"2-1^ v < t r -^a -I/CSB LIBRARY PRACTICAL CALCULATION OF DYNAMO-ELECTRIC MACHINES A MANUAL FOR ELECTRICAL AND MECHANICAL ENGINEERS AND A TEXT-BOOK FOR STUDENTS OF ELECTRICAL ENGINEERING CONTINUOUS CURRENT MACHINERY BY ALFRED E. WIENER, E. E., M. E. M. A. /. E. E SECOND EDITION, REVISED AND ENLARGED NEW YORK McGRAW PUBLISHING CO. 231-241 WEST THIRTY-NINTH STREET COPYRIGHT, 1901, BY ELECTRICAL WORLD AND ENGINEER PREFACE. IN the following volume an entirely practical treatise on dynamo-calculation is developed, differing from the usual text-book methods, in which the application of the various formulae given requires more or less experience in dynamo- design. The present treatment of the subject is based upon results obtained in practice and therefore, contrary to the theoretical methods, gives such practical experience. Informa- tion of this kind is presented in the form of more than a hundred original tables and of nearly five hundred formulae derived from the data and tests of over two hundred of the best modern dynamos of American as well as European make, comprising all the usual types of field magnets and of arma- tures, and ranging in all existing sizes. The author's collection of dynamo-data made use of for this purpose contains full particulars of the following types of con- tinuous current machines: American Machines. Edison Single Horseshoe Type, . . .20 sizes. " Iron-clad Type, . . . .10" " Multipolar Central Station Type, . 10 " " Bipolar Arc Light Type, . . 6 " " Fourpolar Marine Type, . . 4 " " Small Low-Speed Motor Type, . 4 " " Railway Motor Type, . . 3 " Thomson-Houston Arc Light Type, . 9 " " " Spherical Incandescent Type, 4 " " " Multipolar Type, . 3 " " " Railway Motor Type, . 2 " General Electric Radial Outerpole Type, . 12 " Westinghouse Engine Type (" Kodak ") . 12 " Belt Type, . . . 8 " " Arc Light Type, . . 3 " Brush Double Horseshoe ("Victoria") Type, 16 " PREFACE. Sprague Double Magnet Type, . . 13 sizes. Crocker-Wheeler Bipolar Motor Type, . . 6 " " " Multipolar Generator Type, 2 " Entz Multipolar Marine Type, . . 5 " Weston Double Horseshoe Type, . . 3 " Lundell Multipolar Type, . . . 3 " Short Multipolar Railway Motor Type, . 2 " Walker Multipolar Type, . . . 2 " 162 English Machines. Kapp Inverted Horseshoe Type, ... 4 sizes. "Edison-Hopkinson Single Horseshoe Type, . 3 " Patterson & Cooper " Phoenix " Type, . 3 " Mather & Platt " Manchester " Type, . 3 " Paris & Scott Double Horseshoe Type, . 2 " Crompton Double Horseshoe Type, . . i size. Kennedy Single Magnet Type, . . i " " Leeds " Single Magnet Type, . . i " Immisch Double Magnet Type, . . i " " Silvertown" Single Horseshoe Type, . i " Elwell-Parker Single Horseshoe Type, . i " Sayers Double Magnet Type, . . i " 22 German Machines. Siemens & Halske Innerpole Type, . . 3 sizes. " " Single Horseshoe Type, . 2 " Allgemeine E. G., Innerpole Type, . 3 " " " Outerpole Type, . . 3 " Schuckert Multipolar Flat Ring Type, . 3 " Lahmeyer Iron-clad Type, . . . 3 " Naglo Bros. Innerpole Type, . . 2 " Fein Innerpole Type, . . . . . 2 " " Iron-clad Type, 2 " " Inward Pole Horseshoe Type, . . 2 " Guelcher Multipolar Type, . . . 2 " Schorch Inward Pole Type, . . . . i size. Kummer & Co. Radial Multipolar Type, . i " Bollmann Multipolar Disc Type, . . . i " 30 PREFACE. iii French Machines. Gramme Bipolar Type, ..... 3 sizes. Marcel Deprez Multipolar Type, . . 2 " Desrozier Multipolar Disc Type, i size. Alsacian Electric Construction Co. Innerpole Type, ....... i Swiss Machines. Oerlikon Multipolar Type, .... 4 sizes. " Bipolar Iron-clad Type, . . 2 " " Bipolar Double Magnet Type, . 2 " Brown Double Magnet Type (Brown, Boveri &Co 1 2 " VxVS. jf m . . . . 4 Thury Multipolar Type, i size. Alioth & Co. Radial Outerpole Type ("Helvetia"), i " 12 In this list are contained the generators used in the central stations of New York, Brooklyn, Boston, Chicago, St. Louis, and San Francisco, United States; of Berlin, Hamburg, Han- over, Duesseldorf, and Darmstadt, Germany; of London, England; of Paris, France; and others; also the General Electric Company's large power generator for the Intra- mural Railway plant at the Chicago World's Fair, and other dynamos of fame. The author believes that the abundance and variety of his working material entitles him to consider his formulae and tables as universally applicable to the calculation of any dynamo. Although being intended as a text-book for students and a manual fjr practical dynamo-designers, anyone possessing a but fundamental knowledge of arithmetic and algebra will by means of this work be able to successfully calculate and design any kind of a continuous-current dynamo, the matter being so arranged that all the required practical information is given wherever it is needed for a formula. The treatise as here presented has originated from notes prepared by the author for the purpose of instructing his IV PREFACE. classes of practical workers in the electrical field, and upon the success experienced with these it was decided to publish the method for the benefit of others. Since the book is to be used for actual workshop practice, the formula are so prepared that the results are obtained in inches, feet, pounds, etc. But since the time is approaching when the metric system will be universally employed, and as the book is written for the future as well as for the present, the tables are given both for the English and metric systems of measurement. As far as the principles of dynamo-electric machinery are concerned, the time-honored method of filling one-third to one-half of each and every treatise on dynamo design with chapters on magnetism, electro-magnetic induction, etc., has in the present volume been departed from, the subject of it being the calculation and not the theory of the dynamo. For the latter the reader is referred to the numerous text-books, notably those of Professor Silvanus P. Thompson, Houston and Kennelly, Professor D. C. Jackson, Carl Hering, and Professor Dr. E. Kittler. Descriptions of executed machines have also been omitted from this volume, a fairly com- plete list of references being given instead, in Chapter XIV. The arrangement of the Parts and Chapters has been care- fully worked out with regard to the natural sequence of the subject, the process of dynamo-calculation, in general, con- sisting (i) in the calculation of the length and size of con- ductor required fora given output at a certain speed; (2) in the arrangement of this conductor upon a suitable armature; (3) in supplying a magnet frame of proper cross-section to carry the magnetic flux required by that armature, and (4) in determining the field winding necessary to excite the magnet- izing force required to produce the desired flux. Numerous complete examples of practical dynamo calcula- tion are given in Part VIII., the single cases being chosen with a view of obtaining the greatest possible variety of dif- ferent designs and varying conditions. The leakage examples in Chapter XXX. not only demonstrate the practical applica- tion of the formulae given in Chapters XII. and XIII., but also show the accuracy to which the leakage factor of a PREFACE, dynamo can be estimated from the dimensions of its magnet frame by the author's formulae. A small portion of the subject matter of this volume first appeared as a serial entitled " Practical Notes on Dynamo Calculation," in the Electrical World, May 19, 1894 (vol. xxiii. p. 675) to June 8, 1895 (vol. xxv. p. 662), and reprinted in the Electrical Engineer (London), June i, 1894 (vol. xiii.,- new series, p. 640), to July 12, 1895 (vol. xvi. p. 43). This por- tion has been thoroughly revised, and by considering all the literature that has appeared on the subject since the serial was written has been brought to date. It has been the aim of the author to make the book thor- oughly practical from beginning to end, and he expresses the hope that he may have attained this end. The author's thanks are extended to all those firms who upon his request have so courteously supplied him with the data of their latest machines, without which it would not have been possible to bring this work up to date. Due credit, finally, should also be given to the publishers, who have spared neither trouble nor expense in the production of this volume. ALFRED E. WIENER. SCHENECTADY, N. Y., September 20, 1897. PREFACE TO THE SECOND EDITION. In preparing the second edition, it has been the aim to bring this volume up to date in every particular. For this purpose, data of the latest machines of the most prominent manufacturers were procured by the author and compared with the information given in the book. Since the practice in regard to direct-current machinery has changed but little during the past few years, however, only comparatively few changes in the tables have been found necessary. A number of new tables have been inserted, in order to facilitate the work of the inexperienced designer to a still greater extent. The most import of these additions to the text are those to 17 and to 89. The new matter in 17 gives additional guidance in the selection of the conductor-velocity, it having been found that too much uncertainty was formerly left in the assumption of this most important factor. With the added help, even a novice in dynamo designing is now enabled to obtain a practical value of the conductor-velocity for any kind of machine. Table LXXXIXa, 89, serves to check the design with respect to the relation between arma- ture and field. By its use, the performance of a machine in operation can be predicted, thereby avoiding the liability of building a dynamo which would give trouble due to excessive sparking. The importance of such a check will be appreciated by designers who have had experience. Other new matter has been added, referring *o double-cur- rent generators, multi-circliit arc dynamos, secondary gener- ators, etc. Besides these additions to the text, three appendices have been added to the book. Appendix I. gives dimensions and armature data of various types of modern dynamos, thus affording to the student a means of comparing his results with existing machines as he proceeds in the design. Appendix II. contains wire tables and winding data necessary in determining Vlll PREFACE TO THE SECOND EDITION. the windings of dynamos; these tables are added in order to make the book complete in itself, the designer now having close at hand all the necessary data referring to standard wires, rods, cables, etc. Appendix III., finally, in which the causes, localization, and remedies of the usual troubles oc- curring in dynamo-electric machines are compiled, is given for two purposes: first, to enable the designer, by calling his attention to the ordinary short-comings of electrical ma- chinery, to take such preventive measures in designing a machine as will reduce the liability of trouble in operation to a minimum, thus making his dynamo good in performance as well as economical in operation; and second, to assist the attendant of a dynamo plant in going about in a systematic manner in finding the causes of troubles, so that, by their prompt elimination, unnecessary delay or even a shut-down may be obviated. In conclusion, the author takes this opportunity to express his sincere thanks to his professional confreres in this country as well as abroad, for the encouraging comments on the first edition of his book. A. E. W. BROOKLYN, November, 1901. CONTENTS. PAGE LIST OF SYMBOLS, xxv Part I. Physical Principles of Dynamo-Electric Machines. CHAPTER I. PRINCIPLES OF CURRENT GENERATION IN ARMATURE. 1. Definition of Dynamo-Electric Machinery, .... 3 2. Classification of Armatures, 4 3. Production of Electromotive Force, 4 4. Magnitude of Electromotive Force, 6 5. Average Electromotive Force, . 8 6. Direction of Electromotive Force, ...... 9 7. Collection of Currents from Armature Coil, . . .12 8. Rectification of Alternating Currents 13 9. Fluctuations of Commutated Currents 14 Table I. Fluctuation of E. M. F. of Commutated Currents, 19 CHAPTER II. THE MAGNETIC FIELD OF DYNAMO-ELECTRIC MACHINES. 10. Unipolar, Bipolar, and Multipolar Induction 22 n. Unipolar Dynamos, 23 12. Bipolar Dynamos, . 26 13. Multipolar Dynamos, 33 14. Methods of Exciting Field Magnetism, 35 a. Series Dynamo, ......... 36 b. Shunt Dynamo, 37 Table II. Ratio of Shunt Resistance to Armature Resistance for Different Efficiencies, . . 40 c. Compound Dynamo, 41 Part n. Calculation of Armature. CHAPTER III. FUNDAMENTAL CALCULATION FOR ARMATURE WINDING. 15. Unit Armature Induction 47 Table III. Unit Induction, 48 Table IV. Practical Values of Unit Armature Inductions, 50 ix X CONTENTS. PAGE 16. Specific Armature Induction, 51 17. Conductor Velocity, 52 Table V. Average Conductor Velocities, . . 520 Table Va. High, Medium, and Low Dynamo Speeds, 52*$ 18. Field Density, . 52^ Table VI. Field Densities, in English Measure, . 54 Table VII. Field Densities, in Metric Measure, . 54 19. Length of Armature Conductor, 55 Table VIII. E. M. F. Allowed for Internal Resist- ances, 56 20. Size of Armature Conductor 56 CHAPTER IV. DIMENSIONS OF ARMATURE CORE. 21. Diameter of Armature Core, 58 Table IX. Ratio between Core Diameter and Mean Winding Diameter for Small Armatures, 59 Table X. Speeds and Diameters for Drum Arma- tures, . . 60 Table XI. Speeds and Diameters for High-Speed Ring Armatures, ....... 60 Table XII. Speeds and Diameters for Low-Speed ' Ring Armatures, 61 22. Dimensioning of Toothed and Perforated Armatures, . . 61 a. Toothed Armatures 65 Table XIII. Number of Slots in Toothed Arma- tures, , 66 Table XIV. Specific Hysteresis Heat in Toothed Armatures, for Different Widths of Slots, . 69 Table XV. Dimensions of Toothed Armatures, English Measure, 70 Table XVI. Dimensions of Toothed Armatures, Metric Measure 71 b. Perforated Armatures, 71 23. Length of Armature Core, ........ 72 a. Number of Wires per Layer, 72 Table XVII. Allowance for Division-Strips in Drum Armatures, ...... 73 b. Height of Winding Space, Number of Layers, . . 74 Table XVIII. Height of Winding Space in Arma- tures 75 Table XVI I la. Data for Armature Binding, . 75 c. Total Number of Conductors, Length of Armature Core, 76 24. Armature Insulations, 78 a. Thickness of Armature Insulations, 78 . Table XIX. Thickness of Armature Insulation, 82 CONTENTS. XI PAGE b. Selection of Insulating Material, ..... 83 Table XX. Resistivity and Specific Disruptive Strength of Various Insulating Materials, . 85 CHAPTER V. FINAL CALCULATION OF ARMATURE WINDING. 25. Arrangement of Armature Winding, ..... 87 a. Number of Commutator Divisions, 87 Table XXI. Difference of Potential between Com- mutator Divisions, 88 b. Number of Convolutions per Armature Division, . . 89 c. Number of Armature Divisions, ..... 90 26. Radial Depth of Armature Core Density of Magnetic Lines in Armature Body, 90 Table XXII. Core Densities for Various Kinds of Armatures 91 Table XXIII. Ratio of Net Iron Section to Total Cross-section of Armature Core, ... 94 27. Total Length of Armature Conductor, ..... 94 a. Drum Armatures, 95 Table XXIV. Ratio between Total and Active Length of Wire on Drum Armatures, . . 96 b. Ring Armatures, 98 c. Drum-Wound Ring Armatures, 99 Table XXV. Total Length of Conductor on Drum- Wound Ring Armatures, 100 28. Weight of Armature Winding, 100 Table XXVI. Weight of Insulation on Round Copper Wire, ....... 103 29. Armature Resistance, 102 CHAPTER VI. ENERGY LOSSES IN ARMATURE. RISE OF ARMATURE TEMPERATURE. 30. Total Energy Loss in Armature, 107 31. Energy Dissipated in Armature Winding, .... 108 Table XXVII. Total Armature Current in Shunt- and Compound- Wound Dynamos, . . . 109 32. Energy Dissipated by Hysteresis, 109 Table XXVIII. Hysteretic Resistance of Various Kinds of Iron, in Table XXIX. Hysteresis Factors for Different Core Densities, English Measure, . . .113 Table XXX. Hysteresis Factors for Different Core Densities, Metric Measure, . . .115 Table XXXI. Hysteretic Exponents for Various Magnetizations, . . . . . . .116 Table XXXII. Variation of Hysteresis Loss with Temperature, 118 xii CONTENTS. . PAGE 33. Energy Dissipated by Eddy Currents 119 Table XXXIII. Eddy Current Factors for Differ- ent Core Densities and for Various Laminations, English Measure, . . . . . .120 Table XXXIV. Eddy Current Factors for Differ- ent Core Densities and for Various Laminations, Metric Measure, . . ' . . . . 122 34. Radiating Surface of Armature, 122 a. Radiating Surface of Drum Armatures, . . . .123 Table XXXV. Length of Heads in Drum Arma- tures, 124 b. Radiating Surface of Ring Armatures 125 35. Specific Energy Loss, Rise of Armature Temperature, . . 126 Table XXXVI. Specific Temperature Increase in Armatures, 127 36. Empirical Formula for Heating of Drum Armatures, . . 129 37. Circumferential Current Density of Armature, . . . 130 Table XXXVII. Rise of Armature Temperature Corresponding to Various Circumferential Cur- rent Densities 132 38. Load Limit and Maximum Safe Capacity of Armature, . . 132 Table XXXVIII. Percentage of Effective Gap- Circumference for Various Ratios of Polar Arc, 135 39. Running Value of Armatures . . 135 Table XXXIX. Running Values of Various Kinds of Armatures . .136 CHAPTER VII. MECHANICAL EFFECTS OF ARMATURE WINDING. 40. Armature Torque, 137 41. Peripheral Force of Armature Conductors, . . . .138 42. Armature Thrust, 140 CHAPTER VIII. ARMATURE WINDING OF DYNAMO-ELECTRIC MACHINES. 43. Types of Armature Winding, 143 a. Closed Coil Winding and Open Coil Winding, . . 143 b. Spiral Winding, Lap Winding, and Wave Winding, . 144 44. Grouping of Armature Coils 147 Table XL. Symbols for Different Kinds of Arma- ture Winding, 150 Table XLI. E. M. F. Generated in Armature at Various Grouping of Conductors, . . .151 45. Formula for Connecting Armature Coils, 152 a. Connecting Formula and its Application to the Different Methods of Grouping 152 CONTENTS. xin PAGE b. Application of Connecting Formula to the Various Prac- tical Cases, . . . 153 46. Armature Winding Data, . 155 a. Series Windings for Multipolar Machines, . . . 155 Table XLII. Kinds of Series Winding Possible for Multipolar Machines, . . . . .156 b. Qualification of Number of Conductors for the Various Windings, -. 157 Table XLIII. Number of Conductors and Con- necting Pitches for Simplex Series Drum Wind- ings 159 Table XLIV. Number of Conductors and Con- necting Pitches for Duplex Series Drum Wind- ing, 160 Table XLV. Number of Conductors and Con- necting Pitches for Triplex Series Drum Wind- ings, ......... 162 Example showing use of Table XLIII., . . 158 Example showing use of Tables XLIV. and XLV. , 162 Example of Multiplex Parallel Windings, . . 167 CHAPTER IX. DIMENSIONING OF COMMUTATORS, BRUSHES, AND CURRENT-CONVEYING PARTS OF DYNAMO. 47. Diameter and Length of Commutator Brush Surface, . . 168 48. Commutator Insulation, 170 Table XLVI. Commutator Insulation for Various Voltages 171 49. Dynamo Brushes, 171 a. Material and Kinds of Brushes, 171 b. Area of Brush Contact, 174 c. Energy Lost in Collecting Armature-current; Determina- tion of Best Brush-tension, . . . . . .176 Table XLVII. Contact Resistance and Friction for. Different Brush Tensions, .... 179 50. Current-conveying Parts, ........ 181 Table XLVIII. Current Densities for Various Kinds of Contacts, and for Cross-section of Dif- ferent Materials, 183 CHAPTER X. MECHANICAL CALCULATIONS ABOUT ARMATURE. 51. Armature Shaft, 184 Table XLIX. Value of Constant in Formula for Journal Diameter of Armature Shaft, . .185 Table L. Value of Constant in Formula for Di- ameter of Core Portion of Armature Shaft, . 185 XIV CONTENTS. 5 PAGE Table LI. Diameters of Shafts for Drum Arma- tures, 1 86 Table LII. Diameters of Shafts for High-Speed Ring Armatures, 187 Table L1II. Diameters of Shafts for Low-Speed Ring Armatures, 187 52. Driving Spokes, 186 53. Armature Bearings 19 Table LIV. Value of Constant in Formula for Length of Armature Bearings 190 Table LV. Bearings for Drum Armatures, . . 191 Table LVI. Bearings for High-Speed Ring Arma- tures, . . . i9 2 Table LVII. Bearings for Low-Speed Ring Arma- tures, i9 2 54. Pulley and Belt, ig 1 Table LVIII. Belt Velocities of High-Speed Dy- namos of Various Capacities 193 Table LIX. Sizes of Belts for Dynamos, . . 194 Part III. Calculation of Magnetic Flux. CHAPTER XI. USEFUL AND TOTAL MAGNETIC FLUX. 55. Magnetic Field, Lines of Magnetic Force, Magnetic Flux, Field Density, 199 56. Useful Flux of Dynamo, ........ 200 57. Actual Field Density of Dynamo, 202 a. Smooth Armatures, 204 b. Toothed and Perforated Armatures, .... 205 58. Percentage of Polar Arc, 207 a. Distance between Pole Corners, 207 Table LX. Ratio of Distance between Pole Cor- ners to Length of Gap-Spaces for Various Kinds and Sizes of Dynamos, 208 b. Bore of Polepieces, ' . . . 209 Table LXI. Radial Clearance for Various Kinds and Sizes of Armatures 209 c. Polar Embrace, 210 59. Relative Efficiency of Magnetic Field 211 Table LXII. Field Efficiency for Various Sizes of Dynamos, 212 Table LXIII. Variation of Field Efficiency with Output of Dynamo, 213 Table LXIV. Useful Flux for Various Sizes of Dynamos at Different Conductor Velocities, . 214 60. Total Flux to be Generated in Machine, 214 CONTENTS. XV PAGE CHAPTER XII. CALCULATION OF LEAKAGE FACTOR, FROM DIMENSIONS OF MACHINE. A. Formula for Probable Leakage Factor, 61. Coefficient of Magnetic Leakage in Dynamo-Electric Machines, 217 a. Smooth Armatures, 217 b. Toothed and Perforated Armatures, . . . . .218 Table LXV. Core Leakage in Toothed and Per- forated Armatures 2x9 B. General Formula for Relative Permeances. 62. Fundamental Permeance Formula and Practical Derivations, 219 a. Two Plane Surfaces Inclined to each other, . . . 220 b. Two Parallel Plane Surfaces Facing each other, . . 220 c. Two Equal Rectangular Surfaces Lying in one Plane, . 221 d. Two Equal Rectangles at Right Angles to each other, . 221 e. Two Parallel Cylinders, 221 /. Two Parallel Cylinder-halves, 223 C. Relative Permeances in Dynamo-Electric Machines. 63. Principle of Magnetic Potential, 224 64. Relative Permeance of the Air Gaps, 224 a. Smooth Armature, ........ 224 Table LXVI. Factor of Field Deflection in Dy- namos with Smooth Surface Armatures, . . 225 b. Toothed and Perforated Armature, . . . . . 227 Table LXVII. Factor of Field Deflection in Dy- namos with Toothed Armatures, . . . 230 65. Relative Average Permeance across the Magnet Cores, . .231 66. Relative Permeance across Polepieces, 238 67. Relative Permeance between Polepieces and Yoke, . . 244 D. Comparison of Various Types of Dynamos. 68. Application of Leakage Formulae for Comparison of Various Types of Dynamos, 248 (1) Upright Horseshoe Type, 249 (2) Inverted Horseshoe Type, 250 (3) Horizontal Horseshoe Type 251 (4) Single Magnet Type, 251 (5) Vertical Double Magnet Type. .... 252 (6) Vertical Double Horseshoe Type, .... 252 (7) Horizontal Double Horseshoe Type, . . . 253 (8) Horizontal Double Magnet Type 254 (9) Bipolar Iron-clad Type, 255 (10) Fourpolar Iron-clad Type, . * . . . .225 XVI CONTENTS. | PACK CHAPTER XIII. CALCULATION OF LEAKAGE FACTOR, FROM MACHINE TEST. 69. Calculation of Total Flux '. . 257 a. Magnet Frame Consisting of but One Material, . . 259 b. Magnet Frame Consisting of Two Different Materials, . 260 70. Actual Leakage Factor of Machine, 261 Table LXVIII. Leakage Factors, . . .263 Table LX Villa. Usual Limits of Leakage Fac- tor for Most Common Types of Dynamos, . 265 Part IV. Dimensions of Field-Magnet Frame. CHAPTER XIV. FORMS OF FIELD-MAGNET FRAMES. 71. Classification of Field-Magnet Frames, 269 72. Bipolar Types, 270 73. Multipolar Types, 279 74. Selection of Type, 285 Advantages and Disadvantages of Multipolar Machines, . 287 Comparison of Bipolar and Multipolar Types, . . . 287^ Proper Number of Poles for Multipolar Field Magnets, . 287^ Table LXVIII^. Number of Magnet Poles for Various Speeds, 287^- CHAPTER XV. GENERAL CONSTRUCTION RULES. 75. Magnet Cores, 288 a. Material 288 b. Form of Cross-section, 289 Table LXIX. Circumference of Various Forms of Cross-sections of Equal Area, .... 291 c. Ratio of Core Area to Cross-section of Armature, . . 292 76. Polepieces, 293 a. Material, 293 b. Shape, . * 295 77. Base, 299 78. Zinc Blocks 300 Table LXX. Height of Zinc Blocks for High- Speed Dynamos with Smooth Drum Armatures, 301 Table LXXI. Height of Zinc Blocks for High- Speed Dynamos with Smooth Ring Armatures, 302 Table LXXII. Height of Zinc Blocks for Low- Speed Dynamos with Toothed Armatures, . 302 Table LXXIII. Comparison of Zinc Blocks for Dynamos with Various Kinds of Armatures, 303 79. Pedestals and Bearings 303 80. Joints in Field-Magnet Frame 305 a. Joints in Frames of One Material, 305 CONTENTS. xvil PAGE Table LXXIV. Influence of Magnetic Density upon the Effect of Joints in Wrought Iron, . 307 b. Joints in Combination Frames, 306 CHAPTER XVI. CALCULATION OF FIELD-MAGNET FRAME. 81. Permeability of Various Kinds of Iron, Absolute and Prac- tical Limits of Magnetization, ...... 310 Table LXXV. Permeability of Different Kinds of Iron at Various Magnetizations, . . .311 Table LXXVI. Practical Working Densities and Limits of Magnetization for Various Materials, 313 82. Sectional Area of Magnet Frame, ..... 313 Table LXXVII. Sectional Areas of Field-Magnet Frame for High-Speed Drum Dynamos, . -315 Table LXXVIII. Sectional Areas of Field-Magnet Frame for High-Speed Ring Dynamos, . .315 Table LXXIX. Sectional Areas of Field-Magnet Frame for Low-Speed Ring Dynamos, . . 316 83. Dimensioning of Magnet Cores, 316 a. Length of Magnet Cores, ....... 316 Table LXXX. Height of Winding Space for Dy- namo Magnets, ....... 317 Table LXXXI. Dimensions of Cylindrical Magnet Cores for Bipolar Types, . . . . .319 Table LXXXII. Dimensions of Cylindrical Mag- net Cores for Multipolar Types, . . . 320 Table LXXXIII. Dimensions of Rectangular Magnet Cores (Wrought Iron and Cast Steel), . 321 Table LXXXIV. Dimensions of Oval Magnet Cores (Wrought Iron and Cast Steel), . . 322 b. Relative Position of Magnet Cores, . . . . .319 Table LXXXV. Distance between Cylindrical Magnet Cores 32; Table LXXXVI. Distance between Rectangular and Oval Magnet Cores 324 84. Dimensioning of Yokes, . . 325 85. Dimensioning of Polepieces, ....... 325 Table LXXXVII. Dimensions of Polepieces for Bipolar Horseshoe Type Dynamos, . . . 326 Part V. Calculation of Magnetizing Force. CHAPTER XVII. THEORY OF THE MAGNETIC CIRCUIT. 86. Law of the Magnetic Circuit, 331 87. Unit Magnetomotive Force. Relation between M. M. F. and Exciting Power, 332 xviii CONTENTS. 5 PAGE 88. Magnetizing Force required for any Portion of a Magnetic Circuit, 333 Table LXXXVIII. Specific Magnetizing Forces, in English Measure, 33& Table LXXXIX. Specific Magnetizing Forces, in Metric Measure, 337 CHAPTER XVIII. MAGNETIZING FORCES. 89. Total Magnetizing Force of Machine, 339 Table LXXXIXa. Greatest Permissible Angle of Field Deflection and Corresponding Maximum Ratio of Armature Ampere-Turns to Field Ampere-Turns, 33ga 90. Ampere-Turns for Air Gaps, 33gb 91. Ampere-Turns for Armature Core, 340 92. Ampere-Turns for Field-Magnet Frame, .... 344 93. Ampere-Turns for Compensating Armature Reactions, . . 348 Table XC. Coefficient of Brush Lead in Toothed and Perforated Armatures, . . . .350 Table XCI. Coefficient of Armature Reaction for Various Densities and Different Materials, 352 94. Grouping of Magnetic Circuits in Various Types of Dynamos, 353 Part VI. Calculation of Magnet Winding. CHAPTER XIX. COIL WINDING 'CALCULATIONS. 95. General Formulae for Coil Windings, 359 96. Size of Wire Producing Given Magnetizing Force at Given Voltage between Field Terminals. Current Density in Mag- net Wire, . 363 Table XCII. Specific Weights of Copper Wire Coils, Single Cotton Insulation, . . . 367 97. Heating of Magnet Coils, ........ 368 Table XCIII. Specific Temperature Increase in Magnet Coils of Various Proportions, at Unit Energy Loss per Square Inch of Core Surface, 371 98. Allowable Energy Dissipation for Given Rise of Temperature in Magnet Winding, 370 CHAPTER XX. SERIES WINDING. 99. Calculation of Series Winding for Given Temperature In- crease, 374 Table XCIV. Length of Mean Turn for Cylin- drical Magnets, . ..... 375 roo. Series Winding with Shunt-Coil Regulation 375 CONTENTS. xix S PAGE CHAPTER XXI. SHUNT WINDING. 101. Calculation of Shunt Winding for Given Temperature In- crease, ........... 383 102. Computation of Resistance and Weight of Magnet Winding, 388 103. Calculation of Shunt Field Regulator, 390 CHAPTER XXII. COMPOUND WINDING. 104. Determination of the Number of Shunt and Series Ampere- Turns, 395 Table XCV. Influence of Armature Current on Relative Distribution of Magnetic Flux, . . 398 105. Calculation of Compound Winding for Given Temperature Increase, 399 Part VII. Efficiency of Generators and Motors ; Designing of a Number of Dynamos of Same Type ; Calculation of Electric Motors, Unipolar Dynamos, Motor-Generators, etc.; and Dynamo- Graphics. CHAPTER XXIII. EFFICIENCY OF GENERATORS AND MOTORS. 106. Electrical Efficiency, ......... 405 107. Commercial Efficiency, 406 Table XCVI. Losses in Dynamo Belting, . . 409 108. Efficiency of Conversion, 409 109. Weight- Efficiency and Cost of Dynamos, .... 410 Table XCVII. Average Weight and Weight-Effi- ciency of Dynamos, 412 CHAPTER XXIV. DESIGNING OF A NUMBER OF DYNAMOS OF SAME TYPE. no. Simplified Method of Armature Calculation 4^3 in. Output as a Function of Size, 4 l6 Table XCVIII. Exponent of Output-Ratio in Formula for Size- Ratio, for Various Combina- tions of Potentials and Sizes, . . . . 417 CHAPTER XXV. CALCULATION OF ELECTRIC MOTORS. 112. Application of Generator Formulae to Motor Calculation, . 419 Table XCIX. Average Efficiencies and Electrical Activity of Electric Motors of Various Sizes, . 422 113. Counter E. M. F., 423 114. Speed Calculation of Electric Motors, 424 Table C. Tests on Speed Variation of Shunt Motors, ......... 4 2 7 xx CONTENTS. g PAGE 115. Calculation of Current for Electric Motors, .... 427 a. Current for any Given Load, 4 2 7 b. Current for Maximum Commercial and Electrical Effi- ciency, .... 4 2 8 116. Designing of Motors for Different Purposes 429 Table CI. Comparison of Efficiencies of Two Mo- tors Built for Different Purposes, . . .43 117. Railway Motors, 43 1 a. Railway Motor Construction, 43 1 (1) Compact Design and Accessibility 432 (2) Maximum Output with Minimum Weight, . . 432 (3) Speed, and Reduction-Gearing 433 Table CII. General Data of Railway Motors, . 435 (4) Speed Regulation . 436 (5; Selection of Type 437 b. Calculations Connected with Railway Motor Design, . 438 (1) Counter E. M. F., Current, and Output of Motor, 438 (2) Speed of Motor for Given Car Velocity, . . . 439 (3) Horizontal Effort and Capacity of Motor Equip- ment for Given Conditions 440 Table CIII. Specific Propelling Power Re- quired for Different Grades and Speeds, . 441 Table CIV. Horizontal Effort of Motors of Va- rious Capacities at Different Speeds, . . 442 (4) Line Potential for Given Speed and Grade, . . 442 CHAPTER XXVI. CALCULATION OF UNIPOLAR DYNAMOS. 118. Formulae for Dimensions Relative to Armature Diameter, . 443 119. Calculation of Armature Diameter and Output of Unipolar Cylinder Dynamo, . . . . . . . . 446 1 20. Formulae for Unipolar Double Dynamo, 449 121. Calculation for Magnet Winding for Unipolar Cylinder Dy- namos, 450 CHAPTER XXVII. CALCULATION OF DYNAMOTORS; GEN- KKATORS FOR SPECIAL PURPOSES, ETC. 122. Calculation of Dynamotors, 452 123. Designing of Generators for Special Purposes, . . . 455 a. Arc Light Machines (Constant-Current Generators), . 455 b. Dynamos for Electro-Metallurgy, . . . . . 489 c. Generators for Charging Accumulators, . . . . 461 d. Machines for Very High Potentials, .... 462 e. Multi-Circuit Arc Dynamos, 462^ /. Double-Current Generators 462^ 124. Prevention of Armature Reaction 463 a. Ryan's Balancing Field Coil Method, . . . .464 CONTENTS. xxi $ PAGE b. Sayers' Compensating Armature Coil Method, . . 467 c. Thomson's Auxiliary Pole Method, 469 125. Size of Air Gaps for Sparkless Collection, .... 470 126. Iron Wire for Armature and Magnet Winding, . . . 472 CHAPTER XXVIII. DYNAMO GRAPHICS. 127. Construction of Characteristic Curves, 476 Table CV. Factor of Armature Ampere-Turns for Various Mean Full-Load Densities, . . . 480 Practical Example, 481 128. Modification in the Characteristic Due to Change of Air Gap, 483 129. Determination of the E. M. F. of a Shunt Dynamo for a Given Load, 485 130. Determination of the Number of Series Ampere-Turns for a Compound Dynamo 486 131. Determination of Shunt Regulators, 487 a. Regulators for Shunt Machines of Varying Load, . 487 Practical Example, 488 b. Regulators for Shunt Machines of Varying Speed, . . 490 Practical Example, 492 c. Regulators for Shunt Machines of Varying Load and Varying Speed, 493 Practical Example, 495 d. Regulators for Varying the Potential of Shunt Dynamos, 496 132. Transmission of Power at Constant Speed by Means cf Two Series Dynamos, . 497 133. Determination of Speed and Current Consumption of Rail- way Motors at Varying Load, 500 Practical Example, 501 Part VIII. Practical Examples of Dynamo Calculation. CHAPTER XXIX. EXAMPLES OF CALCULATIONS FOR ELECTRIC GENERATORS. 134. Calculation of a Bipolar, Single Magnetic Circuit, Smooth Ring, High-Speed Series Dynamo (10 KW. Single Magnet Type. 250 V. 40 Amp. 1200 Revs.), .... 505 135. Calculation of Bipolar, Single Magnetic Circuit, Smooth Drum, High-Speed Shunt Dynamo (300 KW. Upright Horseshoe Type. 500 V. 600 Amp. 400 Revs.), . . 527 136. Calculation of a Bipolar, Single Magnetic Circuit, Smooth Drum, High-Speed, Compound Dynamo (300 KW. Up- right Horseshoe Type. 500 V. 600 Amp. 400 Revs.), . 547 137. Calculation of a Bipolar Double Magnetic Circuit, Toothed Ring, Low-Speed Compound Dynamo (50 KW. Double Magnet Type. 125 V. 400 Amp. 200 Revs.), . . . 552 xxii CONTENTS. 5 PAGE 138. Calculation of a Multipolar, Multiple Magnet, Smooth Ring, High-Speed Shunt Dynamo (1200 KW. Radial Innerpole Type. 10 Poles. 150 V. 8000 Amp. 232 Revs.), . . 566 139. Calculation of a Multipolar, Single Magnet, Smooth Ring, Moderate-Speed Series Dynamo (30 KW. Single Magnet Innerpole Type. 6 Poles. 600 V. 50 Amp. 400 Revs.), 580 140. Calculation of a Multipolar, Multiple Magnet, Toothed Ring, Low-Speed Compound Dynamo (2000 KW. Radial Outer- pole Type. 16 Poles. 540 V. 3700 Amp. 70 Revs.), . 5657 Table CVI. Factor of Hysteresis Loss in Arma- ture Teeth, . 592 141. Calculation of a Multipolar, Consequent Pole, Perforated Ring, High-Speed Shunt Dynamo (100 KW. Fourpolar Iron-Clad Type. 200 V. 500 Amp. 600 Revs.), in Metric Units 603 CHAPTER XXX. EXAMPLES OF LEAKAGE CALCULATIONS, ELECTRIC MOTOR DESIGN, ETC. 142. Leakage Calculation for a Smooth Ring, One-Material Frame, Inverted Horseshoe Type Dynamo (9.5 KW. "Phosnix" Dynamo: 105 V. 90 Amp. 1420 Revs.), .... 614 143. Leakage Calculation for a Smooth Ring. One-Material Frame, Double Magnet Type Dynamo (40 KW. " Immisch " Dy- namo: 690 V. 59 Amp. 480 Revs.), ..... 618 144. Leakage Calculation for a Smooth Drum, Combination Frame, Upright Horseshoe Type Dynamo (200 KW. " Ed- ison " Bipolar Railway Generator: 500 V. 400 Amp. 450 Revs.), 621 145. Leakage Calculation for a Toothed Ring, One-Material Frame, Multipolar Dynamo (360 KW. " Thomson-Hous- ton" Fourpolar Railway Generator: 600 V. 600 Amp. 400 Revs.), 624 146. Calculation of a Series Motor for Constant- Power Work (In- verted Horseshoe Type. 25 HP. 220 V. 850 Revs.), . 628 147. Calculation of a Shunt Motor for Intermittent Work (Bipolar Iron-Clad Type. 15 HP. 125 V. 1400 Revs.), . . . 637 148. Calculation of a Compound Motor for Constant Speed at Varying Load (Radial Outerpole Type. 4 Poles. 75 HP. 440 V. 500 Revs.), 644 149. Calculation of a Unipolar Dynamo (Cylinder Single Type. 300 KW. 10 V. 30,000 Amp. looo Revs.), . . . 652 150. Calculation of a Dynamotor (Bipolar Double Horseshoe Type. 5^ KW. 1450 Revs. Primary: 500 V. n Amp. Secondary: 110 V. 44 Amp.) 655 CONTENTS. xxi fi APPENDIX I. TABLES OF DIMENSIONS OF MODERN DYNAMOS. TABLE PAGE CVII. Dimensions of Crocker- Wheeler Bipolar Medium-Speed Ring-Armature Motors, 664 CV1II. Dimensions of Edison Bipolar High-Speed Drum-Arma- ture Dynamos and Motors, ..... 665 CIX. Dimensions of Westinghouse Four-Pole Medium and High-Speed Drum-Armature Dynamos and Motors, 666 CX. Dimensions of General Electric Four-Pole Moderate and High-Speed Ring-Armature Generators, . . 667 CXI. Dimensions of Crocker- Wheeler Multipolar Low, Medium and High-Speed Surface-Wound Ring- Armature Dynamos 668 CXII. Dimensions of General Electric Multipolar Low-Speed Ring-Armature Generators, ..... 669 CXIII. Ring-Armature Dimensions, 670 CXIV. Drum-Armature Dimensions, 671 APPENDIX II. WIRE TABLES AND WINDING DATA. TABLE CXV. Resistance, Weight, and Length of Cool, Warm, and Hot Copper Wire 676-677 CXVI. Data for Armature Wire (D. C. C ) 678 CXVII. Data for Magnet Wire (S. C. C.), 679 CXVI 1 1. Limiting Currents for Copper Wires, .... 680 CXIX. Carrying Capacity of Copper Wires 681 CXX. Carrying Capacity of Circular Copper Rods, . . 682 CXXI. Equivalents of Wires 684-685 CXXII. Stranding of Standard Cables, 686 CXXIII. Number and Size of Wires in Cable of Given Cross- Section 687 CXXIV. Size and Weight of Rubber-Covered Cables, . . 688 CXXV. Iron Wire for Rheostats and Starting Boxes, . . 689 CXXVI. Carrying Capacity of German Silver Rheostat Coils, . 690 APPENDIX III. LOCALIZATION AND REMEDY OF TROUBLES IN DYNAMOS AND MOTORS IN OPERATION. Classification of Dynamo Troubles, 695 i. Sparking at Commutator 695 Causes of Sparking, 696 Prevention of Sparking, 696 Faulty Adjustment, 696 Faulty Construction and Wrong Connection, .... 697 Wear and Tear, 698 Excessive Current 699 xxiv CONTENTS. PAGE 2. Heating of Armature and Field Magnets, .... 699 3. Heating of Commutator and Brushes, 700 4. Heating of Bearings 701 5. Causes and Prevention of Noises in Dynamos, . . . 701 6. Adjustment of Speed, 702 7. Failure of Self-Excitation, 703 8. Failure of Motor, 704 INDEX, 707 LIST OF SYMBOLS. Throughout the book a uniform system of notation, based upon the standard Congress-notation, is adhered to, the same quantity always being denoted by the same symbol. The fol- lowing is a complete list of these symbols, here compiled for convenient reference: AT, at = ampere-turns. AT = total number of ampere-turns on magnets, at normal load, or magnetizing force. AT' total magnetizing force required for maximum output of machine. A T" = total magnetizing force required for minimum output of machine. AT l = total magnetizing force required for maximum speed of machine. AT^ = total magnetizing force required for minimum speed of machine. AT = total magnetizing force required at open circuit. at & = magnetizing force required for armature core, normal load. at &0 = magnetizing force required for armature core, open circuit. at ci = magnetizing force required for cast iron portion of magnetic circuit, normal load. at cio magnetizing force required for cast iron portion of magnetic circuit, no load. af CB = magnetizing force required for cast steel portion of magnetic circuit, normal load. at cs o = magnetizing force required for cast steel portion of magnetic circuit, no load. af g = magnetizing force required for air gaps, normal load. af go = magnetizing force required for air gaps, open circuit. xxvi LIST OF SYMBOLS. af gM = combined magnetizing force required for air gaps, armature core, and reactions. at m magnetizing force required for magnet frame, normal output. af ma = magnetizing force required for magnet frame, open circuit. af v , af po = magnetizing forces required for polepieces. at r magnetizing force required for compensation of armature reactions. at a = magnetizing force required to produce a reversing field of sufficient strength for sparkless collection. at wi = magnetizing force required for wrought iron portion of magnetic circuit, normal load. <7/ wio = magnetizing force required for wrought iron portion of magnetic circuit, no load. at y , at yo = magnetizing forces required for yoke, or yokes. tx = half pole-space angle (also angle of brush-displacement). (B = magnetic flux density in magnetic material, in lines per square centimetre. ($>* = magnetic flux density in magnetic material, in lines per square inch. i &*a = average density of magnetic lines in armature core. (B a ,, (B" a , = maximum density of magnetic lines in armature core. a a > *a minimum density of magnetic lines in armature core. (B c .,., (B'ct = mean density of magnetic lines in cast iron portion of frame. c.s.>*cA = mean density of magnetic lines in cast steel portion of frame. (B,, (B" p = mean density of magnetic lines in polepieces. OS.,,, fl&" pl = maximum density of magnetic lines in polepieces. (B,,.,, (B*,,., = minimum magnetic density in polepieces. (B t , (B* t = magnetic density in armature teeth. .v.i> (S>\-.i.'-= magnetic density in wrought iron portion of mag- netic circuit. b breadth, width. a = breadth of armature cross-section, or radial depth of armature core. b\ = maximum depth of armature core. LIST OF SYMBOLS. xxvii b b = width of commutator brush. B = breadth of belt. k = circumferential breadth of brush contact. b a = width of armature slot. b' a = available width of armature slot. b\ width of armature slot for minimum tooth-density. b$ = smallest breadth of armature spoke (parallel to shaft). l>t = width, at top, of armature tooth. b\ = radial depth to which armature tooth is exposed to mag- netic field. b' t width, at root, of armature tooth. y = breadth of yoke. ft = angle embraced by each pole. /?, = percentage of polar arc. /S'j = percentage of effective arc, or effective field circum- ference. y = electrical conductivity, in mhos. Z>, d, 6 diameter. JD m = external diameter of magnet coil. Z> p = diameter of armature pulley. m " ca. specific magnetizing force of cast steel portion of magnetic circuit. w m , m" m = specific magnetizing force of magnet frame. iti f ,'tn" p = specific magnetizing force of polepieces. w t , m" t specific magnetizing force of armature teeth. m wl ., m" wi = specific magnetizing force of wrought iron por- tion of magnetic circuit. w y , w* y = specific magnetizing force of yoke. yti = magnetic permeability. N, n = number. N = number of revolutions of armature per minute. N' = number of revolutions of armature per second. N l = frequency of magnetic reversals, or number of cycles per second. N 9 = speed of dynamo, when run as motor. A r a = total number of turns on armature. ^V = number of conductors around pole-facing circumference of armature. N m = number of turns on magnets. IV^ = number of series turns. ^V 8h = number of shunt turns. = speed ratio, /'. e. t abnormal divided by normal speed of machine. , = speed ratio for maximum speed. , = speed ratio for minimum speed. a = number of turns per armature coil. n b = number of commutator brushes, at one point of commu- tation. c = number of armature coils, or number of commutator divisions. ' = number of armature slots. LIST OF SYMBOLS. xxxiii j = number of wires stranded in parallel to make up one armature conductor. n t = number of separate field coils in each magnetic circuit. k = number of commutator bars covered by one set of brushes. i = number of layers of wire on armature. m = number of independent armature windings in multiple. p = number of pairs of magnet poles. 'p = number of pairs of parallel branches in armature, or number of bifurcations of current in armature. n* p = number of pairs of brush sets. n r = number of steps, or divisions, in shunt field regulator. n a = number of armature circuits connected in series in each of the parallel branches. n s = total number of spokes in armature spiders. se = number of wires constituting one series field conductor. n w = number of armature wires per layer. z = number of magnetic circuits in dynamo. 2, Sj , 2 2 , . . . = permeances. 2, relative permeance of gap-spaces. 2 a = relative average permeance across magnet cores. 2 S = relative permeance across polepieces. 2 4 = relative permeance between polepieces and yoke. 2' = relative permeance of clearance space between poles and external surface of armature. 2" i= relative permeance of teeth. 2'" = relative permeance of slots. P = electrical energy at terminals of machine; /. t., output of generator, intake of motor. P' = total electrical energy, active in armature, or electrical activity of machine. P" = mechanical energy at dynamo shaft; /". k = energy absorbed by contact resistance of brushes. P m = energy absorbed in magnet windings. P = energy loss due to air-resistance, brush friction, journal friction, etc. P' = energy required to run dynamo at normal speed on open circuit. -fee energy absorbed in series winding. P eh = energy absorbed in shunt winding. P' S k = energy absorbed in entire shunt-circuit, at normal load. P r = energy absorbed in shunt regulating resistance. P" I = any load of a motor, in watts. p s = safe pressure, or working load, of materials, in pounds per square inch. n = ratio of circumference to diameter of circle, = 3.1416. (R = reluctance of magnetic circuit, in oersteds. J?, r = electrical resistance, in ohms. J? = resistance of external circuit. J? & = total resistance of armature wire, all in series. r a armature resistance, cold, at 15.5 Centigrade. r\ = armature resistance, hot, at (15.5 -f 6 a ) degrees Cent. r m = magnet-resistance, cold, at 15.5 Centigrade. r' m = magnet-resistance, warm, at (15.5 -f 9 m ) degrees Cent. r r resistance of shunt field regulator. r^ = resistance of series winding, cold, at 15.5 Centigrade. r'ge = resistance of series winding, warm, at (15.5 + O m ) de- grees Centigrade. r nh = resistance of shunt winding, cold, at 15.5 Centigrade. r'gh = resistance of shunt winding, warm, at (15.5 -f- 9 m ) de- grees Centigrade. r x = extra-resistance, or shunt regulating resistance in circuit at normal load, in per cent, of magnet resistance. r n r u> resistances of coils I, II, ... of series field regulator. LIST OF SYMBOLS. xxxv p k resistivity of brush-contact, in ohms per square inch of surface. An resistivity of magnet-wire, in ohms per foot. S = surface, sectional area. 6" A = radiating surface of armature. S & = sectional area (corresponding to average specific mag- netizing force) of magnetic circuit in armature core. S &1 minimum cross-section of armature core. 6' a2 =: maximum cross-section of armature core. *Sc. i. = sectional area of magnetic circuit in cast iron portion of field frame. Sc.s. sectional area of magnetic circuit in cast steel portion of field frame. S t = actual field area ; /. e., area occupied by effective inductors. S g = sectional area of magnetic circuit in air gaps. S' g = area of clearance spaces in toothed and perforated armature. S^ radiating surface of magnets. 6" M = surface of magnet-cores. S m = sectional area of magnet-frame, consisting of but one material. S p = area of magnet circuit in polepieces of uniform cross- section. S pj = minimum cross-section of polepieces. .Sp, = maximum area of magnetic circuit in polepieces. 6" s = sectional area of armature slot, in metric units. S" a = sectional area of armature slot, in square inches. Sw. i. sectional area of magnetic circuit in wrought iron por- tion of field frame. S y = area of magnetic circuit in yoke. G = factor of magnetic saturation. 7', / time. T = torque, or torsional moment. a = rise of temperature in armature, in degrees Centigrade. 6' a = specific temperature increase in armature, in degrees Centigrade. m = rise of temperature in magnets, in degrees Centigrade. 6' m = specific temperature increase in magnets, in degrees Centigrade, xxx vi LIST OF SYMBOLS. v = velocity, linear speed. z/ B = belt velocity, in feet per minute. z/ B = belt velocity, in feet per second. v c = conductor velocity, or cutting speed, in feet (or metres) per second. v k = commutator velocity, in feet per second. z/ m = velocity of railway car, in miles per hour. W^ wt = weight. lV t = total weight to be propelled by railway motor, in tons. // a = weight of armature winding, bare wire, in pounds. o//' a = weight of armature winding, covered wire. wt m = weight of magnet winding, bare wire. wt' m = weight of magnet winding, covered wire. wt K = weight of series winding, bare wire. wt' K = weight of series winding, covered wire. wf ah = weight of shunt winding, bare wire. wt' ah = weight of shunt winding, covered wire. Xa, Xa. = value of an ordinate corresponding to position, or angle, a. x = any integer, in formula for number of armature con- ductors. Exponent of size ratio to give output ratio of two dynamos. Y = relative hysteresis-heat per unit volume of teeth. y connecting-pitch, or spacing, of armature winding; aver- age pitch. ^5 = back-pitch; *". e., connecting-distance on back of arma- ture. y t front-pitch; /'. e. t connecting distance on front of arma- ture (commutator-side). z = ratio of speed reduction of railway motor; /'. ^^>^^A^ |< I-S.ECOND Fig. 3. Moving Conductor in Uniform Magnetic Field. area, *. e. t by the density of the magnetic lines within that area; the rate at which the lines are cut, therefore, depends upon the length of the inductor, the speed of its motion, the strength of the magnetic field, and upon the angle between the moving conductor and the direction of its motion. If Z, Fig-. 3. is the length of the inductor, a its angle with g 4] CURRENT GENERA TION IN ARM A TURE. 7 the direction of motion, v its linear velocity per second, and 3C the uniform density of the lines, then the total number of lines cut per second, #, is the product of the area swept and of the density, thus: = L X sin a X v X 3C ..... . ____ (1) In practical dynamos the inductors are usually so arranged upon the armature that their axes are perpendicular to the direction of the motion, /. = &xLxvxw, ....... (3) where E = E. M. F. induced in moving inductor; = total number of lines cut per second; L = length of moving inductor; v = linear velocity of inductor per second; 3C = average density of magnetic field; k = constant, whose value depends upon units chosen. Now, the absolute electric and magnetic systems of units are so related with each other that, if the number of magnetic lines cut per second is expressed in C. G. S. units, the result of formula (3) gives directly the E. M. F. induced, expressed in absolute units, or in other words, if an inductor cuts i C. G. S. line per second, the difference of potential induced in its length by the motion causing such cutting, is i absolute unit of E. M. F. In the C. G. S. system, consequently, the constant k = i. The practical unit of E. M. F., i volt, is one hundred million times greater than the absolute unit, which is inconveniently small, and, in consequence, 100,000,000 C. G. S. lines of force cut per second produce one volt of E. M. F. If, therefore, is reckoned in C. G. S. lines, and E is to be measured, as usual, in volts, the value of the constant is T k = IOO.OOO.OOO 8 DYNAMO-ELECTRIC MACHINES. [ 5 and the formula for the E. M. F., in practical units, becomes: E = L x v X 3C X io- 8 volts, (4) and now: L = length of inductor, in centimetres; v = cutting-velocity, in centimetres per second; 3C = density of field, in C. G. S. lines per square centimetre. 5. Average Electromotive Force. If the rate of cutting lines of force is constant, the E. M. F. induced at any instant is the seme throughout the motion of a' Fig. 4. Inductor Describing Circle in Magnetic Field. the conductor, but if either the cutting-speed or the density of the field varies, the instantaneous values of the E. M. F. vary accordingly, and the average E. M. F. generated in the inductor is the geometrical mean of all the instantaneous values. In a dynamo each inductor is carried in a circle through a more or less homogeneous field; in two diametrically opposite positions therefore, at a and a', Fig. 4, its motion is parallel to the lines of force, while at two positions, b and b\ at right angles to a and a', the inductor moves perpendicular to the lines. In positions a and a', consequently, no lines are cut, and the induced E. M. F. is E = o, while at b and b' the maxi- mum number of lines is cut in unit time, and E has its maxi- mum value. Between these two extremes any possible value of E exists, according to the angular position of the inductor 6] CURRENT GENERA TION IN ARM A TURE. 9 The average value of the induced E. M. F. for any movement with a varying number of lines cut is given by the average rate of cutting lines during that movement, and the average rate is the quotient of the total number of lines cut divided by the time required to cut them. The average E. M. F., therefore, is E= ^- x io- 8 volts, (5) where E = average value of E. M. F., in volts; $ = total number of lines of force cut; / = time required to cut lines, in seconds. If the inductor of Fig. 4 is moved with an angular velocity of N revolutions per minute, or of revolutions per second, the number of lines cut in the half- revolution, from a to a' is <, and the time taken by this half-revolution is / = JL seconds; consequently the average E. M. F. for this case is: E = i X io~ 8 = 2 $ N' x io"* (6) = 2< x io-* = 60 3 in which E = average value of E. M. F., in volts; < = total number of lines of force cut; N = cutting speed, in revolutions per minute; N' cutting speed, in revolutions per second. 6. Direction of Electromotive Force. The direction of the current flowing due to the induced E. M. F. in any inductor depends upon the direction of the lines of force and upon the direction of the motion, and can be determined by applying the well-known "finger-rule" of 10 D YNA MO-ELECTRIC MA CHINES. [ Professor Fleming. The directions of the magnetic lines, of the motion, and of the current being perpendicular to each other, three fingers of the hand, placed at right angles to one another, are used to determine any one of these directions when the other two are known. To find the direction of the induced E. M. F. the right hand is employed, being placed in such a position that the t3Cumb points in the direction of the magnetic lines (of density 3C), and the ///iddle finger in the direction of the wotion, Fig. 5, when the/orefinger will indicate Fig. 5. Finger Rule for Direction of Current. (Right Hand.) Fig. 6. Finger Rule for Direction of Motion. (Left Hand.) the direction of the /low of the current. Conversely, the direction of the motion which results if a conductor carrying an electric current is placed in the magnetic field of a magnet, is obtained by using in the same manner the respective fingers of the left hand, as shown in Fig. 6, and then the ;;/iddle finger will point to the direction in which the wotion of the conductor will take place. If, in case of a generator, either the direction of the lines of force or the direction of the motion is reversed, the induced E. M. F. will also be reversed in direction; and if, in case of a motor, either the polarity of the field or the direction of the current in the armature conductors is reversed, the rotation will also change its direction. In the armatures of practical machines the inductors, for the purpose of collecting the E. M. Fs. induced in each, are. elec- trically connected with each othr, and thereby a system of CURRENT GENERA TION IN ARM A TURE. II armature coils is formed. According to the number of inductors in each loop there are two kinds of armature coils. In ring armatures, Fig. 7, each coil contains but one inductor per turn, while in drum armatures, Fig. 8, every convolution of the coil is formed of two inductors and two connecting conductors. A Fig. 7. Fig. 8. Drum Armature Coil. ring armature coil, therefore, when moved so as to cut the lines of a magnetic field, has only one E. M. F. induced in it; in a drum armature coil, however, E. M. Fs. are induced in both the inductors, and these two E. M. Fs. may be of the same or of opposite directions, according to the manner in which the coil Fig. 9. Closed Coil moving Horizontally in Magnetic Field. is moved with respect to the lines of force. If the relative position between the magnetic axis of the coil and the direc- tion of the lines does not change, that is, if the angle enclosed by them remains the same during the entire motion of the coil, as in Fig, 9, the E. M. Fs. induced in the two halves counter- 12 DYNAMO-ELECTRIC MACHINES. act each other, while when the coil is revolved about an axis perpendicular to the direction of the lines of force, as in Figs. 10 and n, the E. M. Fs. in the two inductors have opposite directions, and therefore add each other when flowing around the coil. Since in the former case, Fig. 9, the number of lines through the coil does not change, while in the latter case, Figs. 10 and n, it does, it follows that E. M. F. is indtued in a closed circuit, if this circuit moves in a magnetic field so that the number of lines of force passing through it is altered during the motion. By applying the finger-rule to the single elements of the coil it is found that % y ; Figs. 10 and n. Closed Coil Revolving in Magnetic Field. the direction of the induced current is clockwise, viewed in the direction with the lines, if the motion is such as to cause a decreases the number of lines; and is counter-clockwise, if the motion effects an increase in the number of lines. 7. Collection of Current from Armature Coil. If a coil is revolved in a uniform magnetic field, the number of lines threading through it will twice in each revolution be zero, once a maximum in one direction, and once in the other. If, therefore, the current of that coil is collected by means of collector-rings and brushes, Figs. 12 and 13, it will traverse the external circuit, from brush to brush, in one direction for one- half of a revolution and in the opposite direction in the other half, or an alternating current is produced by the coil. In plotting the positions of the coil in the magnetic field as ordi- nates and the corresponding instantaneous values of the 8] CURRENT GENERA J^iON IN ARMATURE. 1 3 induced E. M. F. as abscissae, the curve of induced E. M. Fs., or, since the electrical resistance of the circuit is constant during the motion of the coil, the curve of induced currents is Figs. 12 and 13. Collection of Armature Current. obtained, Fig. 14. Since the instantaneous value e 9 at any moment is expressed by the product of the maximum value and the sine of the angle through which the coil has moved, Fig. 14. Curve of Induced E. M. Fs. viz., e

=: -2- x j+^ b< sl J o 9] CURRENT GENERATION IN ARMATURE. 21 -E'l - + -( - -cos x +-sin #4-- * ) i 4 T *V 2 r 2 r 2 J^ [ U + (4 The average E. M. F. in this case is: If *^l E ' I _ 2 it I n which is the same as obtained above for the case of a one-coil armature. In the same manner the average E. M. F. is obtained for any number of coils and is invariably found to be .63662 of the maximum E. M. F. produced if all of the inductive wire is wound in but one coil and connected to the external circuit by a two-division commutator. As might be expected from the definition of the average E. M. F., it will be noted that the values of the mean E. M. F., column 5, Table I., for increasing number of commutator divisions, approach the figure .63662 for the average E. M. F. as a limit. CHAPTER II. THE MAGNETIC FIELD OK DYNAMO-ELECTRIC MACHINES. 10. Unipolar, Bipolar, and Multipolar Induction. From the previous chapter it is evident that an E. M. F. will be induced in a conductor: (1) When the conductor is moved across the lines of force of the field in a direction perpendicular to its own axis and per- pendicular to the direction of the lines, Fig. 27; and (2) When the conductor is revolved in the field about an axis perpendicular to the direction of the lines, Fig. 28. In the first case, the inductor aa, Fig. 27, as it cuts the lines Fig. 27. Unipolar Induction. Fig. 28. Bipolar Induction. of the magnetic field but once in each revolution around the axis oo, and in the same direction each time, is the seat of a ttni- directed or continuous E. M. F. In the second case, however, the inductor a, Fig. 28, in revolving about the axis 0, cuts the lines of the field twice in each revolution, and cuts them in the opposite direction alternately; the inductor a, therefore, is the seat of an alternating E. M. F. whose direction undergoes reversal twice every revolution. If the conductor a is made to rotate in a multiple field formed of more than one pair of mag- net poles, Fig. 29, at cuts the lines of all the individual fields, between each two poles, in alternate directions, and an alternating E. M. F. is induced in it, whose direction reverses 11] THE MAGNETIC FIELD. 23 as many times in every revolution as there are poles to form the multiple field. Since the induced E. M. F. in the first case always has the same direction along the length of the con- ductor, in the second case has two reversals in every revolu- tion, and in the third case reverses its direction as many times as there are poles, three different kinds of inductions are dis- Fig. 29. Multipolar Induction. tinguished accordingly, viz. : Unipolar, Bipolar, and Multipolar induction, respectively. As induction due to but one pole cannot exist, the term " uni- polar induction," if strictly interpreted, is both incorrect and misleading, and Professor Silvanus P. Thompson, in the latest (fifth) edition of his " Dynamo-Electric Machinery," there- fore uses the word homopolar (homor=alike) for unipolar, and heteropolar (hetero = different) for bi- and multipolar induction. 11. Unipolar Dynamos. In carrying out practically the principle of unipolar induc- tion, as illustrated in Fig. 27, the poles of the magnet are made tubular and the conductor extended into the form of a disc or of a cylinder ring, Figs. 30 and 31, respectively, in order to cause the unidirected E. M. F. to be maintained continuously at a constant value. The solid disc or solid cylinder-ring inductor is to be considered as a number of contiguous strips, in electrical contact with each other, thus forming a number of conductors in parallel which carry a correspondingly larger DYNAMO-ELECTRIC MACHINES. [H current, but which do not increase the amount of E. M. F. induced. In order to increase the E. M. F. it would be necessary to connect two or more conductors in series, thereby multiplying the inducing length. But heretofore all methods which have been experimented with to achieve the end of grouping in series the conductors on a unipolar dynamo armature have failed, for the reason that the conductor which would have to Fig. 30. Unipolar Disc Dynamo. Fig. 31. Unipolar Cylinder Dynamo. be used to connect the two inductors with each other will itself become an inductor, and, being joined to oppositely situ- ated ends of the two adjoining inductors, will neutralize the E. M. F. produced in a length of inductor equal to its own length. No matter, therefore, how many inductors are placed "in series" on the armature, the resulting E. M. F. will cor- respond to the length of but one of them. By adapting the ring armature to this class of machines, winding the conductor alternately backward and forward across the field which is made discontinuous by dividing up the polefaces into separate projections, loops of several inductors in series can be formed, round which the E. M. F. and current alternate, the character- istic feature of the unipolar continuous current dynamo being thereby lost, and unipolar alternators being obtained. Unipolar dynamos being the only natural continuous current 11] THE MAGNETIC FIELD. 25 machines not requiring commutating devices, it is but a matter of course that attempts are continually being made to render these machines useful for technical purposes; but unless the points brought out in the following are kept in mind, such attempts will be of no avail. 1 From the fact that unipolar dynamos have practically but one conductor, it is evident that its length must be made rather great, and the whole machine rather cumbersome in consequence, in order to obtain sufficient voltage for commer- cial uses. But since a very large amount of current may be drawn from a solid disc or cylinder-ring, it follows that uni- polar dynamos can be practical machines only if built for very large current outputs, such as will be required for metallur- gical purposes and for central station incandescent lighting. Professor F. B. Crocker and C. H. Parmly 2 have recently taken up this subject in a paper presented to the American Institute of Electrical Engineers, and have shown that the only practical manner in which the unipolar dynamo problem can be solved, is by the use of large solid discs or cylinder- rings of wrought iron or steel run at very high speed between the poles of strong tubular magnets. The greatest advantage of such unipolar machines is their extreme simplicity, th^ armature having no winding and \\< commutator. The almost infinitesimal armature resistance not only effects increased efficiency and decreased heating, but also causes the machine to regulate more closely either as a generator or as a motor. Furthermore, there is no hysteresis, because the armature and field are always magnetized in exactly the same direction and 1 See " Unipolar Dynamos which will Generate No Current," by Carl Hering, Electrical World, vol. xxiii. p. 53 (January 13, 1894); A. Randolph, Electrical World, vol. xxiii. p. 145 (February 3, 1894); Bruce Ford, Electrical World, Tol. xxiii. p. 238 (February 24, 1894); G. M. Warner, Electrical World, vol. txiii. p. 431 (March 31, 1894); A. G. Webster, Electrical World, vol. xxiii. p. 491 (April 14, 1894); Professor Lecher, Elektrotechn. Zeitschr., January i, 1895, Electrical World, vol. xxv. p. 147 (February 2, 1895); Professor Arnold, Elektrotechn. Zeitschr., March 7, 1895, Electrical World, vol. xxv. p. 427 {April 6, 1895). 8 " Unipolar Dynamos for Electric Light and Power," by F. B. Crocker and C. H. Parmly, Trans. A. I. E. E.,vo\. xi. p. 406 (May 16, 1894); Electrical World, vol. xxiii. p. 738 (June 2, 1894); Electrical Engineer, vol. xvii. p. 468 ''May 30, 1894). 26 DYNAMO-ELECTRIC MACHINES. [12 to precisely the same intensity. For similar reasons there are no eddy currents, since the E. M. F. generated in any element of the armature is exactly equal to that induced in any other element, the magnetic field being perfectly uniform, owing to the exactly symmetrical construction of the magnet frame. The armature conductor consists of only one single length, conse- quently the maximum magnetizing effect of the armature in am- pere turns is numerically equal to its current capacity, and since the field excitation is considerably greater than this, the arma- ture reaction cannot be great. The armature reaction has the effect of distorting and slightly lengthening the lines of force, so that they do not pass perpendicularly from one pole surface to the other in the air gap and have a spiral path in the iron. For, the field current tends to produce lines in planes passing through the axis, while the armature current acts at right angles to the field current and produces an inclined resultant. There can, of course, be no change of distribution of magnet- ism as a result of armature reaction, which is the really objec- tionable effect that it produces in bipolar and multipolar machines. Unipolar machines having no back ampere turns, an extremely small air gap, and but very little magnetic leak- age, their exciting power needs to be but very small, compara- tively, and they have, therefore, a very economical magnetic field. Machines of the type recommended by Professor Crocker, finally, are practically indestructible, since they are so simple and can be made so strong that they are not likely to be damaged mechanically, while it is almost impossible to conceive of an armature being burnt out or otherwise injured electrically, as the engine would be stalled by the current before it reached the enormous strength necessary to fuse the armature. Machines possessing all these important advantages certainly deserve a prominent place in electrical engineering, whereas they now have practically no existence whatever. 12. Bipolar Dynamos. While the homopolar (unipolar) dynamo is naturally a con- tinuous current dynamo, the heteropolar (bipolar and multi- polar) dynamo is naturally an alternating current machine, and has to be artificially made to render continuous currents by 12] THE MAGNETIC FIELD. 27 means of a commutator. But in heteropolar machines any number of inductors may be connected in series, and con- sequently high E. M. Fs. may be produced with comparatively small-sized armatures. In Fig. 32 a ring armature placed in a bipolar field is shown. The magnetic lines emanating from the A^pole, in passing over to the .S-pole of the field magnet, first cross the adjacent gap-space, then traverse the armature core, and finally pass across the gap-space at the opposite side. The inductors of the armature as they revolve will cut these magnetic lines twice in every revolution, once each as Fig. 32. Ring Armature in Bipolar Field. they pass through either gap. If the rule for the direction of the induced E. M. F., as given in 6, is now applied, it is found that in all the inductors that descend through the right- hand gap-space the direction of the induced current is from the observer, while in all inductors that ascend through the left- hand gap-space it is toward the observer. If an armature is wound as a ring, the currents which are produced in the inductors in the gap-space are added up by conductors carrying the currents through the inside of the ring; when, however, the armature is wound as a drum, the currents simply cross at the ends of the core through connect- ing conductors provided to complete a closed electric circuit. In this manner armature coils are formed, in ring as well as in drum armatures, which are grouped symmetrically around the armature core. In order to yield a continuous current these coils must be connected at regular intervals to the respective bars of a commutator, as illustrated by Fig. 33. The currents 28 D YNAMO-ELECTRIC MA CHINES. [12 induced in the two gap-spaces will then unite at the top-bar b, and will flow together in the upper brush, which, therefore, is the positive brush in this case, and thence will return, through the external circuit, to the lower or negative brush and will there re-enter the armature at the lowest bar b v of the commu- tator, dividing again into two parts and flowing through the two halves of the winding in parallel circuits. The preceding equally applies to a drum winding, but owing to the overlapping p'ig. 33. Commutator Connections of Bipolar Ring Armature. of the two halves of the windings, the paths of the currents cannot be followed up as easily as in a ring winding. By inspection of the diagram, Fig. 33, it is seen that the current after having divided in its two paths goes from coil to coil without flowing down in any of the commutator bars, until both streams unite at the other side and pass down into the bar of the commutator which is at the time passing under the brush. At the instant when one of the commutator segments is just leaving contact with the brush and another one is coming into contact with it, the brush will rest upon two adjacent bars and will momentarily short-circuit one of the coils. While this lasts the two streams will unite by both flowing into the same brush from the two adjacent com- mutator segments. A moment later the short-circuited coil when it has passed the brush will belong to the other half of the armature, that is to say, in the act of passing the brush 12] THE MAGNETIC FIELD. 29 every coil will be transferred from one half of the armature to the other, and will have its current reversed. This is, in fact, the act of commutation, and the conditions under which it takes place govern the proper functioning of the machine when running, as they directly control the presence and amount of sparking at the brushes. The production of sparks is a consequence of the property of self-induction in virtue of which, owing to the current in a conductor setting up a magnetic field of its own, it is im- possible to instantaneously start, stop, or reverse a current. If the act of commutation occurs exactly at the point when the short-circuited coils under the two brushes are not cutting any magnetic lines at all, no E. M. F. is induced in them at the time and they are perfectly idle when entering the other half of the armature winding. On account of the self- induction the current cannot instantly rise to its full strength in these idle coils, and it will spark across the commutator bars as the brushes leave them. From this can be concluded that the ideal arrangement is attained if the brushes are shifted just so far beyond the point of maximum E. M. F. that, while each successive coil passes under the brush and is short-circuited, it should actually have a reverse E. M. F. of such an amount induced in it as to cause a current of the opposite direction to circulate in it, exactly equal in strength to that which is flowing in the other half of the armature which it is then ready to join without sparking. A magnetic field of the proper intensity to cause the current in the short- circuited coil to be stopped, reversed, and started at equal strength in the opposite direction can usually be found just outside the tip of the polepiece, for here the fringe of mag- netic lines presents a density which increases very rapidly toward the polepiece. Since a more intense field is needed to reverse a large current than is required for a small one, it follows that for sparkless commutation the brushes must be shifted through the greater an angle the greater the current output of the armature. Since it takes a certain length of time to reverse a current, the brushes must be of sufficient thickness to short-circuit the coils for that length of time, while on the other hand they must not be so wide as to short- circuit a number of coils at the time, as this again would 30 DYNAMO-ELECTRIC MACHINES, [12 increase the tendency to sparking on account of increased self-induction. From the preceding, then, it is evident that sparkless commutation will be promoted (i) by dividing up the armature into many sections so as to do the reversing of the current in detail; (2) by making the field magnet relatively powerful, thereby securing between the pole tips a fringe of field of sufficient strength to reverse the currents in the short- circuited coils; (3) by so shaping the pole surfaces as to give a fringe of magnetic field of suitable extent; (4) by choosing brushes of proper thickness and keeping their contact surfaces well trimmed. Since the direction of a current causing a certain motion is opposite to the direction of the current caused by that motion, it follows that in a. generator the current induced in the short- circuited coil at a certain position has just the opposite direction with relation to the current flowing in the armature from that induced in the short-circuited coil of a motor in the same position, when rotating in the same direction. That is to say, if in a generator the brushes are shifted so that the current induced in the short-circuited coil has the same direction as the current flowing in the half of the armature it is about to' join, in a motor revolving in the same direction and having its brushes set in exactly the same position, the current in the commuted coil, which absolutely of course has the same direction as in case of the generator, would relatively have a direction opposite to that flowing in the half of the armature to which it is transferred by the act of commutation. While the brushes, in order to attain sparkless commutation, must therefore be shifted with the direction of rotation, or must be given an angle of lead in a generator, in a motor they have to be shifted backward, or have to be given an angle of lag. In a generator the effect of commutation is a tendency to increase the aggregate magnetomotive force and therefore to strengthen the field; in a motor, however, the effect of com- mutation is to decrease the magnetomotive force and to weaken the field. Iron is very sensitive to slight increases of magnetomotive force, while on the other hand it is com- paratively insensible to considerable decrease of magneto- motive force; in generators, therefore, the danger of 12] THE MAGNETIC FIELD. sparking due to improper setting of the brushes is 'much greater than in motors. If the magnetic field is perfectly uniform in strength all around the armature, the E. M. Fs. generated in the separate coils will be all of equal amount; but in actual dynamos the distribution of the magnetic lines in the gaps is always more or less uneven, and the E. M. Fs. in the different coils, therefore, have more or less varying strengths. In well- designed machines, however, the magnetic lines, although unevenly distributed around the armature, are symmetrically Figs. 34 and 35. Methods of Exploring Distribution of Potential around Armature. situated in the two air gaps, and the total E. M. F. of either half of the winding, being the sum of the individual E. M. Fs. of the separate coils, will be equal to the total E. M. F. of the other half, from brush to brush. As the distribution of the magnetic flux around the armature directly affects the distribution of the potential, an examination of the latter will allow conclusions to be drawn as to the former. There are two ways of studying the distribution of the potential around the armature: (i) by observing the voltmeter- deflections caused by the individual coils, a set of exploring brushes being placed, in turn, against every two adjacent com- mutator bars, Fig. 34, and (2) by taking a voltmeter-reading for every bar, the voltmeter being connected between one of the main brushes and an exploring brush sliding upon the commutator, Fig. 35. By plotting the voltmeter readings, in the first case a curve is obtained which shows the relative D YNA MO-ELECTRIC MA CHINES. [12 amount of E. M. F. induced in each armature coil when brought in the various parts of the magnetic field, while the curve received in the second case gives the totalized or " integrated " potential around the armature, such as is found for any point in one of the armature halves by adding up the E. M. Fs. of all the coils from the brush to that point. The investigation of the distribution of the potential around the commutator is very useful in practice, as it may disclose unsymmetrical distribution of the magnetic field due to faulty design of the magnet frame, or to incorrect shape of the pole- pieces, or to other causes. Fig. 36 shows the curves of 90^ 180 S70 J SCO Fig- 36. Curves of Potentials around Armature at No Load. 90 180 270 300 Fig. 37. Curves of Potentials around Armature at Full Load. potentials around an armature rotating in an evenly dis- tributed field, such as will exist in a well-proportioned dynamo when there is no current flowing in the armature, that is to say, when the machine is running on open circuit. In Fig. 37 similar curves are given for a correctly designed dynamo with unevenly but symmetrically distributed field, as distorted by the action of the armature current when running on closed circuit. In both diagrams A is the curve of potentials in each coil, obtained by the first method, and B the curve of inte- grated potential, obtained by the second method of exploring the distribution of potential around the commutator. If either one of the curves A or B is given by experiment, the ordinates of the other may be directly obtained by one of the following formulae given by George P. Huhn: 1 1 " On Distribution of Potential," by George P. Huhn, Electrical Engineer ', vol. xv. p. 186 (February 15, 1893). 13] THE MAGNETIC FIELD. 33 *- \)S i cos a sin a and x a = X X sm a i cos a X X 2/Z,. TC 2 in which X a = ordinate, at angle a from starting position of curve of integral potential; x a = ordinate, at angle a from starting position of curve of potential in each coil; n c = number of commutator divisions. The potentials may also with advantage be plotted out round a circle corresponding to the circumference of the commutator, the reading for each coil being projected radially from the Fig- 3 8 - Distribu- tion of Potential around Commu- tator at No Load. Fig- 39- Distribution of Potential around Commutator at Full Load. Fig. 40. Distribution of Potential around Commutator of Faulty Dynamo. respective commutator division. Fig. 38 shows, thus plotted, the curve of potentials at no load, and Fig. 39 that at full load of a well-arranged dynamo, while Fig. 40 depicts the distribu- tion of potential around the commutator of a badly designed machine. 13. Multipolar Dynamos. While bipolar dynamos offer advantages when small capaci- ties are required, their output per unit of weight does not materially increase with increasing size, and a more economical form of machine is therefore desired for large outputs. In order that the weight-efficiency (output per pound of weight) of a dynamo may be increased without increasing the periphery velocity of the armature, or dangerously increasing the tem- 34 DYNAMO-ELECTRIC MACHINES. [13 perature limit, it is necessary to decrease the reluctance of the magnetic circuit, that is, to reduce the ratio of the length of the air gap to the area of its cross section. Since the length of the armature cannot be increased beyond certain limits governed by mechanical as well as magnetical conditions, the only means of increasing the gap area remains to increase the armature diameter. Increasing the diameter of an armature allows a greater circumference on which to wind conductors, and therefore the depth of the winding may be proportionally decreased. Thus the increase of the armature diameter not only increases the gap area, but also decreases its length, and consequently very effectively reduces the reluctance of the magnetic circuit. With armatures of such large diameters, in order to more evenly distribute the magnetic flux, and to more economically make use of space and weight of the magnet frame, it is advantageous to divide the magnetic circuit, resulting in dynamos with more than one pair of poles, or multi- polar dynamos. For small multipolar dynamos drum armatures are often used ; large machines for continuous current work, however, have always ring armatures. In a multipolar armature there are as many neutral and commutating planes as there are pairs of poles, and, therefore, as many sets of brushes as there are poles. Often, however, all commutator segments that are symmetri- cally situated with respect to the separate magnetic circuits are cross-connected among each other, so that the separate portions of the armature winding corresponding to the separate magnetic circuits are actually connected in parallel within the machine, and then only two brushes, in any two subsequent planes of commutation, are necessary. But unless the arma- ture is in excellent electric and magnetic balance, and all the magnetic circuits of the machine have an equal effect on the armature, excessive heating and sparking are bound to result from this arrangement. This trouble may be avoided by wind- ing the armature so that the current is divided between only two paths, exactly as in a bipolar machine. When such a two-path, or series, winding is used, the wire of each coil must cross the face of the core as many times as- there are field- poles, the turns being spaced at a distance equal to nearly the pitch of the poles. Series-wound multipolar armatures will 14] THE MAGNETIC FIELD. 35 operate satisfactorily regardless of inequalities in the strength of the magnetic circuits. Unless specially arranged, these armatures require only two brushes which are 180 apart in machines having an odd number of pairs of poles, and at an angular distance apart equal to the pitch of the poles in machines having an even number of pairs of poles. Sometimes the commutators of series armatures are arranged with twice as many bars as there are coils in the armature, in which case the extra bars are properly cross-connected to the active bars, so that four brushes may be used in order to give a greater current-carrying capacity. To economize wire in multipolar armatures, it is of advantage to arrange the winding so that no wires have to pass through the inside of the ring, the inductors being connected by conductors on either face of the core. An armature so wound is termed a drum-wound ring armature. If the dynamos are to be directly coupled to the steam engines, particularly low rotative speeds of the armatures are required, and their diameters are then made extra large in order to give them low speed without too great a reduction of periphery velocity. To fully utilize the large armature circum- ference of such low speed multipolar machines, the number of poles is usually made very high, their actual number depending upon the capacity of the machine and the service required of it. Great reductions of rotative speed can, however, only be obtained either by considerable sacrifice of weight-efficiency, or by sacrificing sparkless operation. The former, when carried to an extreme, makes too expensive a machine, and the latter causes increased repairs and depreciation; a mean between the two must therefore be followed in practice. 14. Methods of Exciting Field Magnetism. In modern dynamos the field magnetism is excited by current from the armature of the machine itself. According to the manner in which current is taken from the armature and sent through the field winding, we distinguish, as far as continuous current machines are concerned, the following classes of dynamos: (a) Series-wound, or Series dynamo; (b) Shunt- wound, or Shunt dynamo, and (c) Compound-wound, or Com- pound dynamo. D YNAMO-ELECTRIC MA CHINES. [14 a. Series Dynamo. In the series-wound dynamo the whole current from the armature is carried through the field-magnet coils, the latter being wound with comparatively few turns of heavy copper t. JLJ__? C _J Fig. 41. Diagram of Series-Wound Dynamo. wire, cable, or ribbon, and connected in series with the main circuit, Fig. 41. Denoting by E' = total E. M. F. generated in armature; /' = total current generated in armature; r & = armature resistance; E = terminal voltage, or potential of dynamo; / = useful current flowing in external circuit; R = resistance of external or working circuit; / 8e = current in series field; r^ = resistance of series-field coil; r/ e = electrical efficiency; the following equations exist, by virtue of Ohm's law of the electric circuit, for the series dynamo: T I E 1 /= = /' R ~ F' F I I = f .(8) 14] THE MAGNETIC FIELD. 37 E 1 / iri I r / = jB , I+ r. + ^\> w useful energy , / total energy ' /' , From equations (8) it is evident that an increase in the working resistance directly diminishes the current in the field coils, therefore reducing the amount of the effective magnetic flux, and that on the other hand a decrease of the external resistance tends to increase the excitation and, in consequence, the flux. The constancy of the flux thus depending upon the constancy of the current strength in series-wound dynamos, these machines are best adapted for service requiring a con- stant current, such as series arc lighting. Equation (9) shows that the current generated in the arma- ture of a series dynamo, in order to overcome the resistances of armature and series field, loses a portion of its E. M. F. ; the E. M. F. to be generated in the armature of a series-wound machine, therefore, is equal to the required useful potential, increased by the drops in the armature and in the series-field winding. Series machines having but one circuit the current intensity is the same throughout, and consequently the current to be generated in the armature is equal to the current required in the external circuit. The end result of equation (10) shows that the electrical efficiency of a series dynamo is obviously a maximum when the armature resistance and field resistance are both as small as possible. In practice they are usually about equal. The series-wound dynamo has the disadvantage of not start- ing action until a certain speed has been attained, or unless the resistance of the circuit is below a certain limit, the machine refusing to excite when there is too much resistance or too little speed. b. Shunt Dynamo. In the shunt-wound dynamo the field-magnet coils are wound with many turns of fine wire, and are connected to the brushes of the machine, constituting a by-pass circuit of high D YNAMO-ELECTRIC MACHINES. [14 resistance through which only a small portion of the armature current passes, Fig. 42. Using similar symbols as in the case of the series dynamo, E__i__R J Fig. 42. Diagram of Shunt- Wound Dynamo. the following fundamental equations for the shunt dynamo can be derived: E E' E X I = ; 7 = *L ' = (ID (12) El I* R 14] THE MAGNETIC FIELD. 39 Equations (n) show that in a shunt dynamo an increase of the external resistance, by diminishing the current in the working circuit, increases the shunt current, and with it the magnetic flux, while a decrease of the working resistance increases the useful current, the sum of which and the shunt current is a constant as long as the total current generated in the armature remains the same, thereby reducing the exciting current and ultimately decreasing the magnetic flux. The flux remains constant only when the potential of the machine is kept the same, as then the shunt current, which is the quotient of the terminal pressure and the constant shunt resistance, is also constant; shunt-wound machines, therefore, are best adapted for service demanding a constant supply of pressure, such as parallel incandescent lighting. Since the stronger a current flows through the shunt circuit the less is the current intensity of the main circuit, a shunt machine will refuse to excite itself if the resistance of the main circuit is too low. From (n) and (12) it is seen that the armature current of a shunt dynamo suffers a loss both in E. M. F. and in intensity within the machine; E. M. F. being lost in overcoming the armature resistance, and current intensity in supplying the shunt circuit. In consequence, the E. M. F. to be generated in a shunt dynamo must be equal to the potential required in the working circuit, plus the drop in the armature; and the total current is equal to the useful amperage required, plus the current strength used for field excitation. The efficiency of a shunt dynamo, by equation (13), becomes maximum under the condition ' that r> Inserting this value in (13) we obtain the equation for the max- imum electrical efficiency of a shunt dynamo: r e = =L= = (15) 1 Sir W. Thomson (Lord Kelvin), La Lttmilre Electr., iv., p. 385 (1881). D YN A MO-ELECTRIC MA CHINES. [14 Now, since the armature resistance is usually very small com- pared with the shunt-field resistance, the sum r a -)- r sb may be replaced by r,&, and the quotient may be neglected, when the following very simple approximate value of the efficiency is obtained: (16) and this, by transformation, furnishes ^sh _ / 2 7? e V r* ' ~ \i %J ' (17) By means of equation (16) the approximate electrical efficiency of any shunt dynamo can be computed if armature and magnet resistance are known; and from formula (17) the ratio of shunt resistance to armature resistance for any given per- centage of efficiency can directly be calculated. In the follow- ing Table II. these ratios are given for electrical efficiencies from 7/ e = .8, to rj e = .995, or from 80 to 99.5 per cent. : TABLE II. RATIO OF SHUNT TO ARMATURE RESISTANCE FOR DIFFERENT EFFICIENCIES. PERCENTAGE OP ELECTRICAL EFFICIENCY. RATIO OF SHUNT TO ARMATURE RESISTANCE. PERCENTAGE OF ELECTRICAL EFFICIENCY. RATIO OF SHUNT TO ARMATURE RESISTANCE. 100 >je 2* 100 >je rsh_ ra ra 80 64 QK Kf/ t/tJ. *f/0 1,802 85 128 96 2,304 87.5 196 96.5 3,041 90 324 97 4,182 91 409 97.5 6,084 92 529 98 9,604 93 706 98.5 17,248 94 982 99 39,204 95 1,444 99.5 158,404 14] THE MAGNETIC FIELD. c. Compound Dynamo. Compound winding is a combination of shunt and series excitation. The field coils of a compound dynamo are partly wound with fine wire and partly with heavy conductors, the fine winding being traversed by a shunt current and the heavy winding by the main current. The shunt circuit may be derived from the brushes of the machine or from the terminals of the external circuit; in the former case the combination is termed a short shunt compound winding, or an ordinary compound winding, Fig. 43, in the latter case a long shunt compound wind- ing, Fig. 44. Employing the same symbols as before, the application of Fig. 43- Diagram of Ordinary Compound- Wound Dynamo. Ohm's law furnishes the following equations for the compound dynamo: (i) Ordinary Compound Dynamo (Fig. 43). /'=/+/*=:/..+ / 8 = / X r 4- R r af t I .ii. ....(18) DYNAMO-ELECTRIC MACHINES. . El 7V rj (2) Long Shunt Compound Dynamo (Fig. 44). .(19) (20) L E__L_5. Fig. 44. Diagram of Long Shunt Compound- Wound Dynamo. E .= -- = / X ' (r a + r.) = (21) (22) 14] THE MAGNE7VC FIELD. 43 /' R I (+ ^^ r sh j 1 ^a + ''se , ^ , X ^ ^H hi ' ^ ^sh i T 1 a ' 8e 1 n a 1 3 | V a ' Ml 1 shj By combining the shunt and series windings, the excitation of the dynamo can be held constant, as the main current diminishes and the shunt current increases with increasing working resistance, and the main current rises and the shunt current decreases with decreasing external resistance. A compound-wound dynamo, therefore, if properly proportioned, will maintain a constant potential for varying load. In the case of the ordinary compound dynamo, the potential between the brushes is thus kept constant, in case of the long shunt compound dynamo the potential between the terminals of the working circuit. Although, therefore, the latter arrangement is the more desirable in practice, in a well-designed dynamo it makes very little difference whether the shunt is connected across the brushes or across the terminals of the external circuit. In the ordinary compound dynamo the series winding sup- plies the excitation necessary to produce a potential equal in amount to the voltage lost by armature resistance and by arma- ture reaction; in the long shunt compound dynamo the series winding compensates for armature reaction, and for the drop in the series field as well as for that in the armature. The series winding may even be so proportioned that the increase of pressure due to it exceeds the lost voltage, and then the dynamo is said to be over-compounded, and gives higher voltage at full load than on open circuit. Compound dynamos used for incandescent lighting are usually about 5 per cent, over- compounded in order to compensate for drop in the line from the machine to the lamps. The armature current of a compound dynamo suffering a drop both in potential and in intensity within the machine, in calcu- 44 ^DYNAMO-ELECTRIC MACHINES. [14 lating a compound-wound machine the total E. M. F. to be generated must be taken equal to the required potential plus the voltage necessary to overcome armature and series-field resistances; and the total current strength of the armature equal to the intensity of the external circuit increased by the current used in exciting the shunt field. PART II. CALCULATION OF ARMATURE. CHAPTER III. FUNDAMENTAL CALCULATIONS FOR ARMATURE WINDING. 15. Unit Armature Induction. It is evident that a certain length of wire moving with the same speed in magnetic fields of equal strengths will invariably generate the same electromotive force, no matter whether the said length of wire be placed on the circumference of a drum or of a ring armature, and no matter whatever may be the shape of the field magnet frame, or the number of poles of the different magnetic fields. In order to obtain such a constant, suitable for practical purposes, we start from the definition: " One volt E. M. F. is generated by a conductor when cutting a magnetic field at the rate of 100,000,000 C. G. S. lines of force per second." Since the English system of measurement is still the standard in this country, we will take one foot as the unit length of wire, and one foot per second as its unit linear velocity, and for the unit of field strength we take an intensity of one line of force per square inch. At the same time, however, for calculation in the metric system, one metre is taken as the unit for the length of the conductor, one metre per second as the unit velocity, and one line per square centimetre as the unit of field density. Based upon the law: "The E. M. F. generated in a con- ductor is directly proportional to the length and the cutting speed of the conductor, and to the number of lines of force cut per unit of time," we can then derive the unit amounts of E. M. F. generated in the respective systems of measure- ment, with the following results: " Every foot of inductor moving with the velocity of one foot per second in a magnetic field of the density of one line of force per square inch generates an electromotive force of 144 X io~ H volt" and " Every metre of indue to r cutting at a speed of one metre per second through a field having a density of one line per square centi- metre generates io~* volt." 47 DYNAMO-ELECTRIC MACHINES. [15 The derivation of these two laws from the fundamental defi- nition is given in the following Table III.: TABLE III. UNIT INDUCTIONS. LENGTH OF INDUCTOK. CUTTING VELOCITY. DENSITY OP FIELD. E. M. P. GENERATED. 1 foot 1 foot 1 foot 1 ft. per second 1 ft. per second 1 ft. per second 100,000,000 lines per sq. ft. 100,000,000 lines per sq. in. 1 line per sq. in. 1 Volt 144 Volts 144 X 10- Volt 1 cm. 1 metre 1 metre 1 metre 1 cm. per second 1 m. per second 1 m. per second 1 in. per second 100,000,000 lines per sq. cm. 100,000,000 lines per sq. m. 100,000,000 lines persq. cm. 1 line per sq. cm. 1 Volt 1 Volt 10,000 Volts 10-* Volt If two or more equal lengths are connected in parallel, in each of these wires every unit of length will produce the respec- tive unit of induction, but these parallel E. M. Fs. will not add, but the total E. M. F. generated in one length will also be the total E. M. F. output of the combination. In an Ordinary bipolar armature, now, there are two such parallel branches, each branch generating the total E. M. F. This necessitates one foot of generating wire in each of these two parallel circuits, or altogether two feet of wire, under our unit conditions, in order to obtain an E. M. F. output of 144 X io~ 8 volt; or, in other words: Every foot of the total gen- erating wire on a bipolar armature, at a cutting speed of one foot per second, in a field of one line per square inch, generates 72 X io~* volt of the output-E. M. F. And by a similar consideration we find for the metric system : Every metre of the actual inductive wire on a bipolar armature revolving with a cutting velocity of one metre per second in a field of one line per square centimetre, gen- erates 5 X io~^ volt of the output E. M. F. In nlultipolar armatures the number of the electrically paral- lel portions of the winding generally is 2#' p , the number of pairs of parallel armature circuits, or the number of bifurca- tions of the current in the armature being denoted by #' p , and usually 2#' p is equal to the number of poles, 2# p , the number of pairs of poles being denoted by p . In such armatures it therefore takes 2' p feet of generating conductor to produce 144 x io~ 8 volt of output, or the share of E. M. F. contrib- 15] FUNDAMENTAL CALCULATIONS FOR WINDING. 49 uted to the total output by every foot of the generating wire on the entire pole-facing circumference is 144 x io~ 8 72 x icr volt ; that is, 72 X 10 8 volt per pair of armature circuits, or per pair of poles, respectively. In metric units the share of the E. M. F. contributed to the output of a multipolar arma- ture by every metre of the inductive length of the armature conductor is 5 X io~ 6 volt, or 5 X io~^ volt per bifurcation. These theoretical values of the " unit armature induction" however, have to undergo a slight modification for prac- tical use, owing to the fact that generally only a portion of the total generating or active wire of an armature is effective. "Active" is all the wire that is placed upon the pole-facing surface of the armature, "effective" only that portion of it which is actually generating E. M. F. at any time; that is, the portion immediately opposite the poles and within the reach of the lines of force, at that time. The percentage of effective polar arc, in modern dynamos, according to the number and arrangement of the poles, varies from 50 to 100 per cent, and, usually, lies between 70 and 80 per cent., corresponding to a pole angle of 120 to 144, respectively. The lowest values of the effective arc, 50 to 60 per cent, of the total circumference, are found in the multipo- lar machines made by Schuckert, with poles parallel to the armature shaft, and having no separate pole shoes; in these the space taken up by the magnet winding prevents the poles from being as close together as in machines of other types. The highest figure, 100 per cent., is met in some of the Allgetneine Elektricitaets Gesellschaft dynamos, in which the poles are united by a common cast-iron ring ( Dobro wolsky' s pole bushing. See 76, Chap. XV.). In fixing a preliminary value of this precentage, /? 1} in case of a new design, take 67 to 80 per cent., or ^==.67 to .80, for smooth drum armatures; /?, = .75 to .85 for smooth rings, and D YNA MO-ELECTRIC MA CHINES. [16 /?i = .70 to .90 for toothed and perforated armatures. The lower of the given limits refers to small, and the upper to large sizes, for the final value of ft l is determined with reference to the length of the air gaps, and the latter are comparatively much smaller in large than in small dynamos. Also the num- ber of the magnet poles somewhat affects the selection of /? the smaller a percentage usually being preferable the larger the number of field poles. For these various percentages the author has found the average values of the unit armature induction given in the following Table IV. : TABLE IV. PRACTICAL VALUES OF UNIT ARMATURE INDUCTION. E. M. P. PER PAIR OP ARMATURE CIRCUITS. PERCENTAGE ENGLISH UNITS. METRIC UNITS. OP Volt per Foot. Volt per Metre. POLAR ARC. BIPOLAR MULTIPOLAR BIPOLAR MULTIPOLAR DYNAMOS. DYNAMOS. DYNAMOS. DYNAMOS. ft e e i ! 1.00 72 X 10- 8 72 X 10- 5 X 10-' 5 X10-* .95 71 68 4.9 48 .90 70 65 4.8 4.6 .85 67.5 62.5 4.7 4.4 .80 65 60 4.6 4.2 .75 62.5 57.5 4.4 4 .70 60 55 4.2 3.8 .65 57.5 52.5 4 3.6 .60 55 50 3.8 3.4 .55 52.5 47.5 3.6 3.2 .50 50 45 3.4 3 It will be noticed that the values for multipolar machines run somewhat below those for bipolar ones. This means that, at the same rate of polar embrace, a greater percentage of the total active wire is effective in the case of a bipolar machine, which is undoubtedly due to a greater circumferential spread of the lines of force of bipolar fields, 16] FUNDAMENTAL CALCULATIONS FOR WINDING. 5 1 16. Specific Armature Induction. Knowing the values of the induction per unit length of active armature wire under unit conditions, a general ex- pression can now easily be derived for the "specific armature induction" at any given conductor speed and field density. The induction per unit length of active conductor, in any armature, is *' = 4- X v X 3C", (24) n'p where e' = specific induction of active armature conductor, in volts per foot; e = unit armature induction per pair of armature cir- cuits, in volts per foot, from Table IV. ; n'p = number of bifurcations of current in armature, or number of pairs of parallel armature circuits; n' p has the following values, to be multiplied by the number of independent windings in case of multiplex grouping ( 44): n' p = i for bipolar dynamos and for multipolar ma- chines having ordinary series grouping, n'p = n p for multipolar dynamos with parallel group- ing, p being the number of pairs of mag- net poles, n n'p= - for multipolar dynamo with series-parallel 8 grouping, n a being the number of arma- ture circuits connected in series in each of the 2n'p parallel circuits; v c = conductor-velocity, or cutting speed, in feet per second, from Table V. ; 3C" = field density, in lines of force per square inch, from Table VI. In order to obtain the specific armature induction in the metric system, e is to be replaced by the corresponding value of e l} Table IV. ; the conductor velocity is to be expressed in metres per second, Table V., and the field density, 3C, in lines per square centimetre, from Table VII. ; then (24) gives the specific armature induction in volts per metre of active conductor. $2 DYNAMO-ELECTRIC MACHINES. [17 17. Conductor Velocity. The E.M.F. of a dynamo, according to formula (4), is pro- portional to the velocity v c of the moving conductor; since, therefore, the output of a given dynamo can be raised by simply increasing its speed, it will be best economy to run a dynamo-electric machine at as high a conductor speed as practically possible. The velocity, however, is limited mechanically as well as electrically; mechanically, because the friction in the bearings and the strain in the revolving parts due to centrifugal force, must not exceed certain limits; and electrically, because the heating of the armature caused by the resistance of the wind- ing and by hysteresis and eddy currents in the iron, must be kept reasonably low by limiting the powerless, which increases with the output, and therefore is the greater, the higher the conductor speed is chosen. Furthermore, if the number of revolutions of the armature is given, either by the speed of the engine in case of a direct-driven machine, or otherwise, the above mechanical and electrical limitations alone are not sufficient for choosing the conductor velocity, for, when the number of revolutions is fixed, the diameter of the armature is proportional to the peripheral velocity, and abnormal sizes may be obtained by assuming a value of v c , which is permissible from all the other considerations. The limits of v c established by practice are from 25 to 100 feet per second, according to the kind, size, and revolving speed of the machine. A common value is 50 feet per second, or 3000 feet per minute, which in the metric system corre- sponds to about 15 metres per second, or 900 metres per min- ute. For drum armatures, the average practical values of the conductor velocity range between 25 and 50 feet per second, and for ring armatures, which offer a better ventilation and are lighter than drum armatures of the same diameter, con- ductor velocities up to 100 feet per second are employed. Values near the upper limits are chosen for high-speed machines, in which the selection of a low peripheral velocity would re- sult in too small an armature diameter; the radiating surface, or more properly called the cooling surface, of the armature would consequently be inadequate, and excessive heating would be inevitable. Values near the lower limit, on the g 17] FUNDAMENTAL CALCULATIONS FOR WINDING. S 2a other hand, are taken for low-speed machines, because too large a conductor velocity would in their case excessively increase the diameter of the armature, and in consequence would bring the size of the entire machine out of proportion to its output. The following Table V will serve the unexperienced designer as a guide in selecting the proper value of z/ c for various sizes of drum and ring armature machines. This table is compiled from the data of a great many practical machines, the scope of which can best be seen from the list of machines given in the Preface. The averages given for drum armatures are intended for the usual case of high-speed drum machines, but they hold also good for medium and low-speeds, if it is considered that the figures given in the table are in each case averaged from widely differing actual values of the conductor velocity, so that good practical values of v c for each size may be taken from about 20 to 25 per cent, below to about as much above the TABLE V. AVERAGE CONDUCTOR VELOCITIES. CONDUCTOR VELOCITY, IN FEET CONDUCTOR VELOCITY, IN METRES PER SECOND. PER SECOND. CAPACITY IN Ring Armature. Ring Armature. Drum Drum KILOWATTS. Armature Armature High Medium Low High Medium Low Speed. Speed. Speed. Speed. Speed. Speed. .1 25 50 25 7.5 15 7.5 .25 27 55 27 8 16.5 8 .5 30 CO 30 25 9 18 9 '7.5 1 35 65 30 25 10.5 19.5 9 7.5 2.5 40 70 35 25 12 21 10.5 7.5 5 45 70 40 26 13.5 21 12 8 10 45 75 40 28 13.5 22.5 12 8.5 25 50 75 45 30 15 22.5 13.5 9 50 50 80 50 32 15 24 15 10 100 50 80 50 35 15 24 15 11 200 50 85 50 40 15 25.5 15 12 300 50 85 55 40 15 25.5 16 5 12 500 90 55 45 27 16.5 13.5 1000 90 60 45 27 18 13.5 2000 95 60 - 45 28.5 18 13.5 5000 100 65 50 30 19.5 15 given average. Thus, for instance, the conductor velocity of a 2.5-KW drum armature may be chosen between .75 x 4 = 30 and 1.25 x 40 = 50 feet per second ; and the velocity of drum D YNAMO-ELECTR1C MA CHINES. [17 machines above 25 KW output may be taken within the limits of .75 X 50 = 37.5 and 1.25 X 50 = 62.5 feet per second. In the case of ring armatures, in which the peripheral veloc- ities vary in much wider limits than in drum armatures, separate averages are given for high, medium, and low speeds; and in each case a deviation of about 15 per cent, above or below the given average is within good practical limits. For example, the value of z> c for a 5-KW high-speed ring armature may be selected between .85 X 70 = 60 and 1. 15 x 70 == 80 feet per second. It will be noted that the value of v c for a ring armature of given output varies considerably with the speed at which the machine is run, for the reasons given above. Since the size of the armature, and therefore the general proportion of the entire machine, depends directly upon the value chosen for v c , it is evident that the proper selection of the conductor velocity is one of the most important assumptions to be made by the designer. TABLE Va. HIGH, MEDIUM, AND Low DYNAMO SPEEDS. CAPACITY DRUM ARMATURES. RING ARMATURES. IN High Medium Low High Medium Low KILOWATTS. Speeds. Speeds. Speeds. Speeds. Speeds. Speeds. .1 3000 to 2400 2400 to 1800 1800 to 1200 2600 to 2200 2200 to 1600 .25 2800 " 2200(2200 ' I6uO 1600 ' 10002400 " 2000 2UOO 1400 .5 2600 2000 2000 1500 1500 80022UO 1800 1800 1200 120o"t 600 1 2400 1800 1800 1400 1400 7002000 1600 1500 1000 1000 500 8.5 2>00 1000 1600 1200 1300 600 1800 1400 1400 800 800 400 5 2000 1400 1400 1000 1000 500 1600 12001200 700 700 300 10 1800 1200 1200 800 800 400 1400 10001000 600 600 250 25 1500 1000 1000 600 600 300 1200 850 850 500 500 200 50 1200 800 800 500 500 250 1000 700 700 400 400 150 100 1000 600 600 400 400 200 800 550 550 300 300 125 200 800 450 450 300 300 150 600 400 400 200 200 100 500 200 ion 500 300 300 150 150 80 1000 400 250 250 125 125 70 2000 300 200 200 100 100 60 5000 250 150 150 80 80 50 The diameter of the armature must be of such magnitude that the required length of armature conductor can be placed upon the core, if made of the proper length for that diameter, without causing the winding depth to be too great, or without causing an abnormal length of the armature when 17] FUNDAMENTAL CALCULATIONS FOR WINDING. $* wound to a certain depth proper for the diameter in question. And furthermore, the dimensions of the armature must be such that the size of its superficial area is adequate to liberate the heat generated in the winding and in the core. For these reasons it is an advantage to calculate the armature for several values of the conductor velocity, and to select the best size obtained, all things considered. In Table Va, p. 52/5, the usual speeds of various sizes of dynamos and their classification into high, medium, and low speeds are given. The values of z> c for ring armatures, in Table V., refer to the average of the respective speeds in Table Va. If the dynamo in the given problem is a high-speed machine running near the lower limit, or a medium-speed machine running at a speed near the upper limit given in Table Va, a value of v c about halfway between the high-speed and the medium- speed average is to be taken. If the speed specified for the dynamo to be designed is near the lower medium, or the upper low-speed limit, a value near the mean of the medium and the low-speed values of v c should be selected. For speeds near the upper high-speed or the lower low-speed limits, a value of v c somewhat higher than the high-speed average, or lower than the low-speed average, respectively, should be chosen. For instance, if a ring armature for a 25-KW dynamo is to be designed to run at 800 revolutions per minute, the average conductor velocity is obtained as follows: From Table Va it is seen that the given speed, though found under the head of "medium speed," approaches the lower limit given for high speeds; the average value of v c for medium-speed machines of the size in question is 45; the average for 25-KW high-speed ring armatures is 75; the mean of the two averages is = 60 feet per second. Therefore, in the present case, an average value of v c of about 55 feet per second should be chosen. In order to check the value of the conductor velocity so obtained, the tables of dimensions of modern machines which have been added for the guidance of the student may be used. DYNAMO-ELECTRIC MACHINES. [18 These tables, which will be found in Appendix I., include drum as well as ring armature machines, and give the principal dimensions of armatures and field frames for all ordinary sizes of high-, medium , and low-speed dynamos. Tables CXIII. and CXIV., which contain the armature diameters and lengths of all the machines given in the Dynamo Tables CVII. to CXIL, have been prepared especially for the purpose of checking the conductor velocity and the consequent armature dimensions. The conductor velocity having been ascertained by the method given above, the armature diameter is computed by means of formula (30), p. 58, and is compared with the di- ameter of the machine of nearest size and speed given in Table CXIII. or CXIV., respectively. Thus, for the above example of a 25-KW Soo-revolution dynamo, formula (30) gives a diameter of The nearest machine in Table CXIII. is a 20-KW dynamo running at 700 revolutions, which would furnish 25 KW at 875 revolutions; its diameter is 16 inches. The close agree- ment of the two diameters shows that the conductor velocity chosen is a good value for the case on hand. If Table CXIII. or CXIV. contains no machine of sufficiently near output and speed to allow of a comparison, the required diameter may be obtained by interpolation as shown in Appen- dix I., p. 663. 18. Field Density. The specific strength of the magnetic field is chosen accord- ing to the size of the machine, the number of poles, the form of the armature, and the material of the polepieces. In gen- eral, higher field densities are taken for large than for small dynamos, and in multipolar machines higher values of 5C are admitted than in bipolar ones. In dynamos with smooth-core armatures, the field densities are usually taken somewhat greater than in those with toothed armature bodies, for the reason that in the latter a portion of the lines enters the teeth 18] FUNDAMENTAL CALCULATIONS FOR WINDING. 53 and passes from tooth to tooth without cutting the conductors, and that in such armatures it therefore takes more lines per square inch of pole area to produce the same field density (per square inch of area occupied by armature conductors) than for smooth cores; consequently, smaller field densities must be employed with toothed armatures in order to prevent over- saturation of the polepieces, and, eventually, of the frame. This leakage through the armature teeth takes place in the higher a degree, the greater the width of the teeth compared to that of the slots, and therefore still smaller field densities are to be chosen in case of armature cores with tangentially projecting teeth, and of those with closed slots. Finally, in machines having wrought iron or cast steel polepieces, the densities can be taken about fifty per cent, higher than those with cast iron pole-shoes. Practical average values of 3C" for ordinary dynamos and motors are tabulated in Table VI., which gives the average densities in lines of force per square inch, while Table VII. contains the corresponding values of 3C in lines per square centimetre. The values of JC will also depend on the method to be em- ployed for obviating armature reaction. Modern designers often rely upon a strong magnetic field to assist in preventing the distorting effect of the armature reaction (see 93 and 124), and, therefore, higher gap inductions are generally used now than were a few years ago. If a strong field is desired for the above purpose, a value of the field density about 20 or 30 per cent, in excess of the respective value given in. Table VI. or VII., respectively, is advisable. For machines designed for a very low voltage, such as electro-plating dynamos, battery motors, etc., or for dynamos in which the amperage is very high, comparatively, as in incandescent generators of large outputs, the field density is usually made about two-thirds or three-quarters of the corre- sponding density employed under similar conditions for ordi- nary machines. For machines generating very high voltages, the field density should, on the other hand, be chosen considerably higher than the averages given, values from 25 to 50 per cent, in excess of those given being quite common for such machines. 54 D YNAMO-ELECTRIC MA CHINES. [18 For considerations governing the design of the above and other special kinds of machines, the student is referred to I2 3> PP- 455 to 463- TABLE VI. PRACTICAL FIELD DENSITIES, IN ENGLISH MEASURE. Field Densities. In Lines of Force per square Inch , 3& . Bipolar Dynamos MxilUpolar Dynamos Smooth Toothed Armature Core Smooth Toothed Armature Core fri r 09 Core Straight Teeth Projecting Teeth Core Straight Teeth 1 Projectine, Teeth Is & tfWfmtfflfo MwSwffl/b <^op^ t2w/%ffi!>>. / \iU ^__ ,\Ju ,^ Ira MI|III PoUyUoM Polip.ect* Pol,pi Pokpi'cn Poll !>!"< PoUpitcM P0UpleM PokpitJ PolepiMM Pokpiicn .1 10000 15000 8000 12000 14000 20000 12000 18000 .1 .26 18000 18000 10000 15000 16000 24000 14000 21000 .25 .5 14000 80000 12000 18000 18000 27000 16000 24000 .5 1 15000 22000 13000 19000 8000 18000 19000 88000 17000 25000 10000 15000 1 u 16000 24000 14000 20000 9000 14000 20000 29000 18000 26000 11000 16000 8.5 5 17000 25000 15000 22000 10000 15000 21000 30000 19000 28000 12000 18000 5 7.5 18000 86000 16000 84000 11000 16000 28000 38000 20000 80000 13000 20000 7.5 10 19000 28000 17000 85000 18000 18000 24000 85000 21000 88000 14000 21000 10 86 20000 80000 18000 87000 13000 80000 26000 88000 22000 35000 15000 23000 25 60 22000 33000 20000 30000 14000 22000 28000 41000 23000 88000 16000 24000 50 100 84000 86000 22000 33000 16000 24000 30000 44000 25000 40000 17000 25000 100 800 27000 40000 24000 86000 18000 27000 32000 47000 27000 42000 18000 26000 200 800 30000 46000 27000 40000 20000 30000 35000 50000 29000 44000 19000 88000 300 600 38000 53000 31000 46000 20000 30000 500 1000 41000 56000 33000 48000 22000 82000 1000 8000 ~ ~ ~ ~ 45000 60000 35000 50000. 24000 85000 2000 TABLE VII. PRACTICAL FIKLD DENSITIES, IN METRIC MEASURE. Field Densities, In Lines of Force per sqtmre Centimetre , 5& . Bipolar 'Dynamos Hulttpolar Dynamos < t! Smooth Toothed Armature Core Smooth Toothed Armature Core n H Pore Straight Th Projecting Tteth Armature Core Straight Teeth 1 Projecting Teeth 11 j <^PHP|^ /?5iiiy^5> 4^Ofn^ ^HPil^,, d%$M%fr>\ ^lOGH^ a B Wr-llro M Wr-, Iron Cut Wr-tlron CMt Wr-tln* CM Wt-t lr.nl Cut Wr-tlron Ira Inn or"8u.l| Irob or Bul "'I'"" PebpUni Pokpi~ PelipUoo PtUplMM PoUpl P v TT* * ' ' V ' 4- X * c X 3C" < "c X X *, The length Z a is obtained in feet, if e is given in volts per foot, v c in feet per second, and 5C" in lines per square inch; and is obtained in metres, if e is replaced by e l in volt per metre, v c expressed in metres per second, and if 3C* is replaced by 3C in lines per square centimetre. To find the total electromotive force, ', to be generated by the armature, increase the electromotive force E wanted in the external circuit, by the percentages given in Table VIII. The figures in the second column of this table refer to shunt- wound dynamos, and, therefore, take into account the arma- ture resistance only. The percentages in the third and fourth D YNAMO-ELECTRIC AfA CHINES. [20 columns are to be used for series- and for compound-wound dynamos respectively, and, consequently, include allowances for armature resistance as well as for series field resistance: TABLE VIII. E. M. F. ALLOWED FOB INTERNAL RESISTANCES. ADDITIONAL E. M. P. IN PER CENT. OF OUTPUT E. M. F. CAPACITY IN KILOWATTS. Shunt Dynamos. Series Dynamos. Compound Dynamos. Up to .5 20 % to 12 % 40 % to 25 % 30 % to 20 % 1 12 10 25 20 20 15 2.5 10 8 20 16 15 12 5 8 7 16 14 12 10 10 7 6 14 12 10 8 25 6 5 12 10 8 7 50 5 4 10 8 7 6 100 4 34 8 6 6 5 200 8* 3 6 5 5 4 500 3 81 5 4 4 3 1,000 24 2 4 3 3 24 2,000 2 H 3 8| 24 2 20. Size of Armature Conductor. The sectional area of the armature conductor is determined by the strength of the current it has to carry. For general work the current densities usually taken vary between 400 and 800 circular mils (.25 to .5 square millimetre) per ampere; in special cases, however, a conductor area may be provided at the rate of as low as 200 to 400 circular mils (.125 to .5 square millimetre) per ampere, or as high as 800 to 1,200 circular mils (-5 to -75 square millimetre) per ampere. The low rate refers to machines which only are to run for a short while at the time, as, for instance, motors to drive special machinery (private elevators, pumps, sewing machines, dental drills, etc.), while the high rate is to be employed for dynamos which have a fifteen or twenty hours' daily duty, as is the case for central- station, power-house, and marine generators, etc. Taking 600 circular mils per ampere as the average current density (= 475 square mils, or .000475 square inch per ampere, or about 2,100 amperes per square inch), the sectional area of the armature conductor, in circular mils, is to be 20] FUNDAMENTAL CALCULATIONS FOR WINDING. 57 * =. 600 x = -, (2 7 ) where tf a a = sectional area of armature conductor, in circular mils; S & = diameter of armature wire, in mils; /' = total current generated in armature, in amperes; and n' p = number of pairs of parallel armature circuits. In the metric system, taking .4 square millimetre per am- pere (= 2.5 amperes per square millimetre) as the average current density in the armature conductor, the sectional area of the inductor, in square millimetres, is obtained: (*JL. =^-4-^=.X ^> (28) X -2 -r = .5 \ -r from which, in case of a circular conductor, the diameter can be derived: . .(29) The size of conductor may be taken from the wire gauge tables by selecting a wire, the sectional area of one or more of which makes up, as nearly as possible, the cross-section obtained by formula (27). The total armature current, /', in shunt and compound dynamos is the sum of the current output, /, and the exciting current of the shunt circuit. The latter quantity, however, generally is very small compared with the former, and in all practical cases, consequently, it will be sufficient to use the given /instead of the unknown /' for the calculation of the conductor area. A supplementary allowance may, then, be made by correspondingly rounding off the figures obtained by (27), or by selecting the wires of such a gauge that the actual conductor area is somewhat in excess of the calculated amount. CHAPTER IV. DIMENSIONS OF ARMATURE CORE. 21. Diameter of Armature Core. If the speed of the dynamo is given, the proper conductor velocity taken from Table V. will at once determine the diameter of the armature. Let N denote this known speed, in revolutions per minute, and d' & the mean diameter of the Fig- 45- Principal Dimensions of Armature. armature winding, in inches, then the cutting speed, in feet per second, is _ d' & X * N V ~ ~T 2 X 6o~' from which follows: 12 x 60 v c v c n ~ X ~N~ ~'~ 23 X W ..(30) In the metric system the mean diameter of the armature winding, in centimetres, is given by , 100 x 60 v c v c d'.= - - X -Kf = 1,900 X ~, ..,.(31) 7T N in which v c is to be expressed in metres per second. 58 DIMENSIONS OF ARMATURE CORE. 59 From this mean winding diameter, c da *>c da 2.5 400 25 14 7.5 35 5 350 26 17 8 42 10 300 28 21 8.5 53 25 250 30 27 9 70 50 200 32 36 9.5 90 100 175 35 46 11 115 200 150 40 60 12 150 300 125 42 78 13.25 200 400 100 44 100 13.25 250 600 90 45 115 13.75 290 800 80 45 129 13.75 325 1,000 75 45 138 13.75 350 1,500 70 45 148 13.75 375 2,000 65 45 158 13.75 400 22. Dimensioning of Toothed and Perforated Arma- tures. Armatures with toothed and with perforated core discs, which have been much used in recent years, offer the following advantages over smooth armatures: (i) Excellent means for driving the conductors; (2) mechanical protection of the winding, especially in cores with tangentially projecting teeth, and in perforated bodies; (3) lessening of the resistance of the magnetic circuit, and, therefore, saving in exciting power; (4) prevention of eddy currents in the conductors; (5) lessening of the difference between the amounts of field- distortion at open circuit and at maximum output, and there- fore possibility of sparkless commutation for varying load without shifting brushes; and (6) taking up of the magnetic drag by the core instead of by the conductors. Their dis- advantages are: (i) Increased cost of manufacture; (2) neces- sity for special devices to insulate the winding from the core; (3) eddy currents set up by the teeth in the polar faces; (4) additional heat generated in the iron projections by 62 DYNAMO-ELECTRIC MACHINES. [22 hysteresis; (5) increase of self-induction in short-circuited armature coils due to imbedding them in iron, especially in high amperage machines; (6) increased length of the gap- space and consequent greater expenditure in exciting power when saturation of the teeth takes place; and (7) leakage of lines of force through the armature core, exterior to the winding, particularly in case of projecting teeth and of per- forated cores. Comparing these advantages and disadvantages with each other we find that the conditions that have to be fulfilled in order to bring to prominence certain advantages will also favor the conspicuousness of certain of the disadvantages, and moreover we see that what is an advantage in one case may be a decided disadvantage in another. All considered, therefore, there are no such striking advantages in either the toothed or the smooth core as to make any one of them superior in all cases over the other, and a general decision whether a toothed or a smooth-core armature is preferable, cannot be arrived at. As a matter of fact, in practice it chiefly depends upon the purpose of the machine to be designed whether a smooth or a toothed core is preferably used in its armature. In machines with toothed and with perforated armatures an increase of the load has the effect of increasing the saturation of the iron projections and therewith the reluctance of the air gap; the counter-magnetomotive force of the armature, which also increases with the load, has therefore to overcome a greater reluctance as it increases itself, in consequence of which the demagnetizing effect of the armature is kept very nearly constant at all loads. Hence the distribution of the field in the gap remains nearly the same and the angle inclosed between the planes of commutation at no load and at maximum output is reduced to a minimum. For cases where sparkless commutation is required without shifting the brushes for varying loads, as for instance in rail- way generators, in which due to the continual and sudden fluctuations of the load a shifting of the brushes is impractica- ble, the employment of toothed armatures is preferable, for the attainment of the desired end in this case outweighs all their disadvantages. On the other hand, the self-induction in smooth-core armatures, owing to the absence of iron between 22] DIMENSIONS OF ARM A TURE CORE. 63 the conductors, is much less, and consequently they are chosen in cases of machines in which large currents are commutated at low voltages, such as in central station lighting generators and in electro-metallurgical machines. In the latter case the disadvantage of increased self-induction in the toothed arma- ture is the main consideration and drives it out of competi- tion with the smooth armature, in spite of all advantages which it may have otherwise. Again, in the case of motors, where a large torque is the desideratum, especially in low-speed motors, such as single reduction and gearless railway motors, the toothed armature answers best, as in this instance its advantage of increased drag upon the teeth is considered the prominent one. Toothed armatures must further be em- ployed if, in a series motor, a constant speed under all loads is to be attained, for at light loads the teeth, being worked at a low point of magnetization, offer but little reluctance to the flux through the armature, while at heavy loads the teeth become saturated and considerably increase the reluctance of the magnetic circuit, thereby preventing the induction from increasing with increased field excitation, the result being a motor that comes much nearer being self-regulating than one with a smooth-core armature. In order to more definitely determine the mechanical advan- tage of the iron projections, W. B. Sayers * compared the pull on the conductors in toothed and smooth-core armatures. He found that in toothed armatures the driving force is borne directly by the iron instead of by the conductors as in case of smooth-core machines. Taking the case of an armature in which the thickness of the tooth is equal to the width of the slot, he shows that, when the density in the teeth is 100,000 lines per square inch (= 15,500 lines per square centimetre), that in the slots is about 300 lines per square inch (= 47 per square centimetre), while in a smooth-core armature the field density would be about 50,000 per square inch (= 7,750 per square centimetre), from which follows that the force acting upon the conductors is about 167 times greater in the latter case than in the former. In another example he takes a higher mag- netic density and finds that the pull in case of the toothed arma- 1 London Electrician, April 19, 1895; Electrical World, vol. xxv. p. 562 (May ir, 1895). DYNAMO-ELECTRIC MACHINES. [22 ture is only 16 times as great as in a corresponding smooth armature. If the density is so high that the teeth become satu- rated, the field density in the slots will approach that in the gap of an equally sized smooth armature, and the forces will be about equal in both cases. 1 When a toothed or perforated armature is placed in a mag- netic field, the lines of force concentrate toward the teeth in form of bunches, Fig. 46, and thereby destroy the uniformity Fig. 46. Distribution of Magnetic Fig. 47. Distribution of Magnetic Lines around Toothed Armature Lines around Toothed Armature at Rest. in Motion. of the field. If the armature is now revolved these bunches are taken along by the teeth until a position, Fig. 47, is reached in which the lines have been distorted to such a degree that the reluctance of their path has reached the maximum value the magnetomotive force of the field is able to overcome. At this moment each bunch of lines will com- mence to change over to the next following tooth of the arma- ture, and thus every line of each bunch will in succession cross the slot immediately behind the tooth through which it had passed previously. In this manner every line of force passing through the armature core cuts all the inductors on the armature during each revolution. By the action of chang- ing over from one tooth to the next, an oscillation or quiver- ing of the magnetic lines is caused, which tends to set up eddy currents in the teeth and in the polar faces. In order to obviate excessive heating from this cause it is necessary that 1 See also " On the Seat of the Electrodynamic Force in Ironclad Arma- tures," by E. J. Houston and A. E. Kennelly, Electrical World, vol. xxviii. P- 3 (July 4, 1896). Comment, by Townsend Wolcott, Electrical World, vol. xxviii. p. 271 (September 5, 1896), and by William Baxter, Jr., Electrical World, vol. xxviii. p. 299 (September 12, 1896). 22] DIMENSIONS OF ARMATURE CORE. the teeth must be made numerous and narrow, and that the length of the air gap between the pole face and the top of the iron projection must bear a definite relation to the width of the slot. In practice it has been found that according to the field density employed air gaps having a radial length of from one-fourth to one-half the width of the slot, in large and medium size machines respectively, and a ratio of gap to slot up to i in very narrow slotted small armatures, give the best results. a. Toothed Armatures. The mean winding diameter, d' & , of a toothed armature being determined by means of formula (30), its core diameter or diameter at bottom of slots, d^ Fig. 48, is obtained by deduct- NUMBER OF SLOTS =n' Fig. 48. Dimensions of Toothed Core Disc. ing from d' & the height of the winding space, or, in this case, the depth of the slots, // a , averages for which are given in the fourth column of Table XVIII., 23. The outside diam- eter of the armature, d" M over the teeth, is obtained by adding h^ from Table XVIII. to d\, from formula (30). The number of the slots, n' ct since practice has shown, in accord- ance with the theoretical considerations, that better results are obtained from deep and narrow slots than from shallow and wide ones, should be taken as large as possible, from the mechanical and economical standpoint. In the following Table XIII. good practical limits of the number of slots for armatures of different diameters are given: 66 DYNAMO-ELECTRIC MACHINES. [22 TABLE XIII. NUMBER OF SLOTS IN TOOTHED ARMATURES. DIAMETER OF ARMATURE. d"a. NUMBER OF SLOTS. n' Inches. Centimetres. 5 12.5 2o to 40 10 25 40 70 15 27.5 50 100 20 50 60 150 30 75 80 200 50 125 100 250 100 250 150 300 150 375 200 400 200 500 300 500 As to the width of the slots, b & , Fig. 49, a number of conflict- ing conditions governs its relation to that of the teeth: On account of the tendency of the teeth to create eddy currents Fig. 49. Various Types of Slots for Toothed Armatures. in the pole faces, their width ought to be small compared with that of the slots, or shallow slots and narrow teeth should be used; in .order to reduce the hysteresis loss in the teeth and the heat caused by the same to a minimum, the mass of the teeth should be small and their area perpendicular to the flow of the lines, hence their width should be large, that is, on this account narrow slots and wide teeth should be employed; for the sake of effectively reducing the magnetic reluctance of the circuit, the area at the bottom of the teeth should be large, hence the slots narrow and the teeth wide. 22] DIMENSIONS OF ARM A TURE CORE. 67 L. Baumgardt 1 proposes to calculate the hysteresis heat per unit volume of the teeth for a variety of values for the width of the slot, also to find that width of slot for which the density in the teeth for given armature-diameter, number, and sec- tional area of slots becomes a minimum, and to compare the values so found, choosing a practical width that is not too far from giving minimum hysteresis heat and minimum tooth density. For the purpose of calculating the relative values of the hysteresis heat for a given width of the slot he gives a formula which, when reduced to its simplest form, becomes: (,-*)'( S a X the symbol A standing for the expression; A -. <**" * - 'o X 6. ** ~ ^ n > (32) 2n' X tan n c in which Y = hysteresis heat per unit volume of teeth divided by a constant that depends upon the machine under consideration; d"^ = external diameter of armature (in millimetres) ; n' c = number of slots; b a = width of slots (in millimetres); 6" 8 = sectional area of slot = b a x ^ a O n millimetres). In order to save the trouble of employing this rather com- plicated formula in every single instance, the author has calcu- lated the values of Ffor b~ H = .75 to 25 mm. (1/32 to i inch) for a variety of cases ranging from d" & = 100 mm. (= 4"), n' c = 24, S B =go mm." ( = .14 square inch) to d" & = 5,000 mm. ( = 197^"), ' c = 320, S 8 = 2,500 mm. 2 (=3-875 square inches), and in taking the minimum value of Fin each armature as unity, has, for every case, plotted a curve with the various widths of the slot as abscissae and the value of Y ~y * min 1 " On the Dimensioning of Toothed Armatures," by Ludwig Baumgardt, Elektrotechn. Zeitschr., vol. xiv. p. 497 (September I, 1893); Electrical World, vol. xxii. p. 234 (September 23, 1893). 68 D YNA MO-ELECTRIC MA CHINES. [22 as ordinates. In Fig. 50 these curves are arranged in four groups with reference to the size of the armature, only the two limiting curves of each group being drawn. They show that the specific hysteresis heat at first diminishes slightly as the width of the slot increases and arrives at a minimum point WIDTH OF SLOT Fig. 50. Variation of Hysteresis Heat per Unit Volume of Teeth with Increasing Width of Slot, for different Sizes of Toothed Armatures. which over the whole range lies between the narrow limits of 1/16 and 3/16 inch (1.5 and 5 mm.) width of slot, after which it increases very rapidly in case of small armatures, and more or less slowly in case of large ones. Since a slot of 1/16 inch (1.5 mm.) width is too small for even the smallest armature and one of 3/16 inch (4.5 mm.) is too small for anything but a very small machine, it follows that the minimum of hysteresis heat- ing cannot be reached in practice, but by making the slots narrow and deep the hysteresis effect can be kept within prac- 22] DIMENSIONS OF ARMATURE CORE. 69 tical limits. The width of the slot having been chosen, the limits of the specific hysteresis heat, expressed as multiples of the minimum value, can then be obtained from the curves in Fig. 50, or from the following Table XIV., which has been compiled from the curves given: TABLE XIV. SPECIFIC HYSTERESIS HEAT IN TOOTHED ARMATURES, FOR DIFFERENT WIDTHS OF SLOTS. WIDTH OP SLOT. RELATIVE SPECIFIC HYSTERESIS HEAT IN TEETH. 4' to 10" (100 to 250 mm.) Armature. 10' to 40' (250 to 1,000 mm.) Armature. 40' to 120- (1,000 to 3,000 mm.) Armature. 120- to 200" (3,000 to 5,000 mm.) Armature. Inch. Millimetres. ft i A I i 1 1 0.75 1.5 3 45 6 9.25 12.5 16 18.5 22 25 li to 3 1 it 1 H li 2 li 3 2i 10 4 20 6 25 Iito2i li' 2 1 ' H 1 ' H li' 2 if 3i 2f 6i 3f ' 12 4f ' 18 6 ' 22 Iito2i If 2 l ' H 1 ' H if if li' 2i If 3 2f 4 2f ' 5 3f 7 5 ' 12 Iito2 H' H If H 1 ' U 1 ' H If 1* li' 2 if at li' 3 If 4 2 ' 6 According to this table the specific heat due to hysteresis, if, for instance, a ^ inch (18.5 mm.) slot is used in a 100 inch (2,500 mm.) armature, is from 2^ to 5 times as high as in case of a y& irtch (3 mm.) slot for which, in that group, it is a mini- mum. The value of b e , for which the magnetic density in the teeth becomes a minimum, is found by making the circumferential width at the bottom of the teeth, * (d\ - 2/y - '. X *. - a maximum; and the value of b s which does the latter is 27T X n' (33) DYNAMO-ELECTRIC MACHINES. [22 where b\ = width of slot for minimum tooth density, in inches or in centimetres; S* a = cross-section of slot, in square inches, or in square centimetres; n' c = number of slots. While formula (33) in connection with Table XIV. is very useful for the determination of the best width of the slots in case their cross-section is given, ordinarily the problem is to be attacked by first selecting the number of teeth, then deter- mining the width, and finally the depth of the slot. Consider- ing all the adverse conditions, the author has found it a good practical rule to make the width of the slots d\ X 2 X (34) TABLE XV. DIMENSIONS OF TOOTHED ARMATURES, IN ENGLISH MEASURE. DIAMETER DIMENSIONS OF SLOTS. NUMBER OF CORE WIDTH AT OF SLOTS. DIAMETER, BOTTOM OF ARMATURE, IN INCHES. Depth, in inches. Width, in inches. Ratio of Depth to n'c = IN INCHES. TOOTH, IN INCHES. Width. d a"" * h d\ n* b a 26, . . . fl H W > ? ? 1 gi|||||||222 | a ference. 1 o- Core Edges. d J aas+-n- * * * \ CrjC?U''fCO'')CJi**-CC ^. on Core Faces. H O s6 --S 5 - 5 3 <* ^.s" : : : | s Siiaft Insula- tion. S TO c. 2J E. 3 ^ : 1 Slot Lining. 5 S-iTe o'~>"'' ZI Insulation -t^gl bbbobbbbbbbb g ^ W rt _ 3 CFQ n> E-3c?g. 0.0,W*9K.OO^OtO.- BT -* Layers. 8 o *? p 5- en o o o o o b o o oo w D* 5. ference. 1 +-f Core Edges. i ?I8i ji ' " S8 3 : : : ggggf | 1 2= Core Faces. 3 <" -ft n ^ 5- 1 I'ff ' Soooooooo -f 4-h Shaft Insula- tion. o i' !. s 1 Ok Slot Lining. p M Insulation r* O _ OJ OOOOOOOOOOOQ g S o S | o cr o -"5, gggwo.jctooo^^w p- -* Layers. 5 & j Si -i a 3 1 * Core Circum- ference. ff S B n a* " 1 o< Core Edges. 1 Ml _ -2 S. S. E. : : : gg|ggi|: I Core Faces. CO 0^0. 3 o o- a <+ Shaft Insula- tion. a> B ' 233 B o' S w S : | 2- Slot Lining. i |> e ^. Insulation g s- bbobbbbbbbb. g <^ B 1 5SSo.8gu.O.N-i00 Cf -* Layers. > a- | : | a Core Circum- ference. : 1 Core Edges. . : : : |'ggggg< = | ft on Core Faces. M : : : ill|ggs : : 1 $ Shaft Insula- tion. g oooSoocooo' " p 1 == Slot Lining. 5 CD M 1 ^a between Layers. 24] DIMENSIONS OF ARM A TURE CORE, 3 In the preceding Table XIX. (see page 82) the thicknesses of armature core insulations are compiled for machines of various sizes and for different voltages. b. Selection of Insulating Material. Armature insulations must not only possess high insulating resistance, but also great disruptive strength, that is, the ability to withstand rupturing or puncturing by electric press- ure. Besides these two main properties, successful insulating materials must also be perfectly flexible and elastic, must be non-absorptive, and unaffected by heat. Unfortunately there is no material that in a very high degree possesses all these properties together, and, in selecting armature insulators, such a material is to be chosen in every case which best fulfills the particular conditions, having as its prominent property that which is most desired without being objectionable in other respects. Mica ranks highest in disruptive strength, has a high insu- lating resistance, is non-absorptive and unaffected by heat, but it very easily breaks in bending, and therefore, in spite of being the most perfect armature insulator, cannot be used in places where the insulation is required to be flexible. Paraffined materials are distinguished by their enormous insulation resistance, and have a high disruptive strength; but they cannot stand much bending, and are seriously affected by heat. Rubber has good insulating qualities, and is extremely flexi- ble, but is injured by temperatures above 65 Centigrade (= 150 Fahr.). Insulating materials prepared by treating certain fabrics, such as cotton, linen, silk, and paper, with linseed oil, and oxi- dizing the oil at the proper temperature to expel any moisture, although not being of marked disruptive strength or of ex- tremely high insulating resistance, yet make very satisfactory armature insulation, as they can be made to possess all the properties required of a perfect insulator in a practically suffi- cient degree. By using pure linseed oil, properly treated, and by exercising special care in preparing the surfaces, a comparatively high insulation value, both in resistance and in disruptive strength, can be obtained, while the materials are 84 DYNAMO-ELECTRIC MACHINES. [24 perfectly flexible, practically non-absorptive, and affected only by temperatures far above that which entirely destroys the cotton or silk insulation on the armature wires. In using these materials, care should be taken that their surfaces are perfectly uniform, for, if the oil is not evenly distributed, the disruptive strength and the insulation resistance fall off con- siderably. The greatest thickness of an unevenly coated, oil-insulating material determines the number of layers of it that can be placed into a certain space, while the smallest thickness determines the insulation-value, which often runs as much as fifty per cent, below that of an evenly covered sheet of the average thickness if the surfaces were uniform. Oil insulations made of pure linseed oil are preferable to those in which the ordinary commercial oil is used, since to give the latter its oxidizing properties certain metallic oxides are employed which, although being classed as insulators, have an insulating value far below that of oil. With commercial linseed oil there is, therefore, never any certainty that some of these oxides may not be held in suspension, but it is essen- tial for a high insulation resistance that an insulating material shall not contain any other substance having a lower insulating value than itself. Micanite, which is made of pure India sheet mica cemented together with a cement of very high resistance, can be molded in any desired shape, or in combination with certain other materials can be rendered more or less pliable, thus combin- ing the excellent qualities of mica with the property of flexi- bility, and making a most perfect armature insulating material. Micanite cloth, micanite paper, and micanite plate are varieties of this material. The latter is a combination of sheet mica with pure gum or solution of guttapercha, or with a special cement, the office of the gum or cement being to hold the laminae together but to allow them to slide upon each other when the plate is bent. Vulcanized fibre is comparatively low both in resistance and in disruptive strength, and is seriously affected by exposure to moisture. Vulcabeston, an insulating substance composed of asbestos and rubber, is not affected seriously by high temperatures, and has the advantage that it can be molded like micanite, but 24] DIMENSIONS OF ARMATURE CORE. TABLE XX. RESISTIVITY AND SPECIFIC DISRUPTIVE STRENGTH OF VARIOUS INSULATING MATERIALS. MATERIAL. THICKNESS USED FOR ARMATURE INSULATION. AVERAGE RESISTIVITY AT 30 CENT. SPECIFIC DISRUPTIVE STRENGTH. Limits, in Volts per mil Thickness. Practical Average. Megohms per square inch-mil. Megohms per cm. 2 -mm. inch. mm. Volts per mil. Volts per mm. .004-.020 .008-.025 .010-.030 .012-.050 .005-.012 .006-.015 .006-.015 .012-.020 .015-.025 .030-.075 A-8 .015-.040 .001-. 125 .012-.016 .008-.020 .005-.012 .010-.025 010 075 .1-.5 .2-.6 .25-.7S .3-1.25 .125-.3 .15-.4 .15-.4 .3-.5 .4-.6 .75-2.0 1.5-75 .35-1.0 .025-3.0 .S-.4 2-.5 .125-3 .2S-.6 .25-.2 .2S-.4 .25-.S .125-.75 .1 .15 7 680* 850* 120 10 25 11,800,000 10 25 470 600 6 10,000 33,000 310,000 t 440,000 t 490,000 t 500,000 t 980,000 620,000 t 320,000** 650 tt 1,350 1,600 tt 5 3 2 11,800,000 180 100 3,000,000 30 50 75 50 75 35 15 06 1.800 173.000 216.000 31,000 2,500 6,400 3,000,000.000 2,500 6.400 120,000 150,000 1,500 2,540,000 8.400,000 79,000,000 112.000,000 124,000.000 127,000.000 250,000.000 158.000,000 81,000,000 165,000 340.000 400,000 1,270 760 510 3,000,000,000 45,700 25,400 760,000,000 7,600 12,000 18,000 12,000 18,000 9,000 3,800 15 75 150 100-180 225-190 330-500 150-250 260-340 340-370 380-480 210-240 250-300 150- 325 900-1,300 150-250 750-900 2,000-8.000 240-490 175-310 390-510 280-390 940-1,120 830-1,040 575-790 450-650 550-700 600-960 200-275 190-250 160-200 800-1,000 830-950 100-420 350-600 30-60 350-565 500-570 320-420 420-510 240-265 60-110 10-25 5-20 15-40 125 300 375 175 275 350 400 225 275 200 1,000 175 800 3,000 300 200 425 309 1,000 900 600 500 600 700 225 200 175 900 850 150 400 40 475 525 375 450 250 75 15 10 90 5,000 12,000 15,000 7,000 11,000 14,000 16,000 9,000 10,000 8,000 40,000 7,000 32.000 120,000 12,000 8,000 17.000 12,000 40,000 36,000 24,000 20.000 24,000 28,000 9,000 8.000 7,000 36,000 34,000 6,000 16,000 1,600 19,000 21,000 15.000 18,000 10.000 3,000 600 400 800 " and Muslin, oiled Cotton, Single Covering (on wires) Cotton, Single Covering, shel- Cotton, Single Covering, boiled Cotton Doable Coverin<* Cotton, Double Covering, shel- lacked Hard Rubber Linseed Oil, pure, oxidized Micanite Cloth " flexible Paper *' flexible Plate " flexible, "A" J 'B"T Oiled Cloth (Cotton, Linen, or Muslin) .010-.015 .010-.020 .005-.030 .004-. 006 .006-.010 .003-.006 .004-.008 .005-010 .002-.008 .010-.020 .025-.075 .015-.060 .006-.012 .OOI-.0025 .0015-.004 .0015-.005 .002-.007 .006-.012 .040-. 100 4-4 M H Oiled Paper single coat " " double " .15-.25 .075-. 15 .1-.2 .125-.25 .05-.2 .2S-.5 .6-2.0 .35-1.5 .15-.3 .025-.065 .04-.! .04-.I25 .05-.175 .15-.3 1.0-2.5 3.0-100 3.0-100 3.0-100 " brown Paraffined Paper Pres Board Rubber, Sheet Shellacked Cloth Silk, Single Covering (on wires) " shellacked. " Doable " " " " shellacked. Varnished Cheese Cloth Wood Mahogany " Pine " Walnut * Insulation resistance at 50 C. is about f , at 70 C. about ^, and at too C. about -fa of that at 30 C. ; M.;; & ;; .* , * ; : :: ; :; ;: &:: :; ;: * :: :; ;: ,: :: :: t Mica Laminae, put together by solution of guttapercha (\lica Insulator Co.). ^ " " '* patent cement (Mica Insulator Co.). ** The insulating properties of this material (one of the products of the Mica Insulator Co.) is affected but very little by temperature, its specific resistivity at 50* C. being about .9, at 70" C. about .95, and at 100 C. about .85 of the average resistivity at 30 C. tt Resistivity at 50 d. is about %. at 70* C. about J4, and at 100* C about ^ of that at 30" C. Calculated from tests made by Addenbrooke, see Munroe & Jamieson's " Pocket-Book," tenth edition (1894), page 251. 86 DYNAMO-ELECTRIC MACHINES. [24 both its resistivity and its specific disruptive strength are very small comparatively. The preceding Table XX. gives the insulating properties ot the various insulating materials commonly used, and is aver- aged from information contained in writings by Steinmetz, 1 and by Canfield and Robinson," from a report by Herrick and Burke, 3 and from tests expressly made for the purpose. The values of the disruptive strength are those between parallel surfaces, and, since for the same material the break-down volt- age per mil varies with the thickness in some cases decreasing, in others increasing (according to the nature of the material), as much as 50 per cent, when varying the thickness of the sample from .005 to .025 inch are averaged from tests with different thicknesses. Since the insulation resistance varies considerably with temperature 4 (see notes to Table XX.), and since readings taken with identically the same samples at the same tempera- ture but at different times showed large deviations presum- ably owing to differences in moisture the figures for the resistivity have, chiefly, a comparative value, but may with sufficient accuracy be taken as averages for the computation of the insulation resistance of armatures, commutators, etc., of dynamo-electric machines. ! " Note on the Disruptive Strength of .Dielectrics," paper read before the American Institute of Electrical Engineers by Charles P. Steinmetz. Trans- actions A. I. E. E., vol. x. p. 85 (February 21, 1893); Electrical Engineer, vol. xv. p. 342 (April 5, 1893). '"The Disruptive Strength of Insulating Materials," engineering thesis by M. C. Canfield and F. Gge. Robinson, Columbia College, Electrical Engineer, vol. xvii. p. 277 (March 28, 1894). 8 " Report on Tests of Insulating Materials manufactured by The Mica Insulator Co., Schenectady, N. Y.," by Albert B. Herrick and James Burke, electrical engineers, New York, August 13, 1896. 4 " Effect of Temperature on Insulating Materials," by Geo. F. Sever, A. Monell, and C. L. Perry, Transactions A. I. E. E., vol. xiii. p. 225 (May 20, 1896); Electrical World, vol. xxvii. p. 642 (May 30, 1896), vol. xxviii. p. 41 (July II, 1896); Electrical Engineer, vol. xxi. p. 556 (May 27, 1896). CHAPTER V. FINAL CALCULATION OF ARMATURE WINDING. 25. Arrangement of Armature Winding. By "arrangement" of the armature winding is understood the grouping of the conductors into a number of armature coils, each containing a certain number of turns, or convolu- tions, of the armature wire, and each one corresponding to a division of the collector or commutator. a. Number of Commutator Divisions. The E. M. F. generated by the combination of a series of convolutions, or by a coil, while under the commutator brushes, is not constant, but fluctuates with the rate of its cutting lines of force in the different positions during that period. This fluctuation of the E. M. F. of a dynamo, con- sequently, increases with the angle which is embraced by each coil of the armature, and can be mathematically determined from the measure of this angle. This is extensively treated in 9, and Table I. contained therein shows that in a i2-coil armature, in which the angle inclosed by each coil is 30, the fluctuations of the E. M. F. amount to 1.7 per cent, of the maximum E. M. F. generated; that in an i8-coil armature, in which the coil-angle is 20, they are Y per cent. ; for 24 divisions, corresponding to an angle of 15, about y<2, of i per cent. ; for 36 coils, embracing an angle of 10 each, f of i percent.; for 48 divisions of 7^ each, -jig- of i per cent. ; for 90 divisions with coil-angle of 4, Y^JJ of i per cent. ; and that for a 360 division commutator, finally, for which the angle inclosed by each coil is i, they are reduced to but j^j, of i per cent. From these figures it is apparent that the fluctuations be- come practically insignificant, or the potential of the machine practically steady, if, for bipolar dynamos, armature coils of an angular breadth of less than 10, or what amounts to the same thing, if commutators with from 36 divisions 87 88 D YNAMO-ELECTRIC MA CHINES. [25 upward are used. For low potential machines up to 300 volts it has been found good practice to provide, per pair of armature circuits, from 40 to 60 divisions in the commutator. For high potential dynamos the voltage itself determines the number of commutator bars. For, in these, the self- induction set up in the separate coils, and the sparking at the commutator caused by the potential of this self-induction between two adjacent commutator divisions, are more impor- tant considerations than the fluctuation of the E. M. F. No potential below 20 volts is able to maintain an arc across even the slightest distance between two copper points. The potentials above this figure necessary to carry an arc over a certain distance depend upon the intensity of the cur- rent. In order to maintain, between two copper conductors, an arc of .040 inch length, the usual thickness of the com- mutator insulation for high voltage machines, according to actual experiments made by the author, imitating as nearly as possible the conditions of a commutator, a current of 100 amperes takes 20 volts 50 20 10 5 2 1 21 23 25 30 40 50 From this it can be concluded that, in order to prevent the commutator of a high voltage machine from becoming un- necessarily expensive, allowances have to be made as follows: TABLE XXI. DIFFEBEKCES OF POTENTIAL BETWEEN COMMUTATOR DIVISIONS. CURRENT INTENSITY DIFFERENCE OF POTENTIAL PKB ARMATUKB CIRCUIT. BETWEEN COMMUTATOR DIVISIONS. Over 100 amperes 10 to 20 volts 100 to 50 12 21 50 20 15 23 20 10 20 25 10 5 25 30 5 2 30 40 2 1 35 50 25] FINAL CALCULATION OF WINDING. 89 The respective minimum numbers of commutator divisions, consequently, are: For over looA. p. circuit " 100 to 50 A. " " 50 to 20 A. " " 20 to 10 A. " " 10 to 5 A. " 5 to 2 A. " 2 to i A. " V^c/min E X 2 ' p _ EX *'p 20 10 21 E X 2 'p ^ X ' p (^c)min / \ 23 E x 2 ' p ii-5 ^X' p 25 E X 2 ' p 12.5 ^ X p" \ n c)mia 3 E * 2 'p _ 15 E x ' ( n c)min 40 E X 2n' v 20 X ' p SO 2q Having thus determined the minimum number of divisions that can be used in the commutator without excessive spark- ing, the actual number, n$, to be employed has to be chosen by comparing this value of ( c ) min with the total number of con- ductors on the armature, found by multiplying the rounded result of equation (35), (37) or (38), respectively, with that of formula (39), and dividing the product by the number, n$, of armature wires stranded in parallel. b. Number of Convolutions per Commutator Division. The number of turns, n M of armature conductors per com- mutator division, or the number of convolutions in each armature coil, is then readily obtained by dividing the total number of armature convolutions by the number of coils, n c . The number of armature convolutions, in ring armatures, is identical with the number of armature conductors, while in drum armatures it takes two conductors to make one turn, and, therefore, the number of turns is but one-half the number of conductors. Hence we have for ring armatures: n w x w\ n c X 1^ and for drum armatures or drum-wound ring armatures: 2 X X (46) (47) 90 DYNAMO-ELECTRIC MACHINES. [26 c. Number of Armature Divisions. If the armature is to have spacing strips, or driving horns, the number of the armature divisions for this purpose depends upon the number of armature coils, c , the number of turns per armature coil, n M and the number of conductors in parallel, n. In ordinary machines the number of armature divisions is usually made equal to the number of coils, c , and sometimes especially in drum armatures double the number of coils, 2 c , is taken. For high current output machines often a greater number of armature divisions than that given by the number of coils is chosen. In such a case the total number of single wires, or cables, n c x a X //, is to be suitably arranged in groups. The number of these groups is to be a multiple of the number of coils, c , and since the number of turns per coil, a , in high current dynamos, is usually = i, the problem of grouping, in this case, amounts to subdividing the number of parallel wires, n&. 26. Radial Depth of Armature Core. Density of Mag- netic Lines in Armature Body, Diameter and length of the armature core being deter- mined, its proper radial depth can be readily found by the cross-section to be provided for the passage of the magnetic lines of force. The density of lines permitted per unit area of armature cross-section is limited by the heating of the armature due to hysteresis and eddy current losses. The heat, generated by either of these causes, increases with the density of the lines, and with the number of magnetic reversals per second. The latter number is the product of the number of revolutions per second and the number of magnet poles, and therefore it is obvious that, in order to keep the temperature increase of the armature in its practical limits, in dynamos where this product is great, larger specific sectional areas of the armature core are to be allowed than in machines having a small number of magnetic reversals, or a low "frequency," as half the number of reversals, or the number of complete magnetic "cycles," is called. The former high frequency is the case for high 26] FINAL CALCULATION OF WINDING. speed and multipolar dynamos, the latter low frequency for low speed and bipolar ones. On the other hand, large multipolar machines generally have well-ventilated ring arma- tures, and in these an even considerably larger amount of heat generated will produce a smaller temperature increase than in drum armatures of equal output. TABLE XXII. COKE-DENSITIES FOR VARIOUS KINDS OP ARMATURES. SPECIES op DYNAMO. TYPE OF MACHINE. KIND OF ARMA- TURE. FLUX DENSITY IN MINIMUM CROSS- SECTION OF ARMATURE. Lines per gq. inch. ". Lines per cm.* (*a Incandescent Dy- namos; Railway Generators; Ma- chines for Power- Transmission and Distribution; Sta- tionary and Rail- way Motors. Bi- polar High Speed Drum 50,000 to 70,000 8,000 to 11, 000 Ring 60,000" 80,000 9,000 ' 12,500 Low Speed Drum 60,000" 80,000 9,000 " 12,500 Ring 70,000 " 100,000 11,000 " 15,500 Multi- polar High Speed Drum 35,000 " 50,000 5,500 " 8,000 Ring 50,000" 70,000 8,000 " 11,000 Low Speed Drum 40,000" 60,000 6,000 " 9,000 Ring 60,000 " 80,000 9,000 " 12 500 Series Arc Lighting Dynamos. Bi- polar High Speed Ring 110,000 " 130,000 17,000 " 20,000 Multi- polar High Speed Ring 100,000 " 120,000 15,500 " 18,500 Electroplating and Metallurgical Dy- namos. Bi- polar High Speed Drum 40,000 " 60,000 6,000" 9,000 Ring 50,000 " 70,000 8,000" 11,000 Multi- polar High Speed Ring 3.1,000 " 50,000 5,500 " 8,000 Low Speed Ring 40,000" 60,000 6,000 " 9,000 Accumulator Charging Dyna- mos; Battery Mo- tors. Bi- polar High Speed Drum 35,000 " 50,000 5,500 " 8,000 Ring 40,000 " 60,000 6,000 " 9,000 Multi- polar High Speed Drum 30.000" 45,000 4,500 " 7,000 Ring 35,000 " 50,000 5,500 " 8,000 With dynamos for special purposes still other points have to be considered: In arc lighting dynamos, in order to keep 92 DYNAMO-ELECTRIC MACHINES. [26 the magnetic flux constant at varying load, it is necessary to make the magnetic circuit insensitive to considerable changes in exciting power, and this is achieved by working the entire circuit at a very high saturation; on the other hand, in machines used exclusively for charging accumulators, the saturation of the circuit should be very low, for then, during charging, when the counter E. M. F. of the cells gradually rises, the voltage of the charging dynamo also rises automati- cally instead of remaining nearly constant, as it would do if the magnetism were incapable of further increase. Again, in dynamos for electroplating, electrotyping, electrolytic pre- cipitation of metals and for electro-smelting, and in motors driven by accumulators or primary batteries, on account of the very low terminal-voltage, the field density in the gaps must be kept low (compare 18), and therefore a low saturation through the entire circuit is required. According to these considerations, the values given in Table XXII., page 91, for the flux-densities in the radial cross-section of the armature core are recommended (see 91). The cross-section of the magnetic circuit in the armature core is the product of the net length and the net radial depth of the core, and of the number of poles; and this prod- uct, divided into the total magnetic flux through the arma- tures, gives the density of lines per unit area. In order to obtain the net radial depth, or breadth of the cross-section of any armature core, therefore, the total armature flux is to be divided by the product of the armature density, of the net length of the body, and of the number of poles: ..(48) _ _ 2 p X (B" a X 4 X , The symbols used in this formula denote: b & = radial depth, or breadth of cross-section of armature core, in inches; < = useful flux, in maxwells, or number of useful lines of force cutting armature conductors, the calculation of which is the subject of 56. (B" a = flux density in minimum area of armature core, in lines per square inch, given in Table XXII. ; n v number of pairs of magnet poles. 26] FINAL CALCULATION OF WINDING. 93 / a = length of armature core, in inches, from formula (40); k^ = ratio of net iron section to total cross-section of arma- ture core, see Table XXIII. For calculation in metric measure (B" a is to be replaced by (B a (Table XXII.) and / a to be expressed in centimetres; for- mula (48), then, will furnish b & in centimetres. The constant k^ depends upon the material, and the manner of building up, of the armature core. In order to prevent excessive losses and resulting heating of the armature due to eddy currents in the iron, it is necessary to laminate the body perpendicular to the direction of the active armature con- ductors. In case the active pole faces embrace either the outer, or the inner, or both circumferences of the armature, the active conductors are those parallel to the shaft, and the lamination of the core is to be effected perpendicularly to the shaft; while in case of the poles being at the sides of the armature (flat ring type), the active conductors run per- pendicular to the shaft, and the lamination is to take place parallel to the shaft. In case of the polepieces embracing three sides of the armature section, finally, the active con- ductors are partly parallel and partly perpendicular to the shaft, and the lamination, in consequence, is also to be carried out in both directions. The materials for effecting these various laminations are iron discs, iron ribbon, and iron wire, respectively. The insulation of these laminae, in the majority of machines, has been, and is yet, effected by inserting sheets of thin paper, asbestos, etc., between them, although it has been repeatedly shown by practical experiments ' that such an insulation is not only entirely unnecessary, but, on the con- trary, even disadvantageous. For, in order not to lose too much of the available sectional area of the body, the lamina- tion in such armature is usually made rather coarse, but it is just the fineness of the lamination, and not the thickness of its insulation, that avoids in a higher degree the generation of eddy currents. The oxide coating created by heating the iron is a very effective and suitable insulation of the armature core laminae. 'Ernst Schulz, Elektrotechn. Zeitschr., December 29, 1893. See "Iron in Armatures," Electrical World, vol. xxiii. p. 91 (January 2O, 1894), and p. 248 (February 24, 1894). 94 D YN A MO-ELECTRIC MA CHINES. [27 In the following Table XXIII. values of the ratio a of the net to the total core section are given for various thicknesses of the iron, and for the different modes of insulation now in use: TABLE XXIII. RATIO OF NET IRON SECTION TO TOTAL CROSS SECTION OF ARMATURE CORE. MATERIAL THICKNESS OP IRON. INSULATION OF BETWEEN VALUE OP ARMATURE CORE. LAMINAE. RATIO k a . inch. maa. .080 2 Paper or Asbestos 0.95 to 0.90 Sheet Iron (Discs or Ribbon). .040 .020 .010 1 0.5 0.25 " " Enamel .92 .88 .90 .85 .85 .80 .010 0.25 Oxide Coating .95 .90 .080 2 Cotton Covering .90 .80 Square Wire. .040 .020 1 0.5 Enamel or Varnish .85 .75 .80 .70 .020 0.5 Oxide Coating .90 .85 .080 2 Cotton Covering .80 .70 Round Wire. .040 .020 1 0.5 Enamel or Varnish .75 .65 .70 .60 .020 0.5 Oxide Coating .85 .80 In large ring armatures, for the sake of ventilation, air spaces are provided in modern machines by means of light brass frames inserted in certain intervals between the core discs. In calculating the radial depth, a , of the body, the sum of these distance-pieces is to be deducted from the total length, / a , of the core, the reduced length so found being used instead of / a in formula (48). 27. Total Length of Armature Conductor. The amount of inactive, or "dead," wire required to join the active portions of the armature conductors into continuous turns depends upon the shape of the armature, the height of the winding space, and the manner of winding. In an arma- ture, for instance, having a core section of great length parallel to the pole faces, and but a small thickness perpendicular to 27] FINAL CALCULA TION OF WINDING. 95 the same, this inactive addition to the generating wire will be comparatively small, while in short armatures with great core depth the proportion of the dead to the active length will be considerably greater. Furthermore, if two armatures of same length, same core diameter, and same radial depth have equal lengths of active conductor, but are wound with different heights of the winding space, as will be the case if the one has a smooth core with winding covering the entire circumference and the other a toothed body, then the external diameters, and consequently the lengths necessary to join the active con- ductors, are greater in the latter case, and therefore it is evi- dent that the armature with the higher winding space requires a greater total length of armature conductor. If, finally, two otherwise entirely equivalent armatures are wound by different systems, a considerable difference may be found in the total lengths of wire required to produce equal lengths of active conductor. a. Drum Armatures. The active length of the armature conductor being known, the simplest method of expressing its total length, for a drum armature, is where Z t = total length of armature conductor (wires in parallel considered as one conductor); Z a = active length of armature conductor, from formula (26); 3 = constant, depending upon shape of armature and system of winding. See Table XXIV. The ratio, 3 , of the total to the active length of the arma- ture conductor, in a drum armature, depends chiefly upon the ratio of length to diameter of the armature core. In modern machines the lengths of drum armatures usually vary between one and two diameters; in special designs, however, a value as low as 0.75 or as high as 2.5 may be taken for this ratio. The following Table XXIV. gives average values of the con- stant s for various shape-ratios for smooth as well as for toothed drum armatures: 9 6 DYNAMO-ELECTRIC MACHINES. [27 TABLE XXIV. RATIO BETWEEN TOTAL AND ACTIVE LENGTH OP WIRE ON DRUM ARMATURES. RATIO OF LENGTH TO DIAMETER OF ARMATURE COUB. 'a^a VALUE OF *,. Smooth Armature. Toothed Armature. 0.75 2.50 3.10 0.8 2.45 3.05 0.9 2.40 3.00 1.0 2.35 2.95 1.1 2.30 2.90 1.2 ' 2.25 2.85 1.3 2.20 2.80 1.4 2.15 2.75 1.5 2.10 2.70 1.6 2.05 2.65 1.7 2.00 260 1.8 1.95 2.55 1.9 1.90 2.50 2.0 1.85 2.45 2.25 1.75 2.35 25 1.70 2.25 Another form often used for expressing the total length of wire on a drum armature is indicated bv the formula: Z t = N c X (4 + 4 X <4) = X -r); (50) N c = total number of conductors all around armature circum- ference; > 4 = constant, depending upon system of winding. This formula (50) has the advantage over (49) that no special table is required for its constant, since for a certain type of armature, and a certain system of winding, 4 is very nearly constant for all sizes and shapes. The value of 4 for the smooth drum armatures considered in Table XXIV. lies between 1.3 and 1.7, and as an average 1.5 may be taken, thus making the formula for the total length of conductor for smooth drum armatures: A = x (51) Formula (51), then, means that the additional length of dead wire to every conductor of a smooth drum armature is 27J FINAL CALCULATION OF WINDING. 97 one and one-half times its core diameter, or that the total length of one conductor in a smooth drum is equal to the length of the body plus one and a half times the core diameter. The reason why k t , even for the same type and same winding method, has not the same value for all sizes, is that the pro- portion of the core diameter to the thickness of the armature shaft is very much different for different sizes. In a small drum, for instance, the shaft takes up considerably much more room than in a large one, and therefore the dead lengths are comparatively larger in a small machine. In fact k t = 1.5 gives too high values for small ratios of length to diameter, which occur in large drums, while the values found by (51) for large ratios of length to diameter, which are met in small armatures, are below those given in Table XXIV. For / a : d & = i, or d & : / a = i, for instance, we obtain, by comparison of (49) with (50) and (51): 3 = >- = i + 4 X ~= i + i.S X i = 2.5, *' *a while Table XXIV., which is averaged from actual practice, gives k 3 = 2.35 for this ratio, to which number would corre- spond the small value of k, i 2.35 1 ' T 1C ~ - 1.. ' ft) On the other hand, if / a : d & = 2, or d & : / a = 0.5, we get: k 3 = i + i-5 X 0.5 = 1.75; the table-value for k 3 is 1.85 for this shape-ratio, and therefore the high value of 1.85 - i *= -V ='- 7 would answer in this case. For toothed-drum armatures the numerical value of 4 , in the practical limits of the ratio of shape, lies between 1.9 and 3, the average being about 2.5 ; hence formula (50) for toothed- drum armatures becomes : Z t = Z a x (1 + 2.5 X^M; (52) (""***)' D YNAMO-ELECTRIC MA CHINES. [27 that is to say, the average length to be added to each active conductor in a toothed-drum armature is two and one-half times the core diameter of the drum, or the average dead length in each turn (consisting of two active conductors) is five times the diameter at the bottom of the slots. b. Ring Armatures. In a helically or spirally wound ring armature of a core sec- tion of given dimensions, the ratio of the total to the active length of the conductor depends upon the arrangement of the Fig. 59- ^T if li Fig. 61. Fig. 62. It A. Fig. 65. Fig. 66. Figs. 59 to 66. Various Arrangements of Field-Magnet Frame around Ring Armature. field-magnet frame. There are, altogether, eight different possibilities of arranging the poles around a ring armature; these eight methods, however, can be classified into but five principally different cases, viz. : Case I. Polepieces facing one long armature surface, see Figs. 59 and 60; " II. " " two long armature surfaces, see Figs. 6 1 and 62; " III. " " one long and two short armature surfaces, see Fig. 63; " IV. " two long and one short armature surface, see Figs. 64 and 65 ; " V " " one long and two short, and part of second long surface, see Fig. 66. 27] FINAL CALCULATION OF WINDING. 99 Denoting with / a the length, and with b & the breadth of the cross-section, and assuming the winding-height, // a , to be the same all around the section, we obtain the following formulae for calculating the total length of conductor on a ring armature: Case L: A = i& + *> + * " x A ..(53) II.: A = - -p- -x A ........ (54) *a HI.: Z t = 2 ( / a + ^)+/^a^ xZa TV T \ a ' ' *' ' a v 7" f&fi^ j. v . . y^ t X J^a. VVOy In these formulae / a , a , and Z a are known by virtue of equa- tions (40), (48) and (26), respectively, and h^ can be takeji from Table XVIII., if the actual winding depth is not already known by having previously determined the winding and its arrangement. A formula for Case V. is not given, because, in the first place, the arrangement shown in Fig. 66 is not at all practical, and the makers who first introduced the same have long since discarded it, and, second, because the distance of the internal pole projections depends upon the construction and manner of supporting of the armature core, and, consequently, cannot be definitely expressed. c. Drum- Wound King Armatures. In modern ring armatures of the types indicated by Figs. 59 and 60, the conductors facing two adjacent poles of opposite polarity are often connected in the fashion of a bipolar drum, by completing their turns across the end surfaces of the arma- ture body, thus converting the multipolar ring armature into the combination of as many bipolar drum armatures as there are pairs of poles in the field frame ; see 43. By this arrangement, which is illustrated in Fig. 67, not only a con- 100 D YNAMO-ELECTRIC MACHINES. [28 siderable saving of dead wire is experienced, but also the exchanging of conductors in case of repair is rendered much more convenient, especially when formed coils are used, which is the almost universal practice now. The total length of the armature conductor can, in this case, be calculated by applying, for both smooth and toothed bodies, the above formula (51), replacing in the same the core diam- eter, ^ ?; C . ^ Z o "" 1 .300 7.62 .020 15 2.28 1.0228 "i .289 7.34 020 14 45 2.32 1.0232 2 .284 7.21 .020 14.2 2.33 10233 3 .259 6.58 .020 12.95 2.40 1.024 '2 .258 6.55 .020 12.9 2.40 1024 '4 .238 6.04 .020 11.9 2.50 1.025 . '3 .229 5.82 .020 11.45 2.55 1.0255 5 .220 5.59 O-JQ 11 2.65 1.0265 'i .204 5.18 .012 17" 2.20 1022 !020 10.2 2.85 1.0285 6 .203 5.16 .012 16.9 220 1.022 .020 10.15 2.86 1.0286 .. '5 .182 4.62 .012 15.15 227 1(827 .018 10.1 2.87 1.0287 7 . , .ISO 4.57 .012 15 2.28 1.0228 .018 10 2.90 1.029 8 .165 4.19 .012 13.75 2.33 10233 .018 9.17 3.20 1.032 . . 6 .162 4.12 .010 16.2 2.24 1 1 2i4 .018 9 3.25 10325 9 .148 3.76 .010 14.8 2.30 1-023 .016 9.25 3.15 1.0315 "i .144 366 .010 14.4 232 1.0232 .016 9 3.25 1 0325 10 f . .134 3.40 .010 13.4 2.30 10236 .016 8.4 3.55 1.0355 8 .1285 327 .010 1285 2.40 1.024 .016 8 3.75 1.0375 11 .120 3.05 .010 12 2.50 1.025 .016 7.5 4.10 1041 9 .1144 2.91 .010 11.4 255 1.0255 .016 7.1 4.35 10435 i-i .109 2.77 .010 10.9 2.66 1.0266 .016 6.8 4.60 1.046 io .1112 2.59 .010 10.2 285 1.0285 .016 6.4 5.00 1.05 13 .. .095 2.41 .010 9.5 310 1.031 .016 5.9 5.55 1.0055 11 .091 2.31 .010 9.1 3.25 10325 .016 5.7 5.85 1.0585 u .083 2.11 .007 12 2.50 1.025 .016 5.2 6.60 1.066 i-j .081 2.06 .007 11.6 254 1.0254 .016 5.1 6.80 1.068 is 13 .072 1.83 .007 10.3 2.80 1.028 .016 4.5 7.80 1.C78 16 .065 :.65 .007 9.3 3.15 1.0315 .016 4.1 8.60 1.086 , . 14 .064 1.63 .007 91 3.25 1.0325 .016 4 8.80 1.088 17 .058 1.47 .007 8.3 3.60 1.036 .014 4.1 8.60 1.086 is .057 1.45 .007 8.1 3.70 1037 .014 4.1 8.60 1.086 16 .051 1.30 .007 7.3 420 1.042 014 3.6 9.60 1.096 18 .049 1.25 .007 7 4.40 1.044 .014 8.5 9.80 1.098 17 .015 1.15 .005 9 3.25 1.0325 .012 3.75 9.30 1.093 19 .042 1.07 .005 8.4 3.55 1.0355 .012 3.5 9.80 1098 18 .040 102 .005 8 3.75 1.0375 .012 333 10.10 1.101 19 .036 0.91 .005 7.2 4.30 1.043 .005* 7.2 5.60 1.056 20 035 089 .005 7 440 1.044 .005* 7 6.00 1.06 21 20 032 081 .005 6.4 5.00 1.05 .005* 6.4 6.60 1.066 22 21 .028 0.71 .005 5.6 6.00 106 .004* 7 6.00 1.06 23 22 .025 0.64 .005 5 7.00 1.07 .004* 6.25 7.00 1.07 .24 23 .022 0.56 .005 4.4 8.00 1.08 .004* 5.5 8.00 1.08 25 24 .020 0.51 .005 4 8.80 1.088 .004* 5 8.W) 1.088 26 25 .018 0.46 .005 3.6 9.60 1.096 .004* 4.5 9.60 1.096 27 26 016 0.41 .005 3.2 10.40 1.104 .004* 4 10.40 .104 28 i 27 .014 0.36 .005 2.8 11.25 1 1125 .004* 3.5 11.25 .1125 29 28 .013 033 .005 26 11.65 1.1165 .004* 3.25 11.65 .1165 30 .012 0.31 .005 2.4 12.05 1.1205 .004* 3 12.05 .1205 29 .011 0.28 .005 2.2 12.45 1.1245 .004* 2.75 12.45 .1245 Double silk: i mil of silk insulation taken equal in weight to 1.25 mil of cotton corering. 104 DYNAMO-ELECTRIC MACHINES. [29 In case of a multipolar dynamo with parallel grouping the number of parallel armature branches, 2 n' p , is equal to the num- ber of poles 2 p , and the resistance of each branch becomes 2 n p 2 p see Fig. 68, page 102. The joint resistance of these 2 n' p circuits, that is, the actual armature resistance, will consequently be r&= (TWff = 4 X VP)" ' The total resistance, ^ a , of all the armature wire in series can be calculated from the total length, Z t , and the sectional area, d a 2 , of the conductor by the formula * = A x^, where 10.5 is the resistance, in ohms, at 15.5 C. ( = 60 Fahr.) of a copper wire of i circular mil sectional area and i foot length, and of a conductivity of about 98 per cent, of that of pure copper. The quotient iQ-5 ^ for commercial copper, or iQ.3 2 for chemically pure copper, represents the resistance per foot of the armature conductor, and can, for every standard size of wire, be taken from the wire gauge table. Introducing the value of R & into the above equation, we obtain the following formula for the resistance at 15.5 C. ( = 60 Fahr.) of any armature having a single conductor: r * v I V I I0 '5 \ (fif\\ " 4 x () > c v*r/ r a = resistance of armature winding at 15.5 C., in ohms; n' v = number of bifurcations of current in armature; for special values of n' p in the usual cases see symbols of formula (24), 16; 29] FINAL CALCULATION OF WINDING. 105 Z t = total length of armature conductor, in feet, formulae (49) to (57), respectively; (65) in which P A = total watts absorbed in armature; P & = watts consumed by armature winding, form- ula (68) ; P b = watts consumed by hysteresis, formula (73); P 9 = watts consumed by eddy currents, formula (75). io8 DYNAMO-ELECTRIC MACHINES. [31 31. Energy Dissipated in Armature Winding. The energy required to pass an electric current through any resistance is given, in watts, by the product of the square of the current intensity, in amperes, into the resistance, in ohms. The energy absorbed by the armature winding, therefore, is: A=(/TXr' a , (66) where P & = energy dissipated in armature winding, in watts; /' = total current generated in armature, in amperes; r' & = resistance of armature winding, hot, in ohms; see formulae (60) to (64), respectively. The total current, /', in series-wound dynamos, is identical with the current output I; in shunt- and compound-wound dynamos, however, /' consists of the sum of the external current, and the current necessary to excite the shunt mag- net winding. The amount of current passing through the shunt winding is the quotient of the potential difference, E, at the terminals of the machine, by the resistances of the shunt circuit, r m , that is the sum of the resistance of the shunt winding and of the regulating rheostat, in series with the shunt winding. For the resistance, r' a , of the armature winding, when hot, in order to be on the safe side in determining the armature losses, we will take that at, say 65.5 C. (= 150 Fahr.), or, according to formula (63), the resistance, r M at 15.5 C. (= 60 Fahr.), multiplied by 65-5 - I5-, , _ .5\ = , / The energy dissipated in overcoming the resistance of the armature winding, consequently, for shunt- and compound- dynamos can be obtained from the formula: = 1.3 X I = current-output of dynamo, in amperes; E = E. M. F. output of dynamo, in volts; r a = resistance of armature, at 15.5 C. (= 6p Fahr.), in ohms; 32] ENERGY LOSSES IN ARMATURE. 109 r m = resistance of shunt-circuit (magnet resistance -f- reg- ulating resistance) at 15.5 C. (for series dynamos E If P & is to be computed before the field calculations are made, that is to say, before r m is known, it is sufficiently accurate for practical purposes to express, from experience, the total armature current, /', as a multiple of the current output, I; and, therefore, we have approximately P & = 1.2 x (k 6 X /)' X r & ........ (68) and in this the coefficient k 6 for series dynamos is k t = i, and for shunt- and compound-wound dynamos can be taken from the following Table XXVII. : TABLE XXVII. TOTAL ARMATURE CURRENT IN SHUNT- AND COMPOUND- WOUND DYNAMOS. CAPACITY IN KILOWATTS. SHUNT CURRENT IN PER CENT. op CURRENT OUTPUT. TOTAL CURRENT, AS MULTIPLE OP CURRENT OUTPUT. * .1 15 1.15 .25 12 1.12 .5 10 1.10 1 8 1.08 2.5 7 1.07 5 6 1.06 10 5 1.05 20 4 1.04 30 3.5 1.035 50 3 1.03 100 2.75 1.0275 200 2.5 1.025 300 2.25 1.0225 500 2 1.02 1,000 1.75 1.0175 2,000 1.5 1.015 32. Euergy Dissipated by Hysteresis. The iron of the armature core is subjected to successive magnetizations and demagnetizations. Owing to the mole- cular friction in the iron, a lag in phase is caused of the effected magnetization behind the magnetizing force that produces it, and energy is dissipated during every reversal HO DYNAMO-ELECTRIC MACHINES. [32 of the magnetization. The name of ''Hysteresis" (from the Greek varsptoj, to lag behind) was given by Ewing, in 1881, to this property of paramagnetic materials, by virtue of which the magnetizing and demagnetizing effects lag behind the causes that produce them. Although Warburg, 1 Ewing, 2 Hopkinson, s and others have made numerous researches about the nature of this property of paramagnetic substances, it was not until recently that a definite Law of Hysteresis was established. In an elaborate paper presented to the American Institute of Electrical Engineers on January 19, 1892, Charles Proteus Steinmetz * gave the results of his experiments, showing that the energy dissipated by hysteresis is proportional to the i.6th power of the magnetic density, directly proportional to the number of magnetic reversals and directly proportional to the mass of the iron. This law he expressed by the empirical formula: P\ = r ll x &1' 6 X JV, X M\, where P\ = energy consumed by hysteresis, in ergs; 77, = constant depending upon magnetic hardness of material (" Hysteretic Resistance"); (B a == density of lines per square centimetre of iron; W t = frequency, or number of complete cycles of 2 reversals each, per second; M\ = mass of iron, in cubic centimetres. The values of the hysteretic resistance found by Steinmetz for various kinds of iron are given in Table XXVI1L, page in. For the materials employed in building up the armature core, according to this table, we can take the following aver- age values of the hysteretic resistance: Sheet iron : 77, = .0035, Iron wire : 77, = .040. 1 Warburg, Wiedem. Ann'., vol. xiii. p. 141 (1881) ; Warburg and Hoenig, Wiedem. Ann., vol. xx. p. 814 (1884). 2 Ewing, Proceed. Royal Soc., vol. xxxiv. p. 39, 1882 ; P kilos. Trans., part ii. p. 526 (1885). 3 J. Hopkinson, Philos. Trans. Royal Soc., part ii. p. 455 (1885). 4 Steinmetz, Trans. A. I. E. E., vol. ix. p. 3 ; Electrical World, vol. xix pp. 73 and 89 (1892); vol. xx. p. 285 (1892). 32] ENERGY LOSSES IN ARMATURE. HI TABLE XXVIII. HYSTERETIC RESISTANCE FOR VARIOUS KINDS OF IRON. KIND oir IRON. HITBTKRETIC RESISTANCK. Sheet Iron magnetized lengthwise . . .0025 to .005 .0035 .004 .005 .007 .0035 .040 .0023 .0033 .013 .0137 .0146 .0043 .070 .027 .0165 .012 to .028 .003 to .009 0165" thick ( 42mm) " 015" " ( .38 " ) " .006" " ( .15 " ) magnetized across Lamination ; Iron Wire length-magnetization cross- Wrought Iron Norway Iron ' ' ordinary, mean Cast Iron ordinary, mean containing ^ % Aluminium Mitis Metal Tool Steel glass hard oil hardened annealed Cast Steel hardened annealed Inserting the average values given on page no into Stein- metz's equation, and reducing the latter to our practical units, we obtain for the energy loss by hysteresis in any armature having core built of discs or ribbon : A = io- 7 X .0035 X ( ^ ) X NI X 28,316 X M = 5 X io- 7 X (B'V' 6 X NI X M, (69) and in any armature with core of iron wire : A = 5-7 X 10^ x (BY' 6 X JV, X M, (70) where f b = energy absorbed by hysteresis, in watts ; i watt = io 7 ergs ; (S>" & = density, in lines per square inch, correspond- ing to average specific magnetizing force of armature core, see 91 ; N yV 7 ! = frequency, tn cycles per second, = X p ; JV = number of revs, per min., n p = num- ber of pairs of poles ; M = mass of iron in armature core, in cubic feet,- i cu. ft. = 28,316 cm. 3 112 DYNAMO-ELECTRIC MACHINES. [32 The mass, in cubic feet, for both drum and ring armatures with smooth core is : M - *"* X * X * a X /, X k m ^ _ 1,728 d"\ = mean diameter of armature core, in inches, = d n - ft , see Fig. 45, page 58 ; / a = length of armature core, in inches; a = radial depth of armature core, in inches; k t = ratio of net iron section to total cross section, see Table XXL, 26; 1,728 = multiplier to convert cubic feet into cubic inches. And for toothed and perforated armatures : _ (d'\n X b & - n' c S\) X 4 X *. ,- o . 1,728 J 7,-Hl80 *l ij+480 > rj+480 10,000 1.25 .0026 143 .030 66.000 25.72 .0537 294.0 .613 15,000 2.40 .0050 27.4 .057 67.000 26.34 .0550 301.0 .628 20,000 3.79 .0079 43.3 .090 68.000 26.97 .0563 308.2 .643 25,000 5.42 .0113 62.0 .129 69,000 27.61 .0576 315.5 .658 30,000 7.30 .0152 83.5 .174 70,000 28.26 .0589 322.8 .673 31,000 7.70 .0160 88.0 .183 71,000 28.91 .OiiOS 330.1 .688 32,000 8.10 .0168 92.6 .192 72,000 29.56 .0617 337.6 .704 33.000 8.50 .0177 97.2 .202 73,000 30.22 .0631 345.1 .720 34,000 8.91 .0186 101.8 .212 74,000 30.89 .0645 352.9 .736 35,000 9.33 .0195 106.5 .222 75,000 31.56 .0659 360.7 .752 36.000 9.76 .0204 111.5 .232 76,000 32.23 .(X>73 368.5 .768 37,000 10.20 .0213 116.5 .242 77,000 32.91 .0687 3763 .784 38,000 10.65 .0222 121.6 .253 78,000 33.60 .0701 384.2 .800 39,000 11 JO .0231 126.8 .264 79,000 34.29 .0715 392.1 .817 40,000 11.55 .0240 132.0 .275 80,000 34.99 .0730 400.0 .854 41,000 12.01 .0250 137.2 .286 81,000 3569 .0745 408.0 .a-u 42.000 12.48 .0260 142.5 .297 82,000 36.40 .0760 416.0 .868 43,000 12.96 .0370 148.0 .308 83,000 37.11 .0775 424.0 .885 44,000 13.45 .0280 153.7 .320 84,000 37.82 .0790 432.4 .902 45,000 13.95 .0290 159.4 .332 85,000 38.54 .0805 440.8 .919 46,000 14.45 .0300 165.1 .344 86.000 39.27 .0820 4492 .936 47,000 14.95 .0311 170.8 .356 87,000 40.01 .0835 457.6 .954 48.000 15.45 .0322 176.6 .368 88,000 40.75 .0850 466.0 .972 49,000 15.96 .0:333 182.4 .380 89,000 41.50 .0865 474.5 .990 50,000 16.48 .0344 188.3 .392 90,000 42.25 .0881 483.0 1.008 51,000 17.01 .0355 194.3 .405 91,000 43.00 .0-S97 491.5 1.023 52,000 17.55 .0366 2006 .418 92,000 4376 .0913 500.0 1.042 53,000 18.10 .0377 206.9 .431 93,000 44.53 .0929 509.0 1.064 54,000 18.65 .0388 213.2 .444 94,000 45.30 .0945 518.0 l.OKO 55.000 19.21 .0400 2195 .457 95,000 46.07 .0961 527.0 1.098 56.000 19.78 .0412 226.0 .470 96.000 46.85 .0977 536.0 1.116 57.000 20.35 .0424 888.6 .484 97.000 47.63 .0993 545.0 1.135 58,000 20.92 .0436 no.i .498 98,000 48.41 .1009 554.0 1.154 59,000 21.50 .0448 245.8 .512 99000 49.20 .1025. 5630 1.173 60,000 22.09 .0460 252.5 .526 100,000 50.00 .1041 572.0 1.192 61,000 22.69 .0472 259.4 .530 105,000 54.06 .1127 618.0 1.290 62,000 2329 .0485 266.3 .554 110.000 58.23 .1215 666.0 1.388 63,000 23.89 .0498 273.0 .568 115,000 62.53 .1305 715.0 1.490 64,000 i 24.50 .0511 280.0 .583 120,000 66.95 .1400 765.0 1.595 65,000 25.11 .0524 287.0 .598 125,000 71.50 .1500 817.5 1.705 The values of rj contained in this table are graphically represented in Fig. 69, two different scales, one ten times the other, being used for the ordinates in plotting the curves, as designated. For the metric system, in formula (73) the mass M in cubic D YNAMO-ELECTR1C MA CHINES. [32 feet is to be replaced by M l in cubic metres, from the formula: d'" n X n X b & x / a X k n' c X S. X 4 X > M, =- (74) 1,000,000 1,000,000 the second term of which refers to toothed and perforated armatures only, and in which M l = mass of iron in armature body, in cubic metres; d'" & = mean diameter of armature core, in centimetres; |CO 100 Ir ft" > KM $ 3JO t-so FIG. 69. Hysteresis Factor for Sheet Iron and Iron Wire, at Different Core Densities. d"'i = d & b & , for smooth armatures; = d" & (b & -f- ^ a ) f r toothed armatures; / a = length of armature core, in centimetres; b & radial depth of armature core, in centimetres; ' c = number of slots; S 3 = slot area, in square centimetres; a = ratio 'of magnetic to total length of armature core, Table XXL, 26. Then, formula (73) will give the hysteresis loss in watts, if the factor of hysteresis 77 is replaced by if from the following Table XXX., rj' being calculated from 3.5 X io~ 4 X (B a 16 , in case of sheet-iron, and from 4 x io~ s X (B ft 1-6 , in case of iron wire: 32] ENERGY LOSSES IN ARMATURE. TABLE XXX. HYSTERESIS FACTORS FOR DIFFERENT CORE DENSITIES, IN METRIC MEASURE. WATTS DISSIPATED WATTS DISSIPATED MAGNETIC DENSITY IN AT A FREQUENCY OP ONE COMPLETE MAGNETIC CYCLE PER SECOND. MAGNETIC DENSITY IN AT A FREQUENCY OF ONE COMPLETE MAGNETIC CYCLK PER SECOND. ARMATURE ARMATURE CORE. LINES OF Sheet Iron. Iron Wire. CORE. LINES OF Sheet Iron. Iron Wire. FORCE FORCE (GAUSSES) a per cu. m. per kg. per cu. m. per kg. (GAUSSES) (B a per cu. m. per kg. per en. m. per kg. V V--7,700 V V+7,700 V V+7,700 V ^--7,700 2.000 67.0 .0087 765.1 .0994 12,000 1,177.0 .1529 13,451.0 1.7469 3,00i) 128.1 .0166 1,467.1 .1905 12,250 1,216.5 .1580 13,902.3 1.8054 3.500 163.9 .0213 1,873.1 .2432 12,500 1,256.4 .1632 14.359.0 1.8648 4,000 202.9 .0264 2,319.3 .3012 12,750 1.205.8 .1685 14,821.0 1.9248 4,500 245.0 .0318 2.800.2 .3637 13.000 II I,a37.8 .1737 15,288.7 1.9855 5,000 290.0 .0377 3,314.6 .4305 13.250 1,379.2 .1791 15,701.7 2.0470 5,250 313.6 .0407 3,583.6 .4654 13.500 1,421.0 .1845 16,240.0 2.1091 5,500 337.8 .0439 3,860.5 .5014 13,750 1,463.4 .1901 16,724.0 2.1730 5.750 362.7 .0471 4,145.1 .5383 14.000 1,506.2 .1952 17,213.0 2.2355 6,000 388.3 .0504 4,437.1 .5763 14,250 1,549.4 .2012 17,708.0 2.2997 6.250 414.5 .0538 4.848.0 .6151 14,500 1,593.2 .2069 18,207.4 2.3646 6,500 441.3 .0573 5,043.3 .6550 14,750 1,637.3 .2126 18,712.0 2.4301 6.750 468.8 .0609 5.357.3 .6958 j 15,000 1,681.9 .2179 19.222.0 2.4964 7,000 496.9 .0645 5.678.3 .7375 15,250 1,727.0 .2243 19,742.0 2.5639 7.250 525.6 .0683 6,006.1 .7800 15,500 1.792.6 .2302 20,257.4 2.6309 7.500 554.8 .0721 6.355.3 .8254 15,750 1,818.6 .2362 20,783.0 2.6991 7.750 584.7 .0759 6,682.4 .8679 16,000 1,864.9 .2422 21,313.5 2.7681 8.000 615.2 .0799 7,030.7 .9131 16,250 1,911.8 .2484 21,848.5 2.8375 8,250 646.2 .0839 7,3*5.5 .9592 16,500 i 1.959.0 .2544 22,389.0 2.9076 8,500 677.9 .0880 7.747.0 1.0061 16,750 2,0067 .2606 22.934.0 2.9785 8.750 710.1 .0922 8.114.8 1.0539 17,000 2.054 9 .26''.9 23,484.5 3.0499 9,000 742.8 .0965 8,488.8 1.1024 17,250 2.103.5 .2732 24,039.5 3.1220 9,250 776.1 .1101 8.869.8 1.1152 17,500 2,152 5 .2795 24,599.0 3.1947 9,500 809.9 .1105 9,255.6 1.1202 i 17,750 2,201.9 .2860 25,164.0 3.2681 9.750 844.2 .1110 9649.0 1.2532 18,000 2,251 7 .2924 25.733.6 3.3420 10,000 879.2 .1142 10,047.7 1.3049 18,250 2,301 9 .2990 26,307.6 3.4165 10,250 9146 .1138 10,452.2 1.3574 18,500 2,a52.6 .3055 86,886.0 3.4918 10,500 9.50.5 .1234 10,863.2 1.4108 18,750 2.403.7 .3122 27,470.0 35676 10.750 987.0 .1282 11,284.0 1.4650 19,000 2,4551 .3189 28,058.6 3.6440 11,000 1.024.0 .1330 11.702.5 1.5198 19.250 2.507.1 .3256 28,652.0 3.7210 1IJBO 1,061.5 .1379 12,131.0 1.5755 19,500 | 2,559.3 .3324 29,2486 3.7986 11.500 1.0995 .1428 12,565.3 1.6319 19.750 l| 2,636.2 .3424 29,844.6 3.8760 11,750 1,138.0 .1478 13,005.3 1.6890 20,000 j 2,665.1 .3461 30,458.7 39556 With regard to the exponent of (B" a , in formulae (69) and (70), Steinmetz's value, which in the preceding is given as 1.6 over the whole range of magnetization, has been attacked by Professor Ewing, 1 who by recent investigations has found it to vary with the density of magnetization. In the case of sheet 1 J. A. Ewing and Miss Helen G. Klaassen, Philos. Trans. Roy. Soc.; Elec- trician (London), vol. xxxii. pp. 636, 668, 713 ; vol. xxxiii. pp. 6, 38 (April and May, 1894); Electrical World, vol. xxiii. pp. 569, 573, 614, 680, 714, 740 (April and May, 1894); Electrical Engineer, vol. xvii. p. 647 (May 9, 1894). D YNAMO-ELECTRIC MA CHINES. [32 iron of .0185 inch ( =.47 mm.) thickness, for instance, the hysteretic exponent ranged as follows: TABLE XXXI. HYSTERETIC EXPONENTS FOR VARIOUS MAGNETIZATIONS. DENSITY OF MAGNETIZATION. HYSTERETIC EXPONENT. Lines of Force per Square Inch. "a Linos per cm.* (Gausses.) &a 1,300 to 3,000 3,000 " 6.500 6,500 " 13,000 13.000 " 50,000 60,000 " 90,000 200 to 500 500 " 1,000 1,000 " 2,000 2,000 " 8,000 8,000 " 14,000 1.9 1.68 1.55 1.475 1.7 Although Ewing thus has shown that no formula with a constant exponent can represent the hysteretic losses within anything like the limits of experimental accuracy, he con- cludes that Steinmetz's exponent 1.6 gives values which are nowhere so grossly divergent from the truth as to unfit them for use in practical calculations. This conclusion holds par- ticularly good for the densities applied in dynamo-electric machinery, as from the above Table XXXI. can be seen that for densities between 4 and 14 kilogausses (25,000 and 90,000 lines per square inch, respectively), compare Table XXII., 26, the hysteretic exponent, according to Ewing's experiments, varies from 1.475 * I -7> tne average of which is 1.59, indeed a good agreement with Steinmetz's value. Experiments on the variation of the hysteretic loss per cycle as function of the temperature have been made by Dr. W. Kunz, 1 for the temperatures up to 800 C. ( = 1,472 Fahr.). They show that with rising temperature the hyster- esis loss decreases according to a law expressed by the formula P\ = a + b , where P\ = hysteresis loss per cycle, in ergs; = temperature, in centigrade degrees; a and b = constants for the material, depending upon the temperature and on the maximal density of magnetization. 'Dr. W. Kunz, Elektrotechn. Zeitschr., vol. xv. p. Electrical World, vol. xxiii. p. 647 (May 12, 1894). 194 (April 5, 1894); 32] ENERGY LOSSES IN ARMATURE. 117 The decrease of the hysteretic loss, consequently, consists of two parts: one part, b 0, which is proportional to the in- crease of the temperature, and another part, a, which becomes permanent, and seems to be due to a permanent change of the molecular structure, produced by heating. This latter part, in soft iron, is also proportional to the temperature, thus O " 1OO .200 3OO 4OO 50O 60O 70O 8OO 900 Fig. 70. Influence of Temperature upon Hysteresis in Iron and Steel. making the hysteretic loss of soft iron a linear function of the temperature, 'but is irregular in steel. The curves in the latter case show a slightly ascending line to about 300 C. ( = 572 Fahr. ), then change into a rapidly descending straight portion to about 600 C. (= 1,112 Fahr.), when a second "knee" occurs, and the descension becomes more gradual. The author has refigured all of Kunz's test results, basing the same upon the hysteresis loss at 20 C. ( = 68 Fahr.) as unity n8 D YNAMO-ELECTRIC MA CHINES. [32 in every set of observations. In Fig. 70 dotted lines have then been drawn, inclosing all the values thus obtained, for soft iron and for steel, respectively, and two full lines, one for each quality of iron, are placed centrally in the planes bounded by the two sets of dotted lines, thus indicating the average values of the hysteretic losses, in per cent, of the energy loss at 20 C. Arranging the same in form of a table, the following law is obtained: TABLE XXXII. VARIATION OF HYSTERESIS Loss WITH TEMPERATURE. ENERGY DISSIPATED BY HYSTERESIS IN PER TEMPERATURE. CENT. OP HYSTKRESIS Loss AT 20 C. (=68 FAHR.) In Centigrade Degrees. In Fahrenheit Degrees. Soft Iron. Steel. 20 68 100# 100# 100 212 90 103 200 392 80 106 300 572 70 110 400 752 60 80 500 932 50 50 600 1,112 40 20 700 1,292 30 15 800 1,472 20 10 20 68 70 40 The last row of this table, which gives the hysteresis loss at 20 C., at the end of the test, shows that the energy required to overcome the hysteretic resistance is reduced to about 70 per cent, in case of soft iron and to about 40 per cent, in case of steel, after having been subjected to magnetic cycles at high temperatures. Kunz further found that the hysteretic energy loss can thus be considerably reduced by repeatedly applying high temperatures while iron is under cyclic influence. For soft iron a set of straight lines was obtained in this way, each following of which had a lower starting point, and de- scended less rapidly than the foregoing one, until, finally, after the fourth repetition of the heating process, a stationary condition was reached. For steel, already the second set of tests with the same sample did not show the characteristic form of the, at first 33] ENERGY LOSSES IN ARMATURE. 119 ascending, then rapidly, and finally slowly descending steel curve, but furnished a rapidly descending straight line. For every further repetition, the corresponding line becomes less inclined, and for the fifth test is parallel to the axis of abscissae. Steel, therefore, after heating it but once as high as 800 C. (= 1,472 Fahr.), loses its characteristic properties, and with every further repetition becomes a softer, less car- bonaceous iron. 33. Energy Dissipated by Eddy Currents. From his experiments Steinmetz also derived that the energy consumed in setting up induced currents in a body of iron increases with the square of the magnetic density, with the square of the frequency, and in direct proportion with the mass of the iron: / e = = usefulflux through armature,inmaxwells; 2 ff p = number of poles; Ai X / a X ^ = net area of least cross-sec- tion of armature core, in square centi- metres; (B a = flux density in armature core, in gausses; N = number of revolutions per minute; M\ = mass of armature core, in cubic centimetres; S\ = surface of armature-core, in square centimetres, d& TT = a ^ X 4 + > f r smooth armatures, r/r 2 = ^* ft ^ X 4 -\ > f r toothed and perforated armatures. The numerical constant in this formula is averaged from values ranging between .008 and .012 for smooth-core machines, and between .010 and .0125 for toothed armatures. 'Ernst Schulz, Elektrotechn. Zeitschr., vol. xiv. p. 367 (June 30, 1893); Electrical World, vol. xxii. p. 118 (August 12, 1893). 13 DYNAMO-ELECTRIC MACHINES. [37 Translating (82) into the English system of measurement, we obtain the formula: 8 . = . 00045 X **' X "' X7yxJ/ ; ....(83) > A 9 a = rise of armature temperature, in degrees Centigrade; (B" a = density of magnetization, in lines per square inch; n v = number of pairs of poles; JV = number of revolutions per minute; M = mass of iron, in cubic feet; S' A = armature core surface, in square inches. The value of the constant in the English system, for the type of machines experimented upon by Schulz, varies between the limits .0003 and .0005. The numerical factor depends upon the units chosen, upon the ventilation of the armature, upon the quality of the iron, and upon the thickness of the lamination, and consequently varies considerably in different machines. For this reason it is advisable not to use formula (82) or (83), respectively, except in case of calculating an armature of an existing type for which this constant is known by experiment. In the latter case, Schulz's formula, although not as exact, is even more con- venient than the direct equation (81) which necessitates the separate calculation of the energy losses, while (82) and (83) contain the factors determining these losses, and therefore will give the result quicker, provided that the numerical factor has been previously determined from similar machines. Another empirical formula for the temperature increase of drum armatures, which, however, requires the specific energy- loss to be calculated, and which therefore is not as practical as that of Schulz, and which cannot give as accurate results as can be obtained by the use of Table XXXVI. in connection with formula (81), has recently been given by Ernest Wilson. 1 37. Circumferential Current Density of Armature. An excellent check on the heat calculation of the armature, and in most cases all that is really necessary for an examina- 1 Ernest Wilson, Electrician (London), vol. xxxv. p. 784 (Octobei n, 1895); Elektrotechn. Zeitschr., vol. xvi. p. 712 (November 7, 1895). 37] ENERGY LOSSES IN ARMATURE. 131 tion of its electrical qualities, is the computation of the cir- cumferential current density of the armature. This is the sum of the currents flowing through a number of active arma- ture conductors corresponding to unit length of core-periphery, and is found by dividing the total number of amperes all around the armature by the core circumference: /' c x TW ''=^orf P; ............. (84> / c = circumferential current density, in amperes per inch length of core periphery, or in amperes per centi- metre; N c = total number of armature conductors, all around periphery; /' = total current generated in armature, in amperes; 2 'p = number of electrically parallel armature portions, eventually equal to the number of poles; ' r = current flowing through each conductor, in amperes; 2 n p /' N c x r total number of amperes all around armature; 2; this quantity is called "volume of the armature cur- rent" by W. B. Esson, and " circumflux of the arma- ture" by Silvanus P. Thompson; d & = diameter of armature core> in inches; in case of a toothed armature, on account of the considerably greater winding depth, the external diameter, d" M is to be taken instead of d M in order to bring toothed and smooth armatures to about the same basis; for a similar reason, for an inner-pole dy- namo, the mean diameter, d'" & , should be substituted for d & . By comparing the values of i c found from (84) with the averages given in the following Table XXXVII., the rise of the armature temperature can be approximately determined, and thus a measure for the electrical quality of the armature be gained. The degree of fitness of the proportion between the armature winding and the dimensions of the core is indicated by 132 D YKA MO-ELECTRIC MA CHINES. [38 the amount of increase of the armature temperature. If the latter is too high, it can be concluded that the winding is pro- portioned excessively, and either should be reduced or divided over a larger armature surface: TABLE XXXVII. RISE OP ARMATURE TEMPERATURE, CORRESPONDING TO VARIOUS CIRCUMFERENTIAL CURRENT DENSITIES. ClKCUMFERENTIAIj RISK OF ARMATURE TEMPERATURE, ft . CURRBNT DENSITY, i c . High Speed (Belt-Driven) Low Speed (Direct-Driven) Dynamos. Dynamos. Amperes Amperes per inch. per cm. Centigrade. Fahrenheit. Centigrade. Fahrenheit. 50 to 100 20 to 40 15 to 25 27 to 45 10 to 20 18 to 36. 100 200 40 80 20 35 36 63 15 25 27 45 200 300 80 120 30 50 54 90 20 35 36 63 300 400 120 160 40 60 72 108 25 40 45 72 400 500 160 200 50 70 90 126 30 45 54 81 500 600 200 240 60 80 108 144 35 50 63 90 600 700 240 280 70 90 126 162 40 60 72 108 700 800 280 320 80 100 144 180 50 70 90 126 The difference in the temperature-rise at same circumferen- tial current density for high-speed and low-speed dynamos (columns 3 and 5, or 4 and 6, respectively, of the above table) is due to the fact that, other conditions being equal, in a low- speed machine less energy is absorbed by hysteresis and eddy currents; that, consequently, less total heat is generated in the armature, and, therefore, more cooling surface is available for the radiation of every degree of heat generated. 38. Load Limit and Maximum Safe Capacity of Arma- tures. From Table XXXVII. also follows that, according to the temperature increase desired, the load carried by an arma- ture varies between 50 and 800 amperes per inch (= 20 to 320 amperes per centimetre) of circumference, or between about 150 and 2,500 amperes per inch (=: 60 to 1,000 amperes per centimetre) of armature diameter. As a limiting value for safe working, Esson 1 gives 1,000 amperes per inch diameter ( 600 amperes per centimetre) for ring armatures, and 1,500 1 Esson, Journal I. E. E., vol. xx. p. 142. (1890.) 38J ENERGY LOSSES IN ARMATURE. 133 amperes (= 400 amperes per centimetre) for drums. Kapp 1 allows 2,000 amperes per inch (= 800 amperes, per centimetre) diametral current density for diameters over 12 inches as a safe load. Taking 1,900 amperes per inch diameter (= 600 amperes per inch circumference) as the average limiting value of the arma- ture-load in high-speed dynamos, corresponding to a tempera- ture rise of about 70 to 80 Centigrade (= 126 to 144 Fahrenheit), compare Table XXXVII., we have: /' W* X -r - i,9o X d M ......... (85) z n p and since for the total electrical energy of the armature we can write, see formula (136), 56, in which /" = total electrical energy generated in dynamo, in watts; E' = total E. M. F., generated in armature, in volts; /' total current generated in armature, in am- peres; JV C = number of armature conductors; $ = number of useful lines of force; JV = speed, in revolutions per minute; n' p = half number of parallel armature circuits (eventually also number of pairs of poles); we obtain for the limit of the capacity, by inserting (85) into (86): 1,000 X d & X $ X N 10" X o -=63Xio-"x <4X^X $. (87) But the useful flux, r>t 7 U J A "a A " A ^ io 8 X 3 = 4 X io- 7 X d* X 4 X /3\ X N X OC, . .(89) wherein all dimensions are expressed in centimetres. For low-speed machines the factor 4 in this formula must be replaced by 5.33. Average values for fi\, taken from practice, are given in Table XXXVIII. on the opposite page. In this table the percentages given for toothed arma- tures refer to straight tooth cores only; for projecting teeth a value between the straight tooth and the perforated arma- ture should be taken, proportional to the size of the opening between the tooth projections. 39] ENERGY LOSSES IN ARMATURE. '35 TABLE XXXVIII. PERCENTAGE OP EFFECTIVE GAP CIRCUMFERENCE FOR VARIOUS RATIOS OF POLAR ARC. PERCENTAGE OP POLAR AKC. A PERCENTAGE OF EFFECTIVE GAP CIBCUMFEBENCK. P\ 2 Poles. 4 to 6 Poles. 8 to 12 Poles. 14 to 20 Poles. Smooth or Perforated Armature. Toothed Armature. Smooth or Perforated Armature. Toothed Armature. Smooth or Perforated Armature. Toothed Armature. Smooth or Perforated Armalure. Toothed Armature. 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 .95 .98 .96 .97 .955 .965 .955 .96 .955 .90 .96 .915 .94 .91 .93 .91 .92 .91 .85 .94 .87 .905 .865 .89 .865 .88 .865 .80 .91 .825 .87 .82 .85 .82 .84 .82 .75 .88 .78 .835 .775 .sir, .775 .80. .775 .70 .85 .735 .80 .73 .78 .72.1 .76 .725 .65 .83 .69 , .765 .685 .74 .68 .72 .675 .60 .78 .645 .73 .635 .70 .63 .68 .625 .55 .74 .60 .69 .59 .665 .58 .64 .575 .50 .70 .55 .65 .54 .625 .53 .60 .525 39. Running Value of Armature. In order to form an idea of the efficiency of an armature as an inductor, its "running value" has to be determined. In forming the quotient of the total energy induced by the product of the weight of copper on the armature and the field density, the number of watts generated per pound of copper at unit field density is obtained, an expression which indicates the relative inducing power of the armature: P' = x ..(90) P' & = running value of armature in watts per unit weight of copper, at unit field density; E' = total E. M. F. generated in armature, in volts; /' = total current generated in armature, in amperes; wt & = weight of copper in armature, in pounds or in kilo- grammes, formula (58); 5C" = field density, in lines of force per square inch, or per square centimetre, respectively, DYNAMO-ELECI^RIC MACHINES. [39 The value of P' & for a newly designed armature being found, its relative inductor efficiency can then be judged at by com- parison with other machines. The running value of modern dynamos, according to the type of machine and the kind of armature, varies between very wide limits, and the following are the averages for well-designed machines: TABLE XXXIX. RUNNING VALUES OP VARIOUS KINDS OP ARMATURES. TYPE OF MACHINB. KIND OP ARMATURE. RUNNING VALUE, P' a (Watts per unit weight of copper at unit field density.) English Measure. Metric Measure. Watts per Ib. at 1 line per sq. inch. Watts per kg. at 1 line per cm. a High Speed Bipolar Drum .015 to .03 .045 to. 09 Ring .01 " .02 .03 " .06 Multipolar Drum .01 " .02 .03 " .06 Ring .0075 " .015 .022" .045 Low Speed Bipolar Drum .0075 " .015 .022" .045 Ring .005 " .01 .015" .03 Multipolar Drum .005 " .01 .015" .03 Ring .00375 " .0075 .011 " .022 CHAPTER VII. MECHANICAL EFFECTS OF ARMATURE WINDING. 40. Armature Torque. The work done by the armature of a dynamo can be ex- pressed in two ways: electrically, as the product of E. M. F. and current strength, P' = E' X I' watts; and mechanically, as the product of circumferential speed and turning moment, or torque, 746 P' = 27rxNXTX- - = .142 X W X r watts; 33,000 P' = total energy developed by machine, in watts; E' = total E. M. F. generated in armature, in volts; /' = total current generated in armature, in amperes; N = speed, in revolutions per minute; r = torque, in foot-pounds; 746 = number of watts making one horse power; 33,000 = number of foot-pounds per minute making one horse power. Equating the above two expressions, we obtain: ' x I' = .142 X N X r, from which follows : J? ' v f ' T? 1 v 7' r = .142 X N = 7 - 42 X '^~N foot -P unds - --(91) Or, in metric system, i kilogramme-metre being = 7.233 foot- pounds, *=~ x --w *~* ..... < 93 > Inserting into (91) and (92) the expression for the E. M. F. from 56, viz.: E , _ N c x $ X N n'X io e X 60' 9 137 13 8 DYNAMO-ELECTltlC MACHINES. [41 the equation for the torque becomes: N c x $ X N /' r = 7.042 x -^- - X -XT N ' p X io 8 X 60 JV = 3- X X -A^c X foot-pounds ^ ^ p > (93) 1.625 /' = - if X r X N c X $ kg. -metres J 10 P from which follows that in a given machine the torque depends in nowise upon the speed, but only upon the current flowing through the armature, and upon the magnetic flux. 41. Peripheral Force of Armature Conductors. By means of the armature torque we can now calculate the drag of the armature conductors in a generator, respectively the pull exerted by the armature conductors in a motor. The torque divided by the mean radius of the armature winding gives the total peripheral force acting on the arma- ture; and the latter, divided by the number of effective con- ductors, gives the peripheral force acting on each armature conductor. In English measure, if the torque is expressed in foot-pounds and the radius of the winding in inches, the peripheral force of each conductor is: /* ~ I^f ~ ~ d X*^ X ft' P Unds ( 94: ) - X N c X /?', Inserting into this equation the value of r from formula (91), we obtain: E 1 X /' 24 X 7-042 X - fr /.=- d\ X ^o X fi\ 2 X 7-042 X 7t E' x /' 60 " X N c X /?', or, /> =-7375 X ,. vx * , pounds; ....(95) 41] EFFECTS OF ARMATURE WINDING. 139 f & = peripheral force per armature conductor, in pounds; E' X /' = total output of armature, in watts; z/ c = mean conductor velocity, in feet per second; N total number of armature conductors; ft\ = percentage of effective armature conductors, see Table XXXVIII., 38. A second expression for the peripheral force can be obtained by substituting in the original equation (94) the value of r from formula (93), thus: 24 X 11.74 _ < x n p JV X p , 2.82 /' X # //,x = - r X -i 17 ^- pounds (96) io n p X a* X p l Replacing in this the useful flux 4> by its equivalent, the product of gap area and field density, we find a third formula for the peripheral force: /' X d' & X - X p" t X b* X OC* / a = 2 -^X r ^ ;* io 8 n' v X ' ' and c i /' f* ~ io 8 X ~tT X /a X X kil g rammes ...(100) which correspond to (95), (96) and (97), respectively. 140 DYNAMO-ELECTRIC MACHINES. [42 It is on account of this peripheral force exerted by the magnetic field upon the armature conductors that there is need of a good positive method of conveying the driving power from the shaft to the conductors, or vice versa; in the gener- ator it is the conductors, and not the core discs, that have to be driven; in the motor it is they that drive the shaft. Thus the construction of the armature is aggravated by the condi- tion that, while the copper conductors must be mechanically connected to the shaft in the most positive way, yet they must be electrically insulated from all metallic parts of the core. In drum armatures the centrifugal force still more complicates matters in tending to lift the conductors from the core; in smooth drum armatures it has therefore been found necessary to employ driving horns, which either are inserted into nicks in the periphery of the discs, or are supported from hubs keyed to the armature shaft at each end of the core. In ring armatures the centrifugal force presses the conductors at the inner circumference toward the armature core, and thus helps to drive, while the spider arms, by interlocking into the arma- ture winding, serve as driving horns. If toothed discs are used, no better means of driving can be desired. 42. Armature Thrust. If the field frame of a dynamo is not symmetrical, which is particularly the case in most of the bipolar types (see Figs. 77 to 85), unless special precautions are taken there will be a denser magnetic field at one side of the armature than at the other, and an attractive force will be exerted upon the arma- ture, resulting in an armature thrust toward the side of the denser field. The force with which the armature would be attracted, if only one-half of the field were acting, is: S / 5C \ 8 /=27rXX(-'-\ = .0199 X S g X 3C* dynes, \ 47 V or, since 981,000 dynes = i kilogramme, / = _LJ 2JL x $ x w 2 03 x IO - x s x -je 3 kilogrammes; 90 1,000 Sg = gap area, in square centimetres; 0C = field density, in lines of force per square centimetre. 42] EFFECTS OF ARMAl^URE WINDING. 141 Expressing the gap area by the dimensions of the armature, we obtain: / = 2.03 x io- 8 X ^^ X 4 X /?', X 3C 1 = 32 x io~ 9 x <4 X 4 X /^ X 3C" kilogrammes. . .(101) If, now, both halves of the field are in action, but one half is stronger than the other, the armature will be acted upon by two forces: /! = 32 x io- 9 X <4 X 4 X /3\ X JC,* kilogrammes, and /, = 32 x io- 9 X S2 - G 0M "C ^i^c i^ O.-3 S.T3 ~ ^o ^T3 Gbg S* 5 'H.'O a ~ = ~ *C c = z a a a 'E 9 fc 3* ^ * a^. w s= ^ ^ H ** tg ^ f* 2 1.667 .833 .556 1.667 .833 .556 .067 .033 .022 .067 .033 .022 4 3.333 1.667 1.111 1.667 .833 .556 .267 .133 .089 .133 .067 .044 6 8.0002.500 1.667 1.667 .833 .556 .600 .300 .200 .200 .100 .067 8 6.667 3.333 2 222 1.667 .833 .556 1.067 .533 .356 .267 .133 .089 10 8.8334,167 2.778 1.667 .833 .556 1.667 .833 .556 .333 .167 .111 12 ! 10.000 5.000 '3.333:1. 667 .833 .556 2.400 1.200 .800 .400 .200 .133 14 11. fit;: 5.833 3.889 1.667 .833 .556 3.267 1.633 1.089 .467 .233 .156 16 1 13. 333 6.667 4.444 1.667 .833 .556 4.267 2.133 1.422 .533 .267 .178 Designating the voltages in columns 2 to 7 of this table by 2, however, series grouping is only possible by means of wave winding. III. Series Parallel Grouping. In the mixed grouping the number of bifurcations is greater than T, and must be less than p ; hence, in the connecting formula we have n' p > i and n' p < p . In this case there are either several circuits closed in itself, with separate neutral points on the commutator, or one single closed winding with n' p parallel branches. The latter is the case N if y and - are prime to each other; the former if they have a common factor; this factor, then, indicates the number of independent circuits. b. Application of Connecting Formula to the Various Practical Cases. I. Bipolar Armatures. ( i ) For any bipolar armature the number of pairs of poles, as well as the number of bifurcations is = i; furthermore, the number of coils per commutator-bar is usually = i ; conse- quently // a = T, if in the connecting formula the number of conductors, N c , is replaced by the number of coils, n c . For ordinary bipolar armatures, therefore: P = i, a = ii ' P = i ; y = c T i (107) 154 DYXAAIO-ELECTRIC MACHIXF.S. [45 (2) If the number of commutator segments is half the num- ber of armature coils, /. f., two coils per commutator-bar, then P= it * = 2 ' P = i; -J>'= -f =F i (108) IL Multipolar Armatures with Parallel Grouping. (1) By multiplying thj bipolar method of connecting, we have: *p = i, * m = i, *' = i ; y = n c ^ i (109) This is a spiral winding; beginning and end of neighbor- ing coils are connected with each other, and a commutator connection made between each two coils. The number of sets of brushes is 2 ,,. For multipolar parallel connection and spiral winding with but two sets of brushes, either n c divisions may be used in the commutator, and the bars, symmetrically situated with refer- ence to the field, cross-connected into groups of p bars each, or only -- segments may be employed, and n p coils of same /7 p relative position to the poles connected to each bar by means of n v separate connection wires. (2) In connecting after the wave fashion by joining coils of similar positions in different fields to the same commutator segments, the following formula is obtained : (110) \iy and n c have a common factor, this method of connecting furnishes several distinct circuits closed in itself, the common factor indicating their number. (3) If p similarly situated coils are connected in series between each two consecutive commutator bars, only seg- "v ments, but 2 p sets of brushes are needed; the winding is of the wave type, and the connecting formula becomes: = *p > n p g 46J ARMA TURE WINDING. 155 III. Multipolar Armatures with Series Grouping. (i) If all symmetrically situated coils exposed to the same polarity, by joining the commutator segments into groups of p bars each, are connected to each other, they can be consid- ered as one single coil, and we obtain: Each brush, in this case, short circuits p coils simultaneously. The same formula holds good, if beginning and end of every coil are connected to a commutator-bar each. The latter can always be done if p is an uneven number; but if p is even, the number of coils, c , must be odd. In the case of n p uneven, if c is even, the brushes embrace an angle of 180; but if n c is odd, an angle of only - - is inclosed by the brushes. n p (2) Instead of cross-connecting the commutator, the wind- ing itself can be so arranged that only bars are required. In *t this case the connections have to be made by the formula: (H3) NOTE. In drum armatures the beginning and end of a coil being situated in different portions of the circumference, they should be numbered alike, and yet marked differently, in order to facilitate the application of the above connecting formulae. By designating the beginnings of the coils by i, 2, 3, , and the ends by i', 2 , 3 , , this dis- tinction is attained. 46. Armature Winding Data. a. Series Windings for Multipolar Machines. While a parallel winding for a multipolar armature is always possible if the number of coils is even, the possibility of a series winding depends upon the relation between the number of poles and the number of conductors per armature division, or the number of conductors per slot in case of a toothed or perforated armature, respectively. In the following Table XLII., which is compiled from data contained in Parshall and '56 D YNAMO-ELECTRIC MACHINES. [46 Hobart's work, 1 the various kinds of series windings possible for different cases are given, the symbols shown in Table XL., 44, being employed: TABLE XLII. KLNDS OF SERIES WINDINGS POSSIBLE FOR MULTIPOLAR MACHINES. Conductors per Armature Division or per Slot) Kind of SERIES WINDINGS possible far various numbers of Poles Series Winding 4 Poles 6 Poles 8 Poles 10 Poles 12 Poles 14 Poles 16 Poles i Simplex o o o o o o o Duplex o o GDGD O GDGD o o fflffl O GDffl r& o o GDGD S Triplex &&j* o o o sjQ o o o QG)(S) o o o G> d ffl QG)G) QG)S) o o o sw Guy GuO 2 Simplex o O o o o o o Duplex GDGD o o GDGD o o O ffl ffl ffl Q fflffl o o GDffl 0. GDffl Triplex QQ QG> QQG) QQG) G>G>G) o o o GKSK3) OOQ 4 Simplex o o o Duplex O Q GD GD GDGD Qffl Q G> o o GD ffi GD GD GD G) Triplex O O 15 O G> o o o 2w Guu GA) Q(2)G) 6 Simplex O o o o o Duplex O O GDGD o o ffl GO O Q Qffl O GD GO GD GD Triplex QG)<5) OG> OO(S) OG)S) O S)Q (3) QQ<) O(S)(5) 8 Simplex o o o Duplex oo G)GD GD ffl oo GD G) Triplex (SO QGJQ QG)G) 40 Simplex o O o o O Duplex O GDGD && Q Q Gb o o GDGO O GDGD o o GD6D Triplex (2) 12 Simplex o o Duplex GD& o o GDffl GJGD GDGD O GD60 Triplex fflQS) QCu)(S) OG)(S) 44 Simplex o o o o o Duplex <_& O GDGD (SS> && o o QGD GDGD Triplex o o o QGd&> tow Gut) GJU (SG)Q O O OQO G)G) O O OQO 46 Simplex o Duplex oo Q G> fflCD oo GDGD Triplex O O O QQ OQ OG>&) Singly reentrant Simplex Winding o o ff Duplex " GD Doubly " > 0= Triply Triplex GD 1 ".Armature Windings for Electric Machines," H. F. Parshall and H. M. Hobart, New York, 1895. 46] ARMATURE WINDING. '57 b. Qualification of Number of Conductors for the Various Windings. The approximate number of conductors for the generation of a certain E. M. F. being calculated from formula (104) and Table XXXIX., it is important to find the accurate number which is qualified to give correct connections for the desired kind of winding. In the following, practical rules and a num- ber of tables are given for the various cases. (i) Simplex Series Windings. Simplex series windings may be arranged either so that coils in adjacent fields, or so that coils in fields of same polarity are connected to each other. In Fig. 99. Short Connection Type Series Winding. Fig. 100. Long Connection Type Series Winding. the former case, which is sometimes called the short connection type of series winding, each of the two armature circuits is influenced by all the poles; in the latter case, which is similarly styled the long connection type of series winding, each circuit is controlled by only half the number of poles. In the former, therefore, the E. M. Fs. of the two circuits are always equal, in the latter only then when the sum of all the lines of one polarity is equal to that of the other; a condition which, how ever, is fulfilled in all well designed machines. In Fig. 99 a winding of the first kind, and in Fig. 100 one of the second kind is shown. The formula controlling simple series windings is: N c = 2 (n v y i), for drum armatures, and c = n 9 y i , for ring armatures; in which: IS 8 DYNAMO-ELECTRIC MACHINES. [46 N c = number of conductors; n c = number of coils; n p = number of pairs of poles; y = average pitch. While for the short connection type there are as many com- mutator segments as there are coils, in a ring armature, or half as many as there are conductors, in a drum armature, the number of commutator-bars for the long connection type of series winding is "c It I n v It is preferable to have the pitchy the same at both ends, in order to have all end connections of same length, but the number of conductors is less restricted (when n p > 2), if the front and back pitches differ by 2. Each pitch must be an odd number, so, in order that the winding passes through all conductors before returning upon itself, it must pass alter- nately through odd and even numbered conductors. Also when the bars, as is usually the case, occupy two layers, it is necessary to connect from a conductor of the upper to one of the lower layer, so as to obviate interference in the position of the spiral end connections. The following Table XLIII., page 159, gives formulae for the number of conductors for which simplex series windings are possible in various cases, and also gives the pitches for prop- erly connecting the conductors among each other. The formulae given refer to drum armatures, but can be used for ring armatures by replacing in every case half the number of conductors, c , 2 by the number of coils, n c . Example, showing use of Table XLIII. : A 6-pole simplex series-wound drum armature is to yield 1.25 volt of E. M. F. at 3,000 revolutions per minute, with a flux of 27,000 webers per pole. How many conductors are required, and how are they to be connected? From (104) and Table XLI. we have N c = T - 2 5 X io 10 5 x 3,000 X 27,000 and Table XLIII. shows that the number of conductors in this 46] ARMATURE WINDING. 159 TABLE XLIII. NUMBEU OP CONDUCTORS AND CONNECTING PITCHES FOK SIMPLEX SERIES DRUM WINDINGS. NUMBER OP POLES. 2n p QUALIFICATION OF NUMBER OF CONDUCTORS, _^,. AVERAGE PiTCH.t FRONT PITCH.}: BACK PiTcn4 Equation for JV C * Degree of Evenness. Description. 2 N e =2x 2 Nc even Any even number not divisible by 3. _ N y " ~2~ ' y y' y' 4 k *. fodd Any singly even num- ber, i. e., any odd multiple of 2. HKf^') y y'i 6 8 10 JV c =6aj 2 N c even Any even number not a multiple of 3. -&) y' i y'+l 2V c =8a;2 N c fodd Any singly even num- ber. '=Kf') y' i y'+i u- ^Vo even Any even number, having either 2 or 3 as remainder when divided by 5, i. e., any number having a 2 or an 8 as the unit digit. r*H y' i y y'+l 12 *=,*, fodd Any singly even num- ber not divisible by 3. H(f^) y y'-i y y'+l 14 tf c =14a:2 .ZVc even Any even number having either 2 or 5 as remainder when divided by 7. -;(?-) y y' \ y'+l 16 *wLi ^odd Any singly even num- ber having either 2 or 14 as remain- der when divided by 16. -i(t-) y'+l * General formula: JV C = 2 _ JT 2 ; 2 p = number of poles, .* = any integer. ^c t For ring armatures replace by n. (number of coils). 2 J The front and back pitches must always be odd numbers. If the average pitch, y, is odd, both the front and back pitches are equal to y ; but if y is even, then the front pitch is y i, and the back pitch = y -f- i. If the average pitch is either odd (y) or even (y'). ac- cording to whether the -f- or sign in the formula is used, then two connections are possible, one having the pitches y, y, and the other the pitches y' i, y' -{- i. i6o DYNAMO-ELECTRIC MACHINES. [46 case must fulfill the condition N c = 6 x 2, which, for x = 5, and for the -|- sign makes N c = 30 + 2 = 32 . The same table gives the average pitch ,=!(?*-)-' from which follows that at both ends of the armature each conductor is to be connected to the sixth following (see Fig. 99, Page 157). (2) Multiplex Series Windings. In case of multiplex series drum windings the number of conductors must be We = 2 (p y m) TABLE XLIV. NUMBER OF CONDUCTORS AND CONNECTING PITCHES FOR DUPLEX SERIES DRUM WINDINGS. 00 QUALIFICATION 3 o op NUMBER OP CONDUCTORS, JVJ, M (X 51 O j^ AVERAGE ei Be p t2 S Equation for # .t Degree of Evenness. Description. PlTCH.J EH E O M o K - CO fi 65 -ZV C =4 X 2 ^ odd 2 Any singly even num- ber. y=^ 2 V r * y (2) (&> JV C =4 a; 4 ^even Any multiple of 4. y =~f 2 2/'-1 y+i y=l &+2) 2/ 2/ O O ^ c =8a: ^-even 4 Any multiple of 8. i/5i \ 4 y sl^ 2 J 2/ 2/' \(N C n\ . (><> ^=8 * 4 ^2. odd 4 Any quadruple of an odd integer. ljjft-1 y'-i y'+i O O -ZV C =12 a; 2 ^- odd 2 Any singly even num- ber, not divisible by 8. t 1 TIT v .V y <0(5> -ZV C =32 x 4 *Lodd 4 Any quadruple of an odd integer of the form 8 1. V V 2 **) y'-i y'+i * O O = singly re-entrant duplex winding -(2) (a) = doubly re-entrant duplex winding. t General formula for O O : A'c = 4 p -r (2 p 4); I 2 p = number of poles. General formula for(J)(jD: A'c = 4 D jr4. fjr = any integer. A^. + In case of ring windings replace by c (number of coils). If y is tfrf^both pitches are = y: \{ y is even, the pitches are .y i and y -|- i; if the average pitch has two different ) Q ff/; (/), the pitches may be either^, y, or y 1 i,y* -}- i, respectively. and for ring windings the number of coils c = p 7 ^m , in which m is the number of multiplex windings. The great- est common factor of y and n m indicates the number of re- entrancies. In Tables XLIV. and XLV., pages 160 to 163, data for duplex and triplex series windings, respectively, are given. 162 D YNAMO-ELECTRIC MA CHINES. [46 Example: The flux of a lo-pole dynamo is 8 megalines per pole. It is to give 145 volts at 125 revolutions per minute, with a triplex series drum winding. To find the number of conductors and the winding pitches. The approximate number of conductors is, by (104): N= I4 5 X I0 ' = 522 . 2.778 X 125 X 8,000,000 TABLE XLV. NUMBER OF CONDUCTORS AND CONNECTING PITCHES FOR TRIPLEX SERIES DRUM WINDINGS. NUMBER OP POLES. 2np. VOKIQNIAV sainag n SIM QUALIFICATION OF NUMBER OF CONDUCTORS, Nc. AVERAGE PITCH 4 FRONT PITCH. an | M < A Equation for jVc.t Degree of Evenness. Description. 2 ooo ^c= 6 2 -ZV C even Any even number, not a multiple of 3. v ^ 3 y y'-i :'/ y'+i (2) -ZV = 6 a? 6 ^V c even Any multiple of 6. y - 2 . y ?/'-i y y'+i 4 OOO JT C =12 * 2 ^c IT odd Any singly even num- ber, not a multiple of 3. -l(f-) ^M y y'-i y y*+i (S)(S)(S) -ZV C <=12 a; 6 ^-Odd Any odd multiple of 6. H(f+) H(f-) y y'--i y y'+i 6 ooo N C =1S x Nc even Any multiple of 18. V^o.^ ^-^V"2-+ 3 J V '-V^ 3\ y -3\-2*) y y'-i f y'+i ooo (3) -ZV C =18 ar 6 ^V c even Any even multiple of 3, not divisible by 9. y y'-i .V y'+i 8 000 w- o/i 3. 2 iV c 4 * 1Q $ Any singly even num- ber, not a multiple of 3. V V^iS^ y'-i y y'+i (5)(sa) JV C =24 a; 6 *. Any odd multiple of 6. * 4V 2 'V ?/ y'-i '+i 10 000 jv;=30 J 4 ^7"c even Any even number not divisible by 3, and having either a 4 or a 6 as unit digit. y-^) y y'-i y y'+i o #c=30 a; 6 2V C even Any odd multiple of 6, having either a 4 or a 6 as unit digit. 5V 2 / y y-i ^ y'4-1 46] ARMATURE WINDING. 163 TABLE XLV. NUMBER OF CONDUCTORS AND CONNECTING PITCHES FOR TKIPLEX SERIES DRUM WINDINGS. Continued. K i: 1 fc i - r s? H - * o i 6.3 Sg *l QUALIFICATION OF NUMBER OF CONDUCTORS, ^~ c . AVERAGE PITCH.J H o 1 n PQ Equation for zVc-t Degree of Evenness. Description. 12 OOO ^=36 * 18 fodd Any odd multiple of 18. y= ! ( f +3) y y-i A* 000 ^T c =36 * 6* j- odd Any odd multiple of 6, not divisible by 9. y'-i y 14 000 8 JV C even Any even number, not a multiple of 3, hav- ing either 1 or 6 as remainder when di- vided by 7. rH*tf y'-i (3) 3^=42 x 6 ^V T C even Any multiple of 6, hav- ing either 1 or 6 as remainder when di- vided bv 7. y y' i y i \"\ 16 OOO ^=48 * 10 N e Any singly even num- ber, not a multiple of 3, having either 6 or 10 as remainder when divided by 16. y ^( Nc 3) y' \ '_L1 a e j$e 48 6 -- odd Any odd multiple of 6, having either 6 or 10 as remainder when divided by 16. y y'-\ y'+i * O O O = singly re-entrant triplex winding ;(SX3XS) = triply re-entrant triplex winding. i General formula for O O O : A^c = 6 x f a n^ - 6), or ) N c = 6 x (4 p - 6) ; [ 2 "P= nun ? ber of P les ' General formula for fiS( : N c = 6 .r 6. ) * = any lnte S er - A^ } For ring windings replace _ by c (number of coils). 2 5 If .y is odd^ both pitches are = j>,- if y is rv?, the pitches arey i and y + i ; if the average pitch is -ithe* odd(y), or 'he pitches may be either y,y, or y 1 i,X+ i, respectively. By Table XLV., the number of conductors qualified for a singly re-entrant triplex series drum winding must be either N c 30 x 4, or N e = 30 x 14 , the latter of which, for x = 17, when using the -\- sign, fur- nishes the nearest number, = 3 X 17 + T 4 = 5 2 4, 164 DYNAMO-ELECTRIC MACHINES. [46 for which a singly re-entrant triplex winding is possible. The average pitch, being odd, the front and back pitches are equal, both being the same as the average pitch. If a triply re-entrant triplex winding were desired the num- ber of conductors would have to be determined from ^ = 3 x 6 ; and the two nearest numbers that fulfill this. equation are N c = 30 x 17 + 6 = 5 l6 and N c - 30 x 18 - 6 - 534 . According to whether the former or the latter number of con- ductors is chosen, the average pitch will be either or / = s -^r3^=s4 respectively. In the former case both pitches are y = 51; in the latter case, however, the front pitch has to be taken y' -- i = 53, and the back pitchy -f- i = 55. (3) Simplex Parallel Windings. For simplex parallel wind- ings there may be any even number of conductors, except that in toothed and perforated armatures the number of conductors must also be a multiple of the number of conductors per slot. If it is desired to have exactly the same number of coils in each of the parallel branches, the number of coils must further be a multiple of the number of poles. The pitches in parallel windings are alternately forward and backward, instead of being always forward, as in the series windings. The front and back pitches must both be odd, and should preferably differ by 2; therefore, the average pitch y = '-(-*>} "-V 2 / 46] ARMATURE WINDING. 165 should be even. The average pitch should not be very much different from the number of conductors per pole, For drum fashioned ring windings, or "chord" windings, the average pitch, y, should preferably be smaller than and should differ from it by as great an amount as other con- ditions will permit. Fig. 101. Simplex Parallel Ring Winding. Fig. 101 shows a simplex parallel ring winding for 4 poles and 16 coils. The average pitch is y=- = 4 consequently the front pitch, y i =3, and the back pitch y + * = s- (4) Multiplex Parallel Windings. In multiplex parallel wind- ings the number of conductors, N c , must be even. The con- necting pitches must be odd. If the front pitch is = y' t then the back pitch is = (y 1 -\- 2 n m ), where n m number of mul- tiple windings. The number of conductors (-*V C )> the average pitch (y) and the number of poles (2 p ) should be so chosen that 2 p = y is somewhere nearly = N cy preferably a little smaller than N,.. i66 D YNA MO-ELE C 7 'RIC MA CHINES. [46 The greatest common factor of ^c 77^ and n - indicates the number of re-entrancies of the windings. If the number of conductors per pole, is not divisible by the number of multiple windings, n m , there will be a singly re-entrant winding; and if it is divisible by Fig. 102. Duplex Parallel Drum Winding. m , there will be a doubly re-entrant winding in case of n m = 2 (duplex winding), and a triply re-entrant winding in case of m = 3 (triplex winding). The winding pitches for multiple parallel windings are: Average pitch y = - - X n n Front pitch Back pitch mj; y t - y - In case of a duplex parallel winding y should be chosen an odd number, so as to makejv 2 and y -\- 2 odd numbers also; and in case of a triplex parallel winding the average pitch should be taken even, in order to make the connecting pitches, y 3 and y -j- 3, odd. In Fig. 102 a singly re-entrant multiplex parallel winding is 46] ARMATURE WINDING. 167 given for n p = 2, w' p = 2, n m = 2, and lV e = 28. The pitches in this case are 7 2 = 5, and y -f 2 = 9 . There are two independent singly re-entrant windings, each having 4 parallel branches, making 8 paths altogether; 6 of these paths contain 4 conductors each, and the remaining 2 but 2 conductors each. In order to have an equal number of conductors in all branches, N c must be a multiple of 2 n' p X # m > or in the present example the number of conductors should be either 24 or 32; in the former case each of the 8 parallel branches would have 3, and in the latter case 4, conductors. As further illustrations of the rules given above we take (i) yV c = 486, p = 3, ' p = 3, n m = 2; this is a 6-pole duplex parallel winding; since ^c 486 /: ~~ OI 2 p 6 is not divisible by n m = 2, we have a singly re-entrant duplex winding (oo), for which the pitches are: I(A *)-". = 3 y 2 79, and^v -{- 2 = 83 . (2) .rfV,, = 1,368, ftp = 6, n'p = 6, n m = 3; in this case, which represents a triplex parallel winding for 12 poles, W c i >3 6 8 - = -^ = 144 2 fl p 12 is a multiple of m = 3, and therefore we have a triply re- entrant triplex winding ( ((aJ) ) ; the average pitch for this winding is ') hence the front and back pitches are y 3 = i", and y + 3 = 117, respectively. CHAPTER IX. DIMENSIONING OF COMMUTATORS, BRUSHES, AND CURRENT- CONVEYING PARTS OF DYNAMO. 47. Diameter and Length of Commutator Brusb Sur- face. In small and medium-sized machines the commutator is usu- ally placed upon the shaft concentric with the armature, and has the collecting brushes sliding upon its peripheral surface. In large ring dynamos the armature winding is often performed by means of bare copper bars, and the current is then taken off directly from the winding; thus, in the Siemens Innerpole dy- namo the brushes rest upon the external periphery of the arma- ture, and in the Edison Radial Outerpole machine the two end surfaces of the armature are formed into commutators. If it is not convenient to use part of the armature winding itself as the commutator, in large diameter machines it is of advantage to provide a separate face-commutator, that is, a commutator with the brush surface perpendicular to the arma- ture shaft; for in this case the otherwise unavailable space between the armature periphery and the shaft is made use of, and a saving in length of machine and in weight will be effected. For the peripheral as well as for the face type commutator the same principles of construction hold good; the only differ- ence is that in the latter case the outer diameter of the brush surface is fixed by the external diameter of the armature, and that therewith the top width of the bars is directly given by the number of commutator divisions, while in the former case the dimensions of the brush surface can be chosen between comparatively much wider limits. In low potential machines with small number of divisions, the thickness of the substructure determines the diameter of the commutator; in high potential machines, however, espe- cially those of multipolar type, where the number of commuta- 168 47] COMMUTATORS, BRUSHES, AND CONNECTIONS. 169 tor segments is very great, the width, at top, of the commu- tator bars, their number, and the thickness of the insulation between them fix the outside diameter. The bars must be large enough in cross-section to carry the whole current generated in the armature without undue heat- ing, and shall continue so after a reasonable amount of wear. They must be of sufficient length to allow a proper number of brushes to take off the current. The same brush contact surface may be obtained by employ- ing either a broad thin brush on a small diameter commutator, or a narrow thick one on a large diameter, the number of bars being the same in both cases, their width, consequently, larger in the latter case. With larger diameter and greater conse- quent peripheral velocity there will be more wear of both brushes and segments, and greater consumption of energy due to the increased friction of the brushes. The segments are usually made of copper (cast, rolled, or forged), phosphor bronze, or gun metal, sometimes brass, and even iron being used; the materials for the substructure are phosphor bronze, brass, or cast iron. From all this it will be obvious that a general formula for the diameter of the commutator cannot be established, and that, on the contrary, this dimension has to be properly chosen in every case with reference to the armature diameter to the design of the commutator, to the materials employed, to the strength of the substructure, or the thickness of the bar, respectively, and, finally, with reference to the wear of the segments. The commutator diameter being decided upon, the size of the brushes can now be calculated, as shown in 49, and, from this, the length of the commutator can be found. In order to prevent annular grooves being cut around the commutator, the brushes ought to be so adjusted that the gaps between those in one set do not come opposite the gaps in the other set. Denoting, Fig. 103, the width of each brush by b , their number per set by n b , and the gap between them by /'b, we consequently obtain the total length of the commu- tator brush surface from: /.= (n b + - X K+/' b ) (114) 170 DYNAMO-ELECTRIC MACHINES. This length of brush surface should be available even after the commutator has been turned down to its final diameter; the original diameter must therefore have a somewhat larger con- Fig. 103. Arrangement of Commutator Brushes. tact length. An addition to / c of from ^ to i inch, according to the depth of the bar, is thus necessitated. As to the practical design of commutators, while the same general plan is followed in all, the details of construction are almost numberless. Structural cross-sections and descriptions of the commutators manufactured by the Electron Manufac- turing Company, the Storey Motor and Tool Company, the Royal Electric Company, the Fort Wayne Electric Corpora- tion, Paterson & Cooper, the Glilcher Company, the General Electric Company, the Triumph Electric Company, the Sie- mens & Halske Electric Company, the Walker Company, and others, are given in an article l in American Electrician. 48. Com imitator Insulations. In a commutator the insulation has to form a part of the general structure, and has to take strain in common with other material used; from its natural cleavage and hardness, therefore, mica is particularly suitable for commutator insula- tions, and is, in fact, almost exclusively used for this purpose, only asbestos and vulcanized fibre being employed in rare cases. " Modern Commutator Construction," American Electrician, vol. viii. p. 83 (July, 1896). 49] COMMUTATORS, BRUSHES, AND CONNECTIONS. i?i The thickness of the commutator insulation ought to be proportional to the voltage of the machine, and, for the various Fig. 104. Commutator Insulations. positions with reference to the bars, see h ly h\, h f iy Fig. 104, should be selected within the following limits: TABLE XL VI. COMMUTATOR INSOLATIONS FOB VARIOUS VOLTAGES. POSITION OP INSULATION. THICKNESS OF INSULATION (MICA): Up to 300 Volts. 400 to 700 Volts. 800 to 3,000 Volts. inch. mm. inch. mm. inch. mm. Side Insulation (hi) Bottom Insulation (fi'i) Eud Insulation (k"\) .020 to .040 A " A A " A .5 to 1.0 1.25 " 25 1.5 " 2.5 .030 to .050 A " * A " t .75 to 1.25 1.5 " 3 2.5 " 3 .040 to .060 * " ^ 8 A 1 to 1.5 2.5 " 5 3 "5 49. Dynamo Brushes. 1 a. Material and Kinds of Brushes. For low potential machines having a large current output, it is the practice to employ thick copper brushes, made up either of copper wires, or copper strips, or copper wire gauze, in order to secure a large number of contact points, and to set them so as to make an angle of about 45 with the commutator surface, as shown in Fig. 105. In small dynamos, often springy copperplates are used which are placed tangentially to the commutator periphery, as illustrated in Fig. 106. For high potential machines, especially for railway genera- tors and motors, carbon brushes are used in order to aid in the sparkless collection of the current at varying load. As each 1 " Commutator Brushes for Dynamo-Electric Machines: their selection, their proper contact-area, and their best tension, "by A. E. Wiener, American Elec- trician, vol. viii. p. 152 (September, 1896). 172 D YNAMO-ELECTR1C MA CHINES. [49 commutator segment enters under the brush, the area of con- tact is, at first, very small and, owing to the high specific re- sistance of carbon, a considerable resistance is offered to the passage of the current from the branch of the armature of which that segment at the time is the terminal, into the exter- nal circuit. This gives rise to a considerable local fall of potential, which diverts a comparatively large portion of the armature current through the neighboring coil into which it flows against the existing current, causing the latter to reverse quickly in opposition to the E. M. F. of self-induction, thereby Fig. 105. Sloping Copper Wire (or leaf) Brush. Fig. 106. Tangential Copper Plate Brush. preparing the short-circuited coil to join the successive arma- ture circuit of opposite polarity without sparking. (Compare with sections on sparkless commutation of armature cur- rent, in 13.) The resistance of the carbon brushes cannot be depended upon for the complete commutation of the entire current, but in most generators, especially in those with toothed and perforated armatures, fully half the armature current may be thus commutated. In railway generators it is usual to adjust the brushes so that at no load they are in the neighborhood of the forward pole-tips where the pole- fringe E. M. Fs. generated are sufficient to reverse one-half of the normal current, the remaining half being then taken care of by the brushes. Carbon brushes are either set tangentially (Fig. 107), or radially (Fig. 108), with respect to the commutator circumfer- ence, the latter arrangement having the advantage of admitting of reversal of the rotation, without changing the brushes. To use carbon brushes exclusively on machines of low volt- age would be very bad practice, because carbon has so much 49] COMMUTATORS, BRUSHES, AND CONNECTIONS. 1 73 higher resistance than copper that the drop of potential would be excessive, and too great a percentage of the power of the machine would be used up for commutation. If, therefore, the resistance of an ordinary copper brush is not high enough Fig. 107. Tangential Carbon Brush. Fig. 108. Radial Carbon Brush. for sparkless collection, a copper gauze brush must be em- ployed, which has a much higher resistance than a copper leaf brush, and while there are some mechanical advantages in using it, such as cooling effects and smoother wear of the commutator, yet the principal reason it stops sparking is that it has a higher resistance. In case the resistance is still too low, the next step is the application of a brass gauze brush having about twice the resistance of copper gauze. If that is not enough yet, some form of carbon brush which has its resistance reduced, must be resorted to. Carbon itself cannot have its resistivity changed, but by mixing copper filings with the carbon powder, or by molding layers of gauze in it, the conductivity of the brush can be increased. Instead of arti- \ j COPPER \ V BRUSH COPPER x _- CARBON " Figs. 109 and 1 10. Combination Copper-Carbon Brushes. ficially decreasing the resistance of carbon, combination brushes consisting either in copper brushes provided with carbon tips, Fig. 109, or in carbon brushes sliding upon the commutator and having, in turn, copper brushes resting against themselves, Fig. no, are sometimes employed, and in case of very heavy D YNAMO-ELECTRIC MA CHINES. [49 currents, the addition to each set of copper brushes, of a com- bination brush set somewhat ahead of the copper brushes as shown in Fig. in, has been found to greatly improve the COMBINATION BRUSH V COPPER BRUSH Fig. in. Arrangement of Copper and Combination Brushes for Collection of Large Currents. sparkless running of the machines. With the latter arrange- ment, the tension on the combination brushes should exceed that on the copper brushes sufficiently to enable them to take their full share of the current as nearly as possible. b. Area of Brush Contact. The thickness of the brushes, according to the current capa- city of the machine, to the grouping of the armature coils, to the material and kind of the brush and to the dimensions of the commutator, varies between less than the width of one to Figs. 112 and 113. Circumferential Breadth of Brush Contact. that of three and even more commutator segments. In case the brush covers not more than the width of one bar, as in Fig. 112, only one armature coil is short-circuited at any time, 49] COMMUTATORS, BRUSHES, AND CONNECTIONS. 17$ while in case of brushes thicker than the width of one bar plus two side insulations, Fig. 113, two or even more coils, at times, are simultaneously short-circuited under each set of brushes. The breadth of the brush contact surface in the former case (Fig. 112) is equal to the thickness of the beveled end of the brush measured along the commutator circumference; in the latter case (Fig. 113) is the breadth of the brush bevel dimin- ished by the sum of the thickness of the commutator insula- tions covered by the brush, and can be generally expressed by the formula /-_- \ ........(115) where k = circumferential breadth of brush contact, in inches; n k = number of commutator-bars covered by the thick- ness of one brush; <4 = diameter of commutator, in inches; c = number of commutator-divisions; /*i = thickness of commutator side-insulation, in inches, see Table XLVI. If the brush covers less than one bar, as in Fig. 112, k is a fraction; if the width of the brush is from one bar to one bar plus two side insulations, n k = i; when between two bars plus one insulation and two bars plus three insulations, n k = 2, etc. ; and if the brush covers from one bar plus two insulations to two bars plus one insulation, or from two'bars plus three insula- tions to three bars plus two insulations, etc., the value of n k is a mixed number, consisting of an integer and a fraction. Having decided upon %and having calculated fi k from (115), the width of the contact area, and subsequently the width of the brushes, can be found for a given current output of the dynamo by providing contact area in proportion to the current intensity. In order to keep the brushes at a moderate tem- perature, and the loss of commutation within practical limits, the current density of the brush contact should not exceed 150 to 175 amperes per square inch in case of copper brushes (wire, leaf plate, and gauze), TOO to 125 amperes per square inch for brass gauze brushes, and 30 to 40 amperes per square inch in case of carbon brushes. 176 DYNAMO-ELECTRIC MACHINES. i4y Taking the lower of the above limits of the current densities, the effective length of the brush contact can consequently be expressed by 150 x n\ X ^k for copper brushes, by 4 = - -4- -r (117) 100 X n\ X &* for brass brushes, and by 4= 4 r ( ll8 ) 30 X P X k for carbon brushes, the symbols employed being 4 = effective length of brush contact surface, in inches; = #b X b b (n b = number of brushes per set, b b = width of brush) ; / total current output of dynamo, in amperes; ' p = number of pairs of brush sets (usually either n\ = i, or equal to the number of bifurcations of the armature current, n' v = #' p ). For the purpose of securing a good contact, the length 4 should be subdivided into a set of n b individual brushes, of a width b b each, not exceeding i^ to 2 inches. In small machines, where one such brush would suffice, it is good practice to employ two narrow brushes, even down as low as 3/8 inch each, in order to facilitate their adjusting or exchang- ing while the machine is running. c. Energy- Loss in Collecting Armature Current. Determination of Best Brush Tension. The brushes give rise to two losses of energy: an electrical energy-loss due to overcoming contact resistance, and a mechan- ical loss caused by friction. Both of these losses depend upon the pressure with which the brushes are resting upon the com- mutator, the electrical loss decreasing and the mechanical loss increasing with increasing brush tension. There will, there- fore, in every single case, be one certain pressure per unit area of brush contact, for which the sum of the brush losses will be a minimum. With the object of determining this criti- 49] COMMUTATORS, BRUSHES, AND CONNECTIONS. 1 77 cal pressure, E. V. Cox and H. W. Buck 1 have investigated the influence of the brush tension upon the contact resistance and upon the friction, for various kinds of brushes. They found (i) that the friction increases in direct proportion 4-5 w 5 1 1-5 2 2-5 3 3-5 BRUSH PRESSURE, IN POUNDS PER SQUARE INCH. Fig. 1 14. Contact Resistance and Friction per Square Inch of Brash Surface, on Copper Commutator (dry), at Peripheral Velocity of 1,000 Feet per Minute. with the tension; (2) that the contact resistance decreases at first very rapidly, but that beyond a certain point a great increase in pressure produces only a slight diminution of resistance; (3) that slightly oiling the contact surface, while not perceptibly increasing the electrical resistance, greatly 1 The Relation between Pressure, Electrical Resistance, and Friction in Brush Contact," Electrical Engineering Thesis, Columbia College, by E. V. Cox and H. W. Buck. Electrical Engineer, vol. xx. p. 125 (August 7, 1895); Electrical World, vol. xxvi. p. 217 (August 24, 1895). 178 D YNAMO-ELECTRIC MA CHINES. [49 diminishes the friction; (4) that for a copper brush the friction is greater and the contact resistance smaller than for a carbon brush of same area at the same pressure; (5) that the friction of a radial carbon brush is greater than that of a tangential carbon brush at the same pressure; (6) that for the same brush both the contact resistance and the friction are consid- erably less on a cast-iron cylinder than on a commutator ; and 5 1 1-5 2 2-5 3 3-5 4 BRUSH PRESSURE, IN POUNDS PER SQUARE INCH Fig. 115. Contact Resistance and Friction per Square Inch of Brush Surface, on Cast-iron Cylinder. (7) that for all kinds of brushes the friction is less at high than at low peripheral speeds, while the contact resistance is but slightly increased by raising the velocity. In Figs. 114 and 115 the averages of their results are plotted, the former giving the curves of contact resistance and friction for an ordinary commutator, without lubrication, and the latter the corresponding curves for the case that the commutator is replaced by a cast-iron cylinder. From Fig. 114 the following Table XLVII. is derived, which, in addition to the data obtained from the curves, also 49J COMMUTATORS, BRUSHES, AND CONNECTIONS. 179 contains the brush friction for the case the commutator is slightly oiled: TABLE XL VII. CONTACT RESISTANCE AND FRICTION FOR DIFFERENT BRUSH TENSIONS. BRUSH TENSION IN POUNDS PER SQUARE INCH. CONTACT KESISTANCE PER SQUARE INCH OF BRUSH SURFACE, p k , IN OHM. TANGENTIAL PULL DUE TO BRUSH FRICTION PER SQUARE INCH OF CONTACT AT PERIPHERAL SPEED OF 1,000 FEET PER MINUTE. f ky m POUNDS. Tangential Copper Leaf Brush. Tangential Carbou Brush. Radial Carbou Brash. Commutator Dry. Commutator Oiled. a 3. a "TJ a 3 __ a __.c' "03 S2 'S "3 3 ^ Tangent Copper B &a |1 O ! g. 6 " wo c o o 1* s fl l O .5 .010 .50 .40 .6 .3 .5 .16 .10 .15 1 .009 .24 .20 1.15 .63 1 .32 .20 .30 1.5 .008 .15 .13 TlO~ 1.7 ~2T25 .95 T25 1.5 .48 .30 .45 2 .007 .12 2 .64 .40 .60 2.5 .006 .10 .087 2.8 1.6 2.5 .80 .50 .75 3 .0055 .09 .08 3.4 1.9 3 .96 .60 .90 3.5 .0052 .083 .075 3.95 2.2 35 1.12 .70 1.05 4 .005 .08 .07 4.5 2.5 4 1.30 .80 1.20 The specific pull, f k , due to brush friction, in columns 5 to 10 of the above table, is given for a peripheral velocity of 1,000 feet per minute; at 2,000 feet per minute it is 7/8, at 3,000 feet per minute 3/4, at 4,000 feet per minute 5/8, and at 5,000 feet per minute only 1/2 of what it is for that pres- sure at 1,000 feet per minute, and for any commutator velocity, t' k , can be found from the formula From Table XLVII. the electrical brush loss is calculated by dividing the contact resistance given for the particular brush tension employed, by the contact area, and multiplying the 180 DYNAMO-ELECTRIC MACHINES. [49 quotient by the number of sets of brushes and by the square of the current passing through each set, thus: = .00268 X pkX ^ horse power, ..... (120) * k X #k X # P where P = energy absorbed by contact resistance of brushes; p k = resistivity of brush contact, ohm per square inch surface, from Table XLVII. ; / k x ^ k = contact area of one set of brushes, in square inches; * p = number of pairs of brush sets; / = current output of dynamo. And the frictional loss is obtained in multiplying the tan- gential pull, given for the respective brush tension and cor- rected to the proper peripheral velocity according to formula (119), by the total brush contact area and by the peripheral velocity of the commutator, and dividing the product by 33,000, the equivalent of one horse power in foot-pounds per minute: p - A x 2 **P x 4 x k x y k 33,000 = 6 x io- 6 X /' k X 4 X k X % X v* , ........ (121) in which P t = energy absorbed by brush friction, in HP; y' k = specific tangential pull due to friction, at ve- locity v k , in pounds, see formula (119); 2 * p X 4 X k = total area of brush contact surfaces, in square inches; v k = peripheral velocity of commutator, in feet per minute, _ <4 X TT x N By calculating the amounts of / k and P t , from (120) and (121) respectively, for different brush tensions, the best tension giving a minimum value of the total brush-loss, P k + P t , can readily be found. 50J COMMUTATORS, BRUSHES, AND CONNECTIONS. 181 50. Current-Conveying Parts. Care must also be exercised in the proportioning of those parts of a dynamo which serve to convey the current, col- lected by the brushes, to the external circuit. For, if mate- rial is wasted in these, the cost of the machine is unneces- sarily increased; and if, on the contrary, too little material is used, an appreciable drop in the voltage and undue heating will be the result. In the design of such current-conveying parts, among which may be classed brush holders, cables, conductor rods, cable lugs, binding posts, and switches, the attention should Figs. 116 to 118. Various Forms of Spring Contacts. therefore be directed to the smallest cross-section through which the current has to pass, and to the surfaces of contact transferring the current from one part to another. The max- imum permissible current density in the cross-section, while depending in a small degree upon the ratio of circumference to area of cross-section, is chiefly determined by the choice of the material; that in the area of contact between two parts, how- ever, although the conductivity of the material employed is of some consequence, depends mainly upon the condition of the contact surfaces and upon the amount of pressure that can be applied to the joint. The most usual forms of contact are those shown in Figs. 116 to 125. Figs. 116 to 118 represent spring contacts as used in switches; in Fig. 116 the switchblade is cast in one with the lever, while in Figs. 117 and 118 the levers are provided with separate copper blades. The former is a single switch making and breaking contact between the blade and the clips, the lever itself forming the terminal of one pole; the latter two are double switches, the connection being established between two sets of clips by way of the blade, when the switch is closed. 182 D YNAMO-ELECTR1C MA CHINES. [50 In order to prevent the forming of an arc in opening a switch, especially a double switch, each blade must leave all the clips with which it engages simultaneously over its entire length. For this purpose either the blade, or the clips, or both (Figs. 117, 118, and 116, respectively) have to be cut off at such an angle that, in the closed position of the switch, the enter-line of the blade and the line through the tops of the clips are both tangents to the same circle (shown in dotted lines in Figs. 116 to 1 18), described from the centre of the lever fulcrum. If all clips are then made of equal widths, as in Fig. 117, those FIG. 11 9. -LAMINATED JOINT. FIO. 121. -LUG HELD BETWEEN NUTS ON A SJUD. F , . f22. -LUG'CLAMPED BETWEEN WASHERS. FlO. f24. -TAPER PLUG INSERTED BETWEEN TWO SURFACES. 7la/125.~-T APER PLUG GROUND TO SEAT AND BOLTED. Figs. 1 19 to 125. Various Forms of Screwed, Clamped, and Fitted Contacts. nearest to the fulcrum, in case of a double switch, have less contact area than the remote ones, and in designing such a switch this smaller contact area is to be made of sufficient size to carry half the armature current, if there is but one blade, and one-quarter of the total current when the lever has two blades. By making the clips near the fulcrum correspondingly wider than those at the other end of the blade, as in Fig. 118, all the contact surfaces can, however, be made of equal area. Various forms of screwed or bolted contacts are shown in Figs. 119, 120, and 121; a clamped contact is illustrated in Fig. 122; two common forms of fitted contact in Figs. 123 and 124; and an excellent fitted and screwed contact in Fig. 125. 50] COMMUTATORS, BRUSHES, AND CONNECTIONS. 183 The permissible current densities for all these different kinds of contact as well as for the cross-section of different materials are compiled in the following Table XLVIIL, which more in particular refers to the larger sizes of dynamos, since in small machines purely mechanical considerations lead to much heavier pieces than are required for electrical purposes: TABLE XLVIII. CURRENT DENSITIES FOR VARIOUS KINDS OP CONTACTS AND FOR CROSS-SECTION OF DIFFERENT MATERIALS. KIND OP CONTACT. MATERIAL. CURRENT DENSITY. ENGLISH MEASURE. METRIC MEASURE. Amps, per square inch. Square mils per amp. Amps, per cm. 8 mm.* per ampere. Sliding Contact (Brushes) Copper Brash 150 to 175 5,700 to 6,700 23 to 28 3.5 to 4.5 Brass Gauze Brush 100 to 125 8,000 to 10,000 15 to 20 5 to 7 Carbon Brush 30 to 40 25,000 to 33,300 4.5 to 6 16 to 22 Sprinsr Contact (Switch Blades) Copper on Copper 60 to 80 12,500 to 16,700 9 to 12.5 8 to 11 Composition on Copper 50 to 60 16,700 to 20,000 7.5 to 9.5 11.5 to 13.5 Brass on Brass 40 to 50 20,000 to 25,000 6 to 8 12.5 to 16.5 Screwed Contact Copper to Copper 150 to 200 5.000 to 6,700 23 to 31 3 to 4.5 Composition to Copper 125 to 150 6,700 to 8,000 19 to 23 4.5 to 5.5 Composition to Composition 100 to 125 8,000 to 10,000 15 to 20 5 to 6.5 Clamped Contact Copper to Copper 100 to 125 8,000 to 10,000 15 to 20 5 to 6.5 Composition to Copper 75 to 100 10,000 to 13,000 12 to 16 6 to 8.5 Composition to Composition 70 to 90 11,000 to 14,000 11 to 14 7 to 9 Fitted Contact (Taper Plugs) Copper to Copper 125 to 175 5,700 to 8,000 20 to 28 3.5 to 5 Composition to Copper 100 to I-.TJ 8,000 to 10,000 15 to 20 5 to 7 Composition to Composition 75 to 100 10,000 to 13,000 12 to 16 6 to 8.5 Fitted and Screwed Contact Copper to Copper 200 to 250 4,000 to 5,000 30 to 40 2.5 to 3.5 Composition to Copper 175 to 200 5,000 to 5,700 28 to 31 3 to 3.5 Composition to Composition 150 to 175 5,700 to 6,700 23 to 28 3.5 to 4.5 Cross-section Copper Wire 1,200 to 2,000 500 to 800 175 to 300 .35 to .55 Copper Wire Cable 1,000 to 1,600 600 to 1,000 150 to 250 .4 to .65 Copper Rod 800 to 1,200 800 to 1,200 125 to 175 .55 to .80 Composition Casting 500 to 700 1,400 to 2,000 75 to 110 .90 to 1.35 Brass Casting 300 to 400 2,500 to 3,300 45 to 60 1.60 to 2.25 CHAPTER X. MECHANICAL CALCULATIONS ABOUT ARMATURE. 51. Armature Shaft. The length of the armature shaft, varying considerably foi the different arrangements of the field magnet frame, depends upon the type chosen, and, since the length of the commutator depends upon the current output of the machine, even varies in dynamos of equal capacity and of same design, but of differ- ent voltage, a general rule for the length of the shaft can therefore not be given. Its diameter, however, directly depends only upon the out- put and the speed of the dynamo, and can be expressed as a function of these quantities, different functions, however, being employed for various portions of its length. For, while t -'b *! w//A Fig. 126. Dimensions of Armature Shaft. in the bearing portions, d b , Fig. 126, torsional strength only has to be taken into account, the center portion, d c , between the bearings, which carries the armature core, is to be calcu- lated to withstand the torsional force as well as the bending due to the weight. For steel shafts the author has found the following empirical formulae to give good results in practice: For bearing portions: d b = k t x V^x V*^, (122) where d^ = diameter of armature shaft, at bearings, in inches; P' = capacity of dynamo, in watts; N = speed, in revolutions per minute; k t = constant, depending upon the kind of armature, see Table XLIX. 184 61] MECHANICAL CALCULATIONS. 185 The value of k % varies between .0025 and .005, as follows: TABLE XLIX. VALUE OP CONSTANT IN FORMULA FOR JOUKNAL- DlAMETER OF ARMATURE SlIAFT. KIND OF ARMATURE. VALUE OF High speed drum armature .0025 High speed rinu; " .003 Low speed Ibs. per square inch. " brass ........... = 6,000 " " " phosphor-bronze = 7,000 " " " wrought iron. ... = 10,000 " " aluminum bronze 12,000 " " " cast steel ....... =15,000 " " For spiral windings, now, b s , as stated above, is given by making it as large as possible, and from (125) we therefore obtain: ..... (126) I 9 o DYNAMO-ELECTRIC MACHINES. [53 For windings external to the core, /* s may be fixed and then calculated from: * = ' 8x x ..... (127) For very heavy duty dynamos a larger factor of safety should be taken, say from 6 to 8; this will change the numeri- cal coefficient of formulae (125) and (127) into 27 1036, and that of equation (126) into 5.3 to 6, respectively. 53. Armature Bearings. To determine the size of the armature bearings, ordinary engineering practice ought to be followed. In machine design, on account of the increased heat generation at higher velocities, it is the rule to provide a larger bearing surface the higher the speed of the revolving shaft. This rule may, for dynamo shafts, be expressed by the formula: (128) where / b = length of bearing, in inches; p = diameter of pulley, in inches; # B = belt speed, in feet per minute, see Table LVIII. ; N = speed of dynamo, in revolutions per minute. The belt speed in modern dynamos ranges between 2,000 192 DYNAMO-ELECTRIC MACHINES. [63 TABLE LVI. BEARINGS FOR HIGH-SPEED RING ARMATURES. SIZE OF BEARING. SPEED CAPACITY, IN KILO- WATTS. VALUE OF CONSTANT fao. IN REVS. PER MIN. (FROM TABLE XI.) Diameter (from Table LIT.) Length. Ratio. .1 .1 2,600 i li 5.0 .25 .1 2,400 f 11 5.0 .5 .1 2,200 4.75 1 .1 2,000 i 2f 4.4 2.5 .1 1,700 i 4.1 5 .1 1,500 if 5f 3.9 10 .11 1,250 it 6f 3.85 25 .12 1,000 81 10 38 50 .13 800 3! 13 3.7 100 .15 600 4f 17! 3.7 200 .16 500 6f 23 3.6 300 .17 450 27 3.6 400 .175 400 8! 30 3.5 600 .18 350 10 33! 3.35 800 .19 300 11 36 3.3 1,000 .2 250 12 38 3.2 1,500 .21 225 14 45 3.2 2,000 .225 200 16 51 3.2 TABLE L VII. BEARINGS FOR LOW-SPEED RING ARMATURES. SIZE OF BEARING. SPEED CAPACITY, IN KILO- WATTS. VALUE or CONSTANT ho. IN REVS. PER MIN. (FROM TABLE XII.) jr. Diameter (from Table LIII.) <* b Length. i b = &io x d b x VN. Ratio. * b :rf b 2.5 .15 400 H 3f 3.0 5 .16 350 H 4} 3.0 10 .17 300 2 51 2.9 25 .18 250 3 8f 28 50 .19 200 4i IH 2.7 100 .20 175 5* 15i 2.65 200 .21 150 7f 20 2.6 300 .23 125 9i 23f 2.6 400 .25 100 10 25 2.5 600 .265 90 12 30 2.5 800 .27 80 13| 32* 2.4 1.000 .28 75 15 36 2.4 1,500 .29 70 18 43| 2.4 2.000 .30 65 20 48 2.4 54] MECHANICAL CALCULA TIONS. 193 and 6,000 feet per minute (= 600 and i, 800 metres per minute), as follows: TABLE LVIII. BELT VELOCITIES FOR HIGH-SPEED DYNAMOS OP VARIOUS CAPACITIES. BELT SPEED, V B CAPACITY, IN KILOWATTS. Feet per Minute. Metres per Minute. Up to 5 2.000 to 3000 600 to 900 2.5 " 25 3,000 " 4,000 900 " 1,200 10 " 100 4,000 " 5,000 1 200 " 1,500 50 " 500 5,000 " 0,000 1,500 " 1,800 The pull at the pulley circumference, in pounds, is: _ 33,000 X HP __ 33,000 X HP X 12 Watts 33,ooo X -j^- p , - = 44- 2 X - - . For an arc of belt contact of 180, which can safely be as- sumed for dynamo pulleys, the pull F p , is to be multiplied by 1.4 in order to obtain the tension on the tight side of the belt; hence the greatest strain upon the belt: =,1.4 X P' = 62 X . v. Allowing 300 pounds per square inch as the safe working strain of leather, the necessary sectional area of the belt can be found from b, x A,= = .2 X ; (130) 300 V B b B = width of belt, in inches; // B i= thickness of belt, in inches; FU = greatest strain in belt, /. e., tension on its tight side, in pounds; P' = capacity of dynamo, in watts; z> a = belt speed, in feet per minute, Table LVIII. i 9 4 D YNA MO- ELEC TRIG MA CHINES. [54 The approximate thicknesses for the various kinds of belts are: Single belt h K = T \ inch Light double belt " - & " Heavy double belt " = tt " Three-ply belt " = T \ " Inserting these figures into (130), the width of the belt is obtained: Single belt. Light double belt. . . A = ^f X = .7 X (132) i I 2 ^B ^B TABLE LIX. SIZES OP BELTS FOR DYNAMOS. 1 WIDTH OF BELT, IN INCHES. OUTPUT OP THICKNESS DYNAMO IN I/ , , ,*_ OF BELT, Belt Speed, in Feet per Minute : I\ILO WATTS. 2,000 2,500 3,000 3,500 4,000 4,500 5,000 5,500 6,000 ' f A .8 .7 .6 2 A 1 6 1.3 1.1 3 S 2.3 1.8 1.5 1.8 1.2 5 A 3.1 3.0 2.5 2.1 1.9 7.5 - % 5.4 4.4 36 3.1 2.7 10 13 A 7.1 5.6 4.7 4.0 3.5 s!i 2.S 15 A 10.3 8.3 6.9 5.9 5.2 4.6 4.1 20 13.4 10.7 9.0 7.7 6.7 6.0 5.4 , 25 'to s a TV 10.9 9.4 8.2 7.3 6.6 . . 30 ""* _5 13 11.1 9.7 8.6 7.8 40 A . . 17 14.6 12.8 11.4 10.2 . . 50 A . . 21 18.0 15.8 14 12.7 11.5 10 '.5 60 A 25 21.4 18.8 16.7 15 13.7 12.5 75 A . . . . 31 26.5 23.2 20 18.5 17 15.5 100 I A 30 27 24.4 22.2 20.4 150 .2 .*"*' .. 29 25.7 23 21 19.3 200 . 33 29.2 26.3 24 22 250 313 |t 40.7 36.2 32.6 29.6 27.2 300 Q & 51.3 45.5 41 37.3 34.2 400 t>vfr 48.5 43 38.7 35.2 32.2 500 ec >s 7 60 53.5 48 44 40 54] MECHANICAL CALCULATIONS. 19$ Heavy double belt. ..6 B = - X = .6 X (133) i ^B ^B 2 P' P' Three-ply belt B = ~ X = -45 X (134) lV ^B VB Single belts are used for all the smaller sizes, up to 100 KW output, light double belts up to 200 KW, heavy doubles up to 400 KW, and three-ply belts for capacities from 400 KW up. Based upon the above formulae the author has prepared the preceding Table LIX., from which the belt dimensions for vari- ous outputs and for different belt speeds can readily be taken. The width of the belt being thus determined, the breadth of the pulley-rim is found by adding from ^ inch to 2 inches according to the width of the belt. PART III. CALCULATION OF MAGNETIC FLUX. CHAPTER XI. USEFUL AND TOTAL MAGNETIC FLUX. 55. Magnetic Field. Lines of Magnetic Force. Magnetic Flux. Field-Density. The surrounding of a magnetic body, as far as the magnetic effects of the latter extend, is called its Magnetic Field. According to the modern theory of magnetism, magnetic attractions and repulsions are assumed to take place along certain lines, called Lines of Magnetic Force; the magnetic field of a magnet, therefore, is the region traversed by the magnetic lines of force emanating from its poles. The lines of magnetic force are assumed to pass out from the north pole and back again into the magnet at its south pole; t\\z\r direction, therefore, indicates the polarity of the mag- netic field. The total number of lines of magnetic force in any magnetic field is termed its Magnetic Flow, or Magnetic Flux, and is a measure of the amount, or quantity of its magnetism. The density of the magnetism at any point within the region of magnetic influence of a magnet, or the Field Density of a magnet, is expressed by the number of these magnetic lines of force per unit of field area at that point, measured perpendicu- larly to their direction. The Unit of Field Density that is, the field density of a unit pole is i line of magnetic force per square centimetre of field area, and is called i gauss. A Single Line of Force, or the Unit of Magnetic Flux, is that amount of magnetism that passes through every square centi- metre of cross-section of a magnetic field whose density is unity. To this unit, which was formerly called i weber, the name of i maxwell was given at the Paris Electrical Congress, in 1900. A Magnet Pole of Unit Strength is that which exerts unit force upon a second unit pole, placed at unit distance from the former. The lines of force of a single pole, concentrated in one point, are straight lines emanating from this point to all 199 200 DYNAMO-ELECTRIC MACHINES. [56 directions; /. total number of useful lines, or useful flux, in maxwells; JV == number of conductors all around pole-facing circumference of armature; W c = n o X n & , for ring armatures ; A^c = 2 X n c x a > for drum armatures and for drum- wound ring armatures ; 56] USEFUL AND TOTAL MAGNETIC FLUX. 2OI (where c = number of commutator-divisions, a = number of turns per commutator- division, n c X n & =. total number of convolutions of armature, see 25); N = speed, in revolutions per minute; and n' p = number of bifurcations of current in armature, /'. lines of force, for, the $ lines emanating from all the north poles, after pass- ing the armature core, return to the south poles, hence pass twice across the air-gaps, and, in consequence, are cut twice in each revolution by every armature conductor. The armature makes N_ 60 revolutions in i second, hence, AT i conductor in i second cuts 2 X -r- lines. 60 Each one of the 2 ' p parallel armature portions contains conductors connected in series; in each of these 2 n' p arma- ture circuits, therefore, N N conductors in i second cut 2 $ X ^~ X r~ lines. But, according to the law of the divided circuit, the E. M. F. generated in one of the parallel branches is the output voltage of the machine; the E. M. F. generated by any armature, con- sequently, by virtue of (135), is E 1 = f X f x N t volts, (136) ' p X 60 X io" and from this we obtain the number of useful lines required to produce the E. M. F. of E' volts, thus: f = 6_X ,,' X JT X .0". A" c x N 202 DYNAMO-ELECTRIC MACHINES. [ 57 For dynamos with but one pair of parallel circuits in the armature, /. e (144) In this, Z e depends upon the polar embrace, which, in turn, is determined by the ratio of the distance between pole-cor- 206 DYNAMO-ELECTRIC MACHINES. [57 ners to the length of the air spaces, and can be expressed in terms of the total active length of wire, by Z e = Z a x A ............. (145) Inserting (145) into (144), we obtain the actual field density: ' p X E X io 9 72 x A x A x c where 3C" = actual field density of dynamo, in lines of force per square inch; n' p = number of bifurcations of current in armature; E total E. M. F. to be generated in armature, in volts; fi i = percentage of polar arc, see 58; Z a = length of active armature conductor, in feet, for- mula (26) or (148); v c = conductor speed, in feet per second. The field density in metric units is obtained from 5C = .0,000 X p *S, m , ....... (147) if Z a is expressed in metres and v in metres per second. Since, in a newly designed armature, on account of rounding off the number of conductors to a readily divisible number and the length of the armature to a round dimension, the actual length, Z a , of the armature conductor, in general, is somewhat different from that found by formula (26), (as a rule, a little greater a value is taken), it is preferable to deduce the accurate value of Z from the data of the finished armature: L & = N C X = X -, ...... (148) 12 fit 12 where N c = total number of conductors on armature; 4 = length of armature core, in inches; ;/ w =1 number of wires per layer; ) ! = number of layers of armature wire; > see 23. n$ = number of wires stranded in parallel. ) Formula (146) for the actual field density of toothed and perforated armatures, can also be used for smooth cores, and may be applied to check the result obtained from (142). 58] USEFUL AND TOTAL MAGNETIC FLUX. 207 For th - application to smooth armatures, however, the polar embrace, //, , in formula (146) and (147), is to be replaced by the corresponding value of the effective field circumference, ft l , obtained from the former by means of Table XXXVIII., 38. If it is desired to know the real field area in toothed and perforated armatures, an expression for S t can be obtained by combining formulae (139) and (146), thus: 72 x /?, X A x P, X $ .. . a , : ~W ' p x ' xi* This formula, which gives the mean effective area actually traversed by the useful lines cutting the armature conductors, is very useful for the investigation of the magnetic field of toothed and perforated armatures. 58. Percentage of Polar Arc. The ratio of polar embrace, to which frequent reference has been had in 57, is determined by the distance between the pole-corners and by the bore of the polepieces. a. Distance Between Pole-corners. The mean distance between the pole-corners, / p , Fig. 130, depends upon the length of the gap-space between the arma- Fig. 130. Distance Between Pole-corners, and Pole Space Angle. ture core and the pole face, and is determined by the rule of making that distance from i. 25 to 8 times the length of the two gap-spaces, according to the kind and size of the armature and to the number of poles, see Table LX. Denoting this ratio of the distance between the pole-corners 208 DYNAMO-ELECTRIC MACHINES. [58 to the length of the gaps by n , this rule can be expressed by the formula: 'p = *,,xte-' P varies between 4,000 and 40,000 lines of force per watt at i foot per second, according to the size of the machine, the lower figure corre- sponding to the highest field efficiency; and for outputs from 1/4 KW to 2,000 KW, for bipolar and for multipolar fields, respectively, ranges as per the following Table LXII., which is averaged from a great number of modern dynamos of all types of field-magnets: 212 D YNAMO-ELECTRIC MA CHINES. [59 TABLE LXII. FIELD EFFICIENCY FOR VARIOUS SIZES OF DYNAMOS. CAPACITY, ra KILOWATTS. VALUE OP <2*' P IN MAXWELLS PBB WATT, AT UNIT CONDUCTOR VELOCITY. Bipolar Fields. Multipolar Fields. Up to .25 .25 to 1 1 to 10 10 to 50 50 to 100 100 to 500 500 to 1,000 1,000 to 2,000 15,000 to 40,000 10,000 to 20,000 8,000 to 15,000 7.000 to 12,000 6,000 to 10,000 5,000 to 7,500 10,000 to 20,000 8,000 to 15,000 7,000 to 12,000 6,000 to 10,000 5,000 to 7,500 4,000 to 6,000 For a newly designed machine, the value 3>' p , obtained by means of formula (155), will be within the limits given in this 220x10^ 200 400 600 800 1000 1200 1400 1600 1800 2000 Fig. 131. Average Useful Magnetic Flux at Different Conductor Velocities for Various Outputs. table, provided the armature has been calculated in accordance with the rules and tables furnished in the respective Chapters of Part II. 59] USEFUL AND TOTAL MAGNETIC FLUX. 213 As from Table LXII. follows the self-evident fact that the magnetic fields of large dynamos are more efficient than those of small ones, a curve was plotted in order to examine the rate of this increase. For this purpose the useful fluxes of all the dynamos considered were reduced to the basis of a conductor velocity of 50 feet per second, when the heavy curve, Fig. 131, was obtained by averaging the values of the flux thus found. From this curve a law can be deduced for the increase of the field efficiency with increasing size. In the following Table LXIIL, from the average useful flux for 50 feet con- ductor velocity, as plotted in Fig. 131, the specific flux per kilowatt has been calculated, showing the rate of increase of the field efficiency: TABLE LXIII. VARIATION OF FIELD EFFICIENCY WITH OUTPUT OF DYNAMO. TOTAL SPECIFIC FLUX, CAPACITY AVERAGE USEFUL FLUX IN IN AT VELOCITY MAXWELLS PER KILOWATT, KILOWATTS. OF AT 50 FEET PER SECOND. 50 FEET PER SECOND. .1 100,000 1,000,000 .25 200,000 800,000 .5 350,000 700,000 1 600,000 600,000 2.5 1,300,000 520,000 5 2,300,000 460,000 10 4,800.000 400,000 25 8,500,000 340,000 50 15,500,000 310,000 75 22,000,000 294,000 100 28,000,000 280.000 200 50,000,000 250,000 300 70,000,000 233.000 400 88 000,000 220,000 500 104.000,000 208.000 600 118,000,000 197,000 700 130,000.000 186,000 800 141.000.000 176.000 900 151,000,000 168,000 1,000 160,000.000 160,000 1,200 175,000,000 146.000 1,500 195,000,000 130,000 2,000 220,000,000 110.000 By the law of inverse proportionality between useful flux and conductor velocity, the remaining cprves for 25, 30, 40, 60, 214 D YNA MO-ELECTRIC MA CHINES. [60 75, and 100 feet per second, respectively, were then drawn in Fig. 131. Tabulating all the values thus received, we obtain the fol- lowing Table LXIV., giving average values of the useful flux for various conductor velocities: TABLE LXIV. USEFUL FLUX FOR VARIOUS SIZES OF DYNAMOS AT DIFFERENT CONDUCTOR VELOCITIES. AVERAGE USBFUL FLUX, IN MAXWELLS, AT CONDUCTOR VELOCITY, PEE SECOND, OP: IN KILOWATTS. 25 feet 30 feet 40 feet 50 feet 60 feet 75 feet 100 feet (= 7.5 m.) (= 9 m.) (= 12 m.) (= 15m.) (= 18m.) (= 22.5m.) (r=30m.) .1 200,000 167,000 125,000 100,000 &3,000 .25 400,000 333,000 250,000 200.000 167,000 .5 700,000 r>s:j.iKK) 438,000 a5o,ooo 292,000 1 1,200,000 1,000,000 750,000 600,000 500,000 466,000 2.5 2.600.000 2.200.000 1,600.000 1,300,000 1,100,000 870,000 5 4,600,000 s,Hoo. = useful flux necessary to produce the required E. M. F. under the given conditions, from formula (137); \ = factor of magnetic leakage (see Chapters XII. and XIII). 60] USEFUL AND TOTAL MAGNETIC FLUX. 215 The value of the total magnetic flux in a dynamo directly determines the sectional areas of the various portions of the magnetic circuit in the frame (see Chapter XVI.), and since the magnetomotive force required depends upon the total magnetic flux to be effected \ has a direct influence also upon the magnet winding. In calculating a dynamo-electric machine, therefore, it is of great importance to compute the actual value of the total flux, and, consequently, to predeter- mine with sufficient accuracy the amount of the magnetic leakage. But, since the dimensions of the magnetic circuit depend upon the total flux to be generated, and since the accurate value of the latter is given by the coefficient of magnetic leak- age which in turn for a newly designed machine must be calcu- lated from the dimensions of the magnet frame, it is necessary to proceed as follows: An approximate value of A for the type and size of dynamo in question is taken from Table LXVIII., 70, and the corre- sponding approximate total flux calculated from formula (156). With the value of $' thus obtained the principal dimensions of the magnet frame are determined according to the rules given in Chapter XVI. The dimensions now being known, the probable leakage factor, /\, can be figured from formula (157) or (158), respectively, 61, the single terms of which are found from the respective formulae given in Chapter XII. From formula (156), finally, the accurate value of the total flux is obtained. Should the latter prove so much different from the assumed approximate value of $', as to necessitate a change in the dimensions of the frame, then the calculation of A will have to be partly or wholly repeated. That such a calculation of the probable leakage factor is necessary in every single case, is evident from the fact that not only the leakage in two machines of same general design, and even of approximately the same size, which are merely differently proportioned in their essential parts, may widely differ from each other, but that in one and the same dynamo the amount of the leakage can be considerably varied by using armatures of different core-diameters in its magnetic field. From the same reason it can also be % concluded that the method of assuming a value of A from previous experience 21(5 DYNAMO-ELECTRIC MACHINES. [60 with a certain type, or even with an individual machine, is an entirely unreliable one, and that the calculation of the mag- netomotive force based upon such an assumption cannot be depended upon. The author's method of predetermining, from the dimen- sions of a machine, the probable factor of its magnetic leakage is given in the following Chapter XII., while a practical method used by the author for computing the real leakage coefficient, from the test of an actual machine, is treated in Chapter XIII. Professor Forbes' logarithmic formulae, 1 which are usually given in text-books 4 for the predetermination of magnetic leakage, in the first place are too cumbersome for the practical electrical engineer, and besides leave room for doubt as to their application in special cases; Professor Thompson's for- mula 3 for the case of leakage between parallel cylinders has been shown 4 to be incorrect; and the empirical formulae given by Kapp 5 for the leakage resistance of upright and inverted horseshoe types, although being extremely simple, have not much practical value, as they merely have reference to the size of the machine and are independent of the dimensions and the design of the field frame, and will therefore give correct results only in case of dynamos having exactly the same rela- tive proportions as those experimented upon by Kapp. It is therefore believed that the establishment of the geomet- rical formulae presented in Chapter XII., which are simple in form, concise in application, and accurate in result, has re- moved the principal difficulties heretofore experienced with leakage calculations. 1 George Forbes, Journal Society Telegraph Engineers, vol. xv. p. 531, 1886. 9 S. P. Thompson, "Dynamo-Electric Machinery," fifth edition, p. 156. a S. P. Thompson, " Lectures on the Electro-Magnet," authorized American edition, p. 147. 4 A. E. Wiener, "Magnetic Leakage in Dynamo-Electric Machinery," Electrical Engineer, vol. xviii. p. 164 (August 29, 1894). 6 Gisbert Kapp, " Electric Transmission of Energy," third edition, p. 122. CHAPTER XII. CALCULATION OF LEAKAGE FACTOR FROM DIMENSIONS OF MACHINE. A f FORMULA FOR PROBABLE LEAKAGE FACTOR. 61. Coefficient of Magnetic Leakage for Dynamos with Smooth and with Toothed or Perforated Arma- tures. Since air is a conductor of magnetism, the conditions of the magnetic circuit of a dynamo-electric machine resemble those of a closed metallic electric circuit immersed in a con- ducting fluid. In the latter case, the main current will flow through the metallic conductors, but a portion will pass through the fluid. Similarly, in the dynamo, the main path for the lines of force being the magnetic circuit consisting of the iron field frame, the air gaps, and the armature core, a por- tion of the magnetic flux will take its way through the sur- rounding air. The amount of electric current passing through the surrounding medium, the fluid, depends upon the ratio be- tween the conductances of the main to the shunt paths. In order to calculate the amount of magnetic leakage in a dynamo, therefore, it is, analogically, only necessary to determine the ratio between the permeances of the useful and the stray paths. a. Smooth Armature. The leakage factor in any dynamo having a smooth arma- ture can accordingly be expressed as the quotient of the total joint permeance of the system by the permeance of the useful path. But since the reluctance of the iron portion of the main path is very small compared with that of the air gaps, the sum of their reciprocals, that is, the total permeance of the useful path, is practically equal to the permeance of the gaps; hence the permeance of the gaps can be taken as a sub- stitute of the permeance of the whole magnetic circuit within 217 2l8 DYNAMO-ELECTRIC MACHINES. [ 61 the machine, and we obtain the following formula for the probable leakage factor of any dynamo having a smooth arma- ture : Joint permeance of useful and stray paths Permance of useful path or, ._ 2, + 3. + ^ + .(157) where 5, = relative permeance of the air gaps (useful path) ; 2 = relative average permeance across magnet cores (stray 'path); 2 = relative permeance across polepieces (stray path); 5 4 = relative permeance between polepieces and yoke (stray path). The relative permeances by which are understood the absolute permeances divided by the magnetic potential, and which, therefore, include a constant factor, on account of the units chosen are taken for convenience, for, in each individ- ual case the maximum magnetic potential is the same for all permeances, and a constant numerical factor, if absolute per- meances were used, would be common to all terms in (157), and consequently would cancel. b. Toothed and Perforated Armature. In toothed and perforated armatures a portion of the magnetic lines of the main path enters the iron projections of the core and passes through the armature without cutting the conduc- tors. This portion, therefore, cannot be considered as useful, and has to be taken into account in computing the total leak- age coefficient of the machine. Introducing this leakage into the calculation in the form of a factor, the factor of arma- ture leakage, we obtain the probable leakage factor of any dynamo having a toothed o* perforated armature: v = \ x \ = \ x -?i_A+ VtA . (158) *i The factor, A.,, of this core-leakage, that is, the ratio of the total flux of the useful path passing the air gaps to the actual useful flux cutting the armature conductors, or to the total flux 62] PREDE TERM IN A TION OF MA GNE TIC LEAK A GE. 219 through the gaps minus that portion leaking through the teeth, depends upon the relative sizes of the slots to the teeth, and for armatures otherwise properly dimensioned, has been found to average within the following limits: TABLE LXV. CORE LEAKAGE IN TOOTHED AND PERFORATED ARMATURES. RATIO OF WIDTH OF SLOTS To THEIR PITCH ON OUTER CIRCUMFERENCE b s :- n. FACTOR OP ARMATURE LEAKAGE, \, TOOTHED ARMATURES PERFORATED ARMATURES STRAIGHT TEETH PROJECTING TEETH W*3j> RECTANGULAR HOLES ROUND HOLES I&WWZ 0.35 1.06 to 1.04 .4 1.05 " 1.03 1.10 to 1.04 .45 1.04 " 1.02 1.07 1.03 .5 1.03 1.01 1.05 1.02 1.07 to 1 04 1.10 to 1.06 .55 1.02 1.005 1.03 1.01 1.06 1.03 1.08 "1.05 .6 1.01 ' 1.0025 1.02 1.005 1.05 1.02 1.06 " 1.04 .65 1.04 u 1.01 1.05 1.03 .7 1.03 " 1.01 1.04 " 1.02 B. GENERAL FORMULAE FOR RELATIVE PERMEANCES. 62. Fundamental Permeance Formula and Practical Derivations. In order to obtain the values of the permeances of the vari- ous paths, we start from the general law of conductance: Conductance - i Conductivity ) Area of medium V^UliUUV^Ldll^C i f j f /\ -.-^ . > ( of medium ) Distance in medium Area or, in our case of magnetic conductance: Permeance Permeability x i Since the permeability of air = i, the relative leakage per- meance between two surfaces can be expressed by the general formula: _ _ Mean area of surfaces exposed Mean length of path between them * From this, formulae for the various cases occurring in prac* tice can be derived. 22O D YNA MO-ELECTRIC MA CHINES. [62 a. Two plane surfaces, inclined to each other. In order to express, algebraically, the relative permeance of the air space between two inclined plane surfaces, Fig. 132, the mean path is assumed to consist of two circular arcs joined by a straight line tangent to both circles, said arcs to be de- scribed from the edges of the planes nearest to each other, as Fig. 132. Two Plane Surfaces Inclined to Each Other. centres, with radii equal to the distances of the respective cen- tres of gravity from those edges. Hence: , + xx ~~ 2 ,.(160) o / 18 o' where ,5, , S 3 = areas of magnetic surfaces; c = least distance between them; a l , a t = widths of surfaces S t and ,S 8 , respectively; a = angle between surfaces S l and S t . b. Two parallel plane surfaces facing each other. If the two surfaces S t and S 3 are parallel to one another, - J 33> the angle inclosed is a o, and the formula for Fig. 133. Two Parallel Plane Surfaces Facing Each Other, the relative permeance, as a special case of (160), becomes: 9. - i (5 + -S*,) .(161) 62] PREDETERMINA TION OF MAGNETIC LEAKAGE. 221 c. Two equal rectangular surfaces lying in one plane. In case the two surfaces lie in the same plane, Fig. 134, they inclose an angle of a 180, and the permeance of Fig. 134. Two Equal Rectangular Surfaces Lying in One Plane, the air between them, by formula (160), is: a X 6 ..(162) 7T c + a X a = width of rectangular surface; b = length of rectangular surface; c = least distance between surfaces. d. Two equal rectangles at right angles to each other. If the two surfaces are rectangular to each other, Fig. 135, Fig- !35- Two Equal Rectangles at Right Angles to Each Other, the angle a 90, formula (160), consequently, reduces to a = axl> .-(163) 71 e. Two parallel cylinders. In case the two surfaces are cylinders of diameter, d, and length, /, Fig. 136, the areas of their surfaces are d x n X I; and if they are placed parallel to each other, at a distance, r, apart, the mean length of the magnetic path is c -f- \d; hence the permeance of the air between them: d X TT x / (164) 222 D YNAMO-ELECTRIC MA CHINES. [62 In this formula the expression for the mean length of the path is deduced from Fig. 137, in which it is assumed that the Fig. 136. Two Parallel Cylinders. mean path consists of two quadrants joined by a straight line of length c, and extends between two points of the -cylinder- peripheries situated at angles of 60 from the centre line. Since in an equilateral triangle the perpendicular, dropped from any one corner upon the opposite side, bisects that side, Fig. 137. Leakage Path Between Parallel Cylinders. the perpendicular, from either of the endpoints of the mean path upon the centre line, bisects the radius of the corre- sponding cylinder-circle, and the radius of the leakage-path quadrant is d hence the length of the mean path: 71 x c +y X it = c -f d X 7-1 4 or, approximately: x = c -|- f d . This approximation even better meets the practical truth, as most of the leakage takes place directly across the cylinders. I 6 2] PREDE TERMINA TION OF MA GNE TIC LEA KAGE. 223 and the mean path, therefore, in reality is situated at an angle of somewhat less than 60, which was taken for convenience in the geometrical consideration. f. Two parallel cylinder-halves. If two cylinder-halves face each other with their curved surfaces, Fig. 138, the mean length of the magnetic path is c + -3 ^> where c is the least distance apart of the curved sur- Fig. 138. Two Parallel Cylinder-Halves. faces, and d the diameter of the cylinders, and we have for the permeance : x/ dx *** ( 165 ) -|- -3 " 2 c -\- .6 a The mean length of the path is geometrically found from Fig. 139, as follows: Fig. 139. Leakage Path Between Parallel Cylinder-Halves. 2 z ( d \ d J = \ - ) : z = - A/ \2/ 2 K 2 x = c + 2 y c + .3 d. 224 DYNAMO-ELECTRIC MACHINES. [64 For, in this case, the extent of the leakage field is much smaller than in that of full cylinders, and the mean path can be assumed a straight line meeting the two semicircles at an angle of 45 from the centre line. C. RELATIVE PERMEANCES IN DYNAMO-ELECTRIC MACHINES. 63. Principle of Magnetic Potential. In taking the magnetic potential between two polepieces of opposite polarity as unity for calculating the relative per- meances in dynamo-electric machines, the potentials between various points of the magnetic circuit depend upon the num- ber of magnet-cores magnetically in series between two con- secutive poles of opposite polarity. If, as is the case in- the majority of types, there are two magnets between any north- pole and the next south-pole of the machine, then the magnetic potential between two points of the magnetic circuit separated by but one magnet, is = ; and two points not separated by a magnet core, have no difference of magnetic potential, their potential o. If the circuit consists of but one magnet, or of several magnets magnetically in parallel, then the mag- netic potential between any two leakage surfaces of opposite polarity is = i, /. / I oj>" I <>j>'" ' I 6 1 j>// I (180) e. Multipolar Types. In case of multipolar dynamos of n v pairs of poles, the total permeance across the magnet cores is 2 p times that between each pair of cores. In calculating the latter, it has to be con- sidered that, while the permeance across two opposite side surfaces of the cores does not change by increasing their number, the leakage across two end surfaces is reduced, half of the lines leaking to the neighboring core at one side, and half to that on the other side. For rectangular cores, therefore, we have, with reference to Fig 150: Fig. 150 Multipolar Frame with Rectangular Cores. X / 1 c + b - b X I (181) 234 DYNAMO-ELECTRIC MACHINES. [66 for round cores, according to formula (165): g - - s .- X d X / ^/nrx/ ' ~ ' p X 2(2 <: + .6 ^ ~ //p X 2 r + .6 . l ~ + rr- + 6 i + i X (. = 2 X (4-6 + 1.6 -f i.i) = 14.6. Fig. 182. Vertical Double Horseshoe Type. By (201): , _ (16 x 6f - 14 X 5|) + 14 X 3f , 16 X i _ A. 4 1 = 5 + 10.2 = 15.2. -6 + I 5- 2 262. = 1.37. 192 192 7. Horizontal Double Horseshoe Type, Fig. 183. L Fig. 183. Horizontal Double Horseshoe Type. By (179): 8| X 16 6 X 7f X 16 ' = 45 ' 54 DYNAMO-ELECTRIC MACHINES. By (195): ( 4j X i7j . | X 16 i X 16 2 3 = 2 X ] 61+ 6| X- ~~^ 64 + 4- X n ~ ' 2 4 = 2 X (4-6 + 1.6 + .6) = 13.6. By (201): _ (16 X 6f 80.8) -j- 25 X 16 [68 16 + 11 X 18 = 14-2 +.4-45 +6.15 = 24.8. 192 + 45 + 13-6 + 24.8 _ 275.4 ~ 8. Horizontal Double Magnet Type, Fig. 184. Fig 184. Horizontal Double Magnet Type. , = 192- By (187): X i7j 16 X 25! ~~ + 8 X ~ ~ 16 X 7 X 6* + 7 X - 2 = 8 -5 + 5-i + 5-i + 12.3= 31- i6x 14 5i 192 192 68] PREDE TERM IN A TION OF MA GNE TIC LEA KA GE. 255 9. bipolar Iron-clad Type, Fig. 185. Fig. 185. Bipolar Iron-clad Type. 2, = 192. By (184): + 5iX ? 6f 16 X I 9 2 + 30 _ 222 _ A = = - 1.15. 192 192 10. Fourpolar Iron-dad Type, Fig. 186. By (167): By (185): Fig. 186. Fourpolar Iron-clad Type. i-95 339 1-95 = 174. 256 DYNAMO-ELECTRIC MACHINES. [68 16 X , X (nj-f = 88.8 + 19 = 107.8. A= '74+ IQ7.8 = g,.8_ 174 i74 Taking now the leakage proper, that is, leakage factor minus i, of the bipolar iron-clad type, which is the smallest found, as unity, we can express the amounts of the stray fields of the remaining types as multiples of this unity, thus obtain- ing the following comparative leakages of the types consid- ered: Upright horseshoe type 0.32 Inverted horseshoe type o. 255 Horizontal horseshoe type 0.55 Single magnet type o. 32 Vertical double magnet type 0.47 Horizontal double horseshoe type.. 0.37 Vertical double horseshoe type 0.43 Horizontal double magnet type .... o. 16 Bipolar iron-clad type 0.15 Fourpolar iron-clad type 0.62 0.15 = 2.14 0.15 = 1.70 0.15 = 3- 6 7 0.15 = 2.13 0.15 = 3-i3 0.15 = 2.46 0.15 = 2.87 0.15 = 1.07 0.15 = i 0.15 = 4.14 If, in the latter machine, the stray field of which is some- what excessive, an armature of larger diameter and smaller axial length would be chosen and the dimensions of the frame altered accordingly, the leakage would be found within the usual limits of the fourpolar iron-clad type. CHAPTER XIII. CALCULATION OF LEAKAGE FROM MACHINE TEST. 69. Calculation of Total Flux. The machine having been built, its actual leakage can be determined from the ordinary machine test. It is only neces- sary, for this purpose, to run the machine at its normal speed, and to regulate the field current by changing the series-regu- lating resistance in a shunt dynamo, or by altering the num- ber of turns in a series machine, or by regulating both in a compound-wound dynamo until the required output is ob- tained. Noting then the exciting ampere-turns, we can calcu- late the total magnetic flux, <', through the magnet frame, by a comparatively simple method which is given below; and $' divided by the useful flux, 3>, gives the factor A of the actual leakage. The observed magnetizing force of AT ampere-turns per magnetic circuit made up of T sh shunt turns, through which a current of /gh = amperes r m (E potential at terminals, r m = total resistance of shunt circuit) is flowing, in a shunt machine; or of T^. series turns traversed by a current of 1^ = /amperes (/ = current output of dynamo), in a series machine; or partly of the one and partly of the other, in a compound dynamo is supplying the requisite magnetizing forces used in the different portions of that circuit, viz., the ampere turns needed to overcome the magnetic resistance of the air gaps, of the armature core, and of the field frame, and the magnetizing force required to compensate the reaction of the armature winding upon the magnetic field; hence we have: AT = at e + a/ a + at m + at t , (206) 258 DYNAMO-ELECTRIC MACHINES. [69 where AT total magnetomotive force required per mag- netic circuit for normal output, in ampere- turns, observed; at g = magnetomotive force used per circuit to over- come the magnetic resistance of the air gaps in ampere-turns, see 90; a/ fc = magnetomotive force used per circuit to over- come magnetic resistance of armature core in ampere-turns, see 91; at m = magnetomotive force used per circuit to over- come magnetic resistance of magnet frame, in ampere-turns, see 92; at t magnetomotive force required per circuit for compensating armature reactions, in ampere- turns, see 93. Since the magnet frame alone carries the total flux gen- erated in the machine, while the air gaps and the armature core are traversed by the useful lines, only the ampere-turns used in overcoming the resistance of the magnet frame depend upon the total magnetic flux, and all others of these partial magnetomotive forces can be determined from the useful flux. The latter, however, is known from the armature data of the machine by virtue of equations (137) and (138), respectively; consequently, from (206) we can determine at m , and this, in turn, will furnish the value of the total flux, ", divided by the mean sectional area, S m , of one mag- netic circuit in the field frame, or *Jm we obtain the total magnetic flux per magnetic circuit of the machine from the simple formula & = S m x ", in an indirect manner, as follows: The useful flux, <2>, being known by virtue of formula (137) or (138), respectively, an assumption can be made of the total flux per circuit, $", by adding to the useful flux per circuit, (n z being the number of the magnetic circuits in the machine), from 10 to 100 per cent., according to the size and the type of the dynamo (see Table LXVIIL, p. 263, and Table LXVIILz, p. 265). In dividing this approximate value of Stf3O Ci- ^ fee e a 3 B \ OJ c t/! i s s rt 6 c "o V in a u net frame w to obtain to "3 i u u v2 I) "S 5 -!2 , u it H opposite ms O 1 M rt u rS rt "o "rt O smooth-ring _c u 4 . o o **H u * S o c a M 1 * CJJ _G ^ i M "3 j rt a S ^ " 8 u (/> o 'Q V a u '.n E s 3 t/1 (9 S ^ 3 B . rt o ,g rt J a 1 r a smooth-core armati reference to drum art c 3 g, o 5 ,M ,2 or perforated armatur< er percentage referrin materially reducing t ro to 20 per cent, may OJ w a ^ rt D (/] *T | rt J>> "v e TJ 5 'Ec S C e ta p rt X "5 c, "S rS 2 S w - as j^ -c 2 i 3 " b "rt o o CJ 6 rt _O 5 ^ u 5 rt M D rt 0- o hi _o 1 r3 0) .S fa OJ *o C a o ^< D *c ' . . t ~| v 5.J . 31 264 DYNAMO-ELECTRIC MACHINES. [70 distances of the leakage surfaces much smaller than in large dynamos; the permeance of the air gaps, therefore, is relatively much smaller, while the permeances of the leakage paths are considerably larger, comparatively, than in large machines, and formula (157), in consequence, will produce a high value of the leakage coefficient for a small dynamo. It further follows from Table LXVIII. that the leakage factor for various types and sizes of dynamos varies within the wide range of from i.io to 2.00, which result agrees with observa- tions of Mavor, 1 who, however, seems not to have considered capacities over 100 KW. By comparing the values of A. for any one capacity, the rela- tive merits of the various types considered may be deduced. Thus it is learned that, as far as magnetic leakage is con- cerned, the Horizontal Double Magnet Type (column 6) and the Bipolar ilron-clad Type (column 7) are superior to any of the other types, which undoubtedly is due to the common feature of these types of having the cores of opposite magnetic potential in .'ine with each other on opposite sides of the arma- ture, thus reducing the magnetic leakage between them to a minimum. Next in line, considering bipolar dynamos, are the Inverted Horseshoe Type (column 2), the Single Magnet Type (column 4), the Upright Horseshoe Type (column i), and the Vertical Double Horseshoe Type (column 8). Of multipolar machines the two best forms, magnetically, are, respectively, the Innerpole Type (column 13), and the Radial Multipolar Type (column 12). In the first named of these types the magnet cores form a star, having a common yoke in the centre and the polepieces at the periphery; thus the dis- tances of the leakage paths increase the direct proportion to the difference of magnetic potential, a feature which is most desirable, and which accounts for the low values of \ for the type in question. The most leaky of all types seem to be the Horizontal Single Horseshoe Type (column 3), and the Axial Multipolar Type (column 15). 1 Mavor, Electrical Engineer (London), April 13, 1894 ; Electrical World, vql. xxiii. p. 615, May 5, 1894. 70] CALCULA TION OF ACTUAL MA GNE TIC LEAK A GE. 265 In the former type the excessive leakage is due to the mag- netic circuit being suspended over an iron surface extending over its entire length, while in the latter type it is due to the comparatively close relative proximity of a great number of magnet cores (two for each pole) parallel to each other. When making the allowances for improvements referred to in the note to Table LXVIII., the following Table LXVIIIa is obtained, which gives the usual limits of the leakage factor for various sizes of the most common types of continuous current dynamos: TABLE LX Villa. USUAL LIMITS OP LEAKAGE FACTOR FOB MOST COM- MON TYPES OP DYNAMOS. Capacity of Dynamo in Kilo- watts. Ordinary Horseshoe Type. n Inverted Horseshoe Type. Double Magnet Type. Bipolar Iron Clad Type. Fonrpolar Iron Clad Type. Mnltipolar Ring Type. .1 .25 .5 1 2.5 5 10 25 50 100 200 300 500 1,000 2,000 1.50 1.45 1.40 1.35 1.30 1.25 1.22 1.20 1.18 1.16 1.14 1.12 to 2.00 1.40 to 1.75 1. .801 .701 !eb i .55 1 .501 .45 1 .401 .851 .35 .30 1.25 .20 .18 .16 .14 .12 .10 1.601.45 to 2.00 1.501.40 1.45 1.35 1.401 30 1.351.25 1.301.20 1.25 1.221.16 1.201.15 1.25 1.18 1.90 1.80 1 7t 1.60 1.55 1.5< 1.4* 1. 4d 1 .25 to .22 .90 .18 '.14 ,ia .10 .00 .08 1.35 to 1.75 .28 .251.32 .22 1.30 .20,1.28 .181.26 .151.24 1.22 1.20 1.20 to 1.50 1.65 1.60 1.55 1.18 1.16 1.15 1.501.14 1.15 1.13 1.401.12 1.35 1.11 1.10 1.09 .. 1.08 1.40 1.35 1.32 1.30 1.28 1.25 1.22 1.20 1.18 1.15 PART IV. DIMENSIONING OF FIELD MAGNET FRAME. CHAPTER XIV. FORMS OF FIELD MAGNETS. 71. Classification of Field Magnet Frames. With reference to the type of the field magnet frame mod- ern dynamos may be classified as follows: /. Bipolar Machines. 1. Single Horseshoe Type. a. Upright single horseshoe type (Fig. 187). b. Inverted single horseshoe type (Fig. 188). c. Horizontal single horseshoe type (Fig. 189). d. Vertical single horseshoe type (Fig. 190). 2. Single Magnet Type. a. Horizontal single magnet type (Figs. 191 and 192). b. Vertical single magnet type (Fig. 193). c. Single magnet ring type (Fig. 194). 3. Double Magnet Type. a. Horizontal double magnet type (Figs. 195 and 197). b. Vertical double magnet type (Figs. 196 and 199). c. Inclined double magnet type (Fig. 198). d. Double magnet ring type (Fig. 200). 4. Double Horseshoe Type. a. Horizontal double horseshoe type (Fig. 201). b. Vertical double horseshoe type (Fig. 202). 5. Iron-clad Type. a. Horizontal iron-clad type (Figs. 203 and 204). b. Vertical iron-clad type. a. Single magnet vertical iron-clad type (Figs. 205 and 206). ft. Double magnet vertical iron-clad type (Fig. 207). //. Multipolar Machines. i. Radial Multipolar Type. a. Radial outerpole type (Fig. 208). b. Radial innerpole type (Fig.. 209). 269 270 DYNAMO-ELECTRIC MACHINES. [72 2. Tangential Multipolar Type. a. Tangential outerpole type (Fig. 210). b. Tangential innerpole type (Fig. 211). 3. Axial Multipolar Type (Fig. 212). 4. Radi-tangent Multipolar Type (Fig. 213). 5. Single Magnet Multipolar Type. a. Axial pole single magnet multipolar type (Fig. 214). b. Outer-innerpole single magnet multipolar type (Fig. 5). 6. Double Magnet Multipolar Type (Fig. 216). 7. Multipolar Iron-clad Type (Fig. 217). Horizontal fourpolar iron-clad type (Figs. 218 and 220). Vertical fourpolar iron-clad type (Fig. 219). 8. Multiple Horseshoe Type (Figs. 221 and 222). 9. Fourpolar Double Magnet Type (Fig. 223). 10. Quadruple Magnet Type (Fig. 224). 72. Bipolar Types. The simplest form of field magnet frame is that resembling the shape of a horseshoe. Such a horseshoe-shaped frame may be composed of two magnet cores joined by a yoke, or may be formed of but one electromagnet provided with suit- ably shaped polepieces. The former is called the single horse- shoe type, the latter the single magnet type. A single horseshoe frame may be placed in four different posi- tions with reference to the armature, the two cores either being above or below the armature, or situated symmetrically. one on each side, in a horizontal or in a vertical position. The upright single horseshoe type, Fig. 187, is the realization of the first named arrangement, having the armature below the cores, and is therefore often called the " under type." This form is now used in the Edison dynamo, 1 built by the General Electric Co., Schenectady, N. Y., in the motors of the "C & C" (Curtis & Crocker) Electric Co., 2 New York, and is fur- ther employed by the Adams Electric Co., Worcester, Mass.; 1 Electrical Engineer, vol. xiii. p. 391 (1891); Electrical World, vol. xix. p. 220 (1892). 2 Martin and Wetzler, " The Electric Motor," third edition, p 230, 72] FORMS OF FIELD MAGNETS. 271 by the E. G. Bernard Company, Troy, N. Y. ; by the Detroit Electrical Works, 1 Detroit, Mich. ("King" dynamo); the Com- FlQ. 205 FlQ. 206 FlQ. 207 Figs. 187 to 207. Types of Bipolar Fields. mercial Electric Co.* (A. D. Adams), Indianapolis, Ind. ; the Novelty Electric Co., 3 Philadelphia, Pa.; the Elektron Manu- 1 Electrical World, vol. xxi. p. 165 (1893). 9 Electrical World, vol. xx. p. 430 (1892). 8 Electrical World, vol. xvi. p. 404 (1890). 2? 2 DYNAMO-ELECTRIC MACHINES. [72 facturing Co. 1 (Ferret), Springfield, Mass.; by Siemens Bros., 2 London, Eng. ; Mather & Platt 3 (Hopkinson), Man- chester, Eng. ; the India-rubber, Guttapercha and Telegraph Works Co., 4 Silvertown, Eng., and by Clarke, Muirhead & Co., London. fc The inverted horseshoe type, Fig. 188, having the armature above the cores, is also called the "overtype." Of this form are the General Electric Co. 's "Thomson-Houston Motors," the standard motors of the Crocker-Wheeler Electric Co., 6 Ampere, N. J.; further, machines of the Keystone Electric Co.,' Erie, Pa.; the Belknap Motor Co., 7 Portland, Me.; the Holtzer-Cabot Electric Co., 6 Boston, Mass.; the Card Electric Motor and Dynamo Co., 8 Cincinnati, O. ; the La Roche Elec- trical Works, 10 Philadelphia, Pa.; the Excelsior Electric Co., 11 New York; the Zucker & Levett Chemical Co., 14 New York (American " Giant" dynamo); the Knapp Electric and Nov- elty Co., 13 New York; the Aurora Electric Co., 14 Philadelphia, Pa.; the Detroit Motor Co., 15 Detroit, Mich.; the National Electric Manufacturing Co., 18 Eau Claire, Wis. ; Patterson & 1 Electrical Engineer, vol. xiii. p. 8 (1892). 2 Silv. P. Thompson, " Dynamo-Electric Machinery," fourth edition, p. 509. 3 Silv. P. Thompson, " Dynamo-Electric Machinery," fourth edition, pp. 519 and 522. 4 Electrical World, vol. xiii. p. 84 (1889). 8 Electrical World, vol. xvii. p. 130 (1891); Electrical Engineer, vol. xiv. p. 199 (1892). Electrical World, vol. xix. p. 220 (1892). 7 Electrical World, vol. xxi. p. 470 (1893); Electrical Engineer, vol. xiv. p. 2io (1892). 8 Electrical Engineer, vol. xvii. p. 291 (1894). 9 Electrical World, vol. xxiii. p. 499 (1894); Electrical Engineer, vol. xi. p. 13(1891). (This company is now the Bullock Electric Manufacturing Company.) 10 Electrical World, vol. xvii. p. 17 (1893); Electrical Engineer, vol. xiv. p. 559 (1892); vol. xv. p. 491 (1893). 11 Electrical Engineer, vol. xiv. p. 240 (1892). 12 Electrical Engineer, vol. xiv. p. 187 (1892); Electrical World, vol. xxii. p. 210 (1893). (Now the Zucker, Levett & Loeb Company.) 18 Electrical World, vol. xxi. pp. 286, 306, 471 (1893). 14 Electrical World, vol. xv. p. n (1890). 15 Electrical World, vol. xvi. p. 437 (1890); Electrical Engineer, vol. x. p. 695 (1890). 18 Electrical World, vol. xvi. pp. 121, 419 (1890); vol. xxiv. p. 22O (1894); Electrical Engineer, vol. xviii. p. 178 (1894). 72] FORMS OF FIELD MAGNETS. 273 Cooper 1 (Esson), London; Johnson & Phillips 2 (Kapp), Lon- don; Siemens & Halske, 3 Berlin, Germany; Ganz & Co.,* Budapest, Austria ; Allgemeine Elektricitats Gesellschaft,' Berlin; Berliner Maschinenbau Actien-gesellschaft, vorm. L. Schwartzkopff," Berlin; and Zuricher Telephon Gesellschaft, 7 Zurich, Switzerland. Machines of the horizontal single horseshoe type, Fig. 189, in which the centre lines of the two magnet cores and the axis of the armature lie in the same horizontal plane, are built by the Jenney Electric Co.*, 8 New Bedford, Mass. ("Star" dynamo), by the Great Western Manufacturing Co.* (Bain), Chicago, 111., and by O. L. Kumtner & Co., 10 Dresden, Germany. The vertical single horseshoe type, Fig. 190, finally, having the axes of magnet cores and armature in one vertical plane, is employed by the Excelsior Electric Co. 11 (Hochhausen), New York, and by the Donaldson-Macrae Electric Co., 12 Baltimore, Md. Single core honseshoe frames may be designed by placing the magnet either in a horizontal or in a vertical position, or by joining two polepieces of suitable shape by a magnet of circu- lar form. The types thus obtained are the horizontal single magnet type, the vertical single magnet type, and the single magnet ring type. In the horizontal single magnet type, Figs. 191 and 192 respect- ively, the armature may either be situated above or below the core. Machines of the former type (Fig. 191) are built by the I S. P. Thompson, " Dynamo-Electric Machinery," plate v. 9 S. P. Thompson, " Dynamo-Electric Machinery," plates i and ii. 3 Elektrotechn. Zeitschr., vol. vii. p. 13 (1886); Kittler, " Handbuch," vol. i. p. 851. 4 Zeitschr. f. Electrotechn., vol. vii, p. 78 (1889); Kittler, " Handbuch," vol. i. p. 930. 5 Grawinkel and Strecker, " Hilfsbuch," fourth edition (1895), p. 287. 'Grawinkel and Strecker, " Hilfsbuch," fourth edition, p. 288. * Grawinkel and Strieker, " Hilfsbuch," fourth edition, p. 328. 8 Electrical World, vol. xix. p. 172 (1892); Electrical Engineer, vol. xiii. p. 182 (1892). 9 Electrical Engineer, vol. xvii. p. 421 (1894). (Now the Western Elec- tric Co. ) 10 Kittler, " Handbuch," vol. i. p. 949. II Electrical Engineer, vol. xvii. p. 465.(i8g4). 18 Electrical Engineer, vol. xiii. p. 397 (1892). 274 DYNAMO-ELECTRIC MACHINES. [72 Jenney Electric Motor Co./ Indianapolis, Ind. ; the Porter Standard Motor Co., New York; the Fort Wayne Electric Corp., 4 Fort Wayne, Ind. ; the United States Electric Co., New York; the Holtzer-Cabot Electric Co., 8 Boston; the Card Electric Motor and Dynamo Co., 4 Cincinnati, O. ; the Simp- son Electrical Manufacturing Co., B Chicago; the Chicago Electric Motor Co.," Chicago; the Bernstein Electric Co., 1 Boston; and by the Premier Electric Co., 8 Brooklyn. The latter type, Fig. 192, is employed by the Elektron Manufac- turing Co., 9 Springfield, Mass.; by the Riker Electric Motor Co., 10 Brooklyn; and by the Actiengesellschaft Elektricitat- werke, vorm. O. L. Kummer & Co., 11 Dresden. The vertical single magnet type, Fig. 193, is used by the "D. & D." Electric Manufacturing Company, 12 Minneapolis, Minn. ; the Packard Electric Company, 13 Warren, O. ; the Bos- ton Motor Company, 14 Boston; the Elbridge Electric Man- ufacturing Company, Elbridge, N. Y. ; the Woodside Electric Works 16 (Rankin Kennedy), Glasgow, Scotland; by Greenwood & Batley, 18 Leeds, England ; by Goolden & Trotter 17 (Atkinson), England; and by Naglo Bros., 18 Berlin. 1 Electrical Engineer , vol. xiii. p. 182 (1892.) J Electrical Engineer, vol. xiii. p. 408 (1892); Electrical World, vol. xxviii. P. 394 (1896). 3 Electrical World, vol. xix. p. 107 (1892). 4 Electrical World, vol. xxiii. p. 499 (1894). 8 Electrical World, vol. xxii. p. 30 (1893). 6 Electrical World, vol. xxii. p. 31 (1893). 7 Electrical World, vol. xix. p. 283 (1892). 8 Electrical World, vol. xix. p. 186 (1892). 9 Electrical Engineer, vol. xv. p. 540 (1893). 10 Electrical Engineer, vol. xvi. p. 436 (1893). "Grawinkcl and Strecker, " Hilfsbuch," fourth edition, p. 277. 12 Electrical World, vol. xx. p. 183(1892); Electrical Engineer, vol. xiv. p. 272 (1892). 13 Electrical World, vol. xx. p. 265 (1892), Electrical Engineer, vol. xiv. p. 414(1892). 14 Electrical World, vol. xxi. p. 471 (1893). 15 The Electrician (London), March I, 1889 ; Electrical World, vol. xiii., April, 1889. 16 Silv. P. Thompson, " Dynamo-Electric Machinery," fourth edition, p. 531. "Silv. P. Thompson, " Dynamo-Electric Machinery," fourth edition, p. 615. '"Grawinkel and Strecker, " Hilfsbuch," fourth edition, p. 314. 72] FORMS OF FIELD MAGNETS. *75 Fig. 194 shows the single magnet ring type, which is employed by the Mather Electric Company, 1 Manchester, Conn. Two magnets, instead of forming the limbs of a horseshoe, can also be set in line with each other, one on each side of the armature, or may be arranged so as to be symmetrical to the armature, but with like poles pointing to the same direction, instead of forming a single magnetic circuit with salient poles; the frame will then constitute a double circuit with consequent poles in the yokes joining the respective ends of the magnet cores. In both of these cases the cores may be put in a hori- zontal or vertical position, and in consequence we obtain two horizontal double magnet types, Figs. 195 and 197, and two vertical double magnet types, Figs. 196 and 199. The salient pole horizontal double magnet type, Fig. 195, is em- ployed by Naglo Bros., 4 Berlin, and by Fein & Company, Stutt- gart, Germany ; and the salient pole vertical double magnet type, Fig. 196, by the Edison Manufacturing Company, 3 New York; and by Siemens & Halske, 4 Berlin. The consequent pole horizontal double magnet type, Fig. 197, is used in the Feldkamp motor, built by the Electrical Piano Company, 5 Newark, N. J. ; and in the fan motor of the De Mott Motor and Battery Company;* and the consequent pole vertical double magnet type, Fig. 199, by the Columbia Electric Company, 7 Worcester, Mass. ; the Keystone Electric Company, Erie, Pa. ; the Akron Electrical Manufacturing Company, 8 Akron, O. ; the Mather Electric Company, 8 Manchester, Conn.; the Duplex Electric Company, 10 Corry, Pa.; the Gen- 1 Electrical Engineer, vol. xvii. p. 181 (1894). 2 Kittler, " Handbuch," vol. i. p. 908; Jos. Kramer, " Berechnung der Dy- namo Gleichstrom Maschinen." 3 " Composite" Fan Motor, Electrical Engineer ; vol. xiv. p. 140(1893) ; Elec- trical World, vol. xxviii. p. 375 (1896); Electrical Age, vol. xix. p. 269 (1897^ 4 Grawinkel and Strecker, " Hilfsbuch," fourth edition, p. 326. 5 Electrical World, vol. xxi. p. 240 (1893). 6 Electrical World, vol. xxi. p. 395 (1893). 1 Electrical World, vol. xxiii. p. 849(1894). 8 Electrical World, vol. xx. p. 264 (1892). 9 Electrical World, vol. xxiv. p. 112 (1894); Electrical Engineer, vol. xviii. p. 99 (1894). 10 Electrical World, vol. xix. pp. 107, 171 (1892); Electrical Engineer, vol xiii. p. 198(1892). 276 DYNAMO-ELECTRIC MACHINES. [72 eral Electric Traction Company (Snell), England; Mather & Platt (Hopkinson), 1 Manchester, England; Immish & Com- pany,* England; Oerlikon Works (Brown), 3 Zurich, Switzer- land; Helios Company, 4 Cologne; and by Naglo Bros./ Berlin. If in the latter form the magnets are made of circular shape, the double magnet ring type. Fig. 200, is obtained, which is built by the " C & C " Electric Company,' New York, and which has been used in the Griscom motor 7 of the Electro-dynamic Company, Philadelphia. The inclined double magnet type, illustrated in Fig. 198, forms the connecting link between the double magnet and the single horseshoe types; it is employed by the Baxter Electrical Manu- facturing Company, 8 Baltimore, Md. ; by Fein & Company," Stuttgart; and by Schorch 10 in Darmstadt. The combination of two horseshoes with common polepieces furnishes two further forms of field magnet frames. Fig. 201 shows the horizontal double horseshoe type, and Fig. 202 the ver- tical double horseshoe type. Machines of the former type (Fig. 201) are built by the United States Electric Company n (Weston), New York; the Brush Electric Company, 12 Cleveland, O. ; the Ford-Washburn Storelectric Company, Cleveland, O. ; the Western Electric Company, 13 Chicago, 111.; the Fontaine Crossing and Electric Company (Fuller), Detroit, Mich. ; by Crompton & Com- pany, 14 London, England; by Lawrence, Paris & Scott, Eng- land, and by Schuckert & Company, Nuremberg, Germany. The latter form (Fig. 202) is employed in dynamos of Fort 1 Silv. P. Thompson, " Dynamo-Electric Machinery," fourth edition, p. 496. 2 Gisbert Kapp, " Transmission of Energy," p. 272. 3 Kittler, " Handbuch," vol. i. p. 921. 4 Kittler, " Handbuch," vol. i. p. 904. 5 Grawinkel and Strecker, " Ililfsbuch," fourth edition, p. 312. 4 Electrical World, vol. xxii. p. 247 (1892). T Martin and Wetzler, " The Electric Motor," third edition, p. 126. I Martin and Wetzler, " The Electric Motor," third edition, p. 228. 9 Kittler, " Handbuch," vol. i. p. 944. 10 Jos. Kramer, " Berechnung der Gleichstrom Dynamo Maschinen."" II Kittler, " Handbuch," vol. i. p. 879. 19 Electrical Engineer ; vol. xiv. p. 50 (1892). 13 Electrical Engineer, vol. xvi. p. 323 (1893). 14 Kapp, " Transmission of Energy," p. 292. 72] FORMS OP FIELD MAGNETS. 277 Wayne Electric Corporation 1 (Wood), Fort Wayne, Ind.; La Roche Electric Works, 2 Philadelphia; Granite State Electric Company,' Concord, N. H. ; Onondaga Dynamo Company, Syracuse, N. Y. ; Electric Construction Corporation 4 (Elwell- Parker); and Crompton Company, 6 London, England. If one or both the polepieces of a consequent pole double magnet type are prolonged in the axial direction, that is, to- ward the armature, and the winding is transferred from the cores to these elongated polepieces, then a type is obtained in which the magnet frame forms a closed iron wrappage with in- wardly protruding poles. Forms of this feature are known as iron-clad types, and, according to the number of magnets and to their position, are single magnet and double magnet, horizontal and vertical iron-clad types. Fig. 203 shows the horizontal iron-clad type, having two hori- zontal magnets. It is used by the General Electric Com- pany,' Schenectady, N. Y. (Thomson-Houston Arc Light type), Detroit Electric Works, 7 Detroit, Mich.; Eickemeyer Com- pany," Yonkers, N. Y. ; Fein & Company,' Stuttgart; and Aachen Electrical Works I0 (Lahmeyer), Aachen, Germany. A modification of this type consists in letting the poles pro- ject parallel to the shaft, one above and one below, or one on each side of the armature; the only magnetizing coil required in this case will completely surround the armature. This spe- cial horizontal iron clad form, which is illustrated in Fig. 204, is realized in the Lundell machine, 11 built by the Interior Con- duit and Insulation Company, New York. I Electrical World, vol. xxiii. p. 845 (1894); vol. xxviii. p. 390(1896); Elec- trical Engineer, vol. xvii. p. 598 (1894). 4 Electrical Engineer, vol. xiii. p. 439 (1892). 3 Electrical Engineer, vol. xvi. p. 45 (1893). 4 Electrical Engineer, vol. xv. p. 166 (1893). 5 Silv. P. Thompson. " Dynamo-Electric Machinery," fourth edition, p. 486. 'Silv. P. Thompson, " Dynamo-Electric Machinery," fourth edition, p. 465. 7 Electrical World, vol. xx. p. 46 (1892); Electrical Engineer, voL xiv. p. 27(1892). 8 Kittler, " Handbuch," vol. i. p. 941. ' Kittler, " Handbuch," vol. i. p. 944. 10 Kittler, " Handbuch," vol. i. p. 917. II Electrical World, vol. xx. pp. 13, 381 (1892); vol. xxiii. p. 32 (1894); Electrical Engineer, vol. xiii. p. 643 (1892); vol. xiv. p. 544(1892); vol. xvii. p. 17 (1894.) 27 8 DYNAMO-ELECTRIC MACHINES. [72 In Figs. 205 and 206 the two possible cases of the vertical single magnet iron-dad type are depicted, the magnet being placed above the armature in the former and below the armature in the latter case. The single magnet iron-clad overtype, Fig. 205, is adopted in the street-car motors of the General Electric Com- pany, Schenectady, N. Y. ; in the machines of the Muncie Electrical Works, 1 Muncie, Ind. ; of the Lafayette Engineering and Electric Works, 2 Lafayette, Ind., and in the battery fan motor of the Edison Manufacturing Company, 3 New York. Machines of the single magnet iron-clad undertype, Fig. 206, are built by the Brush Electrical Engineering Company * (Mor- dey), London, and by Stafford and Eaves, 8 England. The vertical double magnet iron-clad type, Fig. 207, having two vertically projecting magnets, one above and one below the armature, is employed in the machines of the Wenstrom Elec- tric Company," Baltimore; the Triumph Electric Company, 7 Cincinnati, O. ; the Shawhan-Thresher Electric Company, 8 Dayton, O. ; the Card Motor Company, 9 Cincinnati, O. ; the Johnson Electric Service Company, 10 Milwaukee, Wis. ; the Erie Machinery Supply Company, 11 Erie, Pa.; O. L. Kummer & Company, 12 Dresden ; Deutsche Elektrizitats-Werke" (Garbe, Lahmeyer & Co.), Aachen; Schuckert & Company, 14 Nuremburg, Germany; Oerlikon Works, 16 Zurich; and the Zurich Telephone Company, 1 ' Zurich, Switzerland. There are various other bipolar types, which, however, ^Electrical Engineer ; vol. xv. p. 606 (1893). 2 Western Electrician, vol. xviii. p. 273 (1896). 3 Electrical World, vol. xxi. p. 347 (1893). 4 Elektrotec An. Zeitschr., vol. xi. p. 135 (1890). 6 S. P. Thompson, " Dynamo-Electric Machinery," fourth edition, p. 202. ' Elektrotec hn. Zeitschr., vol. xi. p. 122 (1890). 1 Electrical Engineer, vol. xvii. p. 314 (1894). * Electrical World, vol. xxiii. p. 191 (1894). 9 Electrical World, vol. xxii. p. 15 (1893). 10 Electrical Engineer, vol. xvii. p. 290(1894). "Electrical World, vol. xix. p. 283 (1892). 1S Grawinkel and Strecker, " Hilfsbuch," fourth edition, p. 278. 13 Grawinkel and Strecker, " Hilfsbuch," fourth edition, p. 293. 14 Grawinkel and Strecker, " Hilfsbuch," fourth edition, p. 299. 15 Grawinkel and Strecker, " Hilfsbuch," fourth edition, p. 320. 16 Elektrotechn. Zeitschr., vol. ix. pp. 181, 347, 410 and 485 (1888). 73] FORMS OF FIELD MAGNETS. 279 mostly are out of date, and, therefore, of very little practical importance. These can easily be regarded as special cases of the types enumerated above. 73. Multipolar Types. Multipolar field magnet frames can have one or two mag- nets for every pole, or each magnet can independently supply FIG. 21 3 FIG. 21 4 FIG. 21 5 FIG. 21 6 FIG. 21 7 FIG. 218 FIG. 219 FIG. 220 FIG. 221 FIG. 222 FIG. 223 FIG. 224 Figs. 208 to 224. Types of Multipolar Fields. two poles, or one single magnet, or two magnets, may be pro- vided with polepieces of such shape as to form the desired number of poles of opposite polarity. 280 DYNAMO-ELECTRIC MACHINES. [73 If the number of magnets is identical with the number of poles, the magnets may either be placed in a radial, a tangetial, or an axial position with reference to the armature, and in the two first-named cases they may be put either outside or inside of the armature. The Radial Outerpole Type is shown in Fig. 208; this form has been adopted as the standard type for large dynamos of the General Electric Company, 1 Schenectauy, N. Y. ; of the Westinghouse Electric and Manufacturing Company, 2 Pitts- burg, Pa.; the Crocker- Wheeler Electric Company, 3 Ampere, N. J. ; the Riker Electric Motor Company, 4 Brooklyn; the Stanley Electric Manufacturing Company, 5 Pittsfield, Mass.; the Fort Wayne Electric Company, 6 Fort Wayne, Ind. ; the Eddy Electric Manufacturing Company, 7 Windsor, Conn.; the Belknap Motor Company, 8 Portland, Me.; the Shawhan- Thresher Electric Company, 9 Dayton, O. ; the Great Western Electric Company 10 (Bain), Chicago ; the Walker Manufactur- ing Company, 11 Cleveland, O. ; the Mather Electric Com- pany, 18 Manchester, Conn.; the Claus Electric Company, 13 New York; the Commercial Electric Company, 14 Indianapolis; 1 Electrical World, vol. xxi. p. 335 (1893); vol. xxiv. pp. 557 and 652 (1894); Electrical Engineer, vol. xiii. p. 165 (1892) ; vol. xiv. p. 562 (1892); vol. xviii. pp. 426, 507 (1894). * Electrical World, vol. xxi. p. 91 (1893); vol. xxiv. p. 421 (1894); Electrical Engineer, vol. xviii. p. 330 (1894). 8 Electrical World, vol. xxiii. p. 307 (1894); Electrical Engineer, vol. xvii. p. 193 (1894). 4 Electrical World, vol. xxiii. p. 687 (1894); Electrical Engineer, vol. xvii. p. 442 (1894). 5 Electrical World, vol. xxiii. p. 815 (1894); Electrical Engineer, vol. xvii. p. 507 (1894). Electrical World, vol. xxiii. p. 878 (1894); vol. xxviii. p. 395 (1896). I Electrical World, vol. xxv. p. 34 (1895). 8 Electrical Engineer, vol. xvii. p. 502 (1894). 9 Electrical Engineer, vol. xvii. p. 463 (1894). 10 Electrical World, vol. xxiii. p. 161 (1894). II Electrical World, vol. xxiii. pp. 475 and 785 (1894); vol. xxviii. p. 423 (1896); Electrical A ge, vol. xviii. p. 605 (1896). 12 Electrical Engineer, vol. xiv. p. 364 (1892). 13 Electrical Engineer, vol. xvi. p. 3 (1893). 14 Electrical World, vol. xxiv. p. 627 (1894); vol. xxviii. p. 437 (1896); Elec- trical Engineer, vol. xviii. p. 506 (1894). 73] FORMS OF FIELD MAGNETS. 281 the Zucker. Levitt & Loeb Company, 1 New York; the All- gemeine Electric Company 2 (Dobrowolsky), Berlin, Germany; O. L. Kummer & Company, 3 Dresden; Garbe, Lahmeyer & Company, 4 'Aachen; Elektricitats Actien-Gesellschaft, vor- mals W. Lahmeyer & Company, 5 Frankfurt a. M. ; Schuckert & Company,' Nuremburg; C. & E. Fein, 7 Stuttgart; Naglo Bros., 8 Berlin; the Zurich Telephone Company, 9 Zurich; the Oerlikon Machine Works, 10 Zurich, Switzerland; R. Alioth & Company, 11 Basel, Switzerland; the Berlin Electric Construc- tion Company (Schwartzkopff), 12 Berlin, Germany; and numer- ous others. In Fig. 209 is represented the Radial Innerpole Type, which is used by the Siemens & Halske Electric Company, 13 Chicago, 111., and Berlin, Germany; by the Alsacian Electric Construc- tion Company, 14 Belfort, Alsace; by Naglo Bros., 15 Berlin, Germany; by Fein & Co., 18 Stuttgart, Germany; and by Ganz & Co., 17 Budapest, Austria. The Tangential Outerpole Type, Fig. 210, is employed by the Riker Electric Motor Company, Brooklyn; by the Baxter Motor Company, 18 Baltimore, Md. ; the Mather Electric Com- pany, 19 Manchester, Conn.; the Dahl Electric Motor Com- 1 "Improved American Giant Dynamo," Electrical Age, vol. xviii. p. 600 .(Oct. 17, 1896). 8 Electrical Engineer, vol xii. p. 596 (1891); vol. xvi. p. 103 (1893) 3 Grawinkel and Strecker, " Hilfsbuch," fourth edition, p. 278. 4 Grawinkel and Strecker, " Hilfsbuch," fourth edition, p. 291. 5 Grawinkel and Strecker, " Hilfsbuch," fourth edition, p. 294. * Grawinkel and Strecker, " Hilfsbuch," fourth edition, p. 299. I Grawinkel and Strecker, " Hilfsbuch," fourth edition, p. 304. 8 Grawinkel and Strecker, " Hilfsbuch," fourth edition, p. 311. 'Grawinkel and Strerker, " Hilfsbuch," fourth edition, p. 327. 10 Electrical Engineer, vol. xii. p. 597 (1891). II Kittler. " Handbuch," vol. i. p. 934. 14 Kittler, " Handbuch," vol. i. p. 939. 13 Electrical World, vol. xxii., p. 61 (1893); Electrical Engineer, vol. xii. p. 572(1891); vol. xiv. p. 313 (1892). 14 f.'Electricien, vol. i. p. 33 (1891). 15 Kittler, " Handbuch," vol. i. p. 916. Ztitschr. f. Elektrotechn., vol. v. p. 545 (1887). 11 Electrotechn. Zeitschr., vol. viii. p. 233 (1887). 18 Hering, " Electric Railways," p. 294. 19 Electrical World, vol. xxiv. p. 134 (1894)} Electrical Engineer, vol. xviii. p. 177 (1894). 282 DYNAMO-ELECTRIC MACHINES. [73 pany, ' New York; the Electrochemical and Specialty Com- pany, 2 New York ("Atlantic Fan Motor "), and by Cuenod, Sauter & Co. 3 (Thury), Geneva, Switzerland; generators of this type are further used in the power station of the General Electric Company, 4 Schenectady, N. Y., and in the Herstal, 8 Belgium, Arsenal. Machines of the Tagential Innerpole Type, Fig. 211, are built by the Helios Electric Company, 6 Cologne, Germany. In the Axial Multipolar Type, Fig. 212, there are usually two magnets for each pole, one on each side of the armature, in order to produce a symmetrical magnetic field. This form is used by the Short Electric Railway Company, 7 Cleveland, O. ; Schuckert & Co., 8 Nuremberg, Germany; Fritsche & Pischon, 9 Berlin, Germany; Brush Electric Engineering Company, 10 London, England ("Victoria" Dynamo); by M. E. Desro- ziers, u Paris, and by Fabius Henrion, 12 Nancy, France. The type recently brought out by the C. & C. Electric Company, 13 New York, has but one magnet per pole, and the polepieces are arranged opposite the external circumference of the armature. Fig. 213 shows the Raditangent Multipolar Type, which is a combination of the Radial and Tangential Outerpole Types, Figs. 208 and 210 respectively, and which is employed by the Standard Electric Company, 14 Chicago, 111. 1 Electrical World, vol. xxi. p. 213 (1893). 2 Electrical World, vol. xxi. p. 394 (1893). 3 Kittler, " Handbuch," vol. i. p. 936. 4 Thompson, "Dynamo-Electric Machinery," fourth edition, p. 517. 6 500 HP. Generator, Electrical World, vol. xx. p. 224 (1892). 'Kittler, " Handbuch," vol. i. p. 905. "i Electrical World, vol. xviii. p. 165 (1891). 8 Elektrotechn. Zeitschr., vol. xiv. p. 513 (1893); Electrical Engineer, vol. xii. p. 595 (1891). 9 Electrical World, vol. xx. p. 308 (1892); Electrical Engineer, vol. xii. p. 572 (1891). 10 Thompson, " Dynamo Electric Machinery," fourth edition, p. 498. 11 Electrical Engineer, vol. xiv. p. 259 (1892); vol. xv. p. 340 (1893). 12 Grawinkel and Strecker, " Hilfsbuch," fourth edition, p. 317. 13 Electrical World, vol. xxviii. p. 372 (1896). 14 Electrical World, vol. xxiii. pp. 342, 549 (1894); Electrical Engineer, vol. xvii. pp. 189, 379 (1894). 73] FORMS OF FIELD MAGNETS. 283 If only one magnet is used in multipolar fields, the pole- pieces may be so shaped as to face the armature in an axial or in a radial direction. In the former case the Axial Pole Single Magnet Multipolar Type, Fig. 214, is obtained, which is used by the Brush Electrical Engineering Company l (Mordey), London, England, and by the Fort Wayne Electric Company * (Wood), Fort Wayne, Ind. In the latter case the Outer-Inner Pole Single Magnet Type, Fig. 215, results, in which the polepieces may either all be opposite the outer or the inner armature surface, or alter- nately outside and inside of the armature; the latter arrange- ment, which is the most usual, is illustrated in Fig. 215, and is employed by the Waddell-Entz Company, 3 Bridgeport, Conn., and by the Esslinger Works, 4 Wurtemberg, Germany; the all outerpole arrangement is employed in the direct con- nected multipolar type of the C & C Electric Company, 5 New York. If two magnets furnish the magnetic flux, they are placed concentric to the armature, and the two sets of polepieces so arranged that adjacent poles on either side of the armature are of unlike polarity, but that poles facing each other on opposite sides of the armature have the same polarity. Such a Double Magnet Multipolar Type is shown in Fig. 216; it is that designed by Lundell, 8 and built by the Interior .Conduit and Insulation Company, New York. In giving the yoke of the Radial Multipolar Type (Fig. 208) such a shape as to form a polepiece between each two consec- utive magnets, an iron-clad form is obtained having alternate salient and consequent poles, and requiring but one-half the number of magnets as a radial multipolar machine of same number of poles. Fig. 217 shows a field frame of the Multipolar Iron-clad Type, having six poles, which is the form employed in the gearless street car motor of the Short Electric Railway Com- 1 Thompson, " Dynamo Electric Machinery," fourth edition, p. 678. 2 Electrical Engineer vol. xv. p. 46(1893). 3 Electrical World, vol. xix. p. 13 (1892); vol: xxii. p. 120(1893). 4 Kittler, " Handhuch," vol. i. p. 945. s Electrical World, vol. xxv. p. 33 (1895). * Electrical World, vol. xx. p. 85 (1892). 284 DYNAMO-ELECTRIC MACHINES. [73 pany, 1 Cleveland, O. In Figs. 218 and 219, two special cases of this type are depicted, both representing Fourpolar Iron- clad Types, and differing only in the position of the magnets. The Horizontal Fourpolar Iron-clad Type, Fig. 218, is used in the Edison Iron-clad Motor 4 (General Electric Company), and in the dynamos of the Wenstrom Electric Company, 3 Balti- more, Md. The Vertical Fourpolar Iron-clad Type, Fig. 219, is employed by the Elliott-Lincoln Electric Company, 4 Cleve- land, O. Fig. 220 shows a special case of the Horizontal Fourpolar Iron-clad Type, obtained by symmetrically doubling the frame illustrated in Fig. 204, and providing four poles instead of two. The cores are so wound that the centre of the cylindri- cal iron wrappage has one polarity and the ends the opposite polarity. Two oppositely situated polepieces are joined to the middle, and the two sets of intermediate ones to the ends of the magnet frame; the lower half of Fig. 220, consequently, is a section taken at right angles to the upper half, the diamet- rically opposite section being identical. This type has been developed by the Storey Motor and Tool Company, 5 New York. Multipolar fields may also be formed by a number of inde- pendent horseshoes arranged symmetrically around the outer armature periphery. Figs. 221 and 222 show two such Mul- tiple Horseshoe Types, double magnet horseshoes being employed in the former, and single magnet horseshoes in the latter type. Multiple horseshoe machines of the double magnet form (Fig. 221) have been designed by Elphinstone & Vincent, and by Elwell-Parker Electric Construction Corporation, 8 England; while the single-magnet form (Fig. 222) is employed by the Electron Manufacturing Company' (Ferret), Springfield, Mass. 1 Electrical World, vol. xx. p. 241 (1892); Electrical Engineer, vol. xiv. p. 395 (1895). * Electrical Engineer, vol. xii. p. 598 (1891). * Electrical World, vol. xxiv. p. 183 (1894). 4 Electrical World, vol. xxi. p. 193 (1893); vol. xxii. p. 484 (1893). 5 Electrical World, vol. xxi. p. 214(1893); Electrical Engineer, vol. xv. p. 263 (1893). ' The Electrician (London), vol. xxi. p. 183 (1888). T Electrical Engineer, vol. x. p. 592 (1890); vol. xiii. p. 2 (1892). 74] FORMS OF FIELD MAGNETS. 285 Further forms of multipolar fields can be derived from the bipolar horizontal and vertical double magnet types respec- tively. If, in the Vertical Double Magnet Type, Fig. 196, an additional polepiece is provided at the centre of the frame so as to face the internal surface of the armature at right angles to the outer polepieces, the Fourpolar Vertical Double Magnet Type is created, which, when laid on its side, will constitute the Fourpolar Horizontal Double Magnet Type, Fig. 223. If, in the Vertical Double Magnet Type, Fig. 199, the two cores are cut in halves and additional polepieces inserted at right angles to the existing ones, the Vertical Quadruple Magnet Type, Fig. 224, is obtained; the same operation performed with the Hori- zontal Double Magnet Type, Fig. 197, will give the Horizontal Quadruple Magnet Type. Fourpolar Horizontal Double Magnet Dynamos, Fig. 223, are built by the Zurich Telephone Company, 1 Zurich, Switzerland; and Vertical Quadruple Magnet Machine, Fig. 224, by the Duplex Electric Company, 4 Corry, Pa. Numerous other multipolar types have been invented and patented, but either are of historical value only, or have not yet come into practical use. 74. Selection of Type. If the type is not specified, the field magnet frame for a large output machine should be chosen of one of the multipolar types, as in these the advantage of a better proportioning and a higher efficiency of the armature winding, and the possibility of a symmetrical arrangement of the magnetic frame, results in a saving of copper as well as of iron; while for smaller machines below 10 KW capacity the bipolar forms are pref- erable on account of the great complication caused by the increased number of armature sections, commutator-divisions, field coils, etc., necessary in multipolar machines, and on account of the narrowness of the neutral or non-sparking space on a multipolar commutator. The field, moreover, should have as few separate magnetic 'Kittler, " Handbuch," vol. i. p. 947. * Electrical World, vol. xx. p. 14(1892); Electrical Engineer, vol. xiv. p. I (1892). 286 DYNAMO-ELECTRIC MACHINES. [74 circuits as possible; thus, in the case of a bipolar type, it should be a single magnetic circuit rather than the consequent pole type which is formed by two or more magnetic circuits, of one or two magnets each, in parallel, because the former is more economical in wire and in current required for excita- tion. In two-circuit consequent pole machines, for instance, such as the double magnet types, Figs. 197, 199, and 200, and the double horseshoe types, Figs. 201 and 202, according to Table LXIX., 75, there is 1.41 times the length of wire, and consequently also 1.41 times the energy of magnetization required than in a single 'circuit, round cores being used in both cases, and the single circuit having exactly twice the area of each of the two parallel circuits in the consequent pole ma- chines. Triple and quadruple magnetic circuits, *". e., 3 or 4 cores, or sets of cores, magnetically in parallel, are still more objectionable, requiring, when the cores are of circular cross- section, 1.73 and 2.00 times as much wire, respectively, as a single magnetic circuit having a round core of equal total sec- tional area. If a machine has several magnetic circuits, each of which, however, passes through all the magnets in series, then the frame is to be considered as consisting of but one single cir- cuit, for the subdivision only takes place in the yokes, and it is immaterial as to the length of exciting wire whether the return path of a single circuit is formed by one yoke, or by a number of yokes magnetically in parallel. The above-named objection to divided circuit types, consequently, does not apply in the case of the iron-clad forms, Figs. 203 to 207. According to Table LXVIII., 70, the horizontal double magnet type, Fig. 195, and the horizontal iron-clad type, Fig. 203, are the best bipolar forms, magnetically. The iron- clad types, furthermore, possess the mechanical advantage of having the field windings and the armature protected from external injuries by the frame of the machines, which makes them eminently adaptable to motors for railway, mining, and similar work. The inverted horseshoe type, Fig. 188, which ranks very highly, as far as its magnetic qualities are concerned, has the centre of its armature at a comparatively very great distance from the base, requiring very high pillow-blocks, which have 74] FORMS OF FIELD MAGNETS. 287 to carry the weight as well as the downward thrust of the armature inherent to the inverted forms having the field wind- ings below the centre of revolution; see 42. The side pull of the belt with a high centre line of shaft tends to tip the machine, and the changes in the pull due even to the undula- tions of the belt will cause a tremor in the frame which jars the brushes, and, eventually, loosens their holders, and which has a disastrous influence upon the wearing of the commutator. On this account the inverted forms, or " under-types," can only be used for small and medium-sized machines, in which the height of the pillow-blocks remains within practical limits. In selecting a multipolar type, Table LXVIII. shows that the radial innerpole type, Fig. 209, offers the best advantage with regard to the magnetical disposition; with this type, however, are connected some mechanical difficulties, due to the necessity of supporting the frame from one of its ends, laterally, and the armature from the other. In the outerpole types the armature core can be supported centrally from the inner circumference, and the frame suit- ably provided with external lugs or flanges resting upon the foundation, a most desirable arrangement for mechanical strength and convenience. The most favorite of the out- erpole forms is the radial outerpole type, Fig. 208, on account of its superiority, magnetically, over the tangential and axial multipolar types. In all dynamo designs the consideration is especially to be borne in mind that the whole machine as well as its various parts should be easily accessible for inspection, and so arranged that they can conveniently be removed for repair or exchange. A large number of machines owe their popularity chiefly to their good disposition in this respect. The shape of the frame in all cases is preferably to be so chosen that the length of the magnetic circuit in the same is as short as possible. Advantages and Disadvantages of Multipolar Machines. The advantages of multipolar over bipolar dynamos can be summarized as follows: (i) By the multipolar construction a saving in weight of DYNAMO-ELECTRIC MACHINES. [74 material is effected both in the armature and in the field magnet, due to the subdivision of the magnetic circuit. (2) Multipolar machines have a more compact and sym- metrical form, because the component parts of the magnet frame are much smaller than a corresponding bipolar magnet, and are evenly spaced around the armature. (3) Since there are as many openings around the armature as there are poles, the ventilation of the armature is much better; and since a number of small cores have a greater sur- face than one large core of equal cross-section and length, the dissipation of heat is facilitated, so that under the same condi- tions multipolar machines run cooler than bipolar ones. (4) For armatures of the same diameter, the individual parts of the field frame are much smaller and more easily handled in the multipolar than in the bipolar type. The disadvantages of multipolar machines are: (1) Greater complication in constructing, fitting, winding, and connecting, owing to the increased number of parts and consequent larger number of magnetic and electrical circuits. (2) Strong magnetic side pull on the armature in case of eccentricity of field; much greater than in bipolar machines. (3) Greater difficulty in balancing field; with multiple-cir- cuit armature winding, the flux must be exactly the same for each pole, otherwise the E. M. F. of the circuits will be un- equal, producing wasteful currents in them which, in turn, cause excessive sparking and heating. This difficulty, how- ever, is not present in two-circuit windings. Comparison of Bipolar and Multipolar Types. The saving in material effected by the multipolar construc- tion is seen by comparing the three designs shown in Fig. 224^7, representing armatures of equal size in bipolar, four-pole, and eight-pole fields. Assuming that in all three cases the poles cover a like portion of the armature periphery, and that the gap induction is the same, then evidently the total armature flux is the same in the three designs. In practice, the gap density is usually less in bipolar than in multipolar machines, but this difference is not a necessity, and need not be con- sidered in this comparison. In the bipolar type, it will be seen that the armature must 74] FOXASS OF FIELD MAGNETS. carry the total flux between its shaft and periphery, while in the four-pole machine the armature cross-section is only required to carry the total flux, hence the radial depth. B of the armature core in the four-pole machine need be only one-half as great as A in the bipolar type, thus reducing its weight. The flux passing through each core of the four-pole machine is |, and that passing through its yoke ring is | of the corresponding bipolar flux, as is indicated by the dotted lines, each of which represents of the total flux. Owing to this subdivision of the flux, the weight of the multipolar magnet frame is less than that of the bipolar. The difference is still more marked when we compare the eight-pole machine shown in Fig. 2240 with the bipolar and Fig. 224. Comparison of Bipolar and Multipolar Types. four-pole types. The radial thickness of the field ring in the eight-pole machine is only \ as much as in the four-pole machine, and \ as great as the thickness of the yoke in the bipolar machine, and the armature may be hollowed out to a radial thickness C of only { that of the bipolar armature, A, as shown, the total flux being the same for all three designs. Proper Number of Poles for Multipolar Field Magnets. If a multipolar field has been adopted, the best number of poles must next be decided upon. This is a question, partly, of selecting a size and number of field cores, coils, etc., con- venient for making and handling, but it is chiefly a matter of the number of magnetic cycles occurring in the armature core. The number of cycles per second, as stated on p. in, is N, = X D , 2S-JC D YNA MO- ELEC TRIG MA CHINES. if N is the number of revolutions per minute, and n v the number of pairs of magnet poles. Direct-current machinery is designed, generally, so that N is between 10 and 35 cycles per second. This limits the number of poles, the object being to reduce the core losses due to hysteresis and eddy currents, the former, as we have seen in 32, being proportional to JV lt whereas the latter increase with the square of .A 7 ",, ' see 33. The lower frequency of about 10 or 15 cycles applies to low-speed machines for direct connection to engines, and the higher frequency of 30 or 35 is adopted in high-speed belt-connected generators and motors. By transformation of the above formula for N^ it therefore follows that, for instance, the maximum speed of a four-pole machine, having 2 pairs of poles, should be , r 60 v N 60 X 35 N = ' = - -1-iLl = ^50 revs. p. mm. "v In some instances, four-pole machines are run at higher speeds than this, for example 1200 revs, per min., which gives 40 cycles. But this is rather too high a frequency, and should not be adopted except for special reasons. If the values n 9 - i, 2, 3, 4, etc., and JV t = 10, 15, 25, and 35, respectively, be inserted into the above formula for IV, the following table of dynamo speeds for various numbers of poles is obtained, from which the proper number of poles for any particular speed can be taken: TABLE LXVIII6. NUMBER OP MAGNET POLES FOR VARIOUS SPEEDS. LIMITS op SPEED. NUMBER OP Low-Speed Machines. Medium-Speed Machines. High-Speed Machines. POLES. NI = 10 to 15 cycles. NI = 15 to 25 cycles. N! = 25 to 35 cycles. 2 600 to 900 900 to 1500 1500 to 2100 4 300 450 450 750 750 1050 6 200 300 300 500 500 700 8 150 225 225 375 375 525 10 120 180 180 300 300 420 12 100 150 150 250 250 350 14 85 130 130 215 215 300 16 75 115 115 190 190 260 18 70 100 100 170 170 230 20 60 90 90 150 150 210 74] FORMS CF FIELD MAGNETS. Generally speaking, the bipol.tr type is used for high speeds, such as 1500 revs, per min. or more. A further reason for selecting the bipolar type for very high speeds is the fact that machines running at 1500 revolutions, or more, are usually quite small. For speeds between 400 and 900 revs, per min., the four-pole construction is especially suitable, giving fre- quencies from 13^ to 30 cycles. This includes nearly all belted dynamos and motors, from the large sizes of 200 KW, or more, down to about 10 KW, below which the bipolar form is generally used for the reasons given. Between 200 and 400 revs, per min., six poles are commonly adopted, the corresponding frequencies being from 10 to 20 cycles. This range of speed comprises practically all generators directly connected to high-speed engines, from the largest to the smallest, excepting combinations with very high speed engines of 600 revs, per min., or more, for which four poles would be preferable. When a dynamo is directly driven by a steam turbine, at an extremely high speed without reducing gear, the field should be of the bipolar type. For speeds below 200 revs, per min. the number of poles is generally increased to eight, or more. This applies to most generators directly con- nected to low-speed engines. In some cases motors of various sizes, even down to i or 2 HP, are required to run at low speeds in order to be con- nected directly to the machines which they drive. For this purpose six poles are suitable for speeds from 200 to 400 revs, per min., and eight, or more, poles, if the speed is below 200 revs, per min. Railway motors are nearly always con- structed vi\ih four poles, the speed being very variable, but hav- ing a maximum value in most cases of about 800 revs, per min. This gives a rather high frequency of a6| cycles, but as the maximum speed is rarely maintained for more than a few minutes at a time, the heating due to hysteresis and eddy currents in the armature core does not rise above the limit allowed. The average speed corresponds to a moderate frequency of 15 to 20 cycles. CHAPTER XV. GENERAL CONSTRUCTION RULES. 75. Magnet Cores. a. Material. The field cores should preferably be of wrought iron, or of cast steel, in order to economize in magnet wire, for the use of cast iron, on account of its low permeability, would require cores of at least i|, /'. e., almost twice the cross-section, and therefore a much greater length of wire, to obtain the neces- sary magnetizing force. With the smaller wrought-iron cures the leakage would also be less. In spite of the decided advantage of wrought-iron cores, cast-iron field magnets are very common, since the temptation to use castings instead of forgings is very great. Where weight and bulk are of no consequence, a cast-iron field mag- net may prove nearly as economical as one of wrought iron costing considerably more, but the former requires from ^ to times more wire to encircle it than a wrought-iron one of similar magnetic density, in case of circular cross-section, and it is evident that this, by introducing additional electrical resistance, will prove a constant source of unnecessary running expense. As to the use of steel in dynamos, H. F. Parshall, in a paper delivered before the Franklin Institute, 1 states that magnet frames made of cast steel are 25 per cent, cheaper than those of cast iron, but possess the disadvantage of being not as uni- form in magnetic qualities as cast iron. He further asserts that good cast steel should not have greater percentages of impurities than .25 per cent, of carbon, .6 per cent, of man- ganese, .2 per cent, of silicon, .08 per cent, of phosphorus, and .05 per cent, of sulphur. The effect of carbon is to lessen the magnetic continuity and to greatly reduce the permeability; 1 Electrical World, vol. xxiii. p. "14, February 17, 1894. % 75] GENERAL CONSTRUCTION RULES. 289 carbon, therefore, is the most objectionable impurity, and, if possible, should be restricted to smaller amounts than the maximum above quoted. Manganese, in quantities larger than stated, seriously reduces the magnetic susceptibility of the steel, a 12 per cent, mixture having scarcely greater suscepti- bility than air. Silicon is objectionable through facilitating the formation of blowholes, and from its hardening effect. E. Schulz, 1 in comparing two dynamos differing only in the material of the field frame and in the magnet winding, finds that the weight of a cast-steel magnet frame is about one-half of that of cast iron, and that the weight of the copper for the magnets, on account of the smaller cross-section and the greater permeability of the cast steel, is reduced to somewhat less than one-half. The price of the frame will accordingly be about \\ times that of the cast-iron one, but, on account of the reduction of the copper weight, the cost of the whole ma- chine will be less for a cast-steel than fora cast-iron frame, the total weight being less than one-half in the former case. According to Professor Ewing" the permeability of good cast steel at low magnetic forces is less than that of wrought iron, but the reverse is the case with high forces. In a specially good sample tested by G. Kapp and Professor Ewing, a magnetic density of 18,000 lines per square centimetre ( 116,000 lines per square inch) was reached, with but little more than one-half the magnetizing force as is necessary for the same induction in ordinary wrought iron. b. Form of Cross- Section. The best form of cross-section fora magnei-core is undoubt- edly that which possesses the smallest circumference for a given area, and this most economical section is the circle. It is, however, often preferable on account of reducing the dimen- sion of the machine perpendicular to the armature shaft, to use cores of other than circular section; in this case either rectangular, elliptical; or oval cores are employed, or several 1 Elektrisches Echo, August II, 1894; Electrical World, vol. xxiv., p. 238 (September 8, 1894). 2 Electrical Engineer, London, October 5, 1894 < Electrical World, voL xxiv. p. 446 (October 27, 1894). 290 DYNAMO-ELECTRIC MACHINES. [75 round cores are placed side by side and connected in parallel to each other, magnetically. The latter method, however, is not recommendable for the reason that the magnetizing effects of the neighboring coils partly neutralize each other, because of the currents of equal polarity flowing in opposite lateral directions in the parts of the coils facing each other, as indi- cated by arrows in Fig. 225. There is, consequently, a double ooo Fig. 225. Direction of Current in Parallel Magnet Cores of same Polarity. loss connected with this arrangement, a larger expenditure of copper, connected with higher magnet resistance, and decrease of the magnetizing effects by mutual influence of the coils. Besides the forms mentioned, also square cores and hollow magnets of ring-section are frequently used. An idea of the economy of the form of cross-section to be chosen can be formed by means of the following Table LXIX., which gives the circumferences for unit area of the various forms of cross-sections employed in modern machines, and compares the same with the circumference of the most eco- nomical form, the circle. In the case of rectangular and elliptical cores, four forms each are considered, the lengths being, re- spectively, 2, 3, 4, and 8 times the width of the sections. For oval cores three sections are examined, the semicircular end portions being attached to a centre portion formed of i, 2, and 4 adjacent squares, respectively. Next come four sections consisting of several round cores in parallel, namely, 2, 3, 4, and 8 separate circles. Of hollow cores, finally, five cases are con- sidered, the internal diameter being, respectively, i, 2, 3, 4, and 8 times the radial thickness of the cross section. Hollow Magnets are used in some special types, such as shown in Figs. 84, 94, 95, 96, and 100, where large circumfer- ences of the cores are required but not the total area inclosed by these circumferences, and where the armature or its shaft has to pass through the centre of the magnet. As to the use of holloiv magnets in place of solid ones, Profes- 75] GENERAL CONSTRUCTION RULES. 291 TABLE LXIX. CIRCUMFERENCE OF VARIOUS FORMS OF CROSS SECTIONS OF EQUAL AKEA. Form of Cross-Section Description Circumference for Unit Area Relative Circumference (Circle =1) Circle 3.545 1 H Square 4.000 1.13 Rectangle, 1:2 4.243 1.2O 1:3 4.62 1.305 1:4 5.OO 1.41 mmmxm 1:8 6.364 1.80 Elfipse, 1:2 3.87 1.09 1:3 4.35 1.23 1:4 4.84 1.37 1:8 6.53 1.84 Oval.lsqu.2^; 3.85 1.085 ,. 2 " 2 " 4.28 1.21 mvMmz .. 4 .. 2 " 5.09 1.44 ^ 2 Circles 5.01 1.41 3 " 6.14 1.73 4 " 7.09 2.00 G G O O 8 " 10.03 2.83 15 Ring, 1:1 3.85 1.085 o 1:2 4.O9 1,t55 o " 1:3 4.43 t25 1:4 4.76 1.34 1:8 5.91 1.67 sor Grotrian 1 states that with weak magnetizing forces only the outer layers of the iron, next to the winding, are magnetized. 1 Elektrotechn. Zeitschr., vol. xv. p. 36 (January 18, 1894); Electrical World, vol. xxiii. p. 216 (February 17, 1894). 292 DYNAMO-ELECTRIC MACHINES. [75 E. Schulz, 1 however, showed by practical experiments that the magnetization is exactly proportional to the area of the core- section, even at the low induction due to the remanent mag- netism; from this can be concluded that Professor Grotrian's results do not apply to the case of dynamo magnets under prac- tical conditions. A. Foppl 2 claims that the theory of Professor Grotrian is correct, i. e., that the flux gradually penetrates the magnet from its circumference, and that under certain cir- cumstances it may not reach the centre of the core, but he admits that this theory has no practical bearing upon such magnets as are now used in practical dynamo design. c. Ratio of Core-area to Cross-section of Armature. The relation between the cross-section of iron in the magnet cores to that of the armature core is a very important one, as on its proper adjustment depends the attainment of maximum output per pound of wire with minimum weight of iron. According to tests made at the Cornell University under the direction of Professor Dugald C. Jackson, 3 the best area of cross-section of the magnet cores for drum machines is i^ times that of least cross-section of armature, if the cores are of good wrought iron, or about 2^ times the minimum arma- ture section if cast iron cores are used. According to Table XXII., 26, the maximum core den- sity in ring armatures is from i-^ to if times that of drum armatures; for equal amounts of active wire, therefore, the former require i^ to if times as great a magnetic flux as the latter, and the cross-sections of the magnet cross, con- sequently, have to be taken correspondingly greater in case of ring machines, namely, i|- to 2^ times the minimum armature section in case of wrought iron cores, and 3 co 4 times the arma- ture section for cast iron field magnets. Professor S. P. Thompson, in his " Manual on Dynamo- 1 Elektrotechn. Zdtschr., vol. xv. p. 50 (February 8, 1894); Electrical World, vol. xxiii. p. 337 (March IO, 1894). 2 Elektrotechn. Zeitschr., vol. xv. p. 206 (April 12, 1894); Electrical World, vol. xxiii. p. 680 (May 19, 1894). 3 Transactions Am. lust of El. Eng., vol. iv. (May 18, 1887); Electrical Engineer, vol. iii. p. 221 (June, 1887). 76] GENERAL CONSTRUCTION RULES. 293 Electric Machinery," ' gives 1.25 for wrought iron and 2.3 for cast iron as the usual ratio in drum machines, and 1.66 and 3 respectively, in ring-armature dynamos. In the experiments conducted by Professor Jackson, ten different armatures, all of same length and same external diameter, but of different bores, were used in the same field, thus including a range of from .5 to 1.4 for the ratio of least armature section to core area. The curves obtained show that the total induction through the armature increased quite rapidly when the armature was increased in area from .5 of that of the magnets to about .75 of the core area. From. 75 to .9 there is still an increase of induction with increase of armature section, though comparatively small, and beyond .9 the increase is of no practical importance. 76. Polepieces. a. Material. The polepieces, if the shape and the construction of the magnet frame permits, should be of ivrought iron or cast steel, in order to reduce their size, and therefore their magnetic leak- age, they being of the highest magnetic potential of any part of the magnetic circuit. In forging, care should be taken that the "grain" or texture of the iron runs in the direction of the lines of force. The polepieces, however, usually have to em- brace from .7 to .8 of the armature surface (compare 15), and are, therefore, particularly in the case of bipolar machines, often comparatively large. If in such a case their cross-sec- tion, in order to give sufficient mechanical strength, is to be far in excess of the area needed for the magnetic flux, there is no gain in using wrought iron or cast steel, and the pole- pieces should be made of cast iron. The cast iron used should be as soft and free from impurities as possible. It is prefer- able, whenever practicable, to have it annealed, and, if not too large in bulk, to have it converted into malleable iron; this is especially to be recommended for small machines. An admixture of aluminum has been found to increase the permeability of the cast iron; by adding i per cent., by weight, of aluminum, the maximum carrying capacity of the 'S. P. Thompson, " Dynamo-Electric Machinery,"' fifth edition, p. 378. 294 DYNAMO-ELECTRIC MACHINES. [7.6 cast iron is increased about 5 per cent.; by 3 per cent, admix- ture it is increa-eed 7 per cent.; and by adding 6 per cent, of aluminum, the induction increases about 9 per cent. ; above 7 per cent, of admixture the permeability decreases, and at 12 per cent, addition of aluminum the gain in magnetic conduc- tivity falls down to 7 per cent. From this it follows that an addition of from 6 to 7 per cent., by weight, of aluminum is the proper admixture for the purpose of improving the mag- netic qualities of cast iron, which is explained by the fact that the latter percentage is the limit from which up the hardening influence of the aluminum upon the cast iron becomes appre- ciable. In large multipolar machines combination frames consisting of wrought-iron magnet cores, cast-iron yokes, and cast-steel polepieces give excellent results, having the advantages of the high permeability and uniformity in the magnetic qualities of the wrought iron, of cheapness of the cast iron, and of re- duction in size of the cast-steel polepieces, and being easier to machine, requiring less chipping, and being more easily fin- ished than a magnet frame made entirely of cast steel. A material which a few years ago was quite a favorite with dynamo builders, but which since has to a great extent been displaced by the cheaper cast steel, is the so-called "Mitts metal," or cast ivrought iron, obtained by melting down scrap wrought iron in crucibles, and by rendering it fluid by the addition of a small quantity of aluminum. The trouble with this material was that a great many extra precautions had to be taken to procure sound castings, and that as a rule the castings were rough and difficult to work on account of their toughness. The magnetic value of Mitis iron differs very little from that of cast steel, its permeability at the inductions used in practice being but a trifle lower than that of the latter. Edges and sharp corners are to be avoided as much as pos- sible, for if they protrude sufficiently they will act to a certain extent as poles, and give cause to a source of loss. In cast- ings thin projections are apt to chill while being cast, thus making them quite hard and destroying their magnetic quali- ties; when necessary for mechanical reasons, they should, therefore, be cast quite thick and massive, and may afterward be planed or turned down to the required size. 76J GENERAL CONSTRUCTION RULES. 295 b. Shape. The polepieces have for their object the transmission to the armature of the magnetic flux set up by the field magnet, and the establishment of a magnetic field space around the armature. The shape to be given to them must, therefore, effect the concentration of the lines of force upon the arma- ture, and not their diffusion through the air. This, in general, is achieved by making the polar surfaces as large as possible, and bringing them as near to the armature as mechanical con- siderations permit, and by reducing the leakage areas of the free pole surfaces as much as possible. For practical rules of fixing the distance between the pole corners and the clearance between armature surface and polepieces for various kinds and sizes of armatures, see Tables LX. and LXI., 58, re- spectively. Since eddy currents are produced in all metallic masses, either by their motion through magnetic fields or by variations in the strength of electric currents flowing near them, the pole- pieces of a dynamo-electric machine are. seats of such currents, which form closed circuits of comparatively low resistance, and thereby cause undue heating. These currents are strong- est where the changes in the intensity of the magnetic field or of the electric current are the greatest and the most sudden; this is the case, and consequently the eddy currents are strong- est at those corners of the polepieces from which the arma- ture is moved in its rotation, for, owing to the distortion of the magnetic field by the revolving armature, a density greater than the average is created at the corners where the armature leaves the polepieces, and a density smaller than the average at the corners where it enters. In order to reduce and eventually to avoid the generation of these eddy currents in the polepieces, as well as in the armature conductors, it is therefore necessary to prevent the crowding of the mag- netic lines toward the tips of the polepieces, and to so arrange the poles that the magnetic field does not suddenly fall off at the pole corners, but gradually decreases in strength toward the neutral zone. This object in a smooth arma- ture machine can be attained (i) by gradually increasing the air gap from the centres of the poles toward the 296 D YNAMO-ELECTKIC MA CHINES. [76 neutral spaces in boring the polar faces to a diameter larger than their least diametrical distance apart, thus giving an elliptical shape to the field space, as illustrated in Fig. 226; (2) by providing wrought iron polepieces with cast iron tips form- ing the pole corners and terminating the arcs embraced by the pole faces (see Figs. 227 and 228); or (3) by establishing a magnetic shunt between two neighboring poles in connecting the polepieces, either by a cast-iron ring of small sectional FiQ 226 FiQ. 227 FlQ. 228 FiQ 229 FIG. 235 FIG. 236 FIG. 237 Figs. 226 to 237. Types of Polepieces. area (Dobrowolsky's pole-bushing} or by placing thin bridges across the neighboring pole corners, as shown in Figs. 229 and 230, respectively. The ellipsity of the field space has the advantage that it con- fines the lines of force within the sphere of the pole faces by proportionately increasing the reluctance toward the pole cor- ners, thus preventing an increase of the magnetic density at any particular portion of the polepiece. The application of cast-iron pole tips with wrought iron (or cast-steel) polepieces does not prevent the crowding of the lines at the pole corners, but, by reason of the low permeability of the cast iron, re- duces their density to a figure below that in the wrought iron, and consequently effects a graduation of the field strength near the neutral space, the maximum density being in the 76] GENERAL CONSTRUCTION RULES. 297 wrought iron at the point where the cast-iron tips are joined. In the pole bushing or its equivalent, the pole bridges, the reach of the magnetic field is greatly increased, the percentage of the polar arc being practically = 100, and also a more or less gradual decrease of the field strength at the neutral point is obtained, but the length of the non-sparking space is greatly reduced and thereby its uncertainty increased, thus making the proper setting of the brushes a very difficult operation. It has also been recommended to laminate both the polepieces and the magnet cores in the direction parallel to the armature shaft, in order to prevent the production of eddy currents, but this can only be applied to small dynamos, as the additional cost connected with such a lamination in large machines would be in no proportion to the small gain obtained. Besides, there is another reason against lamination : a laminated magnet frame is very sensitive to the fluctuations in the load of the machine, which naturally react upon the magnetic field, and in following these fluctuations an unsteady magnetization is pro- duced, which, in turn, again tends to increase the fluctuations causing its variability; while in a solid magnet frame the eddy currents induced by the changes of magnetization caused by the fluctuations of the load tend to counteract the very changes producing them, and therefore exercise a steadying influence upon the field, thus reducing the fluctuations in the external circuit of the machine. An expedient sometimes used instead of laminating the pole- pieces is to cut narrow longitudinal slots in- the polepieces, Fig. 231, thus laminating a portion of the polepieces only. These slots at the same time serve to increase the length of the path traversed by the lines of force set up by the action of the armature current, and to thus reduce the armature reaction upon the magnetic field, checking the sparking connected therewith. When the commutator brushes, after having short-circuited an armature coil, break this short circuit, the sudden reversal of the current in the same, produced in passing the neutral line of the field, together with the self-induction set up by the extra current on breaking, causes a spark to appear at the brushes, which may be considerable, since in the comparatively low resistance of the short-circuited coil a small electromotive 298 DYNAMO-ELECTRIC MACHINES. [76 force is sufficient to produce a heavy current. If a dynamo, therefore, is otherwise well designed, that is, if the armature is subdivided into a sufficient number of sections, if the field is strong enough so as not to be overpowered by the armature, and if the thickness of the brushes is so chosen as to not short- circuit more than one or two armature sections each simulta- neously, and as not to leave one commutator-bar before making connection with the next strip, then the sparking at the com- mutator can be reduced to a practically unappreciable degree by so shaping the pole surfaces as to give a suitable fringe of magnetic field of graduated intensity, thus not only causing the current in the short-circuited coils to die out by degrees, but also compelling the coils to enter the field of opposite polarity gradually. This is achieved by giving the pole corners an oblique, or a double conical, or a hyperbolical form, as illus- trated by top views in Figs. 232, 233, and 234, respectively. For the purpose of counteracting the magnetic pull due to the armature thrust in bipolar machines, see 42, the pole- pieces are often mounted eccentrically, leaving a smaller gap- space at the side averted from the field coils than at the side toward the same, Fig. 235, or in case of wrought-iron or steel polepieces, cast-iron pole tips are used at the side toward the exciting coils, and wrought-iron or steel tips at the other, Fig. 236. Both the eccentricity of the pole faces and the cast-iron pole tips, if suitably dimensioned, have the effect of increasing the reluctance of the stronger side of the field in the same propor- tion as the density rises on account of the dissymmetry of the field, thus making the product of density and permeance the same in both halves. In a very instructive paper, entitled "On the Relation of the Air Gap and the Shape of the Poles to the Performance of Dynamo-electric Machinery," Professor Harris J. Ryan 1 has demonstrated the importance of making the polepieces of such shape that saturation at the pole corners cannot occur even at full load; for, the armature ampere turns cannot change the total magnetization established by the field when the pole cor- ners are unsaturated. He further proved by experiment that for a sparkless operation at all loads of a constant current 1 Transactions A . I. E. E., vol. viii. p. 451 (September 22, 1891); Electrical World, vol. xviii. p. 252 (October 3, 1891). 77] GENERAL CONSTRUCTION RULES. 299 generator, it is necessary that the air gap be made of such a depth that the ampere turns required to set up the magnetiza- tion through the armature without current, and for the produc- tion of the maximum E. M. F. of the machine, shall be a little more than the ampere turns of the armature when it furnishes its normal current. As long as the brushes were kept under the pole faces the non-sparking point was wherever the brushes were placed, no matter whether the armature core was satu- rated or not. In order to enable currents to be taken from a machine at various voltages, Rankine Kennedy' has proposed to subdivide the pole faces by deep, wide slots parallel to the armature shaft, Fig. 237, thus providing a number of neutral points on the commutator, at which brushes may be placed without sparking. If, for instance, there are two such grooves in each polepiece, the total voltage of the machine is divided into three equal parts, and by employing an intermediate brush at one of the additional neutral spaces, two circuits can be sup- plied by the machine, one each between the intermediate brush and one of the main brushes, one having two-thirds and the other one-third of the total voltage furnished by the dynamo. 77. Base. The base is the only part of the machine where weight is not only not objectionable but very beneficial, and it should there- fore be a heavy iron casting, especially as the extra cost of plain cast iron is insignificant as compared with the entire cost of the machine. A heavy base brings the centre of gravity low, and consequently gives great stability and strength to the whole machine. Besides this mechanical argument in favor of a massive cast- ing, there is a magnetical reason which applies to all types in which the base constitutes a part of the magnetic circuit, as is the case in the inverted horseshoe type, Fig. 188, in the -ver- tical single-magnet type, Fig. 193, in the inclined and vertical double-magnet types, Figs. 198 and 199, respectively, in the iron-clad types, Figs. 203, 205, 206, 207, 218, and 219, respec- tively, and in the vertical quadruple magnet machine, Fig. 224, 1 English Patent No. 1640, issued April 4, 1892. 300 DYNAMO-ELECTRIC MACHINES. [78 In these and similar types a heavy base of consequent high permeance reduces the reluctance of the entire magnetic cir- cuit, and effects a saving in exciting power which usually is sufficient to repay the extra expense involved, and often even reduces the total cost of the machine. If the base forms a part of the magnetic circuit of the ma- chine, constituting either the yoke or one of the polepieces, its least cross-section perpendicular to the flow of the mag- netic lines should be dimensioned by the rules given for cast- iron magnets that is, it should be at least i| to 2 times the area of the magnet cores, if the latter are of wrought iron or cast steel, and at least of equal area if they are of the same material as the base, /. e., of cast iron. 78. Zinc Blocks. In some forms of machines, such as the upright horseshoe type, Fig. 187, the horizontal single-magnet types, Figs. 191 and 192, the consequent pole, horizontal double magnet type, Fig- 197, the tangential multipolar type, Fig. 210, etc., the magnet frame rests upon two polepieces of opposite polarity, and if these were joined by the iron base, the latter would con- stitute a stray path of very much lower reluctance than the useful path through air gaps and armature, and the lines of force emanating from these two polepieces would thus be shunted away from the armature, instead of forming a mag- netic field for the conductors. In order to prevent such a short-circuiting of the magnetic lines it is necessary either to use material different from iron for the base, or to interpose blocks of a non-magnetic substance between the polepieces and the bed-plate. The former method can be applied to small machines only, and in this case the magnet frame is mounted upon a base of either wood or brass. For large ma- chines a wooden base would be too weak and too light, and a brass one too expensive, and resort has to be taken to the second method of interposing a non-magnetic block, zinc being most usually employed. These zinc blocks must be of the necessary strength, not only to carry the weight of the frame, but also to withstand the tremor of the machine, and must be made high enough to introduce a sufficient amount of reluc- tance into the path of leakage through the base. The reluctance 78] GENERAL CONSTRUCTION RULES. 301 required in that path must be at least four times, and preferably should be up to ten or twelve times that of the air gaps; that is, its relative permeance calculated from formula (161), 62, according to the size of the machine, should range between and J^ of the relative permeance of the air gaps, as found from formula (167) or (168), 64, the amount of leakage through the iron base being thereby limited to 25 per cent, of the useful flux in small dynamos, and to 8 per cent, in the largest machines. This condition is fulfilled if the height of the zinc blocks, according to the kind and the size of the machine, is from three to fifteen times greater than the radial length of the gap-space. The following Tables, LXX., LXXL, and LXXII., give the value of this ratio, the consequent height of the zinc blocks, and the corresponding approximate leakage through the base for high-speed dynamos with smooth-core drum armatures, for high-speed dynamos with smooth-core ring armatures, and for low-speed machines with toothed and perforated armatures, respectively: TABLE LXX. HEIGHT OF ZINC BLOCKS FOR HIGH-SPEED DYNAMOS WITH SMOOTH-CORE DRUM ARMATURES. CAPACITY J* 1> ai ^ || bi Is -3 |bo ^^ 2 > o* .-M.2 MG-2 '5 '-5 5 c if! 1 Clearanci Pable LXi: al Length ap-Space. Inch. M*. - - = gj .2"5| r | S^ccT OS 35 .5 S i. M '! =' t; s - l| ^'- 2 ^I'jj"* KILOWATTS. P = 3 <3 o ^r S *0 sj 1 - 5 a a^_ 0^06 ~N~ -"il^ 1 _ o v - / *l OS o S^ " O _1 o 1 2 7" - 8 .25" .25 .03" .OS .045" .045 .325" .325 8 9 3 15X 14 3 9* .275 .04 .06 .375 9i 8| 14 5 11 .3 .04 .' 6 .4 10 4 12 10 14 .325 .05 .075 .45 11 5 12 15 15 .325 .05 .075 .45 11 r> 12 20 16 .35 .06 .09 5 12 6 10 25 18 .35 .06 .09 .5 12 6 10 30 20 .375 .07 .13 .575 12 7 10 50 24 .4 .07 .13 .6 13i 8 9 75 28 .425 .07 .155 .65 14i 9i 9 100 32 .45 .07 .155 .675 15i io| 8 150 36 .475 .07 .18 .725 16 HI 8 TABLE LXXII. HEIGHT OF ZINC BLOCKS FOR LOW-SPEED DYNAMOS WITH TOOTHED AND PERFORATED ARMATURE. ,-, M CAPACITY IN KILOWATTS. Diameter of Armature Core (from Table XII. Height of Winding Space (from Table XVIII Radial Clearance (from Table LXI. Maximum Radial Length of Gap-Spa< Inch. Ratio of Height of Zinc Block to Maximum LengI of Gap-Space. Height of Zinc Blocks. Inches. Approximate Leakage through Base in p. c. of Useful Flux. 2 12" H" .. 1-3-4-" 3 31" 15^ 3 15 H 5 lyV 3 4 15 5 17 if A IT^ 3| 5 12 10 21 1* A Iff 3f 6 12 15 23 if 5 Iff 4 8f 10 20 25 1 111 41 71 10 25 27 if Iff 4-| 8 10 30 30 HI * ill 44 8| 8 50 36 1* i 2 4| 91 8 From the comparison of the above Tables LXX., LXXI. and LXXII., it follows that the height of the zinc blocks increases in a nearly direct proportion with the diameter of the armature 79] GENERAL CONSTRUCTION RULES. 33 core, and that, for the same armature diameter, a smooth- drum machine requires a higher, and a toothed or perforated armature machine a lower zinc than a smooth-ring dynamo. By compiling the results of Tables LXX., LXXL, and LXXIL, the following Table, LXXIII., is obtained, from which it can be seen that the heights of zinc blocks for smooth-ring machines are from 18 to 30 per cent, less than for smooth-drum dyna- mos, and those for machines with toothed and perforated armatures are from n to 20 per cent, less than for smooth-ring armature dynamos: TABLE LXXIII. COMPARISON OF ZINC BLOCKS FOR DYNAMOS WITH VARIOUS KINDS OF ARMATURE. HEIGHT OF ZIKC BLOCKS. DIAMETER OF Smooth Armature. Toothed ARMATURE CORE. or Perforated | Drum. Ring. Armature. Inches. Inches. Inches. Inches. 3 H 4 2 6 2f '2 'if 8 4 3 24 10 5 34 3 12 5| 44 34 15 6* 5 4 18 74 6 5 21 Si 7 6 24 9i 8 7 27 11 9 8 30 . . 10 8i 36 114 94 79. Pedestals and Bearings. In the design of the base, especially when the portion of *he field frame above the armature centre cannot be lifted off, care should be taken that the armature can easily be withdrawn longitudinally by removing one of the bearing pedestals, which, therefore, should be a separate casting. In machines where the lowest point of the armature periphery is at a con- siderable height above the base, as for instance in dynamos of 304 DYNAMO-ELECTRIC MACHINES. [79 the overtypes, Figs. 188, 191, 198, and 206, respectively, fur- ther of the vertical double types, Figs. 197, 202, 207, 219, and 224, respectively, and of the radial and tangential outerpole types, Figs. 208 and 210, respectively, it is preferable that the pedestals should be made of two parts, the upper part, which should have a depth from the shaft centre a little in excess of the radius of the finished armature, being removable, while the lower portion, which may be cast in one with the base, will form a convenient resting place for the armature in removal. In most cases this problem of making high pedestals of two parts can practically be solved by boring out the pedestal seats together with the polepieces, thus providing a cylindrical seat for the pillow blocks, as shown in Fig. 238. This design is particularly advantageous also for machines in which the base forms one of the polepieces, as for example, the forms shown in Figs. 193, 199 and 219, as in this case, outside of the finish- ing of the core seats, this boring to a uniform radius is the only tooling necessary for the base. If the field frame is symmetrical with reference to the hori- zontal plane through the armature centre, the frame of the machine is usually made in halves, and the armature, in case of repair, can be removed by lifting it from its bed without disturbing the bearing pedestals. The bearing boxes must for this purpose be made divided so that all parts of the machine above the shaft centre are removable. This design affords the further advantage that the bearing caps can be taken off at any time and the bearings inspected, and it has for this reason become a general practice in dynamo design to employ split bearings, even for types in which the armature cannot be lifted. It is, further, of great importance that the bearing should not only be exactly concentric, but that they also should be accurately in line with each other; for large machines it is therefore advisable to effect automatic alignment by providing the bearings with spherical seats. This can be attained either by giving the enlarged central portion of the shell a spherical shape, Fig. 239, or in providing the bottom part of the box with a spherical extension fitting into a spherical recess in the pedestal, Fig. 240. In order to prevent heating of the bearings, the shells in modern dynamos are usually furnished with some automatic 80] GENERAL CONSTRUCTION RULES. 35 oiling device, the most common form of which, shown in Fig. 241, consists of a brass ring or chain dipping into the oil chamber of the box and resting upon and turning with the shaft, thereby causing a continuous supply of oil at the top of the shaft. A further improvement of this self-oiling arrange- ment, patented in 1888 by the Edison General Electric Com- pany, is illustrated in Fig. 242. In this the interior of the FIG. 238 FIG. 239 FIG. 240 ; A C SECTION A-B I SECTION C-D FIG. 242 Figs. 238 to 242. Pedestals and Bearings. shell is provided with spiral grooves filled with soft metal and forming channels for conveying oil from each end of the bear- ing to a circumferential groove which surrounds the shaft at the centre of the shell, and which communicates with the oil chamber beneath the bearing. These grooves not only effect a steady supply, but a continuous circulation of oil, the latter being lifted from the reservoir into the shell by the oiling rings, thence forced by the spiral channels into the central groove, from where it flows back into the oil chamber. 80. Joints in Field Magnet Frame. a. Joints in Frames of One Material. Magnet frames consisting of but one material may either be formed of one single piece or may be composed of several parts. If the frame is of cast iron or cast steel, in small 3o6 DYNAMO-ELECTRIC MACHINES. [80 dynamos usually the former is the case, /. e., the whole frame is cast in one, while in large machines it generally consists of two castings; if, however, wrought iron is used, it is, as a rule, much more convenient to forge each part separately and to build up the frame by butt-jointing the parts. In so joint- ing a magnet frame, it is of the utmost importance to accu- rately adjust and finish the surfaces to be united, so as to make the joint as perfect as possible, for every poorly fitted joint, by reduction of the sectional area at that point, introduces a considerable reluctance in the magnetic circuit. If, however, the contact between the two surfaces is as good as planing and scraping can make it, a practically perfect joint is obtained, and the additional reluctance, which then only depends upon the degree of magnetization, is entirely inappreciable for such high magnetic densities as are employed in modern dynamos. Experiments have shown that at low densities the additional magnetomotive force required to overcome the reluctance of a joint is very much greater, comparatively, than at high in- ductions, which is undoubtedly due to the pressure created by the magnetic attraction of the two surfaces across the joint, this pressure being proportional to the square of the density. The following Table LXXIV. shows the influence of the den- sity of magnetization upon the effect of a well-fitted joint in a wrought iron magnet frame, the induction in the iron ranging from 10,000 to 120,000 lines per square inch, and indicates that the reluctance of the joint becomes the less significant the nearer saturation of the iron is approached. At a magnetic density of ($>" m = 10,000 lines of force per square inch, each joint in the circuit is equivalent to an air space of .0016 inch, or has a reluctance equal to that of an additional length of 3 inches of wrought iron; at (B" m 100,000 lines per square inch, the thickness of an equivalent air space is only .00065 inch, which corresponds to the reluctance of .22 inch of wrought iron at that density; and at or above (B" m = 120,000, finally, a good joint is found to have no effect whatever upon the reluctance of the circuit. b. Joints in Combination Frames. For magnet frames consisting of two or three different mate- rials the same rule as for frames of one material holds good as 80] GENERAL CONSTRUCTION RULES. 37 to the nature of the joint, but since the ordinary butt-jointing would limit the capacity of the joint to that of the inferior magnetic material, it is essential in the case of combination frames to increase the area of contact in the proportion of the relative permeabilities of the" two materials joined. Thus, if wrought and cast iron are butt-jointed, the capacity of the joint is reduced to that of the cast iron, whereby the advantage of the high permeability of the wrought iron is destroyed and the permeance of the circuit is considerably increased; and in order to have the full benefit of the wrought iron, the contact area of the joint must be increased proportionally to the ratio of the permeability of the wrought iron to that of the cast iron at the particular density employed. TABLE LXXIV. INFLUENCE OP MAGNETIC DENSITY UPON THE EFFECT OF JOINTS IN WROUGHT IRON. PRESSURE MAGNETIZING FORCE EQUIVALENT OF JOINT ON JOINT REQUIRED FOR 1 INCH. DIFFER- DENSITY op MAGNET- IZATION. DUK TO MAGNETIC ATTRAC- ENCE DUB TO JOINT, Air Space, Length of Iron, '. TION. V Solid. 3C Jointed. TP 3C = TC X. X oc Lines per sq. in. 72,134,000 uv, Amp. JV 2 Amp. Jv 2 JV-, Amp. .3133X(B" m X IDS. turns. tarns. turns. Inch. Inch. per. sq. in. 10,000 1.4 1.7 6.7 5 .0016 3.0 20.000 5.5 3.2 12.6 9.4 .00155 2.9 30,000 12.5 5 19.1 14.1 .0015 2.8 40,000 22 7 25.2 18.2 .00145 2.6 50,000 35 9.5 31.4 21.9 .0014 2.3 60,000 50 12.7 38.1 25.4 .00135 2.0 70,000 68 18.3 45.7 27.4 .00125 1.5 80,000 89 27.6 55.2 27.6 .0011 1.0 90,000 112 508 76.2 25.4 .0009 0.5 95,000 125 68 91.8 23.8 .0008 .35 100,000 139 90 110 20 .00065 .22 105,000 153 134 150 16 .0005 .12 110,000 168 288 300 12 .00035 .04 112,500 176 391 400 9 .00025 .023 115,000 183 500 506 6 .00016 .012 117,500 192 600 603 3 .00008 .005 120,000 200 700 700 .00000 .000 For a density in wrought iron of 100,000 lines of force per square inch, for example, a magnetomotive force of 90 ampere- turns is required per inch length of the circuit, and the same 3 o8 D YNA MO-ELECTRIC MA CHINES. [80 specific magnetomotive force is capable of setting up about 40,000 lines per square inch in cast iron; the contact area of a joint between wrought iron and cast iron in this case must therefore be increased in the ratio of 100,000 : 40,000, or must be made z\ times the cross-section of the wrought iron in order to reduce the permeability of the joint to that of the wrought iron. In practice this problem of providing a sufficiently large con- tact area between a wrought and a cast iron part of the mag- FIQ. 243 FlQ.,244 Fn.245 FIQ. 246 FlQ. 247 FIG 248 FlQ. 249 FIQ 250 Figs. 243 to 250. Joints in Magnetic Circuits. netic circuit may be solved either by setting the wrought iron into the casfiron, or by extending the surface of the wrought iron part near the joint by means of flanges; or, finally, by in- serting an intermediate wrought-iron plate into the joint. In Figs. 243, 244, 245 and 246 are shown four methods of increasing the area of the joint by means of projecting the wrought-iron core into the cast-iron yoke or polepiece, differing only in the manner of securing a good contact between the parts, the first one employing a set-screw, the second one a wrought-iron nut, and the third one using a conical fit with draw-screw for this purpose, while in the fourth one the threaded projection of the core itself forms the tightening screw. Fig. 247 illustrates a modification of the method shown in Fig. 246, a separate screw- stud being used instead of the threaded extension of the wrought-iron core. In case of rectangular magnet cores the arrangement shown by plan in Fig. 248 effects an excellent 80] GENERAL CONSTRUCTION RULES. 309 joint; in this the cores are inserted into the base from the sides, thus offering three surfaces to form the contact area. The manner of supplying the necessary joint surface by flanged ex- tensions of the wrought-iron core is illustrated in Fig. 249, which shows the method of fastening employed in large multi- polar machines, feather-keys being used to secure exact rela- tive position of the cores. In Fig. 250, finally, a joint is shown in which a wrought-iron contact plate is inserted between the wrought-iron core and the cast-iron yoke or polepiece with the object of increasing the area of the joint and of spreading the lines of force gradually from the smaller area of the wrought iron to the larger of the cast iron. CHAPTER XVI. CALCULATION OF FIELD MAGNET FRAME. 81. Permeability of the Various Kinds of Iron. Ab- solute and Practical Limits of Magnetization. The field magnet of a dynamo has the function of supplying to the interpolar space in which the armature conductors revolve magnetic lines of force in a number sufficient either to cause the generation of the required electromotive force, in case of a generator, or to produce a motion of the desired power, in case of a motor. The cross-sections of the various parts of the field magnet frame, that is, of the iron structure consti- tuting the path or paths, for the flow of these magnetic lines, consequently, must be dimensioned with reference to the num- ber of lines of force to be carried, and to the magnetic con- ductivity of the material used. The number of lines which by a certain exciting power or magnetomotive force can be passed through a portion of a magnetic circuit depends upon the area of the cross-section and on the magnetic conductivity of the material of that part of the circuit. The various magnetic materials, according to their hardness, have a different capability of conducting magnetic lines, the softest material being the best magnetic conductor. The specific magnetic conductance of air being taken as unity, the relative magnetic conductance, or the rela- tive permeance, of the various magnetic materials is indicated by the ratio of the number of lines of force produced in unit cross-section of these materials to the number of lines set up by the same magnetizing force in unit cross-sections of air. This ratio, or coefficient of magnetic induction, is called the magnetic conductivity, or the permeability of the material. The number of lines per square centimetre of sectional area set up by a ceftain magnetizing force in air is conventionally designated by JC, that in iron by (B, and the permeability by 81] CALCULATION OF FIELD MAGNET FRAME. 311 the symbol /t ; between these three quantities, therefore, exists the relation = , or (B = u X 3C. oe (215) Since for air the permeability yu = i, the number of lines of force per square centimetre of air is numerically equal to the magnetizing force in magnetic measure, /". e., in current-turns. Permeability is therefore often also denned as the ratio of the magnetization produced to the magnetizing force producing it. TABLE LXXV. PERMEABILITY OF DIFFERENT KINDS OF IRON AT VAR- IOUS MAGNETIZATIONS. DENSITY OF MAGNETIZATION. PERMEABILITY, it.. Lines per sq. inch (B" Lines per cm*. (B Annealed Wrought Iron. Commercial Wrought Iron. Gray Ca*t Iron. Ordinary Cast Iron. 20,000 3,100 2,600 1.800 850 650 25,000 3,875 2,900 2,000 800 700 30,000 4,650 3,000 2,100 600 770 35,000 5,425 2,950 2,150 400 800 40,000 6,200 2,900 2,130 250 770 45,000 6.975 2,800 2.100 140 730 50,000 7,750 2,650 2,050 110 700 55.000 8.525 2,500 1,980 90 600 60,000 9,300 2.300 1,850 70 500 65.000 10,100 2,100 1,700 50 450 70,000 10,850 1,800 1,550 35 350 75,000 11,650 1,500 1,400 25 250 80.000 12,400 1,200 1,250 20 200 85,000 13,200 1,000 1,100 15 150 90,000 14,000 800 900 12 100 95.000' 14,750 530 680 10 70 100,000 15.500 360 500 9 50 105,000 16,300 260 360 .... .... 110.000 17,400 180 260 .... .... 115,000 17,800 120 190 .... ... 120,000 18,600 80 150 .... .... 125.000 19,400 50 120 .... ... 130,000 20,150 30 100 .... .... 135,000 20.900 20 85 ... 140,000 21,700 15 75 . . . .< While the permeability of air and of all non-magnetic sub- stances is a constant (for air it is i, and for diamagnetic mate- rials slightly less than i) for all stages of magnetization, that of magnetic materials varies with the degree of saturation. 312 DYNAMO-ELECTRIC MACHINES. [81 The more lines a certain cross-section of iron carries, the less permeable is it for additional lines, as is evident from the preceding Table LXXV. containing the average permeabilities of different kinds of iron at various degrees of magnetization. At a certain limit, for every kind of iron, a very material in- crease in the magnetizing forces does not appreciably increase the magnetization induced, and the iron is then saturated with lines of force. This limit of magnetization in annealed wrought iron is reached at a density of about ($>"= 130,000 lines per square inch, or (B = 20,200 lines per square centimetre; in soft steel at (B*= 127,500 lines per square inch, or (B = 19,800 lines per square centimetre; in mitts iron at ($>"= 122,500 lines per square inch, or (B = 19,000 lines per square centimetre; in fast iron with a 6.5 per cent, admixture of alii minum at ($>" = 87,500 lines per square inch, or (B = 13,500 lines per square centimetre, and in ordinary cast iron at (B";= 77,500 lines per square inch, or (B 1 2,000 lines per square centimetre of cross- section. The magnetizations, however, to which these mate- rials are subjected in practical electromagnets are taken far below the actual limits of absolute saturation, since "saturation curves" indicating the variation of the induction (B, with in- creasing magnetizing force, 3C, show that from a certain point, the "knee "of the curve, the magnetization increases much slower than the magnetizing force which causes it. In wrought iron, for instance, an induction of (B = 13,580 requires a mag- netizing force of JC = 25, an induction of (B = 16,000 a magneto- motive force of 3C = 50, and density of (B = 16,500 necessitates an exciting power of JC =100; and an increase of 100 per cent, in the magnetizing force, consequently causes a rise in density of 18^ per cent, at the lower magnetization, while again doubling the magnetomotive force at the higher induction only causes an increase in magnetic density of about 3 per cent. In practice, therefore, the limits of the magnetic densities of the different materials are to be fixed with regard to the reh - tive economy of iron and copper. Taking the practical limit of saturation too low means a small saving of copper at a large expense of iron, while too high a density effects a compara- tively small saving of iron at a large expense of copper! Since copper costs many times more than iron, the densities should be limited rather low, the tendency toward the former extreme 82] CALCULATION OF FIELD MAGNET FRAME. being preferable to that toward the latter. With this point in view, the ''Practical Working Densities " given in the follow- ing Table LXXVI. are recommended for use in dynamo designing, while under the heading of "Practical Limits of Magnetization" the highest densities are tabulated that the author would advise to allow in magnet frames of dynamo- electric machines. For sake of completeness the "Absolute Saturation" of the various materials, as given above, are added in Table LXXVI. : TABLE LXXVI. PRACTICAL WORKING DENSITIES AND LIMITS OF MAG- NETIZATION FOR VARIOUS MATERIALS. MATERIAL. PRACTICAL WORKING DENSITY. PRACTICAL LIMIT OF MAGNETIZATION. ABSOLUTE SATURATION. Lines p. sq. inch. fc"m Lines p. sq. cm. (B m Lines p. sq. inch. Lines p. sq. cm. Lines p. sq. inch. Lines p. sq. cm. Wrought Iron yo,ooo 85.000 80,000 45000 40.000 14.000 13,200 12,400 7,000 6.200 105,000 100,000 95,000 55,000 50,000 16,300 15,500 14,750 8,500 7,750 130,000 1^7,500 12^,500 87,500 77,500 20,200 19.800 19,000 13,500 12000 Cast Steel Mins Iron Cast Iron, containing 6.5% Aluminum Cast Iron, ordinary .. . 82. Sectional Area of Magnet Frame. The magnet frame carries the total flux generated in the machine; according to 81, consequently, the cross section of any portion of it must be X &' (216) S" m = Area of magnet frame, in square inches; #' = Total flux generated in machine, from formula (156), 60; < = Useful flux necessary to produce the required E. M. F., from formula (137), 56; A. = Factor of magnetic leakage, preliminary value from Table LXVIII., 70, final value from for- mula (i57), 61; (B* m = Magnetic density in magnet frame, from Table LXXVI., 81. 314 DYNAMO-ELECTRIC MACHINES. [82 If only one material is used the value found from formula (216) is the uniform cross-section of the whole frame, i. e., of the cores, the yoke, and the polepieces; in case of combina- tion frames, however, the area for each material must be calculated separately: For Wrought iron, S" m = ; .... (217) 90,000 "Cast steel, S ' = J^' ............ < 218 ) ............ < 319 > Cast iron, con- taining 6. 5$ A x of aluminum, S" m =' ~ Ordinary cast , * In combining the averages for the useful flux, taken from Table LXIV. , 59, for the practical conductor velocities given in Tables X., XI. and XII., respectively, with the leakage coefficients compiled in Table LXVIII., 70, the average total flux, 0, for dynamos of various kinds and sizes is obtained, and, then by applying formulae (217) to (221), the sectional areas of the field frame for various kinds and sizes of machines can be found. In this manner the following Tables LXXVIL, LXXVIIL, and LXXIX., have been prepared, which give the cross sections of field magnet frames of different materials for high-speed drum machines, high-speed ring dynamos, and low speed ring machines, respectively. The figures given for the areas directly apply to single circuit bipolar dynamos only; for double circuit bipolar, and for multipolar machines they represent the total cross-section of all the magnetic circuits in parallel, or for frames of only one material, the total area of all the cores of same free polarity, the cross-sections of the various portions of the field magnet frame are therefore obtained in dividing these figures by the number of magnetic circuits, /. e., by the number of pairs of magnet poles: 82] CALCULATION OF FIELD MAGNET FRAME. 315 TABLE LXXVII. SECTIONAL AREA OP FIELD MAGNET FRAME FOR HIGH-SPEED DRUM DYNAMOS. g AREA OF FIELD MAGNET FRAME. i "^ Average ' .t? 5 >?1 Useful Flux. Leak'ge total Cast Cast H s > Table Coeffi- flux, Wr'ght Cast Mitis Iron. Iron, Z,'~ c o|5 t. LXIV. cient. f. Iron, Steel, Iron, 6.5* Al. ordiii'y O K/l u-2 & Lines of Table Lines of Sm Sm Sm Sm Sm PC "2^^" force. LXVIII force. 550,000 1.60 4,080,000 45.5 48 51 91 102 10 50 4.000.000 1.55 6,200,000 69 73 77.5 138 155 15 50 5,700,000 1.50 8,550,000 95 101 107 190 214 20 50 7.200,000 1.45 10,400.000 115.5 122 130 231- 260 25 50 8,500.000 1.40 11,900,000 132 140 149 264 298 30 50 9,900.000 1.40 13,850.000 154 163 173 508 346 50 50 15,500,000 1.35 20.900,000 232 246 261 464 522 75 50 22,000,000 1.35 29,700.000 aso 350 371 660 742 100 50 28.000,000 1.30 36,400.000 405 430 455 810 910 150 50 39,500.000 1.30 51,400,000 572 605 643 1,144 1,286 200 50 50.000,000 1.25 62,500.000 695 735 782 1,390 1,564 300 50 70000,000 1.20 84,000,000 933 990 1,050 1,806 2,100 TABLE LXXVIII. SECTIONAL AREA OF FIELD MAGNET FRAME FOR HIGH-SPEED RING DYNAMOS. >, AREA OF FIELD MAGNET FRAME. " 'O G r- Average Av'age Average Capacity in Kilowatts iductor Vel (Table XI 't. per soro Useful Flux. (Table LX1V.) Lines of force. Leak'ge Coeffi- cient. Table LXVIII Total Flux, V. Lines of force. Wr'ght Iron, Sm *' Cast Steel, Sin *> Mitis Iron, Sm V Cast Iron, 6.5* A 1. Sm */ Cact Iron, ordin'y Sm */ * ^ 90,000 85,000 80.000 45.000 40,000 sq. in. sq. in. sq in. sq. in. sq. in. .1 50 100,000 1.80 180.000 2 2.1 2.2 4 45 .25 55 182,000 1.70 310.000 3.5 3.7 3.9 7 ' 7.8 .5 60 292,000 1.60 467,000 5.2 5.5 5.8 10.4 11.6 1. 65 462.000 1.55 715,000 8 8.4 8.9 16 17.8 2.5 70 930,000 1.50 1.400,000 15.5 16.5 17.5 31 35 6 75 1.500,000 1.45 2,180,000 24.2 25.6 27.3 48.4 54.5 10 80 2,500,000 1.40 3.500.000 39 41.2 43.8 78 87.5 25 80 5.320.000 1.35 7,200.000 80 85 90 160 1W 50 85 9,120,000 1.30 11,900,000 132 140 149 264 298 75 85 13,000,000 1.25 16,250,000 180 191 203 360 406 100 85 16,500,000 1.22 20,100,000 224 236 251 448 502 200 88 28,400,000 1.20 34,000,000 378 400 425 756 850 300 90 39,000,000 1.18 46,000,000 512 542 575 1,024 1,150 400 92 47,800,000 1.18 56,500,000 628 665 707 1,256 1,415 600 95 62,000,000 1.17 72,500,000 806 855 905 1,612 1,810 800 95 74,200,000 1.17 87,000,000 967 1,025 1,085 1,0.35 2,170 1,000 95 84,200.000 1.16 97,700.000 1,085 1,150 1,240 2,170 2,480 1,500 100 97,500,000 1.16 113.000,000 1,255 1,330 1.410 2,510 2,820 2,000 100 110,000,000 1.15 126,500,000 ' 1,400 1,490 1,580 2,800 3,160 316 DYNAMO-ELECTRIC MACHINES. [8 TABLE LXXIX. SECTIONAL AREA OF FIELD MAGNET FRAME FOR LOW- SPEED RING DYNAMOS. >, AREA OF FIELD MAGNET FRAME. f "O . o^e ~ sIBs 'Sal X " o,' S l 5-' 3 5 2-S- Average Useful Flux. (Table LXIV.) Av'asje Leak'ge Coeffi- cient. Table Average Total Flux. *'. Lines of Wr'ght Iron, Sm Cast Steel, Sm Mitis Iron, Sm Cast Iron, 6.5* Al. Sm Cast Iron, ordin'y Sm w ^ gb-j LXVIH force. 4>' *' *' *' o 90,000 85,000 80.000 45,000 40,000 sq. in. sq. in. pq. HI. pq in. pq. in. 2.5 25 2,600,000 1.50 3,900,000 43.3 46 48.7 86.6 97.5 5 26 4,420,000 1.45 6,400,000 71.2 75.3 80 142.4 160 10 28 7,150.000 1.40 10,000,000 111 1175 125 222 850 25 30 14,200.000 1.35 19,200,000 213.5 226 240 417 480 50 32 24,200.000 1.30 31,500,000 350 360 394 700 788 75 33 33,500,000 1.25 42.000,000 467 495 525 934 1,050 100 35 40,000,000 1.22 48,800,000 543 575 610 1,086 1.220 200 40 62,500,000 1.20 75,000.000 ass 883 938 1 .666 1.875 300 42 83.300,000 1.18 9S.500.000 1,095 1,160 1,230 2.190 2,460 400 44 100,000,000 1.18 118.000,000 1.310 1,390 1,475 2,620 2.950 600 45 131.000,000 1.17 153.500,000 1.725 1,810 1.940 3,450 3,880 800 45 157,0(10,000 1.17 184,000,000 2,050 2,165 2,300 4,100 4,600 1,000 45 178,000.000 1.16 206,500,000 2.300 2,430 2,580 4.600 5,160 1,500 45 217,000,000 1.16 252.000,000 2,SOO 2,970 3,150 5,600 6.300 2,000 45 245,000,000 1.15 282,000,000 3,140 3,320 3,525 6,280 7,050 For cases of practical design, in which the fundamental con- ditions materially differ from those forming the base for the above tables, the areas obtained by formula (216) may also widely vary from the figures given, but, by proper considera- tion, these tables will answer even for such a case, and will be found useful for comparing the results of calculations. 83. Dimensioning of Magnet Cores. The sectional area of the magnet cores being found by means of the formulae and tables given in 82, their length and their relative position must be determined. a. Length of Magnet Cores. In the majority of types the length of the magnet cores has a more or less fixed relation to the dimensions of the armature, and definite rules can only be laid down for such cases where the length of the magnets is not already limited by the selec- tion of the type. Two points have to be considered in dimensioning the length of the magnets. The longer the cores are made, the less height will be taken up by the magnet winding; the mean length of a convolution of the magnet wire, and, consequently, the total length of wire required'for a certain magnetomotive force will, therefore, be smaller the greater the length of the 83] CALCULATION OF FIELD MAGNET FRAME. 3*7 core. On the other hand, the shorter the cores are chosen the shorter will be the magnetic circuit of the machine, and, in consequence, the less magnetomotive force will be required to set up the necessary magnetic flux. Of these two considerations economy of copper at the ex- pense of additional iron on the one hand, and saving in mag- netomotive force and in weight of iron on the other the latter predominates over the former, from which fact follows the general rule to make the cores as short as is possible without increasing the height of the winding space to an undue amount. In order to enable the proper carrying out of this rule, the author has compiled the following Table LXXX. , which gives practical values of the height of the winding space for magnets of various types, shapes and sizes: TABLE LXXX. HEIGHT OF WINDING SPACE FOR DYNAMO MAGNETS. BIPOLAR TYPES. Hlui/riPoi.AR TYPES. SIZE OF CORE. Cylindrical Rictaii;,'ular I'ylindricul Kei tanjjular Cores. or Oval Cores. Cores. or Oval Cores. ^ 5 s E 5-3 . C OJ o ep 8* 2 jj g a' 6 - = S3 Diameter Area -'5- 4J Q. bjCy 1 d-c'a)*- C. - W 3 of of 3 CC Offi -= 00 i- ... ?^ao I 33 c/. "= ~ 11 Circular Cross-Section. Rectangular or Oval Section. -3 -5 ~ i 5 5 l.i| a ^ c Iff 'S o c K c |B| s _o i "c 3 .:: ^ O * S3 5 Ins. cm. Sq inp. Sq. cm. III!. Inch. Inch. Incli. 1 2 5 g 4 9 ,/ .50 o/ 75 2 5.1 8.1 20.4 o .375 .... .'so' 1*1 .625 Hi .75 3 7.6 7.1 45.4 1 .33 i4 .42 1^1 .58 2 .67 4 10.2 12.6 81.7 ]1X .31 s .38 2 .50 2*^ .625 6 15.3 28.3 184 l*s .25 2 .33 2*4 .375 294 .46 8 20.3 50.3 324 1% .22 2J^ .31 2V| .31 3 .375 10 25.5 78.5 511 1^1 .19 2-M .275 2-M .28 3*4 -.33 12 30.5 113.1 731 2 .17 3 .25 8 .25 3*3 .29 15 38.1 1T6.7 1140 2*6 .14 3M .22 3*4 .22 3% .25 18 45.7 254.5 1640 2*4 .125 3*o .20 3*2 .205 30 762 707 45 KjV>f MO-ELECTRIC MA CHINES. [83 In bipolar machines, such as the various horseshoe types, in which the length of the magnet cores is not limited by the form of the field magnet frame, the radial height of the magnet winding in case of cylindrical magnets varies from one-half to one-twelfth the core diameter, according to the size of the magnets, and in case of rectangular or oval magnets, is made from .5 to .15 of the diameter of the equivalent circular cross- section. For multipolar types, in which the length of the mag- nets is of a comparatively much greater influence upon size and weight of the machine, it is customary to set the limit of the winding height considerably higher, in order to reduce the length necessary for the magnet winding. For cylindrical mag- nets to be used in multipolar machines, therefore, the prac- tical limit of winding height ranges from .75 to .14 of the core diameter, and for rectangular or oval magnets, from .75 to .195 of the diameter of the equivalent circular area, according to the size. In case of emergency the figures given for rectangular cores may be used in calculating circular magnets, or those given for multipolar types may be employed for bipolar machines. In order to keep the winding heights within the limits given in Table LXXX. the lengths of cylindrical magnets have to be made from 3 to i times the core diameter for bipolar types, and from i to the core diameter for multipolar types; those of rec- tangular magnets from i| to the equivalent diameter for bipolar types, and from i^ to f the equivalent diameter for multipolar types; and the lengths of oval magnets, finally, from i to the diameter of the equivalent circular area for bipolar types, and from i J to -| the equivalent diameter for multipolar types. In the following Tables LXXXI., LXXXIL, LXXXIIL, and LXXXIV., the dimensions of cylindrical magnet cores for bipolar types, of cylindrical magnet cores for multipolar types, of rectangular magnet cores, and of oval magnet cores, respec- tively, have been calculated. In the former two of these tables the lengths and corresponding ratios are given for cast- iron as well as for wrought-iron and cast-steel cores ; in the latter two for wrought iron and cast steel only. From Tables LXXXI. and LXXXII. it follows that cast-iron cores are made from 20 to 10 per cent, longer, according to the size, than wrought-iron 83] CALCULATION Of FIELD MAGNET FRAME. 31$ or cast-steel ones of the same diameter, the lengths of cast-iron cores of rectangular or oval cross-section can therefore be easily deduced from the figures given in Tables LXXXIII. and LXXXIV. TABLE LXXXI. DIMENSIONS OP CYLINDRICAL MAGNET CORES FOR BIPOLAR TYPES. DIMENSIONS OP MAGNET CORES, IN INCHES. TOTAL FLUX, Wrought Iron and Cast Steel. Cast Iron. IN WEBERS. Dinm. Length. Ratio Diam. Length. Ratio 70,000 150,000 1 11 3 8| 3.0 2.5 11 41 3.0 2.56 275,000 2 44- 2.25 3 7 2.33 425,000 21 5" 2.0 3| 8* 2.20 600,000 3 5f 1.92 41 91 2.11 850,000 31 61 1.86 5* 10f 2.05 1,100,000 4 71 1.87 6 12 2.0 1,700,000 5 9 1.80 71 14J 1.9 2,500,000 6 101 1.75 9 161 1.83 3,300.000 7 12 1.72 10.V 18 1.71 4,500,000 8 131 1.70 12 20 1.67 5,500,000 9 15 1.67 131 22 1.63 7,000,000 10 16 1.60 15 24 l.(50 8,500,000 11 17 1.55 161 251 1.55 10,000,000 12 18 1.50 18 27 1.50 15,000,000 15 22 1.46 221 32 1.42 22,500,000 18 25 1.39 27 37 1.37 30,000,000 21 28 1.33 311 41 1.30 40,000,000 24 31 1.29 36 45 1.25 50,000,000 27 34 1.26 .... .... 60,000,000 30 36 1.20 .... .... .... 75,000,000 33 38 1.15 .... .... .... 90,000,000 36 40 1.11 b. Relative Position of Magnet Cores. The majority of types having two or more magnets, the rela- tive position of the magnet cores is next to be considered. In a great number of forms, having the magnets arranged symmet- rically with reference to the armature circumference, the exact relative position of the magnet cores is given by the shape of the field magnet frame; in other types, however, having parallel 320 DYNAMO-ELECTRIC MACHINES. [83 magnsts on the same side of the armature, diametrically or axially, the shape of the frame does not fix their relative position, and the distance between them is to be properly determined. This is done by limiting the magnetic leakage across the cores to a certain amount, according to the size of the machine, namely, from about 33 per cent, of the useful flux in small machines, to 8 per cent, in large dynamos. The relative amount of the leakage across the magnet cores is determined by the ratio of the permeance between the cores to the permeance of the useful path, and the percentage of the core leakage is kept within the limits given above, if the average permeance of the space between the magnet cores does not exceed one-third of the permeance of the gap-space in small machines, and one-twelfth of the gap permeance in large dynamos, or if the reluctance across the core is at least three to twelve times, respectively, that of the gaps. TABLE LXXXII. DIMENSIONS OF CYLINDRICAL MAGNET CORES FOR MULTIPOLAR TYPES. DIMENSIONS OP MAGNET CORES, IN INCHES. TOTAL FLUX PER Wrought Iron and Cast Steel. Cast Iron. MAGNETIC CIRCUIT, IN MAXWELLS. Diam. <4i Length. /. Ratio. An' <4> Diam. d m Length. /. Ratio. tm'-dm 275,000 2 2 1.00 3 31 1.17 600,000 3 Sf .92 4* 4* 1.00 1.100,000 4 i| .875 6 5* .92 1,700,000 5 4 .80 7i 8| .90 2.500,000 6 4* .75 9 8 .89 4,500.000 8 6 .75 12 101 .875 7,000.000 10 7* .75 15 13 .87 10,000,000 12 9 .75 18 15 .83 15.000.000 15 11 .73 221 18 .80 22,500,000 18 13 .72 27 20 .74 30,000,000 21 141 .69 311 22 .70 40,000,000 24 16 .67 36 24 .67 50,000,000 27 17 .63 .... .... 60,000,000 30 18 .60 .... .... 75,000,000 33 19 .58 .... .... .... 90,000,000 36 20 .56 83] CALCULATION OF FIELD MAGNET FRAME. 321 TABLE LXXXIII. DIMENSIONS OF RECTANGULAR MAGNET CORES. (WROUGHT IRON AND CAST STEEL.) CROSS-SECTION. LENGTH. TOTAL FLUX PER o> XI Diam. Bipolar Types. Multipolar Types. MAGNETIC CIRCUIT, a m 3 A s J3 '- 3 "3 o of Equiv. Circular MAXWELLS. a ca '"' ~ ** & Area Length Ratio Length Ratio 0" CO * An ': PERI-ORATED ARMATURE. a Dram. Ring- Diameter of Arm Inches. Radial Length of Gap Space. Least Distance between Cores. Ratio of Distance Apart to Length of liap. Approx. Leakage between Cores p. c. of Useful Flux. Radial Length of Gap Space. Least Distance between Cores. Ratio of Di.tance Apart to Length of Gap. Approx. Leakage between Cores p. c. of Useful Flux. Max. Radial Length of Gap Space. Least Distance between Cores. Ratio of Distance Apart Max. Length of Gap. Approx. Leakage between Cores p. c. of Useful Flux. a c ^ _a g ,.. 2 5.8 33* 3 6 oa^ 6 H 4 4 4% 3.5 3.8 4.0 13 12 11 15 34 8^ 11.3 14 15 r 14.9 11 "'' ' 4.2 10 18 13 i(T 123 12 IA 8}4 16.5 10 1/^2 Si 4.3 10 21 56 12 13.5 10 9J< 16.9 94 u2 THs 4.6 $* 25 IS 14 15 9 & 11 17.6 9 l n2 4.9 9 30 1 16 16 8 H 13 18.9 $4 1% 10 5.3 8U 40 I 18 16 8 M 15 20 8 2 12 6 8 In case of inclined cylindrical magnets the figures given in Table LXXXV. for the least distances apart are to be consid- ered as the mean least distances, taken across the magnets midway between their ends. (Compare formula 180, 65.) 324 DYNAMO-ELECTRIC MACHINES. [83 In dynamos with rectangular and oval cores the leakage across, for the same distance apart, is greater than in case of circular cores of equal sectional area, increasing in proportion to the ratio of the width of the cores to their breadth. For rectangular and oval cores, therefore, the distance apart is to be made greater than for round cores in order to limit the leakage between them to the same amount; and the distance must be the greater the wider the cores are in proportion to their thickness. The following Table LXXXVI. gives the minimum, average and maximum values of the ratio of the dis- tance across rectangular and oval cores of various shapes of cross-sections to the distance which, between round cores of equal sectional area, effects approximately the same leakage, in small, in medium-sized, and in large dynamos, respectively: TABLE LXXXVI. DISTANCE BETWEKN RSCTANGULAU AND OVAL MAGNET CORES. RATIO OP THICKNESS Distance between Rectangular and Oval Magnet Cores, as compared with that between Round Cores of Equal Area, causing approximately the same leakage across. OP CORES. Minimum. Maximum. (Small Machines.) Average. (Large Machines.) 1 1 1.0 1.0 1.0 3 4 1.05 1.07 1.1 2 3 1.1 1.15 1.2 1 2 1.15 1.22 1.3 1 3 1.2 1.3 1.4 1 4 1.25 1.37 1.5 1 5 1.3 1.45 1.6 1 6 1.35 1.55 1.75 1 7 1.4 1.65 1.9 1 8 1.5 1.75 2.05 1 9 1.6 1.9 2.25 1 10 1.7 2.1 2.5 In order to determine the proper distance apart of rectan- gular and oval magnet cores, the corresponding distance be- tween round cores of equal cross-section is taken from Table LXXXIIL, in multiplying the radial length of the gap-space by the ratio of distance apart to length of gap for the particu- lar size of armature. The distance thus obtained is then mul- tiplied by the respective figure found for the shape in question from Table LXXXVI. 85] CALCULATION OF FIELD MAGNET FRAME. 3 2 5 81. Dimensioning of Yokes. In bipolar types the dimensions of the magnet cores being given by Tables LXXXL, LXXXIII. or LXXXIV., 83, and their least distance apart by Table LXXX. or LXXXVL, 83, thus fixing the length of the yoke, and the sectional area of the yokes being found from formula (216), 82 the dimen- sioning of the yoke consists in arranging its cross-section with reference to the shape of the section of the cores, and, for the case that its material is different from that of the cores, in providing a sufficient contact area, conforming to the rules given in 80. In multipolar types the total cross-section found for the frame from formula (216), 82, is to be divided by the total number of magnetic circuits in the machine and multiplied by the number of circuits passing through any part of the yoke in order to obtain the sectional area required for that part of the yoke; otherwise the above rules also govern the dimen- sioning of the yokes for multipolar machines. 85. Dimensioning of Polepieces. In dimensioning the polepieces, three cases have to be con- sidered: (i) the path of the lines of force leaving the pole- pieces has the same direction as their path through the magnets (Fig. 251); (2) the path of the lines leaving the pole- FlQ. 251 FIQ. 252 FiQ. 253 FiQ. 254 FIG. 255 Figs. 251 to 255. Various Kinds of Polepieces. pieces makes a right angle to that through the cores (Fig. 2*5 2); and (3) the path of the lines leaving the polepieces is parallel but of opposite direction to that through the cores, making two turns at right angles in the polepieces (Fig. 253). In the first case, Fig. 251, which occurs in dynamos of the iron-clad, the radial and the axial multipolar types, the shape 326 DYNAMO-ELECTRIC MACHINES. [85 of the cross-section is fixed by the form of the magnet core at one end and by the axial length or the radial width of the armature, respectively, and the percentage of polar arc at the other, while the height, in the direction of the lines of force, is to be made as small as possible, in order not to increase the total length of the magnetic circuit more than necessary. TABLE LXXXVII. DIMENSIONS OF POLEPIECES FOR BIPOLAR HORSE- SHOE TYPE DYNAMOS. DRUM ARMATURE. RING ARMATURE. to 1 B Dimensions of Polepiece. CD C Dimensions of Polepiece. o H o ^ O a Thick- S 8 IH 3 Hs 3 3^ ness in E 9 . Area in Centre H ^ * D . ^ K - & tag C'eijtre. "^ Q. 5 * Square Inches. to 5 ".r^ ~ - o j 5 Inches. i*.p| 2 - S g o s o o ._ a * -111 Si c * o o " 5 4 > 5 2g 2 a^ s tj) Si"* 5 'Slq 2 * 2 i S Wrought Cast 5 *> .5* 3 *s S^5 ^ S 33 "S Iron. Iron. o P 3 a ^ ^ etc. In this manner the values of at & and at m are obtained, the latter by one single multiplication if the field frame is all of the same .material, or by adding several products if various portions of the magnet frame are made of different materials. The compensating ampere-turns at r , finally, need -not be computed at all, it being sufficiently accurate for the purpose on hand to increase the sum of the gap, armature, and frame ampere turns thus far obtained by 75 or 20 per cent. 90. Ampere Turns for Air Gaps. The magnetizing force required to produce a magnetic den- sity of 3C'' lines of force per square inch in the air spaces, ac- cording to 88, is: at = X 3C" X ^ = .3133 X X" X /' (228) 4 ft 2 -54 , where 3C" = field density, in lines of force per square inch ; from formula (142), 57, for smooth armature # dynamos, and from -^ for machines with toothed ^ g or perforated armatures, the area of the gap- space, S g , to be taken, respectively, from the numerators of equations (174), (175), or (176), p. 230; and 34 DYNAMO-ELECTRIC MACHINES. [91 l" e = length of magnetic circuit in air gaps, in inches; the magnetic length of the gaps is obtained by multiplying twice the distance between arma- ture core surface and polepieces by the factor of field-deflection; see Table LXVI., p. 225, for smooth armatures, and Table LXVII., p. 230, for toothed and perforated armatures, respectively. If the field density is given in lines of force per square cen- timetre, and the length of the circuit in centimetres, the mag- netizing force in ampere-turns is obtained from at e = -^ X OC X l g = .8 X 3C X l e . . . .(229) 91. Ampere-Turns for Armature Core. For the magnetizing force needed to overcome the reluc- tance of the armature core we find, according to formula (226): at & = m\ x l\ , (230) where m" & = average specific magnetizing force, in ampere- turns per inch length, formulae (231) to (235); /" a = mean length of magnetic circuit in armature core in inches, formula (236) or (237), respect- ively. Owing to the cylindrical shape of the armature, the area of the surface presented to the lines when entering and leaving the core is much greater than that of the actual cross-section of the armature body. Hence, since every useful line of force, on its way from a north pole to the adjoining south pole, must pass through the smallest core section, it is evident that the magnetizing force required per unit of path length is smallest near the polepieces and greatest opposite the neutral points of the field, while it gradually increases from the minimum to the maximum value as the flux passes from the peripheral surface opposite the north pole to the neutral cross-section, and grad- ually decreases again to minimum as the flux proceeds from the neutral section to the periphery opposite the south pole. 91] MAGNETIZING FORCES. 341 The average specific magnetizing force, therefore, is obtained by taking the arithmetical mean of the extreme values: '. = ^(\ + V, (231) in which m" ai = maximum specific magnetizing force, for smallest area of magnetic circuit, in armature; see Table LXXXVIII., col- umn for annealed wrought iron; m f M = minimum specific magnetizing force, for largest area of magnetic circuit in arma- ture, Table LXXXVIII. The maximum specific magnetizing force w' ai . corresponds < to the maximum density of (B,^ = lines, and the mini- 5 a i mum specific magnetizing force w" aa to a minimum density of (B"^ = lines; $ being the useful flux of the machine, in A "8 maxwells; S"^ the minimum area of circuit in armature, that is, the net cross-section of the armature core, in square inches; and S"^ the maximum path-area of armature, in square inches. The area of the magnetic circuit in the armature can be ex- pressed by the product of the net length and the depth of the core, and of the number of poles; hence the minimum area: S\^ = 2 n p X 4 X b & X *,, (232) and the maximum area: S\, = 2 p X 4 X b\ x*. , .:....(233) where n p = number of pairs of magnet poles; / a = length of armature core, in inches; b & = radial depth of armature core, in inches; b' & = maximum depth of armature core, in inches; a = ratio of net iron section to total cross-section of armature core, see Table XXIII., p. 94. The maximum depth, b' & , of the armature is determined as follows: In multipolar dynamos the maximum depth, b' M of the core is approximately equal to half the circumferential width of one polepiece; for bipolar machines b ' B is half the largest chord that can be drawn between the internal and external armature per- ipheries. In bipolar smooth armatures, as seen from Fig. 257, 342 D YNAMO-ELECTRIC MA CHINES. ' a is the leg of a. right triangle, the hypothenuse of which is the external radius of the armature core, and whose other leg is the internal radius of the armature; hence by the Pythago- rean Principle it can be expressed by the core diameter, d^ and the radial depth, a , as follows: HrJ -1 Fig. 257. Maximum Core-Depih in Bipolar Smooth Armature. -i. ...(234) For bipolar toothed and perforated armatures we have, similarly, with reference to Fig 258: Fig. 258. Maximum Core-Depth in Bipolar Toothed Armature. \d\ - 2 = J 4 *'* ~ 4 (235) The length of the magnetic circuit in the armature is ob- tained from the following formulae (236) or (237),^ smooth and toothed cores, respectively, which are derived from purely geometrical considerations. 91] ALAGNETIZING FORCES. 343 The path of the magnetic circuit through a smooth armature core is illustrated in Fig. 259, from which it is evident that the length l\ can be expressed by: Fig. 259. Length of Magnetic Path in Smooth Armature Core. 90 < -- \-ct (236) In case of toothed and perforated armatures, Fig. 260, the length of the path is: Fig. 260. Length of Magnetic Path in Toothed Armature Core. /'. = d'\ xxx , ...(237) where m "c.i.-> m "c.a. specific magnetizing forces for- wrought iron, cast iron, and cast steel, re- spectively, from Table LXXXVIIL, or Fig. 256; corresponding to the magnetic densi- ties (B" w .i> (B" c .i. , and (B" cs in the respective materials; m m Jii [ /// Jii * w.i. -J- * 0-4 ~T * C,S. average specific magnetizing force of magnet frame in ampere-turns per inch length; /Vi. > /*c4. > /"c.s. lengths of magnetic circuit in wrought iron, in cast iron, and in cast steel, respectively, in inches; /" m = r wi -J- /" ci + /" C8 = total length of magnetic circuit in magnet frame, in inches. The densities (B lV-i . , (B C . L , and (B C8 are the quotients of the total magnetic flux, <', by the mean total areas, S" vA ., S" c .i t , and S" C-M of the magnetic circuits in the respective materials: (Q." . (Q" _ . (Q" _ /*>QO\ > w.i. o// , "J c .i. o// , u> c<8 . Vw9j w.i. *J c.l. M c.s. If two or more portions of the frame are made of the same material, but of different cross-sections, either each of these portions has to be treated separately, or their average specific magnetizing force must be found, exactly as in the case of dif- ferent materials. Thus, if the path in a certain material, for some mechanical or constructive reason, has different sectional areas, S lt S z , S 3 , . . . in various portions, / x , / 2 , / 3 , ....of its length, the total magnetizing force required for that mate- rial is: 92] MAGNETIZING FORCES. 345 at = m X (/i -|- 4 ~h 4 4" . - - ) = 0*1 x A + 0*8 x / + 0*3 x /B -f . . ., (240) where 7# t X /i + 0*2 X 4 + 0*3 X /s + . . = . . m' = mean specific magnetizing force; #*!, *2, 0/3, . . . = specific magnetizing forces in the different sections of the magnetic circuit. Since the resultant area, S, corresponding to the mean spe- cific magnetizing force m in the above formula, is different from the arithmetical as well as from the geometrical mean of the single areas, S lt S 2 , S 3 ,..., the use of either of these mean areas would lead to an incorrect result. And since, further- more, the specific magnetizing force does not vary in direct proportion with the flux-density, it would also be a fallacy to use the specific magnetizing force corresponding to the aver- age density computed from the separate densities, oi o 2 o 8 by taking their arithmetical or even their geometrical mean. Similarly, if the area presented to the lines of force is not uniform throughout the length of their path in a certain por- Figs. 261 to 263. Polepieces with Gradually Increasing Sectional Area. tion of the field frame, neither the mean area nor the mean flux density, obtained by averaging the respective extreme values, should be used, but the specific magnetizing force for the max- imum and minimum cross-section must be calculated, and 346 D YNAMO-ELECTR1C MA CHINES. [92 either their arithmetical or their geometrical mean be taken, according to whether the -variation in cross-section is a con- tinual or a non-gradual one. The sectional areas of the magnet cores and of the yokes in most cases are uniform throughout their respective lengths; but the cross-section of the polepieces, owing to their peculiar shape, usually varies along their length. In case the sectional area gradually rises from a minimum near the core to a maximum at the poleface, as in Figs. 261, 262, and 263, the average specific magnetizing force is the arith- metical mean of the extreme values: m p = $ (! + m s ), (241) in which m v = average specific magnetizing force, of pole- pieces, in ampere-turns per inch; m l = specific magnetizing force, corresponding to cross-section ^ of polepieces near magnet- core (or to twice the minimum cross-section at center of polepiece, Fig. 262), in square inches; m z = specific magnetizing force, corresponding to pole face area S 2 (maximum cross-section of polepiece), in square inches. If, on the other hand, the area is partly uniform and partly varying, as in the polepieces shown in Figs. 264 and 265, the geometrical mean of the specific magnetizing force of the uniform portion and of the average specific magnetizing force of the varying portion has to be taken as follows: Figs. 264 and 265. Polepieces with Partly Uniform and Partly Varying Cross Section. _ m \ A ~\~ \ ( m i ~h m %) X 4 /p ~ / _i_ / *1 "I" 1-9. (242) 02] MAGNETIZING FORCES. 347 where m =. specific magnetizing force corresponding to area Si of minimum cross-section, in sq. in. ; m a = specific magnetizing force corresponding to pole face area S 2 (maximum cross-section), in sq.in. ; 4 = length of uniform cross-section, in inches; 4 = mean length of varying cross-section, in inches. In formulae (241) and (242) it is assumed that the smallest sec- tion of the polepiece is entered by the entire total flux, #', and that the pole area only carries the useful flux, <. Neither Figs. 266 and 267. Mean Length of Magnetic Circuit in Cores and Yokes. of these assumptions is quite correct (the number of lines entering the polepieces being smaller than >', and the flux at the pole face somewhat larger than <) but, since their devia- tions from the facts are in opposite directions, they practically cancel in forming the arithmetical mean of the respective specific magneting forces and give a result as accurate as can be desired. The mean length of the magnetic circuit in portions of the field frame having a homogenous cross-section (cores andjw&r) is measured along the centre line of the frame, as shown in Fig. 266, if there is but one magnetic circuit through that por- tion. In case of two or more magnetic circuits passing in parallel through any part of the frame, as in Fig. 267, thajt part is to be correspondingly subdivided parallel with the direction of the magnetic lines, and the mean length of-the magnetic circuit, then, is given by the centre-line through a part of the frame thus apportioned to one circuit. In the illustration, Fig. 267, two parallel circuits being shown through each core, the average line of force passes through the cores at a distance from their edges equal to one-quarter of their breadth. 348 D YNA MO-ELE C 7 *RIC MA CHINES. [93 In parts with varying cross-section (polepieces) the mean length of the magnetic circuit, depending altogether upon their shape, can only be estimated, one approximation being Figs. 268 and 269. Mean Length of Magnetic Circuit in Polepieces. the arithmetical mean between the shortest and the longest line of force (see Figs. 268 and 269): I /'P = I (/, + /,), or /*=/, + /,; .... (243) /" p = mean length of magnetic circuit in polepieces, in inches; /, = shortest line of force in polepiece; / a := longest line of force in polepiece. 93. Ampere-Turns for Compensating Armature Re- actions. The armature current in magnetizing the armature core exerts a double influence upon the magnetic circuit: (i) a direct weakening influence upon the magnetic field, due to the lines of force set up by the armature winding, and (2) an indi- rect, secondary influence by shifting the magnetic field in the direction of the rotation, thereby causing greater magnetic density to take place in those portions of the polepieces at which the armature leaves the pole than in those at which it enters. The direct effect of the armature current on the field has been studied experimentally by Professor Harris J. Ryan, 1 who, in his paper presented to the American Institute of Electrical Engineers, on September 22, 1891, has shown that the arina- 1 Harris J. Ryan, Trans. A. I. E. E., vol. viii. p. 451 (September 22, 1891); Electrical Engineer, vol. xii. pp. 377, 404 (September 30 and October 7, 1891); Electrical World, vol. xvii. p. 252 (October 3, 1891). 93] MAGNETIZING FORCES. 349 ture ampere-turns acting directly against the field ampere turns can be expressed by: N* X r k lt X a af * = -- --' where at' T = counter magnetizing force of armature per mag- netic circuit, in ampere-turns, to be compen- sated for by additional windings on field frame; JV & total number of turns on armature, JV & = N c , for ring armatures, N A = 1V C , for drum-wound armatures, (N c = total number of armature conductors); /' = total current-capacity of dynamo, in amperes; 2' p = number of armature circuits electrically connected in parallel; N X I' , = total number of ampere-turns on armature; 2n p 13 x oc = angle of brush lead. For smooth-core armatures the angle of lead is approximately equal to half the angle between two adjacent pole corners, the constant 13 being very nearly = i, and is accurately expressed by formula (245). Since the angle of field-distortion depends upon the relative magnitudes of the armature- and field magnetomotive forces acting at right angles to each other, the direction of the dis- torted field is the resultant of both forces; that is, the diag- onal of a rectangle, having the two determining M. M. Fs. as its sides, as shown in Fig. 270, in which OA represents the direction and magnitude of the direct M. M. F., and OB that of the counter M. M. F. The angle of lead can, con- sequently, be mathematically expressed by: _ OB _ Total Armature Ampere-Turns OA Total Field Ampere-Turns N & X I' = 2 "'p = N * X r , n z X AT 2ri v X n z x AT ' or / N X /' \ a = arc tan ( __.__ ) , (245) \ z// D x n. x -'f J- I 35 D YNA MO-ELECTRIC MA CHINES. [93 the total number of fie.ld ampere-turns being the product of the number, AT, of ampere-turns per magnetic circuit, and of the number, n z , of magnetic circuits. In toothed and perforated machines the weakening effect of the armature magnetomotive force is checked by the presence of iron surrounding the conductors, this checking influence being the stronger the greater the ratio of tooth section to field den- sity, that is, the smaller the tooth density. In a minor degree, th.e coefficient of brush lead depends upon the ratio of gap length to pitch of slots, and upon the peripheral velocity of the armature. In the following Table XC. averages for this co- efficient, / 13 , for toothed and perforated armatures are given, the upper limits referring to small gaps and high-speed arma- tures, and the smaller values to large air gaps and to armatures of low circumferential velocity: TABLE XC. COEFFICIENT OF BRUSH LEAD IN TOOTHED AND PER- FORATED ARMATURES. MAXIMUM DENSITY OP MAGNETIC LINES IN ARMATURE PROJECTIONS AT NORMAL LOAD. COEFFICIENT OF BRUSH LEAD, * Toothed Armatures. Perforated Armatures. Lines per sq. In. Lines per sq. cm. Straight Teeth. Projecting Teeth. 50,000 75,000 100,000 125,000 150,000 7,750 11,600 15,500 19,400 23,250 0.30 to 0.45 .35 " .60 .40 " .80 .50 " .90 .70 " 1.00 0.25 to 0.35 .30 " .45 .40 " .60 .50 " .70 .60 " .90 0.20 to 0.30 .25 " .35 .30 " .45 .40 " .60 .50 " .80 Formula (244) is directly applicable to single magnetic circuit bipolar and to the radial types of multipolar machines. In double circuit bipolar types, and for axial multipolar dynamos, however, in which the number of magnetic circuits per pole space is twice that of the former machines, respectively, the result of (244), must be divided by 2 in order to furnish the direct counter magnetizing force per magnetic circuit. As to the second, indirect, influence of the armature field, the density in the Sections I, I, Fig. 270, of the polepieces, on account of the distortion of the field caused by the action of the armature current, is greater, in the Sections II, II, how- 93] MAGNETIZING FORCES. 351 ever, smaller than the average density obtained by dividing the total flux by the sectional area of the polepieces. i Fig. 270. Influence of Armature Current upon Magnetic Density in Polepieces. If the average density in the polepieces, #' -r- S p , is denoted by (B" p , then the distorted densities are in Sections I, I : ($>" pl = * X - . I ma \ ...... (246) in Sections II, II: (&" = ' r n_ m ,\ This is the total number of ampere-turns by the amount of which the exciting power of each magnetic circuit is to be in- creased in order to compensate for the reactions of the arma- ture current upon the field. Making the above calculation of at r , by formula (249), for a great number of practical machines, the author has found that with sufficient accuracy the complex formula (249) can be re- placed by the simple equation: *^ I A. ^ X X (250) if the following values of the coefficient >& I4 are employed: TABLE XCI. COEFFICIENT OF ARMATURE REACTION FOR VARIOUS DENSITIES AND DIFFERENT MATERIALS. AVERAGE MAGNETIC DENSITY IN POLEPIECES. Coefficient of Armature Reaction v Wrought Iron and Cast Steel. Mitis Iron. Cast Iron. Lines per sq. in. , Lines per pq. cm. &P Lines per sq. in. <, Lines per pq. cm. (B p Lines per sq. in. < Lines per t=q. cm. (B p 80,000* 90,000 100,000 105,000 110,000 115,000 120,000 12,400* 13,950 15,500 16,250 17,000 17,800 18,600 70,'doo* 80,000 90,000 100,000 105,000 110,000 115.000 120,000 10,'850* 12,400 13,950 15,500 16,250 17,000 17.800 18,600 26.000* 30,000 40,000 50,000 55,000 60,000 65,000 70,000 3,100* 4,650 6,200 7,750 8,500 9,300 10.100 10,850 1.25 1.30 1.40 1.50 1.60 1.70 1.80 1.90 2.00 2.10 2.25 * Or less. 94] MAGNETIZING FORCES. 353 91. Grouping of Magnetic Circuits in Various Types of Dynamos. In applying formula (227), 89, for the total magnetizing power of a dynamo, the number of the magnetic circuits and their grouping has to be taken into account. Considering each magnet, or each group of magnet coils wound upon the same core, as a separate source of M. M. F., we can classify the various types of dynamos according to the number of sources of magnetomotive force, and according to their grouping, as follows: (1) One source of M. M. F., single circuit, Figs. 271 and 272; (2) One source of M. M. F., double circuit, Figs. 273 and 274; (3) One source of M. M. F., multiple circuit, Figs. 275 and 276 ; (4) Two sources of M. M. F. in series, single circuit, Figs. 277 and 278; (5) Two sources of M. M. F. in series, double circuit, Figs. 279 and 280; (6) Two sources of M. M. F. in parallel, single circuit, Figs. 281 and 282; (7) Two sources of M. M. F. in parallel, double circuit, Figs. 283 and 284; (8) Two sources of M. M. F. in parallel, multiple cir- cuit, Figs. 285 and 286; (9) Two sources of M. M. F. in series, each also sup- plying a shunt circuit, Figs. 287 and 288; (10) Three or more sources of M. M. F. in parallel, multiple circuit, Figs. 289 and 290; (n) Three or more sources of M. M. F. in series, each having a shunt circuit, Figs. 291 and 292; (12) Four sources of M. M. F., two in series and two in parallel, single circuit, Figs. 293 and 294; (13) Four sources of M. M. F. in series, each pair also supplying a shunt circuit, Figs. 295 and 296; (14) Four or more sources of M. M. F. in series, paral- lel, two sources in series in each circuit, Figs. 297 and 298; 354 DYNAMO-ELECTRIC MACHINES. [94 (15) Four or more sources of M. M. F., all in parallel, multiple circuit, Figs. 299 and 300; (16) Four or more sources of M. M. F., arranged in one or more parallel branches in each of which two separate sources are placed in series with a group of two in parallel, Figs. 301, 302 and 303. In order to facilitate the conception of the grouping of the magnetomotive forces, to the following illustrations of the 16 classes enumerated above the electrical analogues of corre- sponding grouping of E. M. Fs. have been added: FIG. 271 FiQ .272 Fic.'273 FIG 274 Fiq. 275 FIG. 276 FIG. 277 F'G. 278 FIG. 300 FIG. 301 FIG. 302 FIG. 303 Figs. 271 to 303. Grouping of Magnetic Circuits in Various Types of Dyna- mos, and Electrical Analogues. Of the first class, Fig. 271, which has but one magnetic cir- cuit, are the bipolar single magnet types shown in Figs. 191, 192, 193 and 194. In the second class, Fig. 273, there are two parallel magnetic 94] MAGNETIZING FORCES. 355 circuits, each containing the entire magnetizing force; of this class are the single magnet bipolar iron-clad types, illustrated in Figs. 204, 205 and 206. The third class, Fig. 275, has as many magnetic circuits as there are pairs of magnet poles, and each circuit contains the entire magnetizing force; the single magnet multipolar types, Figs. 214 and 215, belong to this class. The fourth class, Fig. 277, has but one magnetic circuit, and is represented by the single horseshoe types, Figs. 187 to 190, and by the bipolar double magnet types, Figs. 195, 196 and 198. In the fifth class, Fig. 279, there are two magnetic circuits, each of which contains both magnets; the bipolar double mag- net iron-clad types shown in Figs. 203 and 207 belong to this class. The sixth class, Fig. 281, has also two magnetic circuits, but each one contains only one magnet; of this class are the bipolar double magnet types illustrated in Figs. 197, 199 and 200. In the seventh class, Fig. 283, there are four parallel mag- netic circuits, each of which contains but one magnet; the fourpolar iron-clad types, Figs. 218, 219 and 220, and the fourpolar double magnet type, Fig. 223, belong to this class. In the eighth class, Fig. 285, the number of magnetic cir- cuits is equal to twice the number of poles, opposite pole faces of same polarity considered as one pole, and each circuit con- tains one magnet; this class is represented by the double magnet multipolar type, Fig. 216. The ninth class, Fig. 287, has three magnetic circuits, two of which contain one magnet each, while the third one con- tains both the magnets. In the tenth class, Fig. 289, there are as many magnetic cir- cuits as there are poles, two circuits passing through each magnet; the multipolar iron-clad type, Fig. 217, is of this class. The eleventh class, Fig. 291, has one more circuit than there are pairs of poles, one circuit containing all the magnets, while all the rest contain but one magnet each; to this class belongs the multiple horseshoe type, Fig. 222. In the twelfth class, Fig. 293, there are two magnetic cir- 35 6 DYNAMO-ELECTRIC MACHINES. [64 cults, each containing two magnets; it is represented by the double horseshoe types, Figs. 201 and 202. Class thirteen, Fig. 295, has three circuits, two containing two magnets each and the third one all four magnets; to this class belongs the fourpolar horseshoe type, Fig. 221. In class fourteen, Fig. 297, there are as many circuits as there are poles, each circuit containing two magnetomotive forces in series; this class of grouping is common to the radial multipolar types, Figs. 208 and 209, and to the axial multipolar type, Fig. 212. In class fifteen, Fig. 299, the number of magnetic circuits is equal to the number of poles, and each circuit contains one magnet; the tangential multipolar types, Figs. 210 and 211, and the quadruple magnet type, Fig. 224, are the varieties of this class. The sixteenth class, Fig. 301, finally, has as many magnetic circuits as there are poles, and each circuit contains three magnets; the raditangent multipolar type which is shown in Fig. 213, represents this class of grouping. Similarly as the total joint E. M. F. of a number of sources of electricity connected in series-parallel is the sum of the E. M. Fs. placed in series in any of the parallel branches, so the total M. M. F. of a dynamo-electric machine is the sum of the M. M. Fs. in series in any of its magnetic circuits. In considering, therefore, one single magnetic circuit for the computation of the magnetizing forces required for over- coming the reluctances of the air gaps, armature core and field frame, the result obtained by formula (227) represents the exciting force to be distributed over all the magnets in that one circuit, and, consequently, the same magnetizing force is to be applied to all the remaining magnetic circuits, pro- vided all circuits contain the same number of magnets. In case of several magnetic circuits with a different number of M. M. Fs. in series, as in classes 9, n and 13, which have one long circuit containing all the magnets, and several small circuits with but one or two magnets, respectively, the total M. M. F. of the machine is either the sum of all M. M. Fs. or the joint M. M. F. of one of the small circuits, according to whether the long, or one of the small circuits has been used in calculating the magnetizing force required for the machine. PART VI. CALCULATION OF MAGNET WINDING. CHAPTER XIX. COIL WINDING CALCULATIONS. 95. General Formulae for Coil Windings, In practice it frequently is desired to make calculations con- cerning the arrangement, etc., of magnet windings, without reference to their magnetizing forces; and it is for the simpli- fication of such computations that the following general for- mulae for coil windings are compiled. In Fig. 304 a coil bobbin is represented, and the following symbols are used: D m = external diameter of coil space, in inches; / HSr^ + T-v- < 258 > The resistance which a coil of wire of known resistivity will offer when wound on a given bobbin, is: r m = An X An ohms, (259) or, by inserting the value of L m from (254): r m = .262 X An X (<4 + /U X /m * /* m . (260) d m The diameter of a wire which shall fill a bobbin of given dimensions and offer a given resistance can be found as fol- lows: The coil space occupied by L m feet of wire having a diameter (insulated) of 6' m inch, is: F ra = 12 L m x 6' m \ (261) while, expressed in the dimensions of the bobbin, the volume is: w 'in S\ '^ / T-v Q T 2\ (,-^rn "m / 4 /, X 7T .(262) 36 2 YNA MO-ELECTRIC MA CHINES. [96 consequently we have: 12 J^ m = . 262 x ^- x (h m d m + V) . ... (263) -^m In order to replace in this formula the unknown length Z m , by the given resistance, r m , we express the latter by the dimensions of the wire. The resistance of a copper rod of one square inch area and one inch length being .000000675 ohm at 15.5 Cent. (=: 60 Fahr.), that of a copper wire of length Z m feet and diameter # m inch, is: r m = .000000675 X I2Zm ........ (264) 6V X I Inserting the value of Z m from (264) into (263), we have: .000000675 X 12 X / m X - r m X 6 * x - u m A 4 m vifi J Mm"), r V rf 2 X ^ m m ' m A "m whence: #m X d' m =4 7.0000027 X X (h m d V r m m + V) (265) In practical cases the diameters # m and S' m are usually very little different from each other, so that with sufficient accuracy we can put d m X <5' m ^m"* an ^, consequently, from (265): fm J m m . which, multiplied by the sectional area of the wire, # m s , gives the cross-section of the wire per unit of current strength, that is, its current density: ft a T The product (# m a x An) of the sectional area (in circular mils) of a wire into its specific resistance (in ohms per foot) gives the resistance of one mil-foot of wire of the given material, /'. \*J that is to say, the area of the requisite magnet wire is the quotient of the number of ampere-inches (/ T being the length of the mean turn in inches) to be wound upon the cores, by the potential between the field terminals. Assuming an ap- proximate value for the mean turn, 4> the minimal limit of which is always given by the circumference of the magnet core, a preliminary value of # m can be quickly determined, and from this the value of 4 is easily adjusted if necessary; a re- calculation with the correct value of 4 will then furnish the final value of the area of the magnet wire. A set of valuable curves which show the relation between ampere-turns and mean length of turn, and between current and total length of wire, respectively, and which can be used for graphically obtaining the results of formula (272) as well as other data concerning the magnet winding, has been devised by Harrison H. Wood. 1 Formula (272) is only approximate, being based upon the assumption that the final temperature of the magnet coils is ' "Curves for Winding Magnets," by H. H. Wood; Electrical World, vol. xxv. pp. 503 and 529 (April 27 and May 4, 1895). 366 DYNAMO-ELECTRIC MACHINES. [96 about 60 C. If the actual rise above 15.5 C. of the magnet temperature is denoted by m , the accurate formula for the area of the wire would be : /. x (i + .004 x m ) , (273) 10.5 being the resistance, in ohms, of a copper wire, one foot long and one mil in diameter, at a temperature of 15.5 C. (= 60 F.). From (273) a very useful formula for the weight of the mag- net winding can be derived. By Ohm's Law we have: p E I V r Y r ^m - m A ' m E> ^ ' m > An in which P m = energy absorbed in magnet winding, in watts (see 98); consequently: /.x^. x (I + . 004 x 8J . m N m But the resistance of the magnet winding can be ex- pressed by: X io 6 . . wt x (i + .004 x e m ) x t' m / i V -r-? x ( -^-r ) , ^16 \m y where wt' m = weight of magnet winding, including insulation, in pounds; k jf> = specific weight of magnet winding, in pounds per cubic inch, depending upon size of wire and thickness of insulation; see Table XCII. Hence: , 12 x IP"* X l, t X AT X 4 X E m X m 4 ^ m X wt' m or, , _ 12 X IP-' X . B X AT X / t X An X -* m and since by (272) we have, approximately: P v^ 2 i^y^/T^v/ *- / m A ''m 1 4 /^ si J. xs'tr %96] COIL WINDING CALCULATIONS. we finally obtain: wf m = 144 X io- 6 X k l6 X - ^, X " or, 367 /ATX / t V \ IOOO / \ _ /_ o * -(274) The constant lg is = 144 x 16 , and can be taken from the following Table XCII. : TABLE XCII. SPECIFIC WEIGHTS OF COPPER WIRE COILS, SINGLE COTTON INSULATION. Total Area Specific Value GAUGE OP WIRE. Diam- eter, Bare, Insula- tion S. C. C. Space Occupied by Wire. of Copper. Square Ratio of Copper Weight of Winding. of Constant in Inch. Inch. Cir. Mils. Mils. to IDS. per Formula Total en. inch. (274). Volume of ( 71 1,385 .627 .201 290 is .040 .005 2025 1,257 .628 .201 29.0 19 .036 .005 1,681 1,018 .607 .194 27.9 20 .035 .005 1,600 962 .601 .1925 27.7 21 20 .03-2 .005 1 369 8 '4 .587 .187 270 22 21 .028 .005 1,089 816 .516 .175 25.2 23 22 .025 .005 900 4*1 .565 .181 26.1 24 23 .022 .005 729 380 .521 .167 24.1 25 24 .020 .005 6'i5 314 .503 .161 23.2 26 25 .018 .005 529 254.5 .48 .1535 22J 27 26 .016 .005 4tl 201 .457 .146 21.0 28 27 .014 .005 361 154 .428 .137 19.8 29 28 .013 .005 324 133 .41 .131 18.9 30 .012 .005 289 113 .391 .125 18.0 29 .011 .005 256 95 .371 .119 17.2 From the above Table it is found that for the most usual sizes of magnet wire (No. 6 B. W. G. to No. 20 B. W. G.) the 3 68 DYNAMO-ELECTRIC MACHINES. [97 average value of k lt is = .21, and that of 16 is = 30, and therefore approximately: (275) m that is to say: /Ampere-feetX 2 I 1000 Weight of winding = - Watts absorbed by Magnet Winding. By means of (275) the weight of wire can be found that sup- plies a given magnetizing force at a fixed loss of energy in the field winding. 97. Heating of Magnet Coils. The conditions of heat radiation from an electro-magnet being similar to those of an armature at rest, with polepieces removed, the unit temperature increase of magnet coils can be obtained by extending Table XXXVI., 35, for the specific increase of armatures, to conform with the above conditions. Plotting for this purpose the temperatures given in the first horizontal row for zero peripheral velocity, as functions of the ratio of pole-area to total radiating surface, and prolonging the temperature curve so obtained until it intersects the zero ordinate, the specific temperature rise 0' m = 75 C. (= 135 F.) for i watt of energy loss pzr square inch of radiating sur- face, is found. The actual temperature increase of any mag- net coil can, therefore, be obtained by the formula: fl m = e 'm X ^=T5X~, (276) where 9 m = rise of temperature in magnets, in Centigrade degrees; /> m = energy absorbed in magnet-winding, in watts; C / m = current in magnet wind- ing, in amperes; E m - E. M. F. between field terminals, in volts; r m = resistance of magnet winding, in ohms; > M = radiating surface of magnet coils, in square inches. -/ l 97] COIL WIXDING CALCULA TIONS. 369 The radiating surface of the magnets depends upon the shape and size of the cores as well as the upon the arrangement of the field frame, and can be readily deduced geometrically from the dimensions of the coil. If the polepieces, or yokes, com- pletely overlap the end flanges of the magnet coils, air has access to the prismatical surface only, and the radiating sur- face is for cylindrical magnets : S* = D m x n X /' m = (d m + 2fi m ) x 7f x /' m ; (277) for rectangular magnets: .S M = 2 X l' m X (/ + b + h m X TT); .. . .(278) and for magnets of oval cross-section (rectangle between two semicircles) : SM = 2 X /' m X \(l-b) + (- + h m \ X n\ . ..(279) In case that also one of the end surfaces of each coil is exposed to the air, or that one-half of each coil flange helps the prismatical surface to liberate the heat developed by the field current, the radiating surface becomes: SM, = ^M + tfrn X / T X h m (280) If there is a clearance between the magnet coils and the yokes and polepieces such as to make both the entire end sur- faces of each magnet coil active in giving off heat, the radiat- ing surface is: S M2 = ^ M + 2 m X /T X h m (281) And when, finally, the yokes and polepieces touch the end flanges of the coils, but the latter project over the former so that heat can radiate from the projecting portions, the radiat- ing surface will be: Sii, = SM + 2 m X h m X (/T - &,) (28?) In the above formulae (277) to (282): SH = radiating surface of prismatic surface of magnet coil; Sit, = radiating surface of prismatic surface plus one end surface per coil; 37 DYNAMO-ELECTRIC MACHINES. [97 SM* = radiating surface of prismatic surface plus two end flanges per coil; Sjii = radiating surface of prismatic surface plus pro- jecting portions of coil flanges; d m = diameter of circular core-section; ) m external diameter of cylindrical magnet coil; ^ m = height of magnet winding, see Table LXXX., 83; /' m = total length of magnet coils per magnetic circuit; / length of rectangular or oval core-section; b = breadth of rectangular or oval core-section; / T =: length of mean turn of magnet wire; by = breadth of yoke, or polepiece; n m = number of separate magnet coils in each mag- netic circuit. If the surface, ,S' M , of the magnet cores is given instead of the radiating surface, 5 M , of the coils, the value of 0' m in (276), instead of being constant at 75 C., ranges between 75 and 4 C. (or 135 and 7 F., respectively), according to the ratio of depth of magnet winding to thickness of core; that is, according to the ratio of radiating surface to core surface. In the following, Table XCI1L, the specific temperature rise, 0' m , is given for round magnets, varying in winding depth from .01 to 2 core diameters, and for rectangular and oval cores ranging in radiating surface from 1.02 to 15 times the surface of the cores. If, for a given type of machine, the approximate ratio of radiating surface to core surface is known, the calculation of the magnet winding can, by means of Table XCIII., directly be based upon the given surface of the magnet cores. 98. Allowable Energy Dissipation for Given Rise of Temperature in Magnet Winding. From formula (276), 97, it is evident that for a given coil the temperature rise depends solely upon the amount of energy consumed, and conversely it follows that by limiting the tern- 97] C0/Z WINDING CALCULATIONS. 37' G M 10 o i~ in 10 100 >om m m mia mm in o sifsi** 050.2 2 M v OS O O ~ S. ** 5 it 'E H s a o 3 i c 01 ^cooo inoinoinooinoioom CSf-jOf8l9^990a o in m i-ii-irHi-ii-irti-J^rHr-ir-Jr-ii-IlNejCOlriQOOJ SS S 3 2 S 3 7 3 3 3 3 S S S S go t- e* o o o go o 10 o o fl o o ^COi-H^OIfWOTTOCOTPincDOOWiO O i^5?ccoooo ^-OJ-TSD inco 37* DYNAMO-ELECTRIC MACHINES. [9d perature increase of the coil, the maximum of its energy dissi- pation is also fixed. By transposition of (276) we obtain: *~ = &XS*, ............ (283) / 3 and (284) where P m = energy dissipation in magnet winding, in watts; m temperature increase of magnet coils, in degrees Centigrade; 6' m = specific temperature rise of magnet coils for one watt per square inch of core-surface; S K = radiating surface of magnet coils, in sauare inches; see formulae (277) to (282); S'x = surface of magnet cores, in square inches. The temperature rise of magnet coils in practice varies be- tween 10 and 50 C., and in exceptional cases reaches 75 C., the latter increase causing, in summer, a final temperature of the magnets of about 100 C., which is the limit of safe heating of coils of insulated wire. For ordinary cases, therefore, the allowable energy dissipation in the field magnets ranges between />= and = X S M = .66 7 5 M , that is, between .133 and .667 watt per square inch (=r .02 to .10 watt per square centimetre), or radiating surface is to be provided at the rate of from 7^ to i^ square inches per watt (= 50 to 10 square centimetres per watt). The arith- metical mean of these limits, .4 watt per square inch (= .062 watt per square centimetre), or 2y 2 square inches ( 16 square centimetres) per watt, is a good practical average for medium-sized machines, and corresponds to a rise of magnet temperature of 30 C. (= 54 F.). The energy dissipation, P m thus being fixed by the temper- 98] COIL WINDING CALCULATIONS. 373 ature increase specified, the working resistance of the magnet winding can be obtained by means of Ohm's Law, thus: E F v / P *& * * J or, ff E -*-^ according to whether the intensity of the current flowing through the field circuit, or the E. M. F. between the field ter- minals, respectively, is given, the former being the case in series-wound machines and the latter in shunt-wound dynamos. In a series machine the field current is equal to the given cur- rent output, 7 m = 7; while in a shunt dynamo the potential between the field terminals is identical with the known E. M. F. output of the machine, E m = ; see 14, Chapter II. CHAPTER XX. SERIES WINDING. 99. Calculation of Series Winding for Given Tempera- ture Increase. The number of ampere-turns, AT, being found by the for- mulae given in Chapter XVIII. , and the field current in a series dynamo being equal to the given current output, 7, of the machine, the number of series turns, ^Vge, can readily be obtained by dividing the former by the latter: (287) The number of turns multiplied by the mean length of one convolution, in feet, gives the total length of the series field wire: A. = N ~* /T > ............. (288) in which the length of the mean turn, in inches, is for cylindrical magnets : 4 = ( In dividing (288) by (294), finally, the specific length A^, in feet per ohm, of the series winding giving a magnetizing force of AT ampere-turns at a rise of the magnet temperature of m degrees Centigrade, is received, viz. : AT / T T -7-X - Ae I 12 86 E v - Y 75 X /' * i -f y/ T v / v 7 - 4M. J. /\ / T /\ ./ , = 6.25 X fl ' X (i + .004 X m X Jj( where ^4 7 1 = ampere-turns required for field excitation, for- mula (227); / T = length of mean turn, in inches, formulae (289) to (292), respectively; / = current output of dynamo, in amperes; 6 m = specified temperature increase of magnet wind- ing, in Centigrade degrees; , = radiating surface of magnet coils, in square inches, formulae (277) to (282). The conclusion of the series field calculation, now, consists in selecting, from the standard wire gauge tables, a wire whose "feet per ohm " most nearly correspond to the result of formula (295). If no one single wire will satisfactorily answer, either n wires of a specific length of feet per ohm each may be suitable stranded into a cable, or a copper ribbon may be employed for winding the series coil. In the latter case it is desirable to have an expression for the sectional area of the series field conductor. Such an expres- sion is easily obtained by multiplying the specific length, A M , by the specific resistance, for, since feet ohms = specific resistance X ; rr-, circular mils 100] SERIES WINDING. 377 we have: circular mils = specific resistance x feet per ohm; the specific resistance of copper is 10.5 ohms per mil-foot, at I 5-5 C.,and the area of the series field conductor, conse- quently, is: tfse 2 = 10.5 X A^ = 65 x X J\ X 7 x (i +.004 x o m ) . ...(296) in A ->,, In formulae (293) to (296), it is supposed that all the mag- net coils of the machine are connected in series. If this, however, is not the case, the main current must be divided by the number of parallel series-circuits, in order to obtain the proper value of /for these formulas. Having found the size of the conductor, the number of turns, jVge, from (287), will render the effective height, h' my of the winding space for given total length, /' m , of coil, by transposition of formula (252), 95, thus: 1 (297) (d'^Y being the area, in square inches, of the square, or rectan- gle, that contains one insulated series field conductor (wire, cable, or ribbon). If /*' m , from (297), should prove materially different from the average winding depth taken from Table LXXX., the actual values of / T and S* should be calculated, and the size of the series field conductor checked by inserting these actual values into formula (295) or (296). The product of the number of turns by the actual mean length of one convolution will give the actual length, L^, of the series field winding, and from the latter the real resistance and the weight of the winding can be calculated. (See 102.) 100. Series Winding with Shunt Coil Regulation. For some purposes it is desired to employ a series dynamo whose voltage can be readily adjusted between given limits. Such adjustment can best be attained by connecting across the terminals of the series field winding a shunt of variable 378 D YNAMO-ELEC TRIG MA CHINES. [100 resistance which is opened if the maximum voltage is desired, while its least resistance is offered for obtaining the minimum voltage of the machine, intermediate grades of resistance being used for regulating the voltage of the machine between the maximum and the minimum limits. The series winding in this case is calculated, according to 99, for the maximum voltage of the machine, and then the various combinations of the shunt-coils are so figured as to produce the desired regu- lation, and to safely carry the proper amount of current. As an example let us take five coils arranged, as shown in Fig. 305, so as to permit of being grouped, by moving the FIG. 305 DIAGRAM OF SERIES WINDING WITH SHUNT COIL REGULATION. FIG. 309 4TH COMBINATION FIG. 310 BTH COMBINATION. Figs. 305 to 310. Shunt Coil Combinations. slider of the adjusting switch into five different combinations, illustrated by Figs. 306 to 310. The resistances and sectional areas of these coils are to be so determined as to enable 60, 66f, 75, 83^, and 90 per cent, of the maximum voltage to be taken from the machine. It is evident that in this case 40, 331, 25, i6|, and 10 per cent., re- spectively, of the maximum field current will have to be absorbed by the respective combinations of the shunt coils, and their resistance, therefore, must be: Resistance first combination 60 = X resistance of series field = i.c r'. 4 Resistance second combination 662 = f- X resistance of series field = 2 r' 33i 100] SERIES WINDING. 379 Resistance third combination 7 1 ? = X resistance of series field = 3 r'. 2 5 Resistance fourth combination 8^J- = |- X resistance of series field = 5 r' K . io-(f o Resistance fifth combination = - X resistance of series field = o r' , 10 For the arrangement shown in Figs. 305 to 310, the first combination consists of coils I, II, and III, in parallel, the second combination of coils II and III in parallel, in the third combination only coil III is in circuit, in the fourth combina- tion coils III and IV are in series, and the fifth combination has coils III, IV, and V in series. In all combinations there are, furthermore, the flexible leads carrying the current from the field terminal to the adjusting slider; these are in series to the group of coils in every case, and their resistance, r x , consequently is to be deducted from the resistance of the combination in order to obtain the resistance of the group of coils alone. Expressing the resistances of the various groups by the resistances of the single shunt-coils, we therefore obtain: First group: - -- =i.$V.-r,; ...... (298) r r r Second group: - -- r = *r' M -r l ', ........ (299) r v 'ii 'm Third group: r m = 3^-ri; ........ (300) Fourth group: >m + r* = 5 r' ee - r, 5 ........ (301) Fifth group: r m + r n + r v = 9^-^ ........ (302) From this set of equations the resistances of the separate shunt-coils can be derived as follows: 3 8 DYNAMO-ELECTRIC MACHINES. [ 100 Inserting (299) into (298): whence: 'se ~ fl) X (l-S^'se ~ = _ 3_^se 3-5 'se r \ -h r \ __ 6 r , _ , *r\ C r r ' se ' se The resistance of the leads being very small, r? can be neglected, hence the resistance of coil I: '1 = 6^- 7'i- - (303) (300) into (299) gives: i i i or: r = (3 ^ M ~ '0 X (2 r' M - r,) 6 r'* 5 r' r, -I- ;-," r,* r!3 o r' S r* -I- -T- . r' "^ -J * ' .' ' se ' se Neglecting again r^, the resistance of coil II is obtained: '11 = 6^ - 5 r, (304) From (300) we have, directly: 'ni = 3''se-'i (305) By subtracting (300) from (301): r iv = 2r' M (306) By subtracting (301) from (302): In the above formulae, r' m is the resistance of the series field, hot, at maximum E. M. F. output of machine; and r, the resistance of the current-leads at the temperature of the 100] SERIES WINDING. 381 room. The resistance /-, is determined by finding the length and the sectional area of the leads, the former being depend- ent upon the distance of the adjusting switch from the field terminal, and the latter upon the maximum current to be car- ried, which in the present case is 40 per cent, of the current output of the machine. The currents flowing through the shunt coils in the various combinations can be obtained by the well-known law of the divided circuit, by virtue of which the relative strengths of the currents in the different branches are directly proportional to their conductances, or in inverse proportion to their resistances. The first combination consists in three parallel branches having the resistances r lt r a , and r m , respectively, and carries a total current of .4 / amperes, hence the currents in the branches: r m + r^ r n . '4 ^n r m + r t r m + ^ r u and 7 _ __ r i- r n _ X 4 /. ~ Inserting into these equations the values of the resistances from (303) to (307), respectively, we obtain: /T = r\) (6r'se sn) (s^se n) + (6^86 jn) (s^ae n) + (Gr'se ^r\) (6^86 X .4^ . T T AT V A T - T/ "" '* 2Sr' r, + yr,* i X .4 7 = X .4 I = 4 and -z6r' 2 T2r' r, -4- ^O', 5 i ,. T J se _ ' i JJ ' vx A T _ v A T 27 111 ~~ T^/^ 1 - T2T/ r 4- 47r 2 X ' 4 ~2" ' 4 ~ 7 2r se -~ I2lr se r l T 47 r l 2 In the second combination there are but two parallel 382 DYNAMO-ELECTRIC MACHINES. [ 100 branches, having the resistances r u and r ln , and the total cur- rent carried is .333 /amperes ; therefore: 7 " = X.333/= 3/8e X.333/ = X -333^ = -I o and 86 - 5 1 - - 7" II * 7" 86 - 5 1 7" 111 ~ 7- jTT~ x '333 y = = -, 7- X .333 * r i\ T r m 9 r se orj = - X -333 7 = - 222 ^- *3 The third, fourth, and fifth combinations are simple circuits only, the current through the coils therefore is identical with the total current flowing through the combination, viz. : .25 /, .167 /and .1 /amperes respectively; the first named current, consequently, flows through coil III when in the third com- bination, the second current through coils III and IV, when in the fourth combination, and the last figure given is the cur- rent intensity in coils III, IV, and V, when in the fifth com- bination. Taking the maximum value for the current flowing in each coil, the following must be their current capacities: Coil I and V: /! = / v = . i / = , ......... (308) " II: 7 n = .in/=-, ........ (309) "III: fm=.*SJ=j, ......... (310) " IV: / IV = .i6 7 /=, ........ (311) By allowing 1000 circular mils per ampere current intensity, the proper size of wire for the different shunt coils can then readily be determined from formulae (308) to (311). The preceding formulas (298) to (311) of course only apply to the special arrangement and to the particular regulation selected as an example, but can easily be modified for any given case [see formulae (457) to (466), 134], the method of their derivation being thoroughly explained. CHAPTER XXI. SHUNT WINDING. 101. Calculation of Shunt Winding for Given Tem- perature Increase. The problem here to be considered is to find the data for a shunt winding which w^ll furnish the requisite magnetizing force at the specified rise of the magnet temperature, and with a given regulating resistance in series to the shunt coils, at normal output. The shunt regulating resistance, or as it is sometimes called, the extra-resistance, admits of an adjustment of the resistance of the shunt-circuit within the limits prescribed, thereby inversely varying the strength of the shunt-current, which in turn correspondingly influences the magnetizing force and, ultimately, regulates the E. M. F. of the dynamo. In cutting out this regulating resistance, the maximum E. M. F. at the given speed is obtained while the minimum E. M. F. obtaina- ble is limited by the total resistance of the regulating coil. By specifying the percentage of extra-resistance in circuit at normal load, and the total resistance of the coil, any desired range may be obtained; see 103. Designating the given percentage of extra-resistance by r lt the total energy absorbed in the shunt-circuit, consisting of magnet winding and regulating coil, can be expressed by: ^. = P.. X . + , = X S X . + , (312) where I P& ^=. -- SK = energy absorbed in the magnet winding alone. 75 The potential between the field terminals of a shunt dynamo being equal to the E. M. F. output, , of the machine, the current flowing through the shunt-circuit is: 3*3 DYNAMO-ELECTRIC MACHINES. [ 101 and the number of shunt turns, therefore: _AT _ATx E By Ohm's Law we next find the total resistance of the shunt- circuit at normal load, viz.: X M X i + ~ This contains the r x per cent, of extra resistance; in order to obtain the resistance of the shunt winding alone, r" eh must be decreased in the ratio of i : and we have: * *' f" v 'sh ' sh A 100 = , ^x L_, (317) 75 y iooy ' too which is the resistance of the magnet winding when hot, at a temperature of (15.5 -f- 6 m ) degrees Centigrade; the magnet resistance, cold, at 15.5 C., consequently, is: X 101] SHUNT WINDING. 385 3 i i X - / v /\ /\ | ^L e V/X4.A1 r-L-^. + ' 75 X M X \ ioo/ h 100 x The division of (315) by (318), then, furnishes the specific length of the required shunt wire: A-sh 8h = ~ ^Sh AT The size of the shunt wire can then be readily taken from a wire-gauge table; if a wire of exactly this specific length is not a standard gauge wire, either a length of Z sh feet of the next larger size is to be taken, and the difference in resistance made up by additional extra-resistance, or such quantities of the next larger and the next smaller gauge wires are to be combined as to produce the required resistance, r ah , by the correct length, Z sh . To fulfill the latter condition, the geo- metrical mean of the specific lengths of the two sizes must correspond to the result obtained by formula (319); thus, if A'gh is the specific length of one size of wire and A" sh that of the other, such proportions, Z' sU and Z" sh , of the total length, Zgh = Z' sh + -"sh are to be taken of each that: 1 I \/ 7" ' | 1 II ^, Til * sh A -^ sh ~T ^ sh A -^ sh -\ , -s> -^ sh ~T "^ sh Since in this equation every term contains a length as a factor, any length, for instance Z' 8h , may be unity, and we have: from which follows the proper ratio of the lengths of the two wires: ( Z V\ _^sh A'sh Tl I Y" 1 . -^ Sh / A Bh ^8h 3^6 DYNAMO-ELECTRIC MACHINES. [101 If the two sizes are combined by their weight, the specific weights, in pound per ohm, are to be substituted for the specific lengths in the above equations. The sectional area of the shunt wire which exactly furnishes the requisite magnetizing power at the given voltage between field terminals, with the prescribed percentage of extra- resistance in circuit, and at the specified increase of magnet temperature, may be directly obtained by the formula: tfh* = IO -5 X A sh AT f r \ - -875 x - x / T x / 1 + ~ ) x (i + .004 x e m ). (322) In the above formulae, E is the E. M. F. supplying the shunt coils of one magnetic circuit, and is identical with the terminal voltage of the machine, if the shunt coils are grouped in as many parallel rows as there are magnetic cir- cuits. But if the number of parallel shunt-circuits differs- from the number of magnetic circuits, the output E. M. F. of the machine, in order to obtain the proper value of E for cal- culating the shunt winding, must be multiplied by the ratio of the former to the latter number. The size, or sizes, of the shunt wire thus being decided upon, by means of formulae (319) or (322), the actual value of ,^ m , and therefrom the real length of the mean turn is to be computed (see formulae (289) to (291)), and to be inserted into formulae (319), or (322), respectively. In case of two sizes of wire being used, the winding depth can with sufficient accuracy in most cases be found by means of the formula: + which, however, on account of the fact that the mean length of a turn of the one size of wire is different from that of the other, and that, therefore, the ratio of the number of turns of the two sizes differs from the ratio of their length, is only approximately correct and gives accurate results in case of 101] SHUNT WINDING. 387 comparatively long and shallow coils only. For short and deep coils, Fig. 311, the heights of the winding spaces for the r A A 4 s i f ;? <=s -rr T C I f4 U3 f ' ; i ^ fi -... ^ Fig. 311. Dimensions of Shunt Coil. two sizes are to be separately determined by formula (257), thus: h - h > " " . -. . /i2 Z' 8h x tfV m ,4 / - ; - T /m X 7T /i y .(324) where // m = total height of winding space, in inches; h' m and h" m = partial heights of winding space occu- pied by wire of first and second size, respectively; d' Bb and d" 8b = diameters of insulated shunt wires, inch; Z'gi, and ZV total length of the two sizes of wire, in feet; d' m = internal diameter of coil formed by first size of wire (= core-diameter plus insulation), in inches; " in which AT = number of ampere-turns required; / t = mean length of one turn, in feet; 6 m specified rise of temperature, in Centigrade degrees; SB = radiating surface of magnets, in square inches. In case of a compound winding, (328) will give the weights of the series and shunt wires, respectively, if A T is replaced by A T^ and AT&, and if the energies consumed by each of the two windings individually are substituted for the total energy loss in the magnets. By transformation, the above formula (328) can be employed to calculate the temperature increase 6 m , caused in exciting a magnetizing force of AT ampere-turns by a given weight, wt m pounds, of bare wire filling a coil of known radiating surface, S M square inches. Solving (328) for 6 m , we obtain: [ U = V '"""A ' J (329) wt m .004 X The weight of copper contained in a coil of given dimen- sions is: wt m = / T X /' m X h m X .21 , (330) where / T = mean length of one turn, in inches; /' m = length of coil, in inches; h m = height of winding space, in inches; .21 = average specific weight, in pounds per cubic inch, of insulated copper wire, see Table XCII., 96. 103. Calculation of Shunt Field Regulator. The voltage of a shunt-wound machine is regulated by means of a variable rheostat inserted into the shunt-circuit. 103] SHUNT WINDING. 391 The total resistance of this shunt regulator must be the sura of the resistances that are to be cut out of, and added to, the shunt-circuit in order to effect, respectively, an increase and a decrease of the exciting current sufficient to cause the normal E. M. F. to rise and fall to the desired limits. The amount of regulating resistance required to produce a given maximum or minimum E. M. F. is obtained, in per cent, of the magnet resistance, by determining the additional ampere-turns needed for maximum voltage, or the difference between the magnet- izing forces for normal and for minimum voltage respectively, for, the magnetic flux, and with it the magnetic densities in the various portions of the magnetic circuit, must be varied in direct proportion with the E. M. F. to be generated. If the dynamo is to be regulated between a maximum E. M. F., '0^ , and a minimum E. M. F., E'^n, the magnet- izing forces required for the resulting maximum and minimum flux are found as follows: The exciting power required for the air gaps varies directly with the field density, hence the maximum magnetizing force, by (228): X OC" / and the minimum magnetizing force: *f* = -3133 x The values of /* ' g in these formulae may differ from each other, and also from that for normal voltage, owing to the fact that the product of field density and conductor velocity may have increased or decreased sufficiently to influence the constant 13 in formula (166). For each value of 3C", there- fore, Table LXVI., 64, must be consulted. For the iron portions of the magnetic circuit the specific magnetizing forces for the new densities are to be found from Table LXXXVIII., 88, and to be multiplied by the length of the path in the frame; thus, for maximum voltage: w *max corresponding to a density of (R" m x ^ 392 DYNAMO-ELECTRIC MACHINES. [ and for minimum voltage: at" m = *w ff m jn X /" m > wVn corresponding to a density of (B" m X J7> *5 min. The magnetizing force required to compensate the armature reactions, finally, is affected by the change of density in the polepieces, the latter determining the constant 16 in formula (250); in calculating the compensating ampere-turns for the maximum voltage, the value of k lb from Table XCI. is to be taken for a density of E' X max E' and in case of the minimum voltage, for a density of pi (nil v/ min p ' lines per square inch. Having determined the maximum and minimum magnetizing forces for the various portions of the circuit, their respective sums are the excitations, A T max and AT min , needed for the maximum and minimum voltage. The number of turns be- ing constant, the magnetizing force is varied by proportion- ally adjusting the exciting current, and this in turn is effected by inversely altering the resistance of the field circuit. The excitation for maximum voltage is AT times that for normal load, hence the corresponding minimum shunt resistance, that is, the resistance of the magnet winding alone, must be AT times the normal resistance of the shunt-circuit, or, the extra- resistance in circuit at normal load is: A T -AT '* = 109 X - 103] SHUNT WINDING. 393 per cent, of the magnet resistance. The magnetizing force for minimum voltage, similarly being AT times that for normal output, the maximum shunt resistance is AT times the normal, or, regulating resistance amounting to ' >< per cent, of the normal resistance, which is ( AT-AT^ . 100 X - r*r I X AT per cent, of the magnet resistance, is to be added to the nor- mal shunt resistance in order to reduce the E. M. F. to the required limit. Expressing the sum of these percentages in terms of the magnet resistance, we obtain the total resistance of the shunt regulator: AT A T AT A T min mn - X This resistance is to be divided into a number of subdi- visions, or "steps," said number to be greater the finer the degree of regulation desired. Since the shunt-current de- creases with the number of steps included into the circuit, material can be saved by winding the coils last in circuit with finer wires than the first ones. At the maximum voltage the shunt-current, by virtue of Ohm's Law, is: (/sh)max = ^, (332) and at minimum voltage we have: / r \ -^mln >) (Ah)min= ~p J~^> (666) the current capacity of any coil of the regulator, therefore, can with sufficient accuracy be determined by proper interpolation 394 DYNAMO-ELECTRIC MACHINES. [103 between the values obtained by formula (332) and (333). Thus, the current passing through the shunt-circuit when n x coils of the regulator are contained in the same, is found: (T \ I T \ V \ sh/max (-'sh/mln /oo/f\ \ J s)i)x ^shjmax n x X - , (oo4r) n t where n r is the total number of the coils, or steps, of the reg- ulator. From (334) we obtain by transposition: ~rr~\ ~ ' l/sh/min r the latter formula giving the number of coils which must be added to the magnet winding in order to cause any given cur- rent, (/gh),, to flow through the shunt-circuit. CHAPTER XXII. COMPOUND WINDING. 104. Determination of Number of Shunt and Series Ampere-Turns. Since in a compound dynamo the series winding is to supply the excitation necessary to produce a potential equal to that lost by armature and series field resistance, and by armature reaction, the number of shunt ampere-turns for a compound- wound machine is the magnetizing force needed on open circuit, and the number of series ampere-turns required for perfect regulation is the difference between the excitation needed for normal load and that on open circuit. The proper number of shunt and series ampere-turns can, therefore, be computed as follows: The useful flux required on open circuit is that number of lines of force which will produce the output E. M. F., , of the dynamo, viz. : _ 6 X n' 9 X E X IP* . ~ N c X N ' hence the ampere-turns needed to overcome, on open circuit, the reluctances of air gaps, armature core, and magnet frame, respectively, are: = .3133 X - X/ = '" x g , and /7/ 1I)o = tn"ws^ X /" w j. + " l "d. X /" c j + >' r c . 8 . X /'c^., in which m" ^ ;//* w .,. o , >" c .i, and > //ff c.s. are the speciric mag- # a. <*> ^o * netizmg forces corresponding to densities^-' ' -^ ^ a *-> w.i. " c .i. A and ~^- r > respectively, A being the leakage factor on open ^ c.s, circuit. No current flowing in the armature, there is no armature re- action on open circuit, and no compensating ampere-turns arc 395 39 6 DYNAMO-ELECTRIC MACHINES. [ 104 therefore needed; consequently the total number of ampere- turns on open circuit, to be supplied by shunt winding, is: AT 8h = AT = at g(> + at &Q + at mQ (336) Next a similar set of calculations is made for the normal output. The useful flux in this case is: <6 6 X ' p X E X 10*. where E' =. E -f- /' r' a -f- 1 * "'&, for ordinary compound wind- ing; see formula (19), 14; and E' = E -f- /' X (r' & -f- r' K ), for long-shunt compound winding; see formula (22), 14. Singe, however, / and /' are very nearly alike, E' is practi- cally the same in either case. Besides, E' can only be approxi- mately determined at this stage of the calculation, since the series field resistance is not yet known. Taking the latter as .25 of the armature resistance, we therefore have for either kind of a compound winding: E'=E+ 1.25 7V' a (337) In case the machine is to be over compounded for loss in the line, the percentage of drop usually 5 percent. is to be in- cluded into the output E. M. F., hence the total E. M. F. generated at normal load, for 5 per cent, overcompounding: E'= i.o$E+ 1.25 1' r\ (338) The magnetizing forces required at normal load, then, are: af = -3133 X ^-X /' g ; at & = m\ x l\\ N x /' k y a and at t = k u X - X - - p 180 w" c .g. are the specific magnetizing forces A ^ A densities -^-' -^ ' ^ ' and ^ o a *3 w.i. *^ c j. *^ \ spectively, A being the leakage factor at normal output. A ^ A , corresponding to the densities -^-' -^ ' -^ ' and ^ re- 104] COMPOUND WINDING. 397 Their sum is the total number of ampere-turns needed for excitation at normal output: AT=at e + at* + af at this is supplied by shunt and series winding combined, conse- quently the compounding number of series ampere-turns: AT ee = AT- AT sb = AT- AT Q ..... (339) In the above formulae for af m& and at m , the factors A and A are the leakage coefficients of the machine on open circuit and E' Figs. 312 and 313. Positions of Exploring Coils for Determining Distribu- tion of Flux in Dynamos. at normal load, respectively. Although the effect of the armature current upon the distribution of the magnetic flux in the different parts of the machine is very marked, as shown by tests made by H. D. Frisbee and A. Stratton, ' the ratio of the total leakage factors in the two cases, especially in com- pound-wound machines, is so small that the factor A, as obtained from formulae (157), can be used for the calculation of both the shunt and the total ampere-turns. Since, however, it is very instructive to note the actual difference between the distribu- tion of the magnetic flux at normal output and that on open circuit, the results of the tests mentioned above are compiled in the following Table XCV., in which all the flux intensities in the various parts of the different machines experimented upon are given in per cent, of the useful flux through the 1 "The Effect of Armature Current on Magnetic Leakage in Dynamos and Motors," graduation thesis by Harry D. Frisbee and Alex. Stratton, Columbia College ; Electrical World, vol. xxv. p. 200 (February 16, 1895). 398 DYNAMO-ELECTRIC MACHINES. [104 p 6 ~. II O 3 O .0 fcl|l 0* " _ -,~ JO "Ijl jj'3 .- O 10 JO JO CO JO o> 5 ^^^^^ ^ ^ s X il II JO JO >O O'OJOiOO-*'* O OO i-iCi -iO JO oo JO 3 g|a Q cs I *- c 2 = a II JO *. , i o H M Hi 0) O .3 Normal Output. JO JO JO >^ Sos'jo'ot-:^-' jo JO jooeog 'o J ** *^" SJ M ^ ^ *O Cu ^ *c? ^ * *"" ' *^ "" *^ 'S ^ S oJ" O ta> -^S^cS ^ ^ - -""' "^ fcOgJsfisp -2 p2 "S^'S* E- 8.^ gg^|gg^4 ^o-r---ga^ IllSlll I 1 Hill Leakage factor, on open ci Leakage factor, at norina Ratio of leakage factors, > a . B lss| CO CO 3 3 H Qo4 x flm - AT 75 / 3 i The number of series turns being readily found from * 86 7- > the total length of the series field conductor is: /' AT T T A/" v IT_ _ ^^se v *jr_ r f -^se iv se A. __ ~ T o ICCL, and this, divided by the series field resistance, furnishes the specific length of the required series field conductor, thus: 400 DYNAMO-ELECTRIC MACHINES. [106 /' T AT 75 7 2 ~ x -- x--x -x (i +.004 x e m ) = 6.25 X <* x (i + .004 x U ..... (342) *^M H v m where /' T mean length of one series turn, in inches. The sectional area of the series field conductor, therefore. analogous to (296), is: = 10.5 x A A T (343) If one single wire of this cross-section would be impractical, one or more cables stranded of n K wires, each of ($' \ ?*. * *' - "se circular mils, may be used, or a copper ribbon may be em- ployed. The actual series field resistance, at 15.5 C., then being: Z = 10.5 X ~= 10.5 X - .875 x * - .875 x - T r ....... (344) "se '*se * \ u fie) the actual energy consumption in the series winding is: ^se - /' X ^ = ' 875 x 7X /T X ( T + - 004 x 6 -)> and, consequently, the energy loss permissible in the shunt winding: P P - P J ah * m -* se = ^rX S M -/' X r ae x (i +.004 X 8 m ) ...... (346) / If the extra-resistance at normal load is to be r K per cent. of the shunt resistance, the total watts consumed by the entire 105] COMPOUND WINDING. 401 shunt-circuit can be obtained by (312); formulae (313) to (317) then furnish the number of shunt turns, the total length, and the resistance of the shunt wire, and from (318) and (319) the specific length and the sectional area are finally received: AT I" / r \ ..-(347) AT / r \ > ........... (352) Compound-wound generator: Series-wound motor: * = E1 ~ ^EI* + ^l ............ < 354 > Shunt-wound motor: *?*= Compound-wound motor . ^/-[ Ve - Since the electrical efficiency does not include waste by hys- teresis, eddy currents, and friction, but is depending upon the energy losses due to heating by the current only, it may be adjusted to any desired value by properly proportioning the resistances of the machine; see formula:! (10), (13), (20), and (23), 14. The electrical efficiency of modern dynamos is very high, ranging from rj e = .85, or 85 per cent., for small machines, to as high as r/ = .99, or 99 percent., for very large generators. 107. Commercial Efficiency. By the commercial or net efficiency of a dynamo-electric machine is meant the ratio of its output to its intake. The intake of a generator is the mechanical energy required to drive it, and is the sum of the total energy generated in the armature and of the energy losses due to hysteresis, eddy cur- rents, and friction; the intake of a motor is the electrical energy delivered to its terminals. The output of a generator is the electrical energy disposable at its terminals; the output of a motor is the mechanical energy disposable at its shaft, and 107] EFFICIENCY OF GENERATORS AND MOTORS. 407 consists in the useful energy of the armature diminished by hysteresis, eddy current, and friction losses. The commercial efficiency of a generator, therefore, is : P P P P" ' P' + P' - P' + A + />. + /> and 77 that of a motor : pn p, _ p,^ p, _ ^ Vc ' P ~ P P (357) in which -rj = commercial or net efficiency of dynamo; P = electrical energy at terminals, /. e., output of generator, or intake of motor; P' electrical activity in armature; P" = mechanical energy at dynamo shaft, /. e., driv- ing power of generator, or mechanical out- put of motor, respectively; P & = energy absorbed by armature winding; .P M = energy used for field excitation; P h = energy consumed by hysteresis; P 6 energy consumed by eddy currents; P = energy loss due to air resistance, brush fric- tion, journal friction, etc. ; P' = energy required to run machine at normal speed on open circuit. Substituting in the above formulae the values of P, P M and /> M , the following set of formulas, resembling (351) to (356), is obtained : Series-wound generator: El - /' (r* + * Shunt-wound generator: El T 11 < j_ / a ID' ' -* r - y r ~ * (359) ,(360) 48 DYNAMO-ELECTRIC MACHINES. [ 107 Compound-wound generator: _ _ El _ = El + /" (r\ + r^ + 7 8h ' r\ + /" ; Series- wound motor: Shunt-wound motor: /'V' 7 Compound- wound motor: In case of belt-driving, the mechanical energy at the dynamo shaft, in foot-pounds per second, can also be expressed by the product of the belt-speed, in feet per second, and of the effect- ive driving power of the belt, in pounds, or, converted into watts : p* - *. y ^H y ( F f\ ~ 55 X 60 X ( * B J* = 1.3564 x v' B x OF B -/B), .................. (365) where V B = belt velocity, in feet per minute; z/ B = belt velocity, in feet per second; f B tension on tight side of belt, in pounds; /B = tension on slack side of belt, in pounds. The commercial efficiency of a generator, therefore, may be expressed by: 770 = ^~'~~ L3564 XZ/BX^B-A)' and the commercial efficiency of a motor, by: - P " -' '-3564 X g/ B X(^ B -/B) "" - The commercial efficiency, ^ c , of a dynamo is always smaller than its electrical efficiency, j? e , since the former, besides the electrical energy-dissipation, includes all mechanical and mag- 108] EFFICIENCY OF GENERATORS AND MOTORS. 4<>9 netic energy losses, such as are due to journal bearing fric- tion, to hysteresis, to eddy currents, and to magnetic leakage. The commercial efficiency, therefore, depends upon the amount of the electrical efficiency, upon the shape of the armature, upon the design, workmanship, and alignment of the bearings, upon the pressure of the brushes, upon the quality of the iron employed in its armature and field magnets, and upon the degree of lamination of the armature core; while the electrical efficiency is a function of the electrical resistances only. The mechanical and magnetical losses vary very nearly proportional to the speed; the no load energy consumption for any speed, consequently, is approximately equal to the open circuit loss at normal speed multiplied by the ratio of the given to the normal speed. The commercial efficiency of well-designed machines ranges from 7/ c = .70, or 70 per cent., for small dynamos, to rf c = .96, or 96 per cent., for large ones. Since in a direct-driven generator the commercial efficiency is the ratio of the mechanical power available at the engine shaft to the electrical energy at the machine terminals, for comparisons between direct and belt-driven dynamos the loss in belting should also be included into the commercial effi- ciency of the belt-driven generator. The following Table XCVI. contains averages of these losses for various arrange- ments of belts: TABLE XCVI. LOSSES IN DYNAMO BELTING. ARRANGEMENT OF BELTS. Loss IN BELTINO IN PER CENT. op POWER TRANSMITTED. Horizontal Belt 5 to 10 per cent. Vertical Belt 7 " 12 Countershaft and Horizontal Belt ". 10 " 15 " Countershaft and Vertical Belt 12 " 20 Main and Countershaft with Belts 20 " 30 108. Efficiency of Conversion. The efficiency of conversion, or the gross -efficiency, is the ratio of the electrical activity in the armature to the mechanical energy at the shaft, or vice versa; that is to say, in a generator 4io DYNAMO-ELECTRIC MACHINES. [100 it is the ratio between the total electrical energy generated and the gross mechanical power delivered to the shaft, and in a motor is the ratio of the mechanical output to the useful electrical energy in the armature. Or, in symbols, for a generator: P' P' P" - P' + P' , ^/ + /"K + P + P & + /> + ' r 746 hp 1.3564 X ' B X and for a w0/0r .- p* P' p' P ( J JT 4 J I /B) (368) P' P- + El - 746 hp _ 1.3564 X v' B X (^ B ~/B) E 1 r E r (369) The efficiency of conversion, rj & is the quotient of the com- mercial and electrical efficiencies, and therefore varies between rf a = = - = .82, or 82 per cent., % -85 for small dynamos, and = ^ = ~ = -97, 97 per cent., Tor large machines. 109. Weight-Efficiency and Cost of Dynamos. As the commercial efficiency increases with the size of the machine, so the weight-efficiency that is, the output per unit weight of the machine in general is greater for a large than for a small dynamo, and the cost of the machine per unit out- put, therefore, gradually decreases as the output increases. If all the different sized machines of a firm were made of the 1O9] EFFICIENCY OF GENERATORS AND MOTORS. 411 same type, all having the same linear proportions, and if all had the same, or a gradually increasing circumferential velocity, and were all figured for the same temperature increase in their windings, then the weight-efficiency would gradually increase according to a certain definite law, and the cost per K\V would decrease by a similar law. In practice, however, such definite laws do not exist for the following reasons: (i) Up to a certain output a bipolar type is usually employed, while for the larger capacities the multipolar types are more economical; this change in the type causes a sudden jump to take place, both in the weight-efficiency and in the specific cost, between the largest bipolar and the smallest multipolar sizes. (2) The machines of the different capacities are not all built in linear proportion to each other, but, in order to economize material, tools, and patterns the outputs of two or three consecutive sizes are often varied by simply increasing the length of armature and polepieces; in this case a small machine with a long armature may be of greater weight-efficiency and of a smaller specific price than the next larger size with a short armature. (3) The conductor-velocity is not the same in all sizes; as a general rule, it is higher in the bigger machines, but often the increase from size to size is very irregular, causing deviation in the gradual increase of the weight-efficiency. (4) Certain sizes of machines being more popular than others, a greater number of these can be manufactured simultaneously, and therefore these sizes can be turned out cheaper than others, and the specific cost of such sizes will likely be smaller than that of the next larger ones. (5) Large generators frequently are fitted with special parts, such as devices for the simultaneous adjustment and raising of the brushes, arrangements for operating the switches, brackets for supporting the heavy main and cross-connecting cables, platforms, stairways, etc., the additional weight and cost of these extra parts often lowering the weight efficiency and increasing the specific cost beyond those of smaller sizes not possessing such complications. These various considera- tions, then, show why prices differ so widely, and why the ratio of weight to output is so varied; and they offer a reason for the fact that the data derived from different makers' price- lists are at such a great variance from each other. D YNA MO-ELECTRIC MA CHINES. [109 In the following Table XCVII. the author has compiled the average weights and weight-efficiencies (watts per pound), for all sizes of high-, medium-, and low-speed dynamos as averaged from the catalogues of numerous representative American manufacturers of high grade electrical machinery: TABLE XCVII. AVERAGE WEIGHT AND WEIGHT-EFFICIENCY OF DYNAMOS. 1 1 icii SPEED. MEDIUM SPUED. Low SPEED. CAPAC- ITY OF DYNA- MO, IN KILO- WATTS. Average Weight (Total, Net). Lbs. Weight per Kilo- watt. Lbs. Output per Pound Watts. A verage Weight (Total, Net). Lbs. Weight per Kilo- watt. Lbs. Output per Pound. Watts. Average Weight (Total, Net). Lbs. Weight per Kilo- watt. Lbs. Output per Pound. Watts. .1 25 250 4 35 350 2.9 50 500 2 .25 55 220 4.5 80 320 3.1 112 450 2.2 .5 100 200 5 150 300 3.3 210 420 2.4 1 190 190 5.3 280 280 3.6 400 400 2.5 2 350 175 5.7 500 250 4 720 360 2.8 5 775 155 6.5 1,150 230 4.4 1,650 330 3 . 10 1,400 140 7.2 2,150 215 4.7 3,000 300 3.3 25 3,000 120 8.3 4,750 190 5.3 7,000 280 3.6 50 5,500 110 9.1 8,500 170 5.9 12,500 250 4 100 10,500 105 9.5 16,000 ICO 6.3 23,000 230 4.4 200 20000 100 10 30,000 150 6.7 41.000 i 205 4.9 300 29,000 97 10.3 42,000 140 7.2 57.000 190 5.3 400 37,500 94 10.7 53,000 133 7.5 72,000 180 5.6 600 54,000 90 11.1 74,500 124 8.1 99,000 165 6.1 800 70,000 87 11.5 93.000 116 8.6 120,000 150 6.7 1,000 85,000 85 11.8 110,000 110 9.1 140.000 140 7.2 1,500 123,000 82 12.2 150000 100 10 180,000 120 8.3 2,000 160,000 80 12.5 190,000 95 10.5 220,000 110 9.1 Since the speeds for the same outputs vary greatly in ma- chines of different manufacturers, there exist considerable deviations from the averages given above. When bearing this in mind, the above table may be effectively employed to check the general proportions and design of the calculated ma- chine. CHAPTER XXIV. DESIGNING OF A NUMBER OF DYNAMOS OF SAME TYPE. 110. Simplified Method of Armature Calculation. In case a number of different sizes of machines are to be designed of the same type, the method " m = magnetic density in magnet cores, in lines per square inch; S m = area of magnet-core, in square inches; d & = diameter of armature core, in inches; / a = length of armature core, in inches; jV c = total number of armature conductors; p = number of pairs of magnet poles; ' p = number of bifurcations of current in armature; JV = speed, in revolutions per minute; z/ c = conductor-velocity, in feet per second; A = factor of magnetic leakage. Expressing the length of the armature core as a multiple of its diameter: *a "-18 X " a , and writing for the number of conductors on the armature : j\r a n v C ~"~ J^ftf ^ 1 9 where d & = diameter of armature core, in inches; d"^ = pitch of conductors on armature circumference, in inches; ! = number of layers of armature conductors; formula (371) becomes: E = 3.82 X Y X x * x * . . .(376) V CB" m X * 1 X ^ c X , Having found the armature diameters for the various sizes, their lengths can then be readily obtained by multiplication with/ lg ; and diameter and length of the armature determine the principal dimensions of the field frame. The calculation of the total magnetizing force and of the field winding, for the number of dynamos of the same type, by similarly extracting from the respective formulas all the fixed quantities, may also be somewhat simplified, but the direct methods given for the field calculation are already so simple that not much can be gained by so doing, and it is therefore preferable to separately consider every single case. 111. Output as a Function of Size. If the ratio of the dimensions of two dynamos of the same type is i : m, the ratio of their respective outputs can be expressed as an exponential function of this ratio of size, as follows: X" = If the exponent x is given for the various practical condi- tions, the dimensions of any dynamo for a required output can, therefore, be calculated from the dimensions, and the known output of one machine of the type in question, from the formula: which gives the multiplier , by which the linear dimensions of the known machine are to be altered in order to obtain the required output. The author, by a mathematical deduction, ' has found the theoretical value of the required exponent to be : x = 2.5. ' " Relation Between Increase of Dimensions and Rise of Output of Dynamos," by Alfred E. Wiener, Electrical World, vol. xxii. pp. 395 and 409 (November 18 and 25, 1893) ; Elektrotech. Zeitschr., vol. xv. p. 57 (February I, 1894). 111] DESIGNING DYNAMOS OF SAME TYPE. 417 In the mathematical determination of x, however, the thick- ness of the insulation around the armature conductor has, for convenience, been neglected. The theoretical value found, therefore, holds good only for the imaginary case that the entire winding space is filled with copper. Since the per- centage of the winding space occupied by insulating material is the larger the smaller the armature, the difference between the actual and the theoretical output will be the greater, com- paratively, the smaller the dynamo, and it follows that the exponent, x, varies with the sizes of the machines to be compared. Furthermore, the area of the armature conductor decreases with the voltage of the machine; in a high-voltage dynamo, therefore, a larger portion of the winding space is occupied by the insulation than would be the case if the same machine were wound for low tension. From this it follows that the output of any dynamo, if wound for low voltage, is greater than if wound for high potential, and the value of the expo- nent x, consequently, also depends upon the voltages of the machines to be compared. Taking up by actual calculation the influence of size and of voltage upon the value of x, the general law was found that the exponent of the ratio of outputs of two dynamos of the same type increases with decreasing ratio of their linear dimensions as well as with decreasing ratio of their voltages; the theoretical value being correct only for the case that the dynamo to be newly designed is to have 10 or more times the voltage, and at least the 8-fold size of the given one. This law is observed to really hold in practice, as can be derived from the following Table XCVIIL, which gives average values of the exponent x for all the different ratios of size and voltage: TABLE XCVIII. EXPONENT OF OUTPUT-RVTTO IN FORMULA FOR SIZE- RATIO FOR VARIOUS COMBINATIONS OF POTENTIALS AND SIZES. RATIO or POTENTIALS, VALUK OP EXPONENT X, FOR RATIO or LINEAR DIMENSIONS, nt = Ito2 3to8 8 and over. Up to* *to4 10 and over 3.00 2.80 2.60 2.85 2.70 2.55 2.70 2.60 2.50 41 8 DYNAMO-ELECTRIC MACHINES. [ 111 The values given in the above table, besides for the com- parison of machines of the same type, are found to hold good also for the comparison of the outputs of similar armatures in frames of different types. But the figures contained in Table XCVIII. are based upon the assumption that the field- densities and the conductor-velocities of the two machines to be compared are identical, a condition which is very seldom fulfilled in practice, particularly not in dynamos of different type, as, for instance, when comparing a bipolar with a multi- polar machine. Hence, any difference in the field-densities and in the peripheral speeds of the two machines to be com- pared must be properly considered, that is to say, the expo- nent x given in the preceding table for the voltage-ratio and the size-ratio in question must be multiplied by the ratio of their products of field-density and conductor-velocity, for, the E. M. F., and therefore the output, of a dynamo is directly proportional to the flux-density of its magnetic field and to the cutting-speed of its armature conductors. CHAPTER XXV. CALCULATION OF ELECTRIC MOTORS. 112. Application of Generator Formulae to Motor Calculation. All the formulae previously given for generators apply equally well to the case of an electric motor; for, in general, a well-designed generator will also be a good motor. Hence the first step in calculating an electric motor is to determine the electrical capacity and E. M. F. of this motor when driven as a generator, at the specified speed. ' Considering a given dynamo as a generator, its output, /*, , in watts, at the terminals, is the total energy, /", generated in its armature by electromagnetic induction, diminished by the amount of energy absorbed between the armature conductors and the machine terminals; that is, by the loss due to inter- nal electrical resistances. In other words, the output is the total electrical energy produced in the armature multiplied by the electrical efficiency of the dynamo. The output, P\, of the same machine, when run with the same speed as a motor, is the useful electrical energy, P', active within its armature in setting up electromagnetic induction, less the energy lost between armature and pulley; that is, less the loss caused by hysteresis, eddy currents, and friction, or is the product of electrical activity and gross efficiency. Conversely, the power, P" l , to be supplied to the generator pulley, must be the total energy, P', produced in the armature, increased by an amount equal to the magnetic and frictional losses, or must be P' divided by the gross efficiency. And the energy, /* a , finally, required at the motor terminals in order to set up in the arma- ture an electrical activity of P' watts, is found by adding to f the energy needed to overcome the internal resistances of 1 "Calculation of Electric Motors," by Alfred E. Wiener, Electrical World, vol. xxviii., pp. 693 and 725 (December 5 and 12, 1896). 420 DYNAMO-ELECTRIC MACHINES. (; 112 the motor, or by dividing P' by the electrical efficiency. Des- ignating the electrical efficiency of the machine, /'. (381).. Where P l , P 3 = electrical energy at terminals of machine, as generator and motor, respectively; P' = electric energy active in armature conduc- tors, being the same in both cases; -^" P\ = mechanical energy at dynamo pulley, for generator and motor, respectively. By transposition of (379) the electrical capacity of the machine can be expressed by the motor output, thus: P" pi a ' *' which is to say that, in order to find the dimensions and wind- ings for a motor of P" hp = ^ horse-power, it is necessary to figure a generator which at the given speed has a total capacity of p , = P\ = 746 x >,f watts 112] CALCULATION OF ELECTRIC MOTORS. 421 The E. M. F. for which the generator is to be calculated, or the Counter E. M. F. of the motor, is the voltage at the motor terminals diminished by the drop of potential within the machine, or: >= E- SX (r'a + r'se), (383) in which E = E. M. F. active in armature, in volts; E = voltage supplied to motor terminals; I = current intensity at motor terminals; r' a = armature resistance,, at working temperature, in ohms; r'ge = resistance of series field, warm, in ohms, for series and compound machines; in case of shunt dynamo r' ge = o. Formula (383), though theoretically accurate, is not prac- tically so, since for the same excitation, armature current and speed, the counter E. M. F. of a motor is greater than the E. M. F. when used as a generator, for the following reason: While in a generator a forward displacement, or a lead, of the brushes has the effect of weakening, and a backward displace- ment, or a lag, that of strengthening the field magnet, in a motor a lead tends to magnetize, and a lag to demagnetize the field. Sparkless running, however, requires a lead of the brushes in a generator and a lag of the same in a motor, so that in both cases the armature reactions weaken the field. Since hysteresis as well as eddy currents have the effect of shifting the magnetic field in the direction of the rotation, thereby increasing the lead in a generator and diminishing the lag in a motor, it follows that for equal magnetizing force, equal current inten- sity, and equal speed the lag in a motor is less than the lead in a corresponding generator. For the purpose at hand, however, formula (383) gives the required counter E. M. F. with sufficient accuracy, particularly because neither the cur- rent strength nor the resistances usually being prescribed, the drop must be estimated by means of Table VIII., 19. By dividing the electrical activity, P', as obtained from formula (382), by the E. M. F., E ', the current-capacity of the corresponding generator is found: ^' = ~ (384) 422 D YNAMO-ELECTRIC MA CHINES. [112 For the purpose of simplifying this conversion of a motor into a generator of equal electrical activity, the following Table XCIX. is given, which contains the average efficiencies, and the active energy for motors of various sizes: TABLE XCIX. AVERAGE EFFICIENCIES AND ELECTRICAL ACTIVITY OP ELECTRIC MOTORS OF VARIOUS SIZES. ELECTRICAL OUTPUT ACTIVITY OF MOTOR ELECTRICAL GROSS COMMERCIAL IN ARMATURE, IN EFFICIENCY. EFFICIENCY. EFFICIENCY. IN KILOWATTS. HORSE-POWER. hp *7e *?g % *?e X ?}% D , _ 746 X hp J. A .85 .82 .70 .08 i .87 .83 .72 .13 i .89 .84 .75 .22 i .90 .87 .78 .43 1 .91 .88 .80 .85 2 .92 .89 .82 1.7 5 .93 .90 .84 4.1 10 .94 .92 .86 8.1 20 .95 .93 .88 16 30 .96 .935 .90 24 50 .97 94 .91 40 100 .975 .945 .92 79 200 .98 .95 .93 157 500 .985 .955 .94 390 1000 .985 .96 .95 780 2000 .99 .97 .96 1540 If a dynamo which has been connected for working as a gen- erator is supplied with current from the mains instead, it will run as a motor, the direction of rotation depending upon the man- ner of field excitation. A series dynamo, since both the arma- ture and field currents are then reversed, will run in the 0//0.r/te'direction from that which it was driven as generator, and must therefore have its brushes reversed and given a lead in the opposite direction; or, if direction in the original gen- erator direction is desired, must have either its armature or its field connections reversed. A shunt dynamo will turn in the same direction when run as a motor, for, while the armature 113] CALCULATION OF ELECTRIC MOTORS. 423 current is reversed, the exciting current will have the same direction as when worked as a generator. A compound dynamo, finally, will run as a motor in the opposite direction, if the series winding is more powerful than the shunt, and in the same sense, if the shunt is the more powerful ; and while the field excitation as a generator is the sum of the series and shunt windings as a motor it is their difference. 113. Counter E. M. F. Whereas in a generator there is but one E. M. F., in a motor there must always be two. If / = current at machine terminals, E = direct E. M. F., E' = counter E. M. F., ft = total resistance of circuit, and r = internal resistance of machine, this difference between a generator and a motor can be best expressed ' by the formulae for the current in the two cases, thus for generator: _ E ~ ' for motor: E - E I - - - , or E = E Ir. r The current and direct E. M. F. are the same in both cases, but the resistance is much less in case of a motor, the differ- ence being replaced by the counter E. M. F., which acts like a resistance to reduce the current. Upon the amount of this counter E. M. F. depend the speed and the current, and therefore the power of an electric motor. For, since the E. M. F. generated by electromagnetic induction is proportional to the peripheral velocity of the armature, it follows that, other factors remaining unchanged, the speed conversely depends upon the counter E. M. F. only. The latter is the case in a series motor run from constant cur- rent supply, since in this the magnetizing force is constant at all loads. In a shunt motor, however, the field current varies with the load, and the speed, therefore, depends upon the field magnetism as well as upon the counter E. M. F. If the exciting current in a constant potential shunt motor is de- creased, the E. M. F. decreases correspondingly, and a rise of 1 "The Electric Motor," by Francis B. Crocker, Electrical World, vol. xxiii. p. 673 (May 19, 1894). 424 DYNAMO-ELECTRIC MACHINES. [ 114 the current flowing in the motor is the consequence, as fol- lows directly from the above equation for the motor current. The speed in this case, therefore, rises until the counter E. M. F. reaches a sufficient value to shut off the excess of current. If the counter E. M. F. is low, which is the case when the motor is starting or running slowly, resistance has to take its place in order to govern the current of the motor. The intro- duction of resistance in series with the armature, the so-called starting resistance, is usually resorted to for this regulation, but this is very wasteful of energy and involves the use of a large and clumsy rheostat, while the counter E. M. F. itself affords a means to easily design a motor to run at the same, or at a higher, speed at full load than when lightly loaded. This may be done by slightly exaggerating the effect of armature reac- tion, so that the field magnetism will be considerably reduced by the large armature current which flows at full load, thus diminishing the counter E. M. F. and increasing the speed in the manner explained above. In this way the remarkable effect of greater speed with heavier load is obtained without any special device or construction; all that is necessary being a slight modification in design, involving no increase in cost or complication. 114. Speed Calculation of Electric Motors. If a generator, which at a speed of ^revolutions per minute produces a total E. M. F. of ',= + I' X (r' & + r'^) volts, is run as a motor having same current strength in armature, the motor armature, in order that no more nor less than this current, /', its full load as a generator, shall flow, must gen- erate a counter E. M. F. of E\ = E - I' X (r\ + r'^ volts. The speed necessary to generate this back voltage, speed being proportional to voltage, is: /?' F _ /' v (r 1 4- r' ^ N :_ s/ ^v" * ^ a i se) N/ jy 2V * ~ E ' ^ ~ E /' X r' r' X " ' 114] CALCULATION OF ELECTRIC MOTORS. 4 2 5 which is the speed of the motor at full load, provided the E. M. F., E, supplied to its terminals is equal to the voltage when run as generator. The speed of the motor for any given E. M. F., applied to its armature terminals, depends (i) upon the load impressed upon the motor armature, or the torque r , it has to exert; (2) on the electrical resistance (r' a -\- r'^), of the armature and the series field; and (3) upon its specific generating power, or its capability of producing counter E. M. F. ; /. = useful flux, in maxwells; JV C =. number of conductors on armature; n'p = number of pairs of armature circuits electrically in parallel; the total counter E. M. F. at the required speed of N^ revolu- tions per minute, will be , - N * x jv. x jv and the current flowing in the armature, therefore, is: E - e" X ^ r = E ~ E> * = _ ........ (388) '. + r> m r' A + r> The activity of this current expended upon the counter E. M. F. will be their product, E\ X /' watts, and this must be equal to the total rate of working, which is the product of circumferential speed and turning moment, or torque; that is, it must be equal to 2 7t X .A 7 . X r X watts , 33,000 where the torque, r, is calculated from formula (93), 40; hence we have: I X ; . = 2 n X ^ ) 426 DYNAMO-ELECTRIC MACHINES. from which N^ = 60 x (~ - 8.52 x (r * + r jti> X \ (389) From (389) follows that, if either the internal resistance or the torque is zero, since the second term in the parenthesis then disappears, the speed of the motor is: *; = ox-= 6 X **- X "'' ..(390) This reduced formula (390), indeed, holds very nearly in practice for very large motors (in which the internal resistance is very small), and also is approximately followed in case of motors running free (the torque then being only that necessary to overcome the frictions). The important requirement of constant speed under variable load may be almost perfectly met by the compound-wound motor, is nearly met by the shunt-wound motor, and is not met without the aid of special mechanism by the series-wound motor. A compound-wound motor will maintain its speed perfectly constant under all loads, if the series winding is so adjusted that the increase of current strength through the series coils and armature shall diminish the M. M. F. of the field magnets to the degree necessary to compensate for the drop of pressure in the armature winding. (See 148.) If constant speed is required, such as is the case in operating silk mills and textile machinery, the compound motor will therefore be found to give the best satisfaction, since in shunt motors, although running with " practically constant " speed, the variation may be too great to be without influence upon the product of manufacture. When started without load the speed of a shunt motor grad- ually increases and reaches a maximum, from which it falls down again as soon as the load is put on. The rise at no load is due to the fact that since the potential at the field terminals is constant, the field current decreases as the resistance of the field coils increases, owing to their heating, thereby decreasing the magnetizing power, and in consequence the counter E. M. F. of the motor. The subsequent decrease of the speed is caused by the increase of the armature current with increas- 115] CALCULATION OF ELECTRIC MOTORS. 427 ing load, and by the heating of the armature due to the passing current, the counter E. M. F. decreasing with increasing drop of voltage in the armature. Tests made by Thomas J. Fay ' with shunt motors of various sizes gave the results compiled in the following Table C. : TABLE C. TESTS ON SPEED- VARIATION OP SHTJNT MOTORS. Normal CAPACITY Speed, at No Load, Increase of Speed from No Load, Cold, to No Load. Hot, Decrease of Speed from No Load, Hot, to Full Load. Hot, Final Change in Speed. Of MOTOR, Cold, Revs, per Due to Heating of Field Coils. Dae to Heating of Armature. 4- = Increase. Decrease. HP. Mm. 3 1400 20* of normal speed 12 % of normal speed + 8 % of normal speed. 5 1200 8^4 *' * 5 -j- 3^ * 71^ 1360 5/4 " ' ' 4 _l_ IJx! ' 10 1200 2 " H% " ' -6% ; 15 1180 2J^s " ' 3U " ' 20 860 j| 4 " -3^ From this table it will be seen that the resistance of the field and of the armature can be so proportioned with relation to each other that the final speed at full load hot is equal to the normal speed at no load cold. But in order to reduce to a minimum the variation of the speed during the period of heat- ing up of the motor, it is necessary that both the increase due to the heating of the magnet coils and the decrease due to the heating of the armature should be reduced as much as possible. For this purpose the field winding should be so proportioned as not to heat very much above the temperature of the sur- rounding air, and the armature resistance should be as low as possible. 115. Calculation of Current for Electric Motors. a. Current for Any Given Load. The current in the armature of a motor for any load, f x watts = 746 X hp^ horse power, at the pulley, since at any in- stant the entire energy supplied to the motor must be equal to the sum of the expenditures, can be found from the equation: E X (/', + / 8h ) = P\ + P* X (r' & + r'^) + E X / 8h + PO, 1 " Constant Speed Motors," by Thomas J. Fay, Electrical Age, vol. xv. p. 38 (January 19, 1895). 428 DYNAMO-ELECTRIC MACHINES. [ 115 which gives: X where ." = line potential supplied to motor terminals, in volts; /' x = current in armature of motor, in amperes, for any given load ; / sh = current in shunt field of motor, in amperes; P" x = useful load of motor, in watts; P = energy required for no load, in watts; r' & =. armature resistance, in ohm; r'gg = series field resistance, in ohm. Formula (391) directly applies to series- and compound- wound motors; in case of shunt-wound motors, r'^ being o, it reduces it to: b. Current for Maximum Commercial and Electrical Efficiency. ' As the energy commercially utilized in a motor is: P\ = E X /' - /' X (r' & + O - P and the entire energy supplied is: P\ = E x /' + P* ; the commercial efficiency can be expressed by and similarly the electrical efficiency, by: _xf'-f"(r' & ' being the energy absorbed in the shunt. ' " Shunt Motors," by W. D. Weaver, Electrical World, vol. xxi. p. I37 t (February 25, 1893). 116] CALCULATION OF ELECTRIC MOTORS. 429 These efficiencies are maxima for: (^ j, (393) and / respectively. Formula (393), therefore, gives the current that must be supplied to the armature of a motor in order to have the maximum commercial efficiency, and formula (394) the current for maximum electrical efficiency. 116. Designing of Motors for Different Purposes. According to the purpose a motor has to serve, its efficiency is desired to either be high and nearly constant over a wide range of its load, or to increase in proportion with the output and be highest at the maximal load the motor can carry. The shape of the efficiency curve of a motor depends upon the proportioning of its various losses. The losses in a motor are of two kinds, fixed and variable. The fixed losses are those due to the shunt field current, hysteresis, and eddy cur- rents, brush friction, bearing friction, and air resistance. The variable losses are those due to armature and series resistance, and to commutation, and increase with the load. If the fixed losses are small compared with the variable ones, the efficiency at light loads will be high and will rapidly drop as the load, and with it the variable loss, increases. If, on the other hand, the fixed losses are very large, and the variable losses small, the efficiency with small loads will be low, but will increase as the load becomes greater, for the reason that the total energy increases proportional to the load while the losses in this case remain nearly constant, increasing but very little with the load. In order to have the fixed losses in a motor small and the . variable losses great, it is necessary to employ a massive mag- netic circuit with few shunt ampere-turns, an ample cross-sec- tion of iron in the armature core, and a large number of turns on armature and series field; hence the energy lost in shunt field excitation, in hysteresis, and eddy currents is small, but that lost by armature and series field resistance and by com- 43 D YNAMO-ELECTRIC MA CHINES. [116 mutation is great. The reverse of these conditions insures an increase in the fixed, or a decrease in the variable, losses. Curves I. and II., Fig. 315, show the variation of the com- mercial efficiency with the load in two motors of different de- sign, both having the same efficiency, rj e = 80 per cent, at 90 z u < Ul 70 60 >-- o 50 uj o 40 U *>i 20g HI 10 | o 8 ^ ^ 94 1 1)4 l^LOAD Fig- 3 T 5- Efficiency Curves of Two Motors of Different Design. normal load, but I. having very high efficiencies at light loads, while II. has very low efficiencies at small loads, but even greater than normal efficiency with overloads: TABLE CI. COMPARISON OF EFFICIENCIES OF Two MOTORS BUILT FOR DIFFERENT PURPOSES. EFFICIENCY AT VARIOUS LOADS. J4 Load. 14 Load. i'.i Load. Normal Load. 25 Per cent. Overload. 50 Per cent,. Overload. Per cent. Per cent. Per cent. Per cent. Per cent. Per cent. I. 70 80 83 80 73 65 II. 40 60 72 80 88 90 An efficiency curve similar to I. is desired in constant power work where the greatest load is put on the motor but once in starting, and where, after the friction of rest has been over- come, the motor is called upon to work on half to three-fourths its normal output continually; motors, consequently, which are to be employed for running printing presses, machine- 117] CALCULATION OF ELECTRIC MOTORS. 43* shop tools, power pumps, etc., must be designed with a heavy frame of low magnetic density, a weak field, small excitation, and a powerful armature. In order to obtain an efficiency curve similar to II., which is preferable in all cases where the motor is not doing steady work, but is called upon to give more than its normal power at frequent intervals, as, for in- stance, in operating electric railways, elevators, cranes, hoists, etc., the motor must be provided with a light frame of high magnetic density, a strong field, powerful excitation, and a weak armature. 117. Railway Motors. a. RAILWAY MOTOR CONSTRUCTION. ' The construction of motors used for railway propulsion deviates in many respects, electrically as well as mechanically, from that of ordinary motors. The principal conditions that must be fulfilled in the design of a railway motor are the fol- lowing: (1) The motor should be extremely compact, so that it may be easily placed in the space available within the truck; yet it must be easily accessible, and all its parts subject to wear must be easily exchangeable. All parts of the machine must furthermore be so designed and the winding so executed that the continual vibrations due to the motion of the car are un- able to loosen the same, or to get them out of working order. (2) A railway motor must be so designed that with minimum weight a maximum output is obtained. (3) The speed of the armature must be properly chosen with regard to the minimum and maximum load, to the speed of the car, the diameter of the car wheels, and the ratio of speed reduction. (4) The regulation of the speed should be simple, reliable, and perfectly adapted to all grades and curvatures of the track. (5) The type of the motor should be so chosen, and the de- sign so carried out, that there is no external magnetic leakage, 1 See " Praktische Gesichtspunkte fur die Konstruction von Motoren fiir Strassenbahnbetrieb," by Emil Kolben, Elektrotechn. Zeilschrifl, vol. xiii. No. 34 and 35 (August 19 and 26, 1892). 43 2 DYNAMO-ELECTRIC MACHINES. [11*7 that at the same time all the vital parts of the motor are pro- tected from mechanical injuries, and that it can be so sup- ported from the truck that, if possible, none of its weight is resting directly upon the car axle. Particular care must also be bestowed upon the selection of insulating materials and the manner of insulation, in order to guard the machine against the influence of dampness, mud, and water. (i) Compact Design and Accessibility. Since it is usual to equip each car with two motors which are directly suspended from the car axles and the frame of the truck, the extreme dimensions of the motor are limited by the diameter of the wheels, their distance apart longitudinally, and by the gauge of the track. The trucks most commonly used have 30 or 33-inch wheels, a wheel base of 6 to 7 feet, and the standard gauge of 4 feet 8 inches. The height of the motor is further limited by the condition that a space of at least 3 inches should be left between the lowest point of the motor and the top of the rails in order to enable the motor to pass over stones or other small obstructions upon the track. The arrangement should be such that the working parts can be easily inspected during the trip from a trapdoor in the flooring of the car. If it is impracticable to provide the car- barn with pits below the tracks, the motor should be so arranged that the armature, the field coils, and the brushes can be taken out through the same trapdoor. In order to facilitate the quick replacing of a disabled armature, it is ad- visable to split the motor frame horizontally, and to make one part revolvable by means of strong hinges. (2) Maximum Output with Minimum Weight. The energy required for propelling a car being proportional to its weight, it must be the aim to make the entire equipment as light as is consistent with strength and durability. In order to reduce the weight of the motor to a minimum, it is of the utmost importance to use only the best materials suitable for the respective parts, namely, the softest annealed sheet iron for the armature core, silicon bronze or drop-forged copper 117] CALCULATION OF ELECTRIC MOTORS. 433 for the commutator segments, and softest cast steel for the field frame. If reduction gears are used, the pinions should be of hard bronze or of good tool steel, and the gear wheels of cast steel, or of fine grain cast-iron. In order to obtain the maximum possible output, the magnetic circuit of the motor should have as small a reluctance as possible, and the magnetic leakage should likewise be reduced as much as pos- sible. The former is attained by the use of toothed or perfor- ated armatures with very small air gaps; and the latter by proper selection of the type. The armature should be made most effective by providing it with a great number of turns; the sparking which would thus result under ordinary condi- tions being checked by the use of carbon brushes which are set radially in order to enable reversibility in the direction of rota- tion of the motor. The weight efficiency of various railway motors is given in Table CII., p. 435. (3) Speed, and Reduction Gearing. The speed of the motor naturally depends upon the car velocity desired, upon the size of the car wheels, and upon the method used for the mechanical transmission of the motion from the armature-shaft to the car axle. The maximum speed of the car, according to local conditions (size of town, amount of traffic in streets, etc.) varies from 8 to 15 miles per hour, the greatest speed of the car axle, therefore, provided that 30- inch wheels are used with the slow, and 33-inch wheels with the fast running cars, ranges between 90 and 150 revolutions, respectively. The methods of transmission most commonly employed in electric railway cars are the double and single spur gearing, and the direct coupling; worm gearing, bevel gearing, link- chains, and crank-rods being used only in single cases. The employment of double spur gearing was necessary with the earlier railway motors which were run at from 1000 to 1200 revolu- tions per minute, and which, therefore, had to have their speed reduced in the ratio of from 10: i to 15: i. High-speed railway motors, however, on account of the noise and wear connected with the presence of four gear wheels for each motor, that is eight gears per car, proved too inconvenient 434 D YNA MO-ELECTRIC MA CHINES. [ 1 1 7 and too expensive to maintain, and low-speed motors of from 400 to 500 revolutions per minute, necessitating but a single spur gearing with a reduction ratio of from 4:1 to 5 : i, were next resorted to. If the spur gears for such single reduction motors are provided with broad and carefully cut teeth, and are run in oil, both noise and wear are very small, and the effi- ciency is comparatively high. Worm gearing can be employed for any speed ratio within the limits of railway motor reduction, and by proper design very high efficiencies may be attained. If the worm is carefully cut from a solid piece of tool steel, and the rim of the worm wheel made of hard phosphor bronze, and if the dimensions are so chosen that an initial speed of 20 to 40 feet per second is obtained, the efficiency when run in oil may reach 90 per cent, and over. ' If no speed reduction at all is desired, that is to say, if the motor is to be directly coupled with the car axle, its normal speed must be between 100 and 150 revolutions per minute. From tests made by Professor S. H. Short, 4 the saving of power consumed in operating a directly coupled, gearless street car motor is found to be from 10 to 30 per cent, as compared with double spur gearing, and from 5 to 10 per cent, as compared with single spur gearing, according to the load. In order to show what has been done in the way of compact design and weight-efficiency of railway motors of various speed reductions, the following Table CII. has been prepared, giving the specific weight, the speed, kind and ratio of reduction, the type and dimensions of the frame, the space-efficiency, and the size of the armature, of the most common railway motors in practical use. The figures given for the dimensions of the field frame do not include any supporting or suspension brackets, lugs, or other extensions that may be attached to, or cast in one with the frame, but relate only to the magnetic portion of the field casting. This is done to bring all the space efficiencies to a common basis, thus enabling a fair com- parison of the various types: 1 See " Schneckengetriebe in Verbindung mit Elektromotoren," by Emil Kolben, Elektrotechn. Zeitschr., vol. xvi. p. 514 (August 15, 1895). 8 " Gearless Motors," by Sidney H. Short, Electrical Engineer, vol. xiii. p. 386 (April 13, 1892) ; Electrical World, vol. xix. p. 263 (April 16, 1892). 117] CALCULATION OF ELECTRIC MOTORS. 435 3 g HJ K fc o o o I S < c a H 7 S Q g -8.100 jo cooo cfe 10 co ao ^ JH -tad 'sut 'no BUI 'O aunuj p^ jCq paidnooo fc o a s~ 5* cc irToTado' so ocxfuj scoTo'o'o s "-> i-T- co* 'mP!A\ 9IXV II u i 15; * x MM iialai o* 4t jo uoipnpna paadg ;o OIBH; - n . * $ 8 5 J -a - g'l! 3 > js 3 a " oo .c 3 * e" 5 I HI *W :H o Ow 03 g ."3 .33 ^ ^-----.S3^*i .-.J---NH RE aO oS^SO & X O "> -^ t* : 5. . "3 x - > - tn ^ ^ s? v "a f 3S^ J -S 13 ^^ ^ 2 T D.O*' - - - - u ft- -S-*-3--C cC* SOCC 005 v. J; Q'GC* - S - 3 ^oji SiISIS3S3 'C 1 "g * *i J s! o 2 O) Tft 05 O3 O5 rnefi f> Oi ?C in ^Q.O oiO i ^ ; '*coco'''fl : ' c3^| 43 6 DYNAMO-ELECTRIC MACHINES. [ 117 (4) Speed Regulation. In order to effect the variation of the speed of railway motors within wide limits it is desirable that their field mag- nets should be series wound. The strength of the magnetic field can then be regulated either by inserting resistance into the main circuit, in connection with partial short-circuiting of the field coils, or by altering the combination of the magnet spools, or by series-parallel grouping of the armatures and field coils of the two motors. In the Resistance Method the insertion of rheostat-resistance into the main circuit, by reducing the effective E. M. F., causes a decrease in the speed of the motor; in this case the cross-section of the magnet wire must be so dimensioned as to carry the maximum current, but the number of turns must be chosen far greater than is required for the production of the requisite number of ampere-turns at maximum current and maximum speed. For, almost the full field strength must be obtained with a comparatively small current-intensity, and it it therefore necessary to short-circuit a portion of the magnet coils at maximum load. That is to say, in order to raise the torque of the motor for increased loads, only one of the two factors determining the same is increased, namely the current strength in the armature, while the field current remains the same. In order to do this without excessive sparking, caused by the fact that the brushes, not being adjustable, are never at the neutral points of the resultant field, carbon brushes must be used, whose large contact resistance considerably re- duces the current in the coils short-circuited by the brushes. The Combination Method of speed regulation consists in suit- ably changing the grouping of the magnet-spools. For this purpose it is necessary to wind the magnet coil in sections, equal portions of which are placed on each magnet, and to connect the terminals of these sections, usually three in num- ber, to a switch, or controller, of proper design. At the max- imum load of the motor the three sections are connected in parallel, and for this combination, therefore, the cross-section of the winding is to be calculated. For starting the car all sections are connected in series, and, if no precaution were taken, the magnet winding would, in consequence, have to 117] CALCULATION OF ELECTRIC MOTORS. 437 carry the full starting current, which may be 4 to 6 times the maximum normal current. In order to avoid overheating and damage due to this starting current, a starting rheostat must be placed in circuit, the resistance of this rheostat being so dimensioned that the starting current is brought down in strength to that of the maximum working current. While with the two former methods of speed regulation the two motors of the car are permanently connected in parallel, in the Series- Parallel Method of control, finally, both the arma- tures and magnet-coils of the two motors can be grouped in any desired combination. The same number of combinations is therefore possible with less elements, and only two sections per magnet-coil are necessitated. Since by placing both arma- tures and all four field-sections in series the starting current is considerably reduced, less resistance is needed in the start- ing rheostat, and a saving of energy is effected by this method. For calculating the carrying capacity of the magnet-wire the last two positions of the series-parallel controller are essential: for maximum speed the two motors, each having one coil cut out, are placed in parallel; and in the position for the next lower speed both motors with their two coils in series are grouped in parallel. (5) Selection of Type. The most important consideration in the selection of the type for a railway motor is the condition that there should be no external magnetic leakage, as otherwise the neighboring iron parts of the truck may seriously influence the magnetic distribution, and, furthermore, small iron objects, such as nails, screws, etc., may be attracted into the gap-space and may injure the armature. In order to protect the motor from dampness and mechanical injuries, such types are to be pre- ferred in which the yoke surrounds the armature, and which therefore can easily be so arranged that the frame completely encases all parts of the machine. The types possessing the latter feature are the iron-clad types, Figs. 203 to 207, 72, and Figs. 217 to 220, 73, the radial outerpole type, Fig. 208, and the axial multipolar type, Fig. 212; and as can be seen from the preceding Table CII., these are in fact the forms of machines that are used in modern railway motor design. 43 8 DYNAMO-ELECTRIC MACHINES. [117 b. CALCULATIONS CONNECTED WITH RAILWAY MOTOR DESIGN.' (i) Counter E. M. F., Current, and Energy Output of Motor. Inserting into the formula for the counter E. M. F., , 7V C N E' = -^ X --X $ X io 8 , P 60 the value of the useful flux from 86 and 87, 4 * y AT - N - X 7 ^eX/ (R (R io (R' X itt 47T where JF = magnetomotive force, in gilberts; AT N^ X I = magnetizing force, in ampere-turns; (R reluctance of magnetic circuit, in oersteds; *" X lH := X X j; , 4 4 7T A* *^m /t = permeability of magnet-frame, at normal load; l' m = length of magnetic circuit, in inches; S m = area of magnet-frame, in square inches; we obtain: E 1 c * * v v v TO* ^Q^ (R' X n p 60 x ] ' ' ' ^) If the internal resistance of the motor, /. e., armature resist- ance plus series field resistance, is designated by r, and the line potential by E, the current flowing in the armature, there- fore is: TV v JV r N _w.xsv mt _/_ x yv T E (R ' 60 y = = *: 1 See "Some Practical Formulae for Street-Car Motors," by Thorburn Reid, Electrical Engineer, vol. xii. p. 688 (December 23, 1891); " Capacity of Rail- way Motors," byE. A. Merrill, Electrical Engineer, vol. xvii. p. 231 (March 14, 1894). 117] CALCULATION OF ELECTRIC MOTORS. 439 and solving for /, we have: N c X & W r+ - -^7-- X -7-X f- X io 9 , 01 p oo Hence the work done by the motor: JV v N P N /> = * x / = -^= x , xx.o'. (397) 7V C , TVge, and n' v are constants of the motor, and 61' varies somewhat with the saturation of the field, but may be consid- ered practically constant; if, therefore, we unite all constants by substituting: _ N c X JVse j_ io 8 X * , ..(402) in which z> m = speed of car, in miles per hour; z = ratio of speed reduction, /'. e., ratio of arma- ture revolutions to those of the car axle; IN MILES PER HOUR, is : OF GRADE, g 8 10 12 15 18 20 25 30 .64 .80 .96 1.21 1.45 1.61 2.01 2.41 1 1.0? 1.34 1 61 2.01 2.41 2.68 3.35 4.02 2 1.50 1 88 225 2.82 3.38 376 4.69 5.63 3 1.93 2^41 2.90 3.62 4.34 4.83 603 7.24 4 2.36 2.95 3.54 4.42 5.31 5.90 7.37 8.85 5 2.78 3.48 4.17 522 6.26 6.97 8.71 10.44 6 3.22 4.02 4.83 6.03 7.23 8.05 10.04 12.06 7 3.65 4.56 5.47 6.84 8.20 9.12 11.40 1367 8 4.07 5.09 6.11 7.63 9.15 1018 12.73 15.28 9 4.50 5.64 6.75 8.43 10.10 11.25 14.07 16.89 10 4.93 6.16 7.39 9.24 11.07 12.32 15.40 18.50 12 5.78 7.23 8.68 10.84 13.01 14.47 18.10 21.70 15 7.07 8.84 10.60 13.25 15.90 17.70 22.10 26.55 From (404) the horizontal pull required to exert a given power at given speed is found thus: ?-?,000 X 60 P* I hp Giving to hp values from 15 to 60 horse-power, and to 7> m from 8 to 30 miles per hour, the following Table CIV. is obtained, which at a glance gives the horizontal effort, or draw-bar pull, exerted by any motor capacity at a given speed, whereupon, from (403), the load Wi, in tons, can be computed, which the equipment under consideration is able to propel at any given grade: 442 D YNAMO-ELECTRIC MA CHINES. [117 TABLE CIV. HORIZONTAL EFFORT OF MOTORS OF VARIOUS CAPACITIES AT DIFFERENT SPEEDS. KATKD CAPACITY PULL AT PERIPHERY OP WHEEL, f^ IN POUNDS, OF AT BATED SPEED OP CAR, V m IN MILES PER HOUR, OF : MOTOR 1 EQUIPMENT. hp 8 10 12 15 18 20 25 30 15 703 563 469 375 313 281 225 188 20 938 750 625 500 417 375 300 250 25 1,172 938 781 625 521 469 375 313 30 1,406 1,125 938 750 625 563 450 375 40 1,875 1,500 1,250 1,000 833 750 600 500 50 2,344 1,875 1,562 1,250 1,043 938 750 625 60 2,812 2,250 1,875 1,500 1,250 1,125 900 750 A simple graphical method of determining the car velocity and the current consumption under various conditions of traffic is shown in 133, Chapter XXVIII. (4) Line Potential for Given Speed of Car and Grade of Track. The E. M. F. required at the motor terminals to drive a car up a particular grade at a certain rate of speed may be found as follows. From (399) we have: = IX(r + KxW) t (406) in which everything is known except E and /. But /can be obtained from formula (400), provided we know the work P" that is to be done by the motor under the prevailing condi- tions. The value of P" being given by (404), the current I can be expressed by transposition of formula (400), and by substituting the expression so found into (406) the required E. M. F. is obtained : E= (r X 2 /h X V n K X M ..(407) Inserting into (407) the value of N found from (402), we have : (i-i * v PT \s 11 v ^ \ / /" v // r+J a ^OW>fj x y'A^. (4M) Knowing ,", we are enabled to determine the size of wire required in the feeders to maintain a certain speed at any point on the line. CHAPTER XXVI. CALCULATION OF UNIPOLAR DYNAMOS. 118. Formulae for Dimensions Relative to Armatnre Diameter. Assuming the armature diameter of a unipolar dynamo as given, the ratio of the working density of the lines in the material chosen for the frame to the flux-density permissible in the air gaps will determine the dimensions of the frame. The armature consisting in a solid iron or steel core without winding, the only air gap necessary is the clearance required for untrue running, and, on account of the short air gaps so obtained, a comparatively high field density, namely, JC* = 40,000 lines per square inch (or 5C 6200 lines per square centimetre) can be admitted. The practical working densi- ties, as given in Table LXXVL, 81, are: (B" = 90,000 lines per square inch ((B = 14,000 lines per square centimetre), for wrought iron, (B" = 85,000 lines per square inch ((B = 13,200 lines per square centimetre), for cast steel, and (B" = 45,000 to 40,000 lines per square inch ((B = 7000 to 6200 lines per square centimetre), for cast iron. By comparison, then, it follows that the area of the gap spaces should be about twice the cross-section of the frame, if wrought iron or cast steel is used, and about equal to the frame section if cast iron is employed. The cylinder type, on account of its smaller diameter and more compact form, being more practical than the disc type of unipolar machines, the former only will here be considered, inasmuch as it will not be difficult to derive similar formulae for the latter. Moreover, since for the same size of armature 443 444 D YNAMO-ELECTKIC MA CHINES. [118 a cast-iron frame requires about twice the weight of a cast- steel one, the use of the former material is limited to special cases, and formulae are given only for machines having cast- steel magnets. Adopting the general design indicated by Fig. 31, n, good practical dimensions of the frame are obtained by making the i * i j j i Fig. 316. Dimensions of Cast Steel Unipolar Cylinder Dynamo. active length of the armature conductor, that is, the length of the poles, see Fig 316: / P = -3<4, ................ (409) <4 being the mean diameter of the armature-cylinder; and by providing for the winding an annular space of length: and height: h m = .id & The gap area, then, will be: S g = d & 7t X -3<4 = - (411) 118] CALCULATION OF UNIPOLAR DYNAMOS. 445 and the cross-section of the magnet frame, in order to have a magnetic density of 85,000 lines per square inch, must be: The radial thickness of the armature, being that of the rim of a pulley of diameter d M is taken : ^ = .21^, ............. (412) which, by adding 5 V^T for clearance, makes the total distance between the two pole faces : p = .25 y^T- ............. (413) Allowing .05 ^ for the recess at the outer pole face, the internal diameter of the yoke is found: and the diameter at the bottom of the annular winding groove, or the diameter of the magnet core is: <4 = <4 - -25 Vd^~ 2 X .i<4 = -&? a - .25 ^7 The thicknesses of the frame section at these diameters must be: ^.Tjfe-R^fes-^*-;- 41 ^ <4U) and X re .& - .25 \ .0 respectively. For the radial thicknesses of the outer and inner tube por- tions of the field frame we have the equations: 446 DYNAMO-ELECTRIC MACHINES. [ 119 and h _ $m _ -444' _ " (4, - A*) (-84 - .25 y-_ 4) 7t - V respectively, from which we obtain, for the radial thickness of the yoke: k, = - J 2 = . 1 254 - . o 3 1/4 , and for the radial thickness of the core portion of the frame: .84 -.251/4 ^ c - - = .264 + .23^ .......................... (417) The total axial length of the frame is : 4 = .34^.1254 + 24 = .6254; ..... (418) and for the mean length of the magnetic circuit in the frame we find by scaling the path: /' m = 1.24 ............... (419) 119. Calculation of Armature Diameter and Output of Unipolar Cylinder Dynamo. All the dimensions of the machine being given, by 118, as multiples of the armature diameter, 4 > the dimensioning of the frame is reduced to the calculation of 4- In order to obtain a formula for the armature diameter, we express the polar area in two ways: electrically, as the quo- tient of flux, 0, and field density, 3C", and geometrically, as a cylinder surface of diameter 4 a d length .34* The number of parallel circuits as well as the number of conductors in the unipolar armature is unity, and the lines are cut but once in each revolution, the useful flux necessary to 119] CALCULATION OF UNIPOLAR DYNAMOS. 447 generate E volts at the speed of N revolutions, therefore, from formula (137), 56, is: _ .6 xx IP* ~AT~ ' '-\ence the gap area can be expressed, electrically, by: c - _ - 6 * E X io 9 ,. 2m * ~ 3C' " ^X OC" ' while geometrically we have from Fig. 316: S g = .3*; _ 6 9 , (426) The corresponding minimum speeds are found by formula (424), as follows: For forged steel armature : N . 33 X For wrought iron or cast steel armature: For cast iron armature : = 33 X ^=.33 X 300 200" _ 13,200 ~~ ~~ (427) The output of the machine is limited only by the carrying capacity of the armature; the current carrying cross-section of the latter is: <4 n X .2\/<4 = - 2 a 1 ^*! and since iron or steel will carry at least 200 amperes per square inch, the current capacity, in amperes, is: 1= 200 x .2 7t v <4* = 125*4*, (428) 120] CALCULATION OF UNIPOLAR DYNAMOS. 449 which, at E volts E. M. F., gives the output of the dynamo, in watts: (429) 120. Formulae for Unipolar Double Dynamo. In duplicating the design shown in Fig. 316, a unipolar dynamo with an armature of twice the effective length of the former is obtained, Fig. 317. Fig- 317. Dimensions of Cast-Steel Unipolar Double Dynamo. The pole area for this type is: S g = 2 x <4 7f x .3*4 = i.s&C, . . . .(430) hence, by equating (430) and (420), the diameter is obtained: 4 = 5 6 4<>o X E N x X." which, for 3C" = 40,000 lines per square inch, becomes: ". (432) The minimum diameter which produces E volts is: d = 282 x jf~r = 49 X f-, ..(433) 45 DYNAMO-ELECTRIC MACHINES. [121 from which, for forged steel armature: d. = X E = 1.22 E; 400 for wrought iron or cast steel armature: d & = X E = \.b\E; 300 and for cast iron armature : d & = x = 2.45 ^. 200 ....(434) For the double machine, the current carrying capacity and the output are found from the same formulae (428) and (429) respectively, as for the single-frame machine, and since the diameter of the frame is smaller, also its current intensity, and, in consequence, its total output will be smaller than that of a single-cylinder machine of the same E. M. F. 121. Calculation of Magnet Winding for Unipolar Cylinder Dynamos. The dimensions of both the single and double cylinder types being generally expressed as multiples of the armature diameter, see Figs. 316 and 317, the magnetizing forces re- quired for the various portions of their magnetic circuit can be computed from the following formulae. The magnetizing force required for the air gaps, their density being 5C" = 40,000, is: <*t g = -3133 X 40,000 X .05 Vd* X 1.2 = 750 Vd* t . .(435) where 1.2 is taken to be the probable factor of field deflec- tion, see Table LXVL, 64. Magnetizing force required for armature: (4.3$) at* = m X . 2 Since CB' a = 40,000 lines, we have: for wrought iron: at & = 1.5 tor cast steel: at A = 1.8 tor cast iron: at & = 17.6 Magnetizing force required for magnet frame (cast steel of density &" m = 85,000): at m = m" m X i.2 to \ X 3C" X ~^- D YNA MO-GRAPHICS. 479 In cases where the armature reaction is small and where the magnetic density in the armature core is low, that is, in all machines except those designed for certain special purposes (see 123), the curves OB and OD are very nearly straight lines, and can be united with curve O A by means of the approx- imate formula: = af at r = .3133 x oc" x i\ + k n x A x + .00001 X ^a X r X 3C" 2 ' x ; = 3C' X ( .3133 X I' g + k n X A x -~ X l\ r .00001 X ^V a X V' thus simplifying the construction of the magnetic characteris- tic into the addition of the abscissae of but a single curve and a Fig. 326. Simplified Method of Constructing Magnetic Characteristic. single straight line. Formula (448) gives practically accurate results if the mean density in the armature core, 91, at maxi- mum load of dynamo, is within 80,000 lines per square inch, or 12,500 lines per square centimetre, and if the values of the 480 DYNAMO-ELECTRIC MACHINES. [127 constant ao for different mean maximum load densities are taken from the following Table CV. : TABLE CV. FACTOR OF ARMATURE AMPERE-TURNS FOR VARIOUS MEAN FULL-LOAD DENSITIES. ENGLISH UNITS. METRIC UNITS. Mean Ampere- Constant Mean Ampere- Constant Density in Armature Core Turns per inch of Magnetic Circuit in Approximate Formula for Armature Density in Armature Core Turns per cm. of Magnetic Circuit in Approximate Formula for Armature at Maximum in Ampere- at Maximum in Ampere- Output. Armature Turup. Output. Armature Turns. Li lies p. sq. in. fO'l Core. n j. \ Lines per cm* /D Core. fi> * (fc a m\ (B"a <&a m & 80 o\ 25,000 4.5 .00018 4,000 1.8 .00045 80,000 5.5 .00018 5,000 2.35 .00047 35,000 6.5 .00019 6,000 2.85 .000475 40,000 7.5 .00019 7,000 3.35 .00048 45,000 8.5 .00019 8,000 3.95 .00049 50,000 9.6 .00019 9,000 4.8 .00053 55,000 11.1 .00020 10,000 6.1 .00061 60,000 13 .00022 10,500 7 .00067 65,000 15.7 .00024 11,000 8 .00073 70,000 19.6 .00028 11,500 9.4 .00082 75,000 24.7 .00033 12,000 10.8 .00090 80,000 31.2 .00039 12,500 12 .00096 For calculations in metric units the coefficient of gap ampere- turns, .3133, must be replaced by .8 (see 90), and the value .0000645 is to be taken for the factor of compensating am- pere-turns, instead of .00001, which has been averaged from a great number of bipolar and multipolar dynamos, having drum as well as ring, and smooth as well as toothed and perforated armatures. In the majority of cases the value of this factor, in English units, ranges between .0000075 anc ^ .0000125, while the actual minimum and maximum limits found were .0000040 and .0000160, respectively. The metric value is derived from the average in English measure by multiplying with the number of square centimetres in one square inch. The simplified process of constructing the characteristic, then, is as follows : The value of the combined magnetizing force, fl/ Kar , calculated from (448) for any one, preferably high, value of the field density, 3C", is plotted as abscissa XA, Fig. 326, with that value, XO, of JC" as ordinate, and the point A 127] DYNAMO-GRAPHICS. 481 thus found is connected with the co-ordinate centre O, by a straight line. Next the saturation curve OC of the field frame is plotted by computing A X OC" X & ^m for a series of values of 3C", multiplying the corresponding magnetizing forces, m" m , taken from Table LXXXVIII., p. 336, or LXXXIX, p. 337, or from Fig. 259, p. 338, for the re- spective material, with the length /" m , of the magnetic circuit in the field frame, and connecting the points so obtained by a continuous curved line OC. In case of a composition frame this process is to be performed according to formula (447), that is to say, by adding all the component magnetizing forces for each value of the density 3C". The required characteristic OE is then obtained by drawing horizontal lines, such as XE in Fig. 326, and making C, measured from curve OC, equal to the distance XA of line OA from the axis OX. Example : To construct the characteristic of a bipolar gen- erator of 125 volts and 160 amperes at 1200 revolutions per minute, having a ring armature and a cast-iron field frame, the following data being given: Length of magnetic circuit in cast iron, /" m = 80 inches; in armature core, l\ = 15 inches; in gap spaces, l" g = i-^g- inch. Mean area in cast iron, S m = 79 square inches; in armature, S a = 50 square inches; in gaps, S g = 158 square inches. Number of armature conductors, N c = 216. Coefficient of magnetic leakage, \ = 1.25. If the field frame, as in the present case, consists of but one material, the magnetization curve for that material of which a supply may be prepared for this purpose can be directly utilized. It is only necessary to multiply the scale of the abscissae by /" m , and to divide that of the ordinates by A. X -^ ; in the present case the magnetizing force per inch *->m length of circuit is to be multiplied by 80 to obtain the total number of ampere-turns, and the density per square inch of field frame is to be divided by x 482 DYNAMO-ELECTRIC MACHINES. [127 in order to reduce the ordinates to the corresponding values of the field density. In this manner the second scales in Fig. 327, marked "Total Number of Ampere-turns" and "Field E oe (B m / ^ON^-fi^ 15 - - 24000 - 60000 / " ^o^- *~"^~~'^ / r*\S*V-x^*"" f*X ^-^^^ 150- / 0^5^ JP*^$ 122000 / s ^"^ UJ _ Z 2 10200 A/ ^C^^r ^^^^ ~ 20000 - < 50000 . ~ v ..._?:::L...__..d/ ^f ^^^^ {0125- >s > U 2 loo- 16000 LJ - - Q; 10000 z // <>x^ u! I E 11000 // ! ,>^ ^ . - 1 p // y LJ 5 12000 - CO 30000 // X ,_ 75- Z B t 10000 UJ Q // / i - - CO O / / / 8 50- U 8000 Q H 20000 UJ - 3 6000 Z -0 // / i til S / / / ** 85- U. 4000 10000 ite C~ 8000 I// AMPE'RE TURNS PER INCH LE ^ ( i i 1 i i i I 1 i i i i 1 i , i i 1 i i , i 1 i YQTH. m" m , , , 1 , , . , li r 1 il , . r= 100 200 300 x> ; I 8000 12000 16000 20000 21000 2 TOTAL NUMBEB QF AMPERE TURNS Fig. 327. Practical Example of Construction of Characteristic. Density," respectively, are obtained, and now the line a/ gar can be plotted. For this purpose the mean density in the arma- ture core at maximum output, and from this the value of the constant k^ must first be determined. From formula (138) we have, for the useful flux, at normal load : _ 6 X (125 + 5) X io 9 _ 2l6 X 1200 3,000,000 maxwells, hence, > 3,000,000 -~ = - = 60,000 lines per square inch, 3* 5 for which Table CV. gives: = .00022. 128] DYNAMO-GRAPHICS. 483 Calculating now the value of af g&T for 3C" == 20,000, we find by formula (448) : = 20,0001 .3133 X I^V + -OOO22 X 1.25 X -~- X 1 5 i6o\ .00001 X 210 X - / 2 = 20,000 (.324 + .013 + .173) = 20,000 x .510 = 10,200 ampere-turns. Plotting this value as abscissa for an ordinate of 3C" 20,000, the point A is obtained, which, when connected with the co- ordinate centre O, gives the line OA, representing the sum of the gap, armature, and compensating ampere-turns for any field density. The addition of the abscissa of this line to those of the curve OB, which gives the magnetizing force, at m , required for the field iframe, furnishes the required characteristic. In order to read the ordinates in volts, a third scale of ;ordinates is yet to be added; since the field density at full load, is <& 3,000,000 ' = 19,000, o g 150 this third scale is obtained by placing " 125 volts " opposite that density, and by subdividing accordingly, the resulting scale giving the output E. M. F. for varying magnetizing force. 128. Modification in the Characteristic Due to Change of Air Gap. 1 In practice it often becomes necessary to change the length of the air gap in order to secure sparkless collection of the current (compare 125), and it is then important to investi- gate the influence of different air gaps upon exciting power and E. M. F. The characteristic OBC, Fig. 328, for the original air gap constructed according to 127, is replaced by the curve ABC, consisting of the straight-line portion, AB, and of the curved 1 Brunswick, L'Eclairage Elec., August 31, 1895; Electrical World, vol. xxvi. p. 349 (September 28, 1895). 484 DYXAMO-ELECTRiC MACHINES. [12S portion, BC. Since for low densities the magnetizing force required for the iron portion of the magnetic circuit is very small, the straight line portion, AB, can be considered as the magnetizing force due to the air gap alone, and therefore the curved portion, BC, as the sum of the elongation, BD, of this straight line plus the magnetizing force due to the iron. Any H K' Fig. 328. Conversion of Characteristics for Different Air Gaps. change in the length of the air gaps will, consequently, for any given ordinate, OE, only alter the abscissa, EF, of the straight line AD, but will leave unaffected the abscissa-difference, EG, between the curve BC and the straight line BD. Hence the new characteristic OC for an increased air gap is obtained by increasing the abscissa EF to EF' , in the ratio of the old to the new air gap, and by adding to the abscissa thus found the original difference between BC and BD, making F'G = EG. Then Off' is the magnetizing force required to produce the E. M. F. OE, corresponding to the point G' on the new characteristic; the portion OK' of the magnetizing force is the exciting power used for the new air gap, and K'H' that for the remaining parts of the magnetic circuit, and is therefore independent of the air gap. 129] D YNAMO-GRAPHICS. 485 129. Determination of the E. M. F. of a Shunt Dy- namo for a Given Load. 1 If E, Fig. 329, is the E. M. F. developed by the machine at no load, viz.: = /!, X and if the E. M. F., E^ , at a certain load corresponding to an armature current of / amperes is to be found, draw OA, by connecting the co-ordinate centre, O, with the points on the Fig. 329. Determination of E. M. F. of Shunt Dynamo for Given Load. characteristic corresponding to the E. M. F. E, then make OB equal to the total drop of E. M. F. caused by the armature current /, or OB = e & = I X r & + e T , where / X r^ is the drop caused by the armature resistance r & , and e r that due to armature reaction. The latter may ap- proximately be taken as half the former, /. e. : e t = $ I X r* , thus making the total drop * a = i-5 X /X r a . 1 Picou, " Traite des Machines dynamo-e'lectriques." 486 DYNAMO-ELECTRIC MACHINES. [ 130 The point B thus being located, draw BC \ OA, and from the intersection, C, of this parallel line with the characteristic curve drop the perpendicular CD upon the axis of abscissae. The portion FD of CD, from its intersection, F, with OA to the axis of abscissae, is the required E. M. F., DF t , while OD = AT^is the corresponding exciting force of the field magnets. The characteristic shows that the drop, CF, is the greater the lower the saturation of the machine. 130. Determination of the Number of Series Ampere- Turns for a Compound Dynamo. Let the E. M. F., which is to be kept constant, be repre- sented by E, Fig. 330. Draw EA parallel to the axis of O AMP. TURNS AT,, AT Fig. 330. Determination of Compound Winding. abscissae, and from A on the characteristic drop the perpen- dicular AB. The length OB then gives the ampere-turns required on open circuit, that is, the shunt excitation AT sh . If e & again denotes the total drop of E. M. F. caused by the armature current at the given load (see 129), then in order to keep the external E. M. F., , constant, an internal E. M. F., E' = E -f- e & , must be generated. Drawing E'C \ OB, and CD J_ OB, we find that the latter requires a total magnetiz- ing force of OD = A T ampere-turns. 131] D YNAMO-GRAPHICS. 487 Hence the number of series ampere-turns necessary for compounding: BD = AT^ = AT - the series excitation being the difference between the total number of ampere-turns required for the generation of ' volts, and the shunt excitation needed for E volts. 131. Determination of Shunt Regulators.' Shunt regulators are employed: (a) to keep the output E. M. F. constant at variable load and constant speed; () to keep the E. M. F. constant for variable speed; (c) to keep the E. M. F. constant if both the load and the speed are var- iable; and (d) to effect any variation in the E. M. F. a. Regulators for Shunt Machines of Varying Load. In Fig. 331, E is the constant potential of the dynamo, r m , the magnet resistance, r r , the resistance of the shunt regula- AMP. T|URNS O A AT AT Fig. 331. Shunt Regulating Resistance for Constant Potential at Varying Load. tor, and JV m the number of convolutions per magnetic circuit. The dynamo is driven by a motor of constant speed, and so 1 " Losung einiger praktischer Fragen iiber Gleichstrom-Maschinen auf graphischem Wege," by J. Fischer-Hinnen, Elektrotechn. Zeitschr., vol. xv. p. 397 (July 19, 1894). 488 DYNAMO-ELECTRIC MACHINES. [131 arranged that at full load all resistance of the regulator is cut out. The resistance is to be found which has to be put in series with the field magnets in order to keep the potential on open circuit the same as at full load. In the manner shown in 129 the exciting current intensi- ties, 7 m and 7' m , at no and full load, respectively, are first de- termined by finding the magnetizing forces AT and AT' , for the E. M. Fs. , and E' = E -\- e & , respectively, and divid- ing the same by the given number of shunt-turns, thus: AT AT' Then, according to Ohm's Law: E 7V m x E = tan and E _N m X E _ ~rT AT' - ...(449) The values of r m and (r m -f- r r ) can be directly found as fol- lows: In the distance OA = N m (Fig. 331) draw AB parallel to the axis of the ordinates; find point F by drawing EF\ OA and E'F \ AB\ and draw the lines OE and OF. These will intersect AB in points E l and 3 , respectively, for which hold the following relations: and: tan a -*- N X tan a _ -- - The required regulating resistance, therefore, is directly: r F - - F r r -c, -c a . Example: A shunt dynamo for 100 volt? and 40 amperes having an armature resistance of r a = .12 ohm, a magnet winding of N m = 4200 turns per magnetic circuit, and the magnetic characteristic shown in Fig. 332, is to be provided with a regulator for constant pressure at variable load. 131] DYNAMO-GRAPHICS. 489 The drop at 40 amperes is: fa. = i-5 X / X r & = 1.5 x 40 X .12 = 7.2 volts, and the characteristic gives, for E = ioo and E' ioo -j- 7.2 = 107.2 volts, respectively: Magnetizing force at no load, AT = 8100 ampere-turns; Magnetizing force at full load, AT' = 10,500 ampere-turns. Hence, by (449) : &m X E 4200 x ioo r+> r = -- - =5 1. 8 ohms, and 8 ioo X E' 4200 X ioo A , A 1 10,500 r p = 51.8 40.0 = i r. 8 ohms. = 40.0 ohms, 100 Z 60 AMPERE TURNS Fig. 332. Practical Example of Graphical Determination of Shunt Regulator for Constant Potential at Varying Load. These values can also be directly derived from the charac- teristic by erecting, at OA = 4200, the perpendicular AB, and by drawing the lines OE and OF\ the resistances can then be read off on AB from the scale of ordinates. 49 DYNAMO-ELECTRIC MACHINES. [ 13l b. Regulators for Shunt Machines of Varying Speed. If TV" is the normal, and N^ the maximal, or minimal abnor- mal speed, as the case may be, then the speed ratio, N, N = n is greater or smaller than i, according to whether the speed- variation is in the form of an increase or of a decrease. In E< N M C AT, AT AT' AT n Fig. 333- Shunt Regulating Resistance for Constant Potential at Increasing Speed. order to obtain the characteristic of the machine for the abnormal speed, all ordinates of the original characteristic, I ) must be multiplied by the speed-ratio, n. The result of this multiplication is shown by curve II, Fig. 333, for increasing, and by curve II, Fig. 334, for decreasing speed. If the point E on curve 7, corresponding to the E. M. F. at normal speed, IV, is connected with O, then the intersec- tion, n , of the line OE with curve /, is the E. M. F. which the machine would yield at the speed N^ . For, in the first moment, the E. M. F. J5, Fig. 333, on account of the increased speed, will rise to the amount E '; at the same time, however, the exciting current rises, and with it the magnetizing force increases from A T to AT', causing an increase of the E. M. F. to ", on account of which the magnetizing power is further increased to AT", and so on, until at n the equilibrium is reached. But the potential of the machine is to be kept con- 131] D YNAMO-GRAPHICS. 49 1 slant; for this purpose, that magnetizing force, AT lt is to be found which produces the E. M. F. E at the speed N^. This, however, can be done without the use of curves II, which therefore need not be constructed at all. For, since the num- Fig. 334. Shunt Regulating Resistance for Constant Potential at Decreasing Speed. ber of ampere-turns required to produce E volts at N^ revolu- tions is identical with the magnetizing force needed to generate Tf E_ n volts at normal speed, N, it follows that it is only necessary to draw EA J_ OA, to make AB E^ = , and to draw E l | OA. The abscissa of the intersection, E^ , of this parallel with the characteristic /is the required number of ampere-turns, AT^ . The latter will be smaller than AT if n > i, and greater if n < i; in the former case, therefore, the excitation must be reduced by adding resistance, while in the latter case it must be increased by cutting out resistance. AT^ being known, the regulating resistance can be computed as follows: For N l > N: E E X JV m E*N m AT. AT. AT 49 2 DYNAMO-ELECTRIC MACHINES. [131 whence: ...(450) For N^ < N: E* t- i_ t- ' m "1~ 'r A T> > ~ or: l -*-^T\ < 51 ) If at distance <9C = N m a parallel, CZ>, to the axis of ordinates is drawn, then resistances can be directly derived graphically, as shown in Figs. 333 and 334. Example: A dynamo of 125 amperes current output, hav- ing the characteristic OA, Fig. 335, is to be regulated to give a constant potential of 120 volts for a speed variation of 9 per cent, below and 10 per cent, above the normal speed; to deter- mine the magnet and regulator resistance, if at normal speed a current consumption of 3.2 per cent, is prescribed. Under the given conditions the speed ratio and correspond- ing E. M. F. for increasing speed is: N, N + o.io N E 120 n -W = ! KT i.i; E= = = 109 volts; N N n i.i and for decreasing speed: N' JV 0.09 N E 120 = -*r = - ~ AT-^ = -91 J E i = = - - = J 3 2 volts - N N n' .91 For these E. M. Fs. the characteristic furnishes the follow- ing magnetizing forces: Ampere-turns at normal speed, AT = 20,000; Ampere-turns at maximum speed, AT l = 15,400; Ampere-turns at minimum speed, AT\ =27,600. Hence: -_ 20,000 . J _. N m = - = 5000 convolutions; m .032 x 125 p and consequently: 131] D YNAMO-GRAPHICS. 50OO X 120 15,400 = 39.0 ohms. 493 5000 X 120 r m = - - = 21.8 ohms. 27,600 r r = 39.0 21.8 = 17.2 ohms. This value is directly given by the ordinate scale in the dia- gram, Fig. 335, being the distance between the lines OF and uo 130 120 110 100 {2 90 80 Z 70 EJ=1 32 V. E; E=1 20 V. F E^ ^ , H E,= 1 09V. 2 ^^ ^ . ^ -^ * ^x x 1 Y ^ ^ D / ' / /- ^ <^N m : = 500 >- ^x / // / * / x^ 5 ui 50 40 39 20 10 / / // / / ' ' / 7 / L / / / / j^ ^ // / ^ i 8 _ ^ S 1 c i AMPERE TUflNS F 'g- 335- Practical Example of Graphical Determination of Shunt Regulator for Constant Potential at Varying Speed. measured on the ordinate CD, in distance OC = N m = 5000 from the co-ordinate centre. c. Regulators for Shunt Machines of Varying Load and Varying Speed. In this case the required resistance must be capable of keeping the potential the same at no load and maximum speed as at full load and minimum speed. The former of these two extreme cases no load and maximum speed, N^ , has already been treated under subdivision b; to consider the latter case full load and minimum speed reference is 494 D YNAMO-ELECTRIC MA CHINES. tiai had to the open circuit curves I and II, Fig. 336, for normal speed, N, and for minimum speed, N^, respectively. If AT ampere-turns are requisite to produce, at normal speed and on open circuit, the potential, , to be regulated, AT AT, Fig. 336. Shunt Regulating Resistance for Constant Potential at Variable Load and Variable Speed. the magnetizing force for minimum speed is found by deter- mining the abscissa AT t for on curve II, which at the same time also is the abscissa for the potential E -^ on curve I, a being the ratio of minimum to normal speed. The value of AT^can therefore be derived without plotting curve II, by adding to E the drop e a , dividing the sum by and finding the abscissa for the potential so obtained. If the magnetizing force for open circuit and maximum speed is A 7 1 , , the desired regulating resistance for variable load and variable speed is: r r = ;V m X E X (-jf - ^] , . (452) where JV m is the number of turns per magnetic circuit. 131] D YNAMO-GRAPHICS. 495 Example: A shunt dynamo having a potential of 60 volts, a drop in the armature of 3 volts, a current-intensity of 50 amperes, 6 per cent, of which is to be used for excitation at full load, and having the characteristic given in Fig. 337, is to 550 o Z10 Z30 ui 20 10 1833 C | AT, | AMPERE TURNS AT, Fig. 337. Practical Example of Graphical Determination of Shunt Regulator for Constant Potential at Varying Load and Varying Speed. be regulated for a speed variation of 10 per cent, above and below normal speed, and for loads varying from zero to full capacity. For no load and maximum speed we have in this case: N, N + .iJV +9 ^ 1 T T l ~JV N '*' E 60 A = ~ = ~ = 54-5 volts, AT t = 2500 ampere-turns (from Fig. 337); and for full load and minimum speed: ' = + e & = 60 + 3 = 63 volts, N. N - . N - -9, E 1 / E. - - = - = 70 volts, ' , -9 496 DYNAMO-ELECTRIC MACHINES. [131 AT t = 5500 ampere-turns (from Fig. 337), N m = -y-i = = 1833 convolutions. -'sh ' OO X 5 Connecting the points A and , in which the 2500 and 5500 ampere turn lines, respectively, intersect the 6o-volt line, with the co-ordinate centre O, and erecting, at OC = 1833, the perpendicular CD, the intersections ^and G are obtained, and the lengths CF and FG give the required resistances of the magnet-winding and of the shunt-regulator, respectively. The result thus found can be checked by the following computation: N m X E 1833 x 60 r m + r r = -5^- -3S-. = 44 ohms, E 60 ~r- = ? - = 20 ohms, 7 sh .06 X 50 r r = 44 20 = 24 ohms; or, directly, by formula (452): r t 1833 X 60 X ( -- '-^ ) = 24 ohms. ^2500 d. Regulators for Varying the Potential of Shunt Dynamos. The potential of the machine is to be adjustable between a minimum limit t and a maximum limit E t , and the ad- justed potential is to be kept constant for varying load. These conditions are fulfilled by so proportioning the magnet- winding and the regulator-resistance that at full load the maximum potential E^ is generated with the regulator cut out entirely, and that at no load the minimum potential E t is pro- duced with all the regulator-resistance in circuit. From the characteristic, Fig. 338, the magnetizing forces AT l , corresponding to the potential E t at no load, and AT^, corresponding to the potential E 9 at full load, or to the internal E. M. F., E\ = 9 -f- For v m = 6.83 miles per hour, the equation for the current takes the following convenient form: /' = .02927 x 6.83 X (30 + 20^) = 2 X (3 + 2^), from which, for: g - o #, i %, 2 #, 3 #, 4 <, 5 % we find: /' = 6, 10, 14, 18, 22, 26 amperes. In order to derive therefrom the actual speeds, and current intensities corresponding to the same, a line AB, Fig. 341, is drawn parallel to the axis of abscissae and at a distance OA = 6.83 from it. Upon this line AB the points x' , x\ , ,...x' t , corresponding to the above values of /' are found and connected with O. Then the co-ordinates of the intersections x^ , x l , ...,x t ol the lines Ox\, Ox' lt ,,..Ox' t with the characteristic are the required amounts of /and v m for the various grades. PART VllL PRACTICAL EXAMPLES OF DYNAMO CALCULATION, CHAPTER XXIX. EXAMPLES OF CALCULATIONS FOR ELECTRIC GENERATORS. 134. Calculation of a Bipolar, Single Magnetic Circuit, Smooth Ring, High-Speed Series Dynamo: 10 Kilowatts. Single Magnet Type. Cast Steel Frame. 250 Volts. 40 Amps. 1200 RCTS. p. Min. a. CALCULATION OF ARMATURE. i. length of Armature Conductor. According to 15, p. 49, the percentage of polar arc, in this case, should be between .75 and .85; the machine being a small one, we take fa = .78, for which, in Table IV., p. 50, we find, by interpolation, a unit ar- mature induction of e = 64 X lo" 8 volt per foot per bifurcation. The number of bifurcations in bipolar machines is ' p = i. Next we consult Tables V. and Va, 17. From Ta- ble Va it is seen that the given speed is the average high speed for 10 KW output. Hence a value of v c near the average conductor velocity given in Table V. for a 10 KW high-speed ring armature must be taken. Though the average, 85 feet per sec., is a very good value for the case under consid- eration, we will here take v c = 80 ft. p. sec., which will result in a somewhat better shape for the armature. Table VI., p. 54, gives an average field density of 3C* = 19,000 lines per square inch, the value for cast iron polepieces being preferable, although the present machine has cast steel poles, because otherwise the magnetizing force required would be rather great to be produced by one single magnet. The total E. M. F., finally, that must be generated in order to yield the required 250 volts at the brushes is found by Table VIII., p. 56, to be about E' = 250 -f .12 x 250 = 280 volts. Hence, by means of formula (26), p. 65, the length of the active arma- ture conductor required is: ' 8 X '' - 64 X 80 X 19,000 505 = 288 feet. 506 DYNAMO-ELECTRIC MACHINES. [134 2. Sectional Area of Armature Conductor, and Selection of Wire. Taking a current density of 500 circular mils per ampere, we find the cross-section of the armature conductor, according to formula (27), 20: 5 * 4 = 10,000 circular mils. Referring to a wire gauge table we find that a single wire of this area would be rather too thick, and therefore difficult to wind on a small armature; we consequently select a gauge of half the above section, taking 2 No. 15 B. W. G. wires having a total sectional area of 2 X 5*84 = 10,368 circular mils. The diameter of No. 15 B. W. G. wire is # a = .072" bare, and d' a = .088" when insulated for 250 volts with a .016" double cotton covering. 3. Diameter of Armature Core. Applying formula (30), 21, the mean winding diameter of the armature, corresponding to the given speed of N = 1200 revolutions per minute, is found: 80 . and from this the core diameter can be deduced by means of Table IX., 21, thus: d & = .98 x 15.3 = 15 inches. Approximately, d & could also have been derived from Table XL, by multiplying the respective table-diameter by the ratio of the table-speed to the speed prescribed : i2;o <4 = i4 X = 14.6". 1200 4. Length of Armature Core. The number of wires per layer, if the entire circumference of the armature were to be occu- pied by winding, is by formula (35), 23: , 15 X Tt _ n *~ .088 ~ 535 Allowing 16 per cent, of the circumference for spaces be- tween the coils, we have : w = .84 x 535 = 448 S 134] EXAMPLES OF GENERATOR CALCULATION. 507 the exact result, 449, being replaced by the nearest even and readily divisible number. Table XVIII., 23, gives the height of the winding space, h = .325", and Table XIX., 24, the thickness of core insulation, a = .040", allowing .040" more for binding (see p. 75), by formula (39) the number of layers is obtained: .125 .080 ~ " ** -y " l ~ .088 - 3> Remembering that the armature conductor consists of 2 wires in parallel, we insert the values found into formula (40) and find the length of the armature core: 12 x 2 x 288 '= 448x3 = 5 i' nches - 5. Arrangement of Armature Winding. The voltage of the machine being below 300, the potential between adjacent com- mutator bars will be within the limit of sparklessness, if the number of armature coils is chosen between 40 and 60. There are three numbers which fulfill this condition, viz. : , = + I4 = 48; and 448 X 3 c = -- * -f- 16 = 42. In practice that number would have to be taken for which the tools, and possibly even the entire commutator, of an ex- isting machine could be used; here, however, although for the smallest number the cost of the commutator as well as that of winding and connecting would be the lowest, we will take n c = 56, because this number is preferable to the others on account of the more symmetrical arrangement of the winding it produces. For, in dividing the total number of wires on the armature, 448 X 3 = 1344, by the different values of n c , we obtain for the number of wires per armature coil the figures 24, 28, and 32, respectively, and as 24 = 8 -f 8 -}- 8, 28 = 9 -j- 9 -}- 10, and 32 10 -)- n -f- n, it follows 5o8 D YNA MO- EL E C TRIC MA CHINES. [134 that in the first case alone the number of wires per layer is uniform, while for each of the two latter windings the number of wires in one of the three layers would differ by i from the other two. Substituting, therefore, c = 56 into (46) the number of convolutions per coil is obtained: = 448 X 3=I = " S^ X 2 " that is to say, the armature winding is composed of 56 coils, each having 12 turns of 2 No. 15 B. W. G. wires. The arrangement of the winding is shown by the diagram, Fig. 342, which represents the cross-section of one armature Fig 342. Arrangement of Armature Winding, IO-KW. Single-Magnet Type Generator. coil. In order to have both ends of the coil terminate at the outside layer, at the inner circumference of the armature, and at the commutator end, as is most desirable for convenience in connecting and for avoidance of crossings, the centre, C, of each coil must be placed at the inner armature circumference on the commutator end, and, starting from C, one-half, C"j, 7', 8, 8'. ... 12 must be wound right-handedly, and the other half, C6', 6, 5', 5 .... i, left-handedly, as indicated. The wind- ing in the interior of the armature is shown arranged in five layers, this being necessary on account of the smaller interior circumference. 134] EXAMPLES OF GENERATOR CALCULATION. 509 6. Radial Depth, Minimum and Maximum Cross- Section, and Average Magnetic Density of Armature Core. The useful mag- netic flux, according to formula (138), 56, being 6 X 280 X io 9 = = 2,083, ooo maxwells, 56 X 12 X 1200 the radial depth of the armature core, by (48), 26, is obtained: 2,083,000 b* = - 5 -: - = 21 inches. 2 x 80,000 X5l X .90 In this the density in the minimum core section is taken at the upper of the limits prescribed by Table XXII., while the ratio k^ is selected from Table XXIII., under the assumption that .010" iron discs with oxide coating are employed. Subtracting twice the radial depth from the core diameter, we find the internal diameter of the armature core: 15 2 x 2^ = 9^ inches, and the arithmetical mean of the external and internal diame- ters is the mean diameter of the core: d"\ = i (15 .4. 9 J) = i2| inches. Inserting the value of b & into formula (234), 91, the maxi- mum depth of the armature core is obtained: *'a = 2 1 X /1 - J = 5.9 2 inches; hence, by (232) and (233), the minimum and maximum cross- sections: -S'aj = 2 x 5i X 2| X .90 = 26.5 square inches, and S'*i 2 x 5i X 5.92 X .90 = 54.7 square inches, respectively. Dividing with these areas into the useful flux, we find the maximum and minimum densities: 2, 08^,000 & a , = ^ - = 78,700 lines per square inch, " O and 2, 083, ooo (B a2 = - - = 38,100 lines per square inch, * I 510 DYNAMO-ELECTRIC MACHINES. [134 for which Table LXXXVIII., p. 336, gives the specific mag- netizing forces m \ = 2 9-5> an d #*"a 2 =7-i ampere-turns per inch. According to formula (231), therefore, the mean specific magnetizing force is: m\ = (29.5 + 7.1) = 18.3 ampere-turns per inch, and to this, according to Table LXXXVIII., corresponds an average density of: (B" a = 68,500 lines per square inch. 7. Weight and Resistance of Armature Winding; Insulation Resistance of Armature. The poles being situated exterior to the armature, as in Fig. 59, 27, formula (53) gives the total length of the armature conductor: Lt = X (5* + + -3'S X x 2g8 = 95 Si" Hence, by (58), p. 101, the bare weight of the armature winding: wt A = .00000303 x 10,368 x 955 = 30 pounds. The same result can also be obtained by means of the specific weight given in the wire gauge table; No. 15 B. W. G. wire weighing. 0157 pound per foot, and two wires being connected in parallel, we have: >4 = 2 X 955 X .0157 = 30 pounds. From this the covered weight of the winding is deduced by means of formula (59) and Table XXVI., thus: wt\ = 1.078 X 30 = 32 pounds. The resistance of the armature winding, at 15.5 C, is ob- tained from (61), 29: r a = ^-r X 955 X ( 4?irr I = 24 ohm. 134] EXAMPLES OF GENERATOR CALCULATION. 511 By Fig. 343 the surface of the armature core is: 2 X (5^ + 2 s) X 12^ X TT = 610 square inches; if oiled muslin whose average resistivity, by Table XX., 24, is 650 megohms per square inch-mil at 30 C., and 650 -j- 25 = 26 megohms per square inch-mil at IOO Q C., is employed to make up the 40 mils of core insulation given by Table XIX., the insulation resistance of the armature is found: 650 x 40 610 and 26 x 40 610 = 42.6 megohms at 30 C, = 1.7 megohm at 100 C. 8. Energy Losses in Armature, and Temperature Increase. The energy dissipated by the armature winding, by formula (68), 31, is found: P^ = 1.2 X 40' X .24 = 460 watts. The frequency is: 1200 jy ' = = 20 cycles per second; 60 the mass of iron in the armature core, from (71), 32: 124 X 7t X 2! x 5 4- X .90 , . , M= ? - , ? = .292 cubic feet; 1728 for (B" a = 68,500, Table XXIX. gives the hysteresis factor: and Table XXXIII., the eddy current factor: = -034- Hence, the energy losses due to the hysteresis and eddy cur- rents, from (73), p. 112, and (76), p. 120, respectively: P* = 2 7-3 X 20 x .292 = 160 watts, P = .034 X 20* X .292 = 4 watts. By ( 6 5)> P- I0 7 then, the total energy dissipation in the armature is: P A = 460 + 1 60 + 4 = 624 watts. S 12 DYNAMO-ELECTRIC MACHINES. [134 The heat generated by this energy, according to (79), 34, is liberated from a radiating surface of Sj, = 2 x 12^ x re X (5^ + 2$ + if) = 715 square inches, whence follows the rise in armature temperature, by (81), p. 127: the specific temperature increase, O' a = 42 C., being taken from Table XXXVI. for a peripheral velocity of 80 feet per second, and for a ratio of pole area to radiating surface of .78 X i5X*r X 5* _ 6 Inserting the above value of 6 a into formula (63), p. 106, the armature resistance, hot, at 15.5 + 36.5 = 52 degrees, Centi- grade, is obtained : r' a = .24 X ( i + ^ 1 = .275 ohm. 9. Circumferential Current Density, Safe Capacity and Run- ning Value of Armature; Relative Efficiency of Magnetic Field. From formula (84), 37, the circumferential current density is obtained: 672 x 20 * c = = 285 amperes per inch, J 5 X 7T for which Table XXXVII. gives a temperature increase of 30 to 50 Cent., the result obtained being indeed within these limits. For the maximum safe capacity we find, by formula (88), 38, and by the use of Table XXXVIII. : pt = I 5 t X 5i X .89 x 1200 x 19,000 X io-' = 23,500 watts, and for the running value of the armature, by formula (90), 39: p> * = r = .0197 watt per pound of copper at unit field density (i line per square inch). 134] EXAMPLES OF GENERATOR CALCULATION. 513 The values of P' and P' & show that the armature is a very good one, electrically, for, according to the former, an over- load of over 100 per cent, can be stood without injury, and by comparing the latter with the respective limits of Table XXXIX. it is learned that the inductor efficiency is as high as in the best modern dynamos. The relative efficiency of the magnetic field, by formula (i55), 59, is: maxwells P er watt at unit velocity, and, according to Table LXIL, page 212, this is within the limits of good design. 10. Torque, Peripheral force, and Lateral Thrust of Arma- ture. By means of formula (93), 40, we obtain the torque: r = 4r X 40 X 672 X 2,083,000 = 65.7 foot-pounds. 10 and by (95), 41, the force acting at each armature con- ductor: Pound. ' The force tending to move the armature toward the magnet core is found by formula (103), 42; the reluctance of the path through the averted half of the armature being about 10 per cent, in excess of that through the armature half nearest to the magnet core, the field density in the former will be about 10 per cent, smaller than in the latter; that is to say, the stronger density, 3C", is about 5 per cent, above, and the weaker density, 3C" a , about 5 per cent, below the average den- sity OC", or 3C", = 19,000 x 1.05 = 20,000, and 5C" a = 19,000 x -95 = 18,000; hence the side thrust: / t = ii X io- 9 X 15 X 5^ X (20,000* 18,000*) = 64J pounds. 5'4 DYNAMO-ELECTRIC MACHINES. [ 134 This pull is to be added to or subtracted from the belt pull, according to whether the dynamo is driven from the magnet or from the armature side. ii. Commutator, Brushes, and Connecting Cables. The in- ternal diameter of the wound armature being 9i 2 x (.040 + 5 X .088) = 8 inches, the brush-surface diameter of the commutator is chosen 4 = 8 2 X | = 7 inches, by allowing |* radially for the. height of the connecting lugs, as shown in Fig. 343. If we make the thickness of the side " 1 Fig. 343. Dimensions of Armature and Commutator, IO-KW. Single-Magnet Type Generator. mica ^ = .030", Table XLVL, 48, and if we fix the number of bars to be covered by the brush as n k = i-J, the circum- ferential breadth of the brush contact, by (115), becomes: = i X *-^ - .o 3 oj = .68*. Adding to this the thickness of one side insulation, which is also covered by the brush, we obtain the breadth of the brush- bevel, .68 -}- - 3 7 1 "? which, for an angle of contact of 45, gives the actual thickness of the brush as = inch. Tangential carbon brushes being best suited for the machine under consideration, formula (118), page 176, gives the effec- tive length of the brush contact surface: 134] EXAMPLES OF GENERATOR CALCULATION. 51$ 4 = ^>T68 = 2 inChCS ' which we subdivide into two brushes of i inch width, each. Allowing i* between them for their separation in the holder, and adding y 1 / for wear, we obtain the length of the brush- surface from (114), page 169, thus: 4 = (2 + ) X (i + i) + T V - 2|| + T "V = 3} inches. The best tension with which the brushes are to be pressed against the commutator is found by means of formulae (119) to (121) and Table XLVIL, as follows: The peripheral velocity of the commutator is: 7 X 7f X 1200 zv ;= -- - - = 2200 feet per minute, 12 hence the speed-correction factor for the specific friction pull, by (119), p. 179: 2200 Inserting the values into (120) and (121), the formulas for the energies absorbed by contact resistance and by friction re- duce to A = .00268 x T-J = 3-15 x A, and P t = 6 X io- 5 x .85 / k X 2 X .68 X 2200 = .1526^. Taking from Table XLVIL the values of fa and / k for brush tensions of i, 2, 2^, and 3 pounds per square inch, respec- tively, for tangential carbon brush and dry commutator, we find: for i Ibs. per sq. in., /> k + P t = 3.15 X .15 + -i5 z6 X -95 = .618 HP.; "2 " " PI + P t = 3.15 X .12 + .1526 X 1.25 = -569 HP.; " 2^ " P k + P t = 3.15 X .10 + .1526 X 1.6 -559 HP.; " 3 " " P* + P t = 3-15 X .09 + .1526 X 1.9 -574 HP., 5*6 DYNAMO-ELECTRIC MACHINES. [134 from which follows that the most economical pressure is about 2J- pounds per square inch of contact. The proper cross-section of the connecting cables, by allow- ing 900 square mils per ampere, in accordance with Table XLVIIL, 50, is found to be: 40 x 900 = 36,000 square mils, or 36,000 x = 46,000 circular mils. Taking 7 strands of 3 X 7 wires each, or a i47-wire cable, each wire must have an area of 46,000 . - = 315 circular mils, J 47 and the cable will have to be made up of No. 25 B. & S. wire, which is the nearest gauge-number. 12. Armature Shaft and Bearings. By (123) and Table L., 31, the diameter of the core portion of the shaft is: <=i.tX 4 = 21 inches; \ 1200 by (122), p. 185, and Table XLVII., the journal diameter: _ 4 _ 4, = .3 X /y/280 X 40 X 4/1200 = 1| inch; and, by (128), p. 190, and Table LIV., the length of the journal: / b = .1 X if X V 1200 = 6J inches. 13. Driving Spokes. Selecting 4-arm spiders, similar to those shown in Fig. 127, 52, the leverage of the smallest spoke- section, determined by the radial depth of the armature, is 4 = 3" r > and the width of the spokes, fixed by the length of the armature core, is b$ = 2"; hence, by formula (126), p. 189, their thickness: / \/ y II.2OO X "?fr . / ^ ^/ A / *-* !5 4 ' 25 X V 80 X 8 X 2 X 7oo 134] EXAMPLES OF GENERATOR CALCULATION. 517 14. Pulley and Belt. Taking a belt-speed of z> B = 3500 feet per minute, Table LVIII., 54, the pulley diameter becomes, by ( I2 9), P- 19*: D 3-7 X 35oo es 1200 the size of the belt, by Table LIX. : ^ B = ^- inch, B = 4 inches, and the width of the pulley: b 9 = 4 -| = 4J inches. b. DIMENSIONING OF MAGNET FRAME. 1. TV/a/ Magnetic Flux. From Table LXVIII., 70, the average leakage factor for a lo-KW single-magnet type machine, with high-speed drum armature and cast-iron pole pieces, is A = 1.40; the present machine having a ring arma- ture and a cast-steel frame, the leakage is about 22 -|- n =33 per cent, less (see note to Table LXVIII., p. 263), and the leakage factor is reduced to A. = 1.27. The total flux, conse- quently, by (156): #' = 1.27 x 2,083,000 = 2,650,000 maxwells. 2. Sectional Area of Magnet Frame. According to formula (216) and Table LXXVIIL, 82, we obtain the cross-section of the magnet frame: 2,650,000 . , Sf- . 3 - = 29.4 square inches. 90,000 The axial length of the frame, limited by the length of the armature core on the one hand and by the length over the armature winding on the other, being chosen / p = 5-J", its thickness is: -~ 5 inches. 5 3. Polepieces and Magnet Core. The bore of the field is found by summing up as follows: DYNAMO-ELECTRIC MACHINES. l134 Diameter of armature core = 15.000 inches Winding 6 x .088 = .528 " Insulation and binding 2 x .080 = .160 " Clearance (Table LXI.).... 2X &= .312 " 16.000 inches I*- --L--16-'- J J I j Fig. 344. Dimensions of Field Magnet Frame, lo-KW Single-Magnet Type Generator. Making the width at the centre of the polepiece one-half the full width, or z\ inches, the total height of the machine is ob- tained 16 -j- 5 = 21 inches, leaving the length of the magnet core: / m = 21 2 x 5 11 inches. The distance between the pole-tips is obtained by formula (150) and Table LX., 58, as: I 'P = 5-5 X (16 15) = 5$ inches. The assumed percentage of polar arc corresponds to a pole angle of ft = 140, or a pole space angle of a = 180 140 = 40, and therefore furnishes: /' p = 1 6 x sin 20 = 5$ inches. If the two values of l' v so obtained differ from each other, the larger figure is preferable on account of smaller leakage. The distance between the magnet core and the adjoining pole-tips is determined by Table LXXX., 83. In this, the height of the magnet-winding for a 28 square inch rectangular core is given as h m = 2 inches; allowing \" clearance, we ob- 134] EXAMPLES OF GENERATOR CALCULATION. 519 tain the desired distance, and making the width of the pole- shoes 16 inches, the total width of the frame becomes: 5 + z\ + 16 = 23 inches. Fig. 344 shows the field magnet frame thus dimensioned. C. CALCULATION OF MAGNETIC LEAKAGE. i. Permeance of Gap- Spaces. The ^actual field-density, by (142), p. 204, being 3C* _ _ _ 2,083,000 j('5 + 16) X~ 2 X -89 X ^(5i + 5l) = 17,500 lines per square inch, the product of field density and conductor velocity is JC" X v c = i7,5 00 X 80 = 1,400,000; hence the permeance of the gaps, by Table LXVI. and formula (167), page 226: - --,-? -^ - 1.19 X (16 - 15) 1.19 2. Permeance of Stray Paths. The area of the pole-shoe end surface, S 2 , Fig. 164, is, according to Fig. 344: X 8i+( 7 f) 2 X + 7| XSl-i6X-StX 54 square inches. Substituting this value into (193), we obtain the total relative permeance of the waste field: 2 X 54 + 5* X ( 8 + j> o ^ _1_ e S . I e 1 , 2j X 5l | 5 1 X 2f ii ^"5^ + 2! = 5-5 + 17-2 + 1.3 -I- 2.0 = 26. 520 DYNAMO-ELECTRIC MACHINES. [134 3. Leakage Factor. From (157), p. 218: 100 100 This being smaller than, and only i per cent, different from, the leakage factor taken for the preliminary calculation of the total flux, we will use the value found from the latter in the subsequent calculations. d. CALCULATION OF MAGNETIZING FORCES. 1. Air Gaps. Length, by (166), p. 224: l\ = 1.19 X (16 15)= 1.19 inch. Area, by (141)* P- 2O 4- S" e = 15$ X ^ X .89 X 5 1 = JI 9 square inches. Density, by (142), p. 204: 2,083,000 .. . , 3C = - = 17,500 lines per square inch. 119 Magnetizing force required, by (228), p. 339: at K = .3133 X 17,500 X 1.19 = 6530 ampere-turns. 2. Armature Core. Length of path, by (236), p. 343: 00 _i_ 20 l\ i2| X n X - ^ h 2 i = J 4i inches. Minimum area of circuit, by (232), p. 341: "1 =2 X 5^ X 2^ X .90 = 26.5 square inches. 2,083,000 ,. . . .*. " p = 78,000 lines per square inch. Magnetizing force required for magnet frame, by (238), P- 344: af m = 57 X 26 + 30.8 X 18 2035 ampere-turns. 522 DYNAMO-ELECTRIC MACHINES. t 4. Armature Reaction. According to Table XCL, 93, the coefficient of armature-reaction for &" p = 78,000, in cast steel, is 14 = 1.25, hence, by formula (250), the magnetizing force required to compensate the magnetizing effect of the armature winding: / r = 1.25 X 6?2 f 4 X ^ = 1870 ampere-turns. 5. Total Magnetizing Force Required. By (227), p. 339, we have: AT= 6530 + 625 + 2035 + 1870 = 10,700 ampere-turns. e. CALCULATION OF MAGNET WINDING. Temperature increase at normal load not to exceed fl m = 30 Centigrade. Voltage to be adjustable between 225 and 250, in steps of 5 volts each. i. Winding Proper (for E = 250 volts). Rounding the total magnetizing force to 11,000 ampere-turns, formula (287), 99> gives the number of series turns: = 275. The length of the mean turn, by (290), being 'T = 2 (5 J + 5) + 2 x n = 28 inches, the total length of the series field wire is obtained, by for- mula (288) p. 374: *1S X .8 12 Formulae (278) and (282) give the radiating surface of the magnet: S M , = 2 x ii X (51 + 5 + 2 X it) + 2 X 2 x (28 - 5|) = 466 square inches, hence by (294) the resistance required for the specified tem- perature increase: r* = 3 X . i X : - - - = .104 ohm, 75 40' i + .004 x 30 134] EXAMPLES OF GENERATOR CALCULATION. 523 and therefore by (294) the specific length of the magnet-wire: 104 = 6170 feet per ohm. The nearest gauge wire is No. 2 B. & S., which is too incon- venient to handle; we therefore take 2 No. 7 B. W. G. wires (.180" + .012" = .192"), which have a joint specific length of 2 X 3 1 3%*6 = 6277 feet per ohm. Allowing | inch at each end of the magnet spool for insulation and discs, formula (297), p. 377, gives an effective winding depth of 2 X .192* * = 2 " x ..-xi = '' 9 mch ' Actual resistance of magnet-winding (from wire gauge table): 642 X = .1025 ohm at 15.5 C, * or r'^ .1025 x 1. 12 = .115 ohm at 45.5 C. Weight of magnet winding, bare: w f m = 2 X 642 x .098 = 126 pounds; weight, covered, from Table XXVI., 28: wt' m 1.0228 X 126 == 130 pounds. 2. Regulator (see diagrams, 100). The difference of 5 volts between each of the five steps being = 2 per cent, of the full load output, 250 the shunt coil regulator has to be calculated for 90, 92, 94, 96. and 98 per cent, of the maximum E. M. F., the resistances of the five combinations, therefore, are: Resistance, first combination ff X r'^ = 9 X r' M , " second " = % 2 - X r'^ =11.5 X r'^, " third " = Y X r'^ = 15.67 X r^, " fourth " = \ 6 - X r'ge = 24 X r'^, " fifth " = Y X r'^ = 49 X A-' 524 DYNAMO-ELECTRIC MACHINES. [ 134 By the proceeding shown in 100 we then obtain the follow- ing formulae for the resistances of the five coils: _ (11.5 r '* - '1) X (9 r'se ^i) ~ (n-S'-'se ~ n) - (9^ - rj _ II3-5 r'~ - 20 -5 ^sen + r{ 2.5 r K = 45-5^-8.2,1; ........................... (457) _ (15-67 r' K - r^ X (11.5 r'n - r^ ~ (15-67 r' - r.) - (11.5 r', - r,) _ 160.2 r'^ 27.2 r'^ r t -f r/ 4- 167 r' K = 38-2 /.e- 6.5 r,; ............................. (458) rjn = resistance of third combination minus res. of leads = 15-67 ^ - r,; .............................. (459) rjy = res. of fourth comb, minus res. third comb. = (24 - 15-67) r'^ =-. 8.33 r' 8e ; ..... ............. (460) r v = res. of fifth comb, minus res. fourth comb. = (49-24)^ = 25^ ..... .. ................ (461) These formulae apply to all cases in which a total regulation of 10 per cent, in five steps of 2 per cent, each, is desired. In the present example, the resistance of the series winding, hot, being r' M .115 ohm, and the resistance of the leads r t = .01 ohm (assuming 4 feet of 4000 circular mil cable, carrying 10 per cent, of the maximum current output, or 4 am- peres), we have: ri = 45-5 X .115 8.2 x .01 = 5.15 ohms, r n = 38.2 x .115 - 6.2 x .01 = 4.32 " >m= 15-67 X .115 - .01 = 1.79 " ^iv = 8.33 X .115 = .96 " r v = 25 X .115 = 2.88 " The currents flowing in the various coils, at the different combinations, are: 1341 EXAMPLES OF GENERATOR CALCULATION, 525 First combination: /, = T^^-T X.I/ r n r m ~r r i r iu ~r r i r u 4.32 x 1.70 X i X 4 4.32 X i-79 + 5- 5 X i-79 + 5- J S X 4-3 2 ^-^ X 4 = -^ X 4 = .8 ampere. 7.73 + 9.22 + 22.35 39.3 r \ r m 0-22 - x .1 / = - -X4 = -95 amp. r \ r m + r \ r a + r n r m 39- 3 r " , ^ ^ X . i / = ^^ X 4 = 2.3 amp. Second combination: / = 7 1 X .o87 = li|2 X 3-2 = -95 ampere. *n + r ui 0.11 7 m = ^ x .08 / = 2 x 3- 2 = 2 -3 amperes. r n + r m - 11 Third combination: / m = .06 7 = 2.4 amperes. Fourth combination: /m = / IV = .04 / = 1.6 amperes. Fifth combination: 7 ni = /^ = 7 V = .02 / = .8 ampere. By comparison, the maximum current passing through each of the five coils, in the present case of a machine of 40 amps, ca- pacity, is found : / x = .8 amp. ; or, for the general case of current output /, we have: 7 t = .2 X .1 /= .02 7, (462) /H = .95 amp. ; or, in general: / = .3 X .08 /= .024 /, (463) /m = 2.4 amp. ; or, in general : 7 m = .06 /, , (464) /iv = 1.6 amp. ; or, in general: / JV =04!, (465) / v .8 amp. ; or, in general : / v = .02 /, (466) From the wire gauge table, finally, the size of the wire suffi- cient to carry the maximum current, and the length and weight of the same, required to make up the necessary resist- ance, is obtained: 526 DYNAMO-ELECTRIC MACHINES. [134 d COIL NUMBER. I'll 00 i! 'o Sectional Area, Cir. Mils. Ofig 8-0 5 2\. !l U" d I .8 No. 21 B. & 8. 810 1012 5.15 400 105 II .95 No. 20 B. & S. 1021 1073 4.32 427 1.29 III 2.4 No. 18 B. W. G. 2401 1000 1.79 414 3.15 IV 1.6 No. 18 B. & 8. 1624 1015 .96 150 .76 V .8 No. 21 B. & 8. 810 1012 2.88 224 .58 f. CALCULATION OF EFFICIENCIES. i. Electrical Efficiency. The electrical efficiency of the above dynamo, by formula (351), p. 405, is: 250 X 40 250 X 40 + 4' X (.275 + .115) 10,000 10,624 = .943, or 94.3 2. Commercial Efficiency and Gross Efficiency. The energy losses due to hysteresis, eddy currents, brush contact, and brush friction were found P b = 160, P 9 =. 4, P^ = .315 x 746 = 235, and P t = .244 X 746 = 182 watts, respectively; as- suming that journal friction and air resistance cause a further energy loss of 500 watts, the commercial, or net efficiency of the machine will be, by (359), p. 361: 10,000 10,624 -f 160 + 4 + 235 + 182 -j- 500 10,000 11,705 = .855, or 85.5 In dividing this by the electrical efficiency, the efficiency of conversion, or the gross efficiency, is obtained : ^=~ = -97, or 90.7 #. 3. Weight Efficiency. The weights of the various parts of our dynamo are as follows : 135] EXAMPLES OF GENERATOR CALCULATION. S 2 7 Armature: Core, .292 cu. ft. of sheet iron, . . 140 Ibs. Winding ( 134, a, 7), core insulation, binding, and connecting wires, . 40 Ibs. Shaft, spiders, pulley, keys, and bolts (estimated), 100 Ibs. Commutator, 7" dia. X 3^* length, . 20 Ibs. Armature, complete, .... 300 Ibs. Frame: Magnet core and polepieces (see Fig. 344 and 134, c, 2), (5 X 26 + 54) X 5^ = 1080 cu. ins. of cast steel, . 300 Ibs. Field winding ( 134, c t i), core insu- lation, flanges, etc., . . . 150 Ibs. Bedplate (cast-iron), bearings, etc., (estimated), ..... 250 Ibs. Frame, complete, .... 700 Ibs. Fittings: Brushes, holders, and brush-rocker, (estimated), . . . . .20 Ibs. Field regulator (winding, see 134, ',2), .15 Ibs. Switches, cables, etc. (estimated), . 15 Ibs. Fittings, complete, .... 50 Ibs. Hence the total net weight of the machine, . 1050 Ibs. The useful output is 10 KW, therefore the weight-efficiency, by 109: 10,000 = 9.5 watts per pound. 1050 135. Calculation of a Bipolar, Single Magnetic Circuit, Smooth-Drum, High-Speed Shunt Dynamo : 300 KW. Upright Horseshoe Type. Wrought-Iron Cores and Yoke, Cast-Iron Polepieces. 500 Volts. 600 Amps. 400 RCYS. per Min. a. CALCULATION OF ARMATURE. i. Length of Armature Conductor. For this machine, since 300 KW is a large output for a bipolar type, we take the upper limit given for the ratio of polar embrace of smooth- 528 D YNAMO-ELECTRIC MA CHINES. [135 drum armatures, namely, /?, = .75. Hence, by Table IV., p. 50: e 62.5 x i~" volt per bifurcation; the number of bifur- cations is ' p = i. The mean conductor velocity, from Table V., p. 52: z/ c = 50 feet per second; and the field density, from Table VI., p. 54: 3C" = 30,000 lines per square inch. The total E. M. F. to be generated, by Table VIII., p. 56: E' = 1.025 x 500 = 512.5 volts. Consequently, by (26) : L = 5i 2 -5 X 10" _ 547 feet a 62.5 x 5 X 30,000 2. Sectional Area of Armature Conductor ; and Selection of Wire. By (27), p. 57: d* = 300 X 600 = 180,000 circular mils. Taking 3 cables made up of 7 No. 13 B. W. G. wires having .095* diameter and 9025 circular mils area each, we have a total actual cross-section of 3 X 7 X 9025 = 189,525 circular mils, the excess over the calculated area amply allowing for the dif- ference between the current output and the total current generated in the armature, see 20. For large drum armatures cables are preferable to thick wires or copper rods, because they can be bent much easier, are much less liable to wasteful eddy currents, and, since air can circulate in the spaces between the single wires, effect a better ventilation of the armatures. In accordance with 24, a, a single covering of .007* is selected for the single wires, and an additional double coating of .016" is chosen for each cable of seven wires, making the total diameter of the insulated cable, see Fig. 345: 1500 X 2 = = 100. 10 Two values of n between these limits can be obtained, viz. : 252 x 2 o = ~ 2 and *- 2 = 84, 252 X 2 c = - -5- 3 = 56. For the latter number of divisions, however, there are three conductors per commutator-bar, and since the armature is a. 53 DYNAMO-ELECTRIC MACHINES. [135 drum, there would be i turn to each coil, which is impossi- ble; therefore, the number of coils employed: c = 84. By (47), P- 89, then: 252 x 2 _ |. = 2 X 84 X 3 ~ hence, summary of armature winding: 84 coils, each consisting of 1 turn of 3 cables made up of 7 No. 13 B. W. G. wires. M FIBRE 84 DIVISIONS Fig. 346. Arrangement of Armature Winding, 3OO-KW Bipolar Horseshoe- Type Generator. One armature division containing the beginning of one coil and the end of the one diametrically opposite, is shown in Fig. 346. 6. Weight and Resistance of Armature Winding. By (5), P- 96: A = 547 X ( i + 1.3 X -r } = 1070 feet. /i + 1-3 X -^-r \ = Here the original value of Z a , without reduction, is used, in regard of the fact that, in a cable, due to the helical arrange- ment of the wires, the actual length of each strand is greater than the length of the cable itself, and under the assumption that 4 per cent, is the proper allowance for this increase in the present case. By (5 8 ), P- 101, then: '/ = .00000303 X 189,525 x 1070 = 615 pounds. By (59), p. 102, and Table XXVI. : wt\ = 1.031 X 615 = 634 pounds. From (61), p. 105: i 4 X X 1070 X .001144 = .0146 ohm, at 15.5 C. 135] EXAMPLES OF GENERATOR CALCULATION. S3 1 7. Radial Depth, Minimum and Maximum Cross- Section, and Average Magnetic Density of Armature Core. By (123), and Table XLVIIL, p. 183: */ y - _ . , see also Table XLIX., p. 185; therefore: o _ Q b & = I (<4 - d c ) = -- ~ = 10 inches, and from (234), p. 342, or Fig. 347 : /"izS b\ = 10 X A/ -- i = 13.4 inches. Fig. 347. Dimensions of Armature Core, 3OO-KW Bipolar Horseshoe- Type Generator. Hence by (232), p. 341: 5* ai = 2 X 37i X 10 X -95 = 712 square inches, and by (233), p. 341: S'a, = 2 X 37| X 13-4 X -95 = 956 square inches. From (138), p. 202 : ^6 x 512.5 X TO' = 6o maxw ells; 2 x 84 X 400 consequently: <&" a = 4 5'_7 6 '^ c 3 64,200 lines per square inch, 712 5 3 2 D YNAMO-ELECTRlC MA CHINES. [136 45,760,000 (S>\ = - l = 47,800 lines per square inch. 95 From Table LXXXVIIL, page 336: m" &i = 15.2 ampere-turns per inch; \= 9- 1 " " " " = 12.15 ampere-turns per inch. A To the latter corresponds a mean density of: \ = 58,000 lines per square inch. 8. Energy Losses in Armature^ and Temperature Increase. By (68), p. 109: P & = 1.2 x 6oo 2 x .0146 = 6307 watts. JV^ = -? = 6.67 cycles per second; By (71), p. 112: 18 X n x 37i X 10 X .9 .. c M=- ^^- - = 11.05 cubic feet; From Table XXIX., (<8>\ = 58,000): rf = 20.92 watts per cubic feet; From XXXIIL, (tf, = .010"): e = .0242 watt per cubic feet. By (73), P- 112: 7> h = 20.92 x 6.67 x 11.05 = 1540 watts. By (76), p. 120: P* = .0242 x 6.67" X 11.05 = 12 watts. By (65), p. 107 : Pt. = 6307 + 1540 + 12 = 7859 watts. From Table XXXV., p. 124: 4 = 35 X 28 + 2 x .8 = n inches. By (78), p. 124: 5 A = (28+ 2 x -8) X ?r(37i+ 1.8 X ni)= 5412 sq. ins. 135] EXAMPLES OF GENERATOR CALCULATION. 533 Ratio of pole area to radiating surface: 30 X 7t X 37^ X .75 -- = '49- 5412 For this ratio and a peripheral velocity of X w x 4 f = 5 if feet per second. 12 60 Table XXXVL, p. 127, gives: 6' a = 44.7C. ; consequently by(8i): 9 a = 44.7 x = 65 Centigrade, and the resistance of the armature, when hot, is: r\ = .0146 X (i + .004 X 65) = .0184 ohm, at 80.5 C. 9. Circumferential Current Density, Safe Capacity, and Run- ning Value of Armature; Relative Efficiency of Magnetic Field. By (84), p. 131 : 84 X 2 X 300 n / = - - - = 572 amperes per inch. 20 x 7t Corresponding increase of temperature, from Table XXXVII., p. 132: a = 60 to 80 C, which checks the above result. By (88), p. 134, and Table XXXVIII. : . P' = 28' X 37i X -88 X 400 X 30,000 X io-' = 310,000 watts. By (90), P. 135: P' & = -jr '-^- - = .0167 watt per pound of copper, at unit field density; this also verifies the calculation, see Table XXXIX., p. 136. By (i55), P- 211 : Q, _ 45 > 7 0,000 x _ 74.50 maxwells per watt, at unit 512.5 X ooo velocity; by Table LXII., p. 212, this is not too high. 534 DYNAMO-ELECTRIC MACHINES. [135 10. Torque, Peripheral Force, and Upward Thrust of Arma- ture. By (93), P- 138: r = II ', x 600 X 168 X 45,760,000 = 5420 foot-pounds. By (95), P- r 33: =30.7 Pound, By (103), p. 141: / t = ii X io- 9 X 28 X 37i X (30,600' 29,400') = 8321bs., under the assumption that the density of the upper half of the field is 2 per cent, above, and that of the lower half 2 per cent. below, the average. b. DIMENSIONING OF MAGNET FRAME. 1. Total Magnetic Flux, and Sectional Areas of Magnet Frame. By (156), p. 214, and Table LXVIII. : #' = 1.20 x 45,760,000 = 55,000,000 maxwells. By (217), p. 314, wrought-iron cores and yoke being used: = 55,000,000 = e . nches 90,000 By (216), p. 313, and Table LXXVI., the minimum section of the cast-iron polepieces: = 55.000,000 = ^^ . nches 50,000 2. Magnet Cores. Selecting the circular form for the cross- section of the magnets, their diameter is: 1 X - = 28 inches. Length of cores, from Table LXXXL, p. 319, by interpola- tion: / = 35 inches. g 135] EXAMPLES OF GENERATOR CALCULATION. 535 Distance apart, from Table LXXXV., p. 323, c = 16 inches. 3. Yoke. Making the width of the yoke, parallel to the shaft, equal to the diameter of the cores, its height is found: -- 20 = 22 inches. SCALED INCH =1 FT. Fig. 348. Dimensions of Field Magnet Frame. 3OO-KW Bipolar Horseshoe- Type Generator. The length of the yoke is given by the diameter of the cores, and by their distance apart, see Fig. 348: / y = 2 x 28 -|- 16 = 72 inches. 4. Polepieces. The bore of the field is the sum of: 536 DYNAMO-ELECTRIC MACHINES. [135 Diameter of armature core, = 28.000 Winding 4 X .322", = 1.288 Insulation and binding, 2 X (-070" + .070") = .280 Clearance (Table LXI., p. 209) 2 X \\ = .50 30.068 or, say, 30 inches. Pole distance, by (150), p. 208, and Table LX. : /' p = 6 X (30 28) = 12 inches. Length of polepieces equal to length of armature core, or: /p = 37f inches. Height of polepieces, same as bore: h p = 30 inches. Thickness in centre, requiring half of the full area: 1 100 = 14.7, say 15 inches. 2 ^^ "2 *7-l- Height of pole-tips: \ inch. Mso - 1/30' - 12' J = 1J i Height of zinc blocks, from Table LXX., p. 301: h z = 11 inches. C. CALCULATION OF MAGNETIC LEAKAGE. i. Permeance of Gap-Spaces. OC" X v c = 30,000 X 50 = 1,500,000, therefore, by (167), p. 226, and Table LXVI. : * X .88 X 37i = 536. i-3S X (30 - 28) ' 2.7 2. Permeance by Stray Paths. y (178), p- 232: 2 _ 28 * n X 35 A 1 ' " 2 x 16+ 1.5 x 28 ~ *' 135] EXAMPLES OF GENERATOR CALCULATION. 537 By (188), p. 239: 7 X [37i X (28 + 15) + 850] \ = = 56, 2 X II the portion of the bed plate opposite one polepiece being esti- mated to have a surface of S = 850 square inches. The pro- jecting area of the polepiece, see Fig. 349, is Fig. 349. Top View of Polepiece. 300 KW Bipolar Horseshoe-Type Generator, Showing Projecting Area. S 3 = 16 x 37 -f 16" X - 28" - = 386 square inches, hence by (199), p. 245: * _ . 386 37$ X 3 35 2 X 35 + (3 + 22) X - = ii + 7.4 = 18.4. 3. Leakage Factor. By (i57), P- 218: A = 536 + 4i.6 4- 56 + 18.4 _ 652 _ 536 " 536 Total flux: #' = 1.215 x 45,760,0-00 = 55,700,000 maxwells. d. CALCULATION OF MAGNETIZING FORCES. i. Air Gaps. Length, by (166), p. 224: l \ l -35 X (30 28) = 2.7 inches. 538 DYNAMO-ELECTRIC MACHINES. Area, by (141), p. 204: [136 7t S g = 29 x - X .88 X 37^ = 1500 square inches. Density, by (142), p. 204: . 4<, 760,000 ,. 3C = - - = 30,500 lines per square inch. Magnetizing force required, by (228), p. 339: a/ g = .3133 x 3,5 X 2.7 = 25,800 ampere-turns. 2. Armature Core. Length, by (236), p. 343, see Fig. 350: /" = 18 X n X -{- 10 = 27.85 inches. Fig. 350. Flux Path in Armature, soo-KW Bipolar Horseshoe-Type Generator. Minimum area, by (232), p. 341 : S",^ = 2 x 37^ X 10 X .95 = 712 square inches. 45,760,000 . . (B ai = - = 64,200 lines p. sq. in. ; m ai = 15.2. Maximum area, by (233), p. 341, and (234), p. 342: S'ag = 2 X 37i X 13.4 X.95 = 956 square inches. 45,760,000 ' . = - - = 47,800 lines p. sq. in. ; m'. = 9. i. 950 Average specific magnetizing force, by (231), p. 341 : 15.2 + 9.1 m a = = 12.15 ampere-turns p. inch. Corresponding average density: (B" a = 58,000 lines per sq. in. 135] EXAMPLES OF GENERATOR CALCULATION. 539 Magnetizing force required, by (230), p. 340: at* 12.15 X 27.85 = 340 ampere-turns. 3. Wrought Iron Portion of Frame (Cores and Yoke).' Length: /' wx = 2 x 35 + 22 + 44 = 136 inches. Area: S\i = 28 8 - = 615.75 square inches. 4 Density and corresponding specific magnetizing force: ieces). Length, by (243), page 348: /'c.i. = 35 + 2 = 37 inches. Minimum area (at center) : S'c.1.! = 15 X 37* = 5 62 -5 square inches. Corresponding maximum density and specific magnetizing force : X lines . Maximum area (at poleface) : S'CA, = (30 X n X ^ + 2 x iH X Z1\ - 1400 sq. ins. Corresponding minimum density and specific magnetizing force : 415,760,000 ,. c.i. a = = 32,7oo lines; m\^ = 57.6. Average specific magnetizing force: **c.i. = -^ = 106.3 ampere-turns per inch. Corresponding average density: OJ" cl = 43,500 lines per square inch. 54 DYNAMO-ELECTRIC MACHINES. [135 Magnetizing force required: af *L = lo6 -3 X 37 = 3930 ampere -turns. 5. Armature Reaction. By ( 2 5) P- 352, and Table XCL: af T = 1.73 x - - X 2 ~- = 5700 ampere-turns. 6. Total Magnetizing Force Required. By (227), p. 339: AT = 25,800 + 340 + 6900 -f 3930 -f 5700 = 41,670 ampere-turns. C. CALCULATION OF MAGNET WINDING. Shunt winding to be figured for a temperature increase of 15 C. Regulating resistance to be adjustable for a maximum voltage of 540, and a minimum voltage of 450. i. Percentage of Regulating Resistance at Normal Load. The maximum output of 540 volts requires a total E. M. F. of 512.5 -f 40 = 552.5 volts, which is 7.8 per cent, in excess of the total E. M. F. gen- erated at normal output; for the maximum voltage, therefore, 1.078 times the normal flux must be produced. The magnet- izing forces required for this increased flux are: Air gaps: at 'g = -3*33 X (30,500 X 1.078) x 2.7 = 27,800 ampere-turns. Armature core: ffi'a = 58,000 x 1.078 = 62,500 lines; m' & = 14.2. at'i= 14.2 X 27.85 = 400 ampere-turns. Wrought iron: 'w.i. = 90,000 X 1.078 = 97,000 lines; w' Wii . = 73.6. a/' wl = 73.6 X 136 = 10,000 ampere-turns. Cast iron: <&'c.i. = 43>500 X 1.078 = 46,900 lines; w' c .i. = '44- fl/' c .j. = 144 X 37 = 5320 ampere-turns. Armature reaction: at' t = 1.77 X 4 X X ~~= 5820 ampere-turns. 2 IOO 135] EXAMPLES OF GENERATOR CALCULATION, 54* The total magnetizing force needed for maximum output, consequently, is: AT' = 27,820 + 400 -f- 10,000 + 5320 + 5820 = 49,340 ampere-turns. This surpasses the normal excitation by 100 X (49,340 - 41,670) = 41,670 that is to say, the extra-resistance in circuit at normal output must be 18 per cent, of the magnet resistance, in order to pro- duce the maximum voltage of 540 with the regulating resist- ance cut out. 2. Magnet Winding (for $00 Volts). The mean length of one turn, by (292), p. 375, and Table XCIV., being 4 = 3-43 X 28 = 96 inches, the specific length of the required magnet wire is directly obtained by (319), p. 385: X - x 1. 18 x (i +.004X15) = 882ft. pr. ohm. The nearest gauge wires are No. 13 B. W. G. (.095* + .010*) and No. n B. & S. (091" -f- .010"), having 874 and 798 feet per ohm, respectively. The former being about 5 percent, above, and the latter about 4 per cent, below, the required figure, the regulating resistance in circuit at full load, when No. 13 B. W. G. were used, would be about 23 per cent., and for No. ii B. & S. would be about 14 per cent, of the magnet resist- ance. In order to obtain the exact amount of regulating resistance desired, the two sizes must be suitably combined. Taking equal weights of each, the resultant specific length is: == .04x9 x 8 74 + .0503 x 798 = 834 feet ohm; .0419 + .0503 where .0419 and .0503 are the resistances per pound of the two wires. This specific length being practically the same as found above, the winding calculated on its basis will, in fact, make r x = 18, which therefore is to be used in the formulae. 542 DYNAMO-ELECTRIC MACHINES. [135 The height of the winding space derived from the above value of / T is : h m = - r ; -- 28 = z\ inches, and this into formula (277), page 369, gives the radiating sur- face of the magnets: SM = (28^ + 2 x 2%) 7t x 2 (35 3) = 6730 square inches, an allowance in length of 3 inches per core being made for flanges, spools, and insulation. Hence by (312), p. 383: ^"sh = ~- X 6730 x 1.18 = 1590 watts, 75 by (314), p- 384: 41,67 TV^ = - and by (315), p. 384: 41,670 X "joo = - 1_2 13,100 shunt-turns. '59 consequently, = 125.5 ohms, resistance of winding, cold (15-5 G.); and by (318), p. 385: r'sh = I2 5-5 X (i + .004 x 15) = 133 ohms, resistance of winding, warm (30.5 C). By (317), P- 384: r \\>. = 133 X 1.18 = 157 ohms, resistance of entire shunt circuit, at normal load; therefore: / sh = - - = 3. 18 amperes, shunt current, at normal load. Dividing the magnet resistance (cold) by the average resist- ance per pound of the two sizes used (equal weights being taken), we obtain the weight of the shunt winding: - (.0419 -f .0503) = 2720 pounds, bare wire, 135] EXAMPLES OF GENERATOR CALCULATION. 543 or, see Table XX VI., p. 103: a'/' gh = 1.03 x 2720 = 2800 pounds, covered wire. By (3 2<5 )> P- 3 8 9> we receive: w/Bh = 3i-3 X io-' X 13,100 X - \ X 834 = 2730 Ibs., which checks the above figure. Formula (257), p. 361, gives: / -95 + -09 1 / 12 X 104,800 x - - /- ( 65 X n = 16. 2 14 = 2.2 inches. Allowing. 3 inch for insulation between the layers, thickness and insulation of bobbins, and clearance, the total height of the magnet winding becomes // m = 2.2 + .3 = 2.5 inches, which is the same as used in calculating the winding. There are, consequently, no errors to be corrected, and the final result of the winding calculation is: 1400 Ibs. (covered) of No. 13 B.W.G. wire (.095' + .010*) and 1400 Ibs. (covered) of No. 11 B. & S. wire (.091* + .010'), each wound in 4 spools of 350 pounds, two spools of each size to be placed on each magnet, see Fig. 348. Total weight of magnet wire, 2800 pounds. 3. Shunt Field Regulator. The amount of regulating resist- ance in circuit at normal load required for the maximum volt- age in the preceding was found to be 18 per cent, of the magnet resistance. In order to reduce the voltage from the normal amount to the minimum of 450, the total E. M. F. gen- erated must be decreased from 512.5 to 512.5 50 = 462.5 volts, or by 9^ per cent.; hence the minimum flux is .9025 of the normal flux, and the magnetizing forces for the minimum voltage are; 544 DYNAMO-ELECTRIC MACHINES. [135 Air gaps: af 'e = -3 X 33 X (30,50 X .9025) X 2.64* = 22,800 ampere- turns. Armature core: "a= 5 8 > 000 X .9025 = 52,350 lines; m\ = 10.3. .-. at\ = 10.3 X 27.85 = 270 ampere-turns. Wrought iron: (B* w .i. 90,000 X -9025 = 8120 lines; /0* w .i. = 33.2. * 0*'w.L = 33-2 X 136 = 4520 ampere-turns. Cast iron: %.i. = 43,5oo X .9025 = 39,260 lines; m" c = 86.8. .-. af' ci = 86.8 x 37 = 3210 ampere-turns. Armature reaction: 84 X 600 2-*i at r = 1.7 X X -~ = 5600 ampere-turns. The total excitation required for minimum voltage is the sum of the above magnetizing forces: AT' 22,800 + 270 + 4520 + 3210 x 5600 = 36,400 ampere-turns. This minimum excitation being IPO x (41,670 - 36,400) _ | "^ l*t UCI L-C11U. 41,670 smaller than the normal excitation, the normal resistance of the shunt circuit, in order to effect the corresponding increase in the exciting current, must be increased by 12.7 per cent., or the magnet resistance by 1.18 x 12.7 = 15 per cent. The total resistance of the regulator, therefore, by formula (33i ) P- 393, is: r r = (.18 + .15) X r' 8h = .33 x 133 = 44 ohms. By (332), P. 393: / r \ 54 (Ah)max = ~ == 4-6 amperes. 133 * For the minimum density the product 3C X "V c being 1,500,000 X .9025 = J, 353.75O, Table LXVI. gives a coefficient of field-deflection k\ s = 1.32, which makes the length of the magnetic circuit in the gaps /"g = 1.32 X (30 28) = 2 64 inches, 135] EXAMPLES Of GENERATOR CALCULATION. 545 By (333), P- 393 : (/8h)mln = 4 = 2 ' 5 Supposing that the regulator is to have 60 contact-steps, so as to give an average regulation of i volt per step, the resist- ance of each coil of the rheostat will be - = .733 ohm; and if iron wire at 6500 circular mils per ampere is employed, the area of the wires for the various coils ranges between 4.06 X 6500 = 26, 390 and 2.54 x 6500 = 16,510 circular mils. The data for the gauge numbers lying between these limits are: GADOB DIAMETER SECTIONAL AREA CARRYING CAPACITY, AMPS. NUMBER. (inch). (Cir. Mils). (6500 Cir. Mile p. A.) N0.6.B.&S ........... 162 ...... 26,251 ............ 4.04 No. 9B. W. G ........... 148 ...... 21,904 ............. 3.38 No. 7B. &8 ............ 144 ...... 20,817 ............. 3.21 No. 10 B. W. G .......... 134 ...... 17,956 ............. 2.76 No.SB.&S ............ 1285.... 16,510 ............ 2.54 Inserting the above values of the current capacities into formula (335), p. 394, we obtain: 4.06 4.04 4.o6 2.54 4.06 3.38 4.06 -- 2.54 4.06 3.21 X 60 = i , X 60 = 27, and 4.06 2.76 X 4 = ~ X 60 = 51, 4.06 - 2.54 4.06 2.154 I6 = - ^ X 60 = 60 ; 4.06 - 2.54 from which follows that coils i to 26 are to consist of No. 6 B. & S. wire, of which about 300 feet are needed for the required resistance of .733 ohm; that coils 27 to 32 are to be of No. 9 B. W. G., length per coil about 250 feet; coils 33 to 50 of No. 7 B. & S., length about 240 feet; coils 51 to 59 of No. 10 546 DYNAMO-ELECTRIC MACHINES. [135 B. W. G., length about 205 feet; and coil 60 of No. 8 B. & S. wire, about 190 feet in length. /. CALCULATION OF EFFICIENCIES. 1. Electrical Efficiency. By (35 2 ) P- 4o6: 500 X 600 __ 300,000 Ve ~ 500 X 600 + 603.18" X .0184 + 3.18' X 157 " 308,280 = .975, or 97.5 #. 2. Commercial Efficiency and Gross Efficiency. The energy lost by hysteresis and eddy currents was found P h -\- P e = 1552 watts; energy losses by commutation and friction estimated at 12,000 watts; hence the commercial efficiency, by (360), p. 407: 300,000 300,000 _ % ~ 308,280 + I 55 2 + 12,000 - 321,832 : ' 932> and the gross efficiency: 3. Weight Efficiency. The net weight of the machine is esti- mated as follows: Armature: Core, 11.05 cu - ft. f wrought iron, 5,300 Ibs. Winding, insulation, binding, etc., . 700 " Shaft, commutator, pulley, etc., . 3,000 " Armature, complete, .... 9,000 Ibs. Frame : Magnet cores, 28* X 70 = 43,100 cu. ins. of wrought iron, 12,075 Ibs. Keeper, 28 X 22 x 72 = 44,35<> cu. ins. of wrought iron . 12,325 " Polepieces, about (18 X 30 X 37i) X 2 = 40,500 cu. ins. of cast iron . . 10,600 " Field winding, core insulation, spools, flanges, etc., . 3,000 " Bedplate, bearings, zinc blocks, et c., ..... 10,000 " Frame, complete, . . . , . 48,000 Ibs. 136] EXAMPLES OF GENERATOR CALCULATION. 547 Fittings: Brushes, holders, and brush rocker, . .... 400 Ibs. Switches, cables, etc., . . . 300 " Fittings, complete, ...... 700 Ibs. Total net weight of dynamo, . . 57,700 Ibs. Hence, the weight efficiency: ^^. = 5.2 watts per Ib. 577oo 136. Calculation of a Bipolar, Single Magnetic Circuit, Smooth- Drum, High-Speed Compound Dynamo: 300 KW. Upright Horseshoe Type. Wrought-Iron Cores and Yoke. Cast-Iron Polepieces. 500 Volts. 600 Amps. 400 Revs, per Min. The armature and field frame calculated in 135 are given; the machine is to be overcompounded for a line loss of 5 per cent. ; temperature of magnet winding to rise 22^ C. ; extra- resistance in shunt circuit to be not less than 18 per cent, at normal load. a. CALCULATION OF MAGNETIZING FORCES. i. Determination of Number of Shunt Ampere- Turns. Use- ful flux required on open circuit: 6 * 5 X10 ' - 44,700,000 maxwells; i 65 X 400 hence by 104 and 135: 44,700,000 . ox ** = -3133 x 4> ; 500 x 1.32 (30 - 28) -3*33 X 29,800 x 2.64 = 24,700 ampere-turns. 44.700,000 44,700,000 .. = ' = 62,700, (B. =r- =46,700. ,-.^ = I4 ' 3 "*" X 27.85 = 11.55 X 27.85 = 320 ampere- 2 turns. 54$ DyNAMO-ELECTRIC MACHINES. [ 136 **n 1-215 X 44,700,000 00 .. 4o lines per square inch; 1400 184.7 -f 63.1 af c .i. - ^ - X 37 = 123.9 x 37 = 4580 amp.-turns. 8/t ' at r = 1.76 X - ^ ""* X ~- 5820 ampere-turns. 2 1 80 AT 27,100 -f- 380 -f 9220 + 4580 -f 5820 = 47,100 ampere-turns. Consequently by (339), p. 397 : 47, IO 35> 000 = 12,100 ampere-turns. 136] EXAMPLES OF GENERATOR CALCULATION. 549 b. CALCULATION OF MAGNET WINDING. i. Series Winding. By (343), P- 400: 47,100 X 600 X 96 , *- *=6SX 4 -' -X (i +.004 X a.}) = 1,267,000 circular mils. Taking 5 cables of 19 No. 9 B. & S. wires each, the actual area is: 5 Xi9 X 13,094 = 1,243,930 circular mils. The number of turns required is: 12 1 2O JV M = - = 20, or 10 turns per core; ooo hence the series field resistance, at 15.5 C., by (344), p. 400: r m = .875 X * * 96 - = .00135 ohm, 5 X 19 X 13,094 and the weight: wt^ = 20 x -J- X (5 X 19 X 13,094) =6031bs., bare wire; or, wt'^ 1.028 x 603 = 620 Ibs., covered wire. 2. Shunt Winding. The potential across the shunt field being 1.05 X 500 = 525 volts, the specific length of the shunt wire, for 18 percent, extra-resistance, and 22^ C. rise in tem- perature, is, by (3x9), p. 385: ? lh = 35i^ x X 1.18 X (i + .004 X 22$) 5 2 5 I2 = 687 feet per ohm. The two nearest gauge numbers are No. n B. & S. (798 feet per ohm) and No. 14 B. W. G. (667 feet per ohm); taking two parts, by weight, of No. 14 B. W. G. to one part of No. n B. & S., we obtain: = .0503 X 79+ X. 07.8 X7 = 703 feet ohm> 53 + 2 X .0718 which is a trifle more than 2 per cent, in excess of the re- quired specific length. By increasing the percentage of extra 550 DYNAMO-ELECTRIC MACHINES. [136 resistance in the same ratio, that is, by making r^ = 20 per cent., formula (319) will give the specific length actually pos- sessed by the combination of shunt wires selected. Hence: by (346), p. 400 : P^ = ~- X 6730 - 600" X .00135 X (i + .004 X 2 2 ) :=: 2O2O 530 = 1490 Watts; by (3 I2 )> P- 3 8 3 : J' ab = 1490 X 1.20= 1788 watts; by (3H), p. 3 8 4: ^= ^|^ = 10,270 turns; by (315). P- 384: Z^ = 10,270 x = 82,160 feet; Weight: ,/* = 82,160 x 2 X - 2 85 + ' 2493 = 1825 Ibs., bare wire, o >/'!, = 1.035 X 1825 = 1890 Ibs., covered wire; Resistance: = 117 ohms, resistance of shunt winding, 15.5 C.; by (318), P- 3 8 5: r' Bh = 117 X (i -f- .004 X 22^) = 127.5 ohms, resistance of shunt winding, 38 C. ; by (317), p- 384: r "*h = 12 7-5 X 1.20 = 153 ohms, resistance of entire shunt circuit, normal load. e 2t .*. 7^= = 3.43 amperes, shunt current, normal load. 3. Arrangement of Winding on Cores. Total weight of series winding: . wt'^ = 620 Ibs. Total weight of shunt winding: . wt'^ 1890 Ibs. . Total weight of magnet winding: . . 2510 Ibs. 136] EXAMPLES OF GENERATOR CALCULATION. 551 The weight of the series wire being just about one-quarter of the total weight, the winding is with advantage placed upon 8 spools, 4 per core, the lower one of each being used for the series wire, one of the upper three being wound with No. ii B. & S., and the remaining two with No. 14 B. W. G. wire; weight of wire per series spool, 310 pounds, per shunt spool, 315 pounds. Each series spool has 5 X to = 50 cables which are arranged in 4 layers, two of which contain 12, and two 13 cables. The diameter of each series cable, consisting of 19 No. 9 B. & S. wires, is 5 X (. 1144" -(- .010") = .622 inch, hence the winding depth in the series spools, 4 X .622" = 2.488 inches, and the length of one layer (13 cables) = 13 X .622" = 8.086 inches. Since the available height of each spool is 35 ~ 2 ^=8| inches, by this arrangement the spool will be just filled. In the shunt bobbins the total 10,270 turns are divided in the ratio of the quantities used and of the specific lengths (feet per pound) of the two sizes of wire, /". e., in the ratio of 2 x 48 : 40. i ; hence there are 10,270 x 2 Q X , 48 = 7240 turns of No. 14 B. W. G. 2 X 48 + 40- I and 10,270 x xx 4 '* = 3030 turns of No. 11 B. & S. 2 X 40 + 40. I Each No. 14 B. W. G. spool, therefore, contains - = 1810 turns, 4 and, the number of turns per layer being 8.125 .083 -f- .010 has a net winding depth of 1810 -87, X .093* = 1.95 inch. 55 2 DYNAMO-ELECTRIC MACHINES. [137 Each of the No. n B. & S. spools has ^L= 1515 turns; 2 the number of turns per layer is: -^5 =80, .091 -(- .OIO and consequently, the net winding depth: x .101" = 1.92 inch. Actual magnetizing force at full load : AMPERE-TURNS. Series magnetizing force, AT^ = 20 x 600 = 12,000 Shunt magnetizing force, AT^ = 10,270 X 3.43 = 35> 22 6 Total magnetizing force, . . . . 47,226 137. Calculation of a Bipolar, Double Magnetic Circuit, Toothed-Ring, Low-Speed Compound Dynamo: 50 KW. Double Magnet Type. Wrought-Iron Cores. Cast-Iron Yokes and Polepieces. 125 Volts. 400 Amps. 200 Revs, per Min. a. CALCULATION OF ARMATURE. 1. Length of Armature Conductor, For /?, = .70 (a = 27), Table IV., p. 50, gives e = 60 X io~ 8 volt per foot; from Table V., p. 520, v c = 32 feet per second; from Table VI., p. 54, 3C* = 20,000 lines per square inch; and from Table VIII., p. 56, E' = 1.064 X 125 = 133 volts; hence by (26), p. 55: Z -=6 J 33X v'' -=346 feet. oo X 32 X 20,000 2. Sectional Area of Armature Conductor, and Selection of Wire. B 7 ( 2 7), P- 57: * = - - = 61 inches. 2 x 80,000 X 10 x .9 Internal diameter of armature core, Fig. 352: 35| - 2 X 6J - 21$ inches. 137] EXAMPLES OF GENERATOR CALCULATION. Mean diameter of core: d'\ = 2i-f + 6| + i^ = 30^ inches. Maximum depth of core, from (234), p. 342: 555 Fig- 352. Dimensions of Armature Core, so-KW Double-Magnet Type, Low-Speed Generator. By (232), p. 341: S^ = 2 X 10 X 6 x .90 = 121 square inches. By (233), p. 341: San = 2 x 10 X 14-8 X .90 = 266 square inches. Therefore: 9,630,000 (B &l = - - 79,600 lines per square inch; /u" _ 9> 6 3> 000 ,- ^ ~ ^6 = 3^> 200 l ines P er square inch. m " a\ = 3-7 ampere-turns; m" &z 6. 7 ampere turns p. inch. By (231), p. 341: 30. 7 4- 6. 7 * a = - - = 18.7 ampere-turns per inch. Corresponding average density: &" a = 60,000 lines per square inch. 556 DYNAMO-ELECTRIC MACHINES. [ 137 7. Weight and Resistance of Armature Winding. By (53) p- 99: 2 X (ic + 61) + iAX* By (58), p. 101: a// a = .00000303 X 137,980 X 1360 = 568 Ibs., bare wire. By (59), P- I02: //' a = i. 066 x 568 = 605 Ibs., covered wire. By (61), p. 105: r & = - - X 1360 X .0015 = .0256 ohm, at 15.5 C. 4 X 20 8. Energy Losses in Armature, and Temperature Increase. By (68), p. 109: P & = 1.2 x 400" X .0256 = 4950 watts. From Fig. 352: X n X 8^ - 138 X i-ft X-^ ) X 10 X .90 M= - 5 - '- - 1728 = 3.61 cubic feet; 200 = 3.33 cycles per second; l from Table XXIX. (&" a = 69,000): rj = 27.61 watts per cubic foot; from Table XXXI. ( 630, ooo x 5800 maxwe lls per watt, at unit i33 X 400 b. DIMENSIONING OF MAGNET FRAME. i. Total Magnetic Flux, and Sectional Areas of Frame. By (156), p. 214, and Table LXVIII. : # = 1.25 x 9,630,000 = 12,000,000 maxwells. 55 8 DYNAMO-ELECTRIC MACHINES. [137 B y (217), p- 314; I2,OOO,OOO -inn n L S w i = - = 133.3 square inches. 90,000 By (220), p. 314: o. I2.OOO.OOO nnn > i S" c i = - = 266.7 square inches. 45,000 2. Magnet Cores. The two cores being magnetically in parallel, each must have, one-half the area *S" w .i. found above for wrought iron, and making their breadth equal to that of the armature core, their thickness is found: 133-3 = 6.67, or say 6 inches. 2 x 10 3. Polepieces. Thickness at ends joining cores: 2 x 6| = 13 inches. Bore, by Table LXI., p. 209: 4 = 3i + 2 X i = 39 inches. Length of centre portion* (equal to diameter of armature core) : 38 inches. Depth of magnet winding (Table LXXX., p. 317): h m = 2f inches. Allowing $ inch clearance between the magnet winding and the pole- tips, the total length of the polepieces is: 38^ + 2 X (2| + ) = 45 inches. Pole-distance: A> = 39 X sin 27 = 15 inches, which is 4.45 times the total length of the gap space (compare with Table LX., p. 208). Thickness in centre, required for mechanical strength only: 3 inches. Thickness of pole-tips: \ (3H ~ V X 39 8 - 15") = 137] EXAMPLES OF GENERATOR CALCULATION. 559 All other dimensions of the frame can be directly derived from Fig. 353. Fig. 353- Dimensions of Field-Magnet Frame, 50 KW Double-Magnet Type, Low-Speed Generator. C. CALCULATION OF MAGNETIC LEAKAGE. i. Permeance of Gap Spaces. t = 3 o -^ = -8765 .4375 = .439 inch ; Ratio of radial clearance to pitch: ^? = - 286; Product of field density and conductor velocity: 20,000 X 32 : = 640,000, hence by Table LXVII., p. 230, the factor of field deflection, n f f- K Vt *'5 and by (174), P- 230: . j [19 X * X .70 + (-439 + -219) X 138 X .85] X io -5 X (39 - - 544. 75 560 DYNAMO-ELECTRIC MACHINES. [ 137 2. Permeance of Stray Paths. P- 242: + 10) X i3i + 3i X io 10 X 18 '15+ - 2 (53.1 +.9) = 108. 3. Leakage Factor. By (157), P- 218: -H *i) 544 Ratio of width of slot to pitch: 4375 _ ."8765 - therefore, by (158), p. 218, and Table LXV. : A' = 1.03 X 1.20 = 1.24. d. CALCULATION OF MAGNETIZING FORCES. i. Shunt Magnetizing Force. = 6 X 125 X 10* = g 060 000 maxwells. 414 X 200 Air gaps: at. = .3X33 X 9 -^^ X .75 = .3133 X 22,200 X -75 400 = 5216 ampere-turns. Armature core: 0.060.000 9,060,000 (B a , = - ~ = 74,8oo lines; (B a2 = - -^ = 34,000 lines; l\ = 28f X n X 9 ,"t 27 " + 6| + 3i = 39 inches; 300 - - J '3. x 39 = 15.5 X 39 = 605 ampere-turns. 2 Magnet cores (wrought iron): 1.24 X 9,O6O,OOO 01- t, ($>" . = - = 83,300 lines per square inch; 2 X 6f X 10 .'.af w , = 36.5 X 3 8 = X 3 8 7 ampere-turns. 137J EXAMPLES OF GENERATOR CALCULATION. 561 Polepieces (cast iron with admixture of aluminum) : The pole- pieces consist of two end portions of uniform cross-section and of a centre portion of varying cross-section. The com- bined length of the uniform portions is, from Fig. 353: l\= 2 X 3i = 6 i inches, and the mean length of the varying cross-section, by (243), p. 348: _ x i. - 22 inches. The flux-densities and the corresponding magnetizing forces are: = i. 24 X 9 060,000 = , 1,225,000 = Hnes 2Xi 3 *Xio 270 S q. inch; 0,060,000 0,060,000 -- 05 '*. = m' eA = 79 amp. -turns p. inch; m' cl = 25.4amp.-turns. p. inch. 1<> o Hence, according to formula (242), page 346: a/ cl = 79 X 6 -j- -- X 22 = 1662 ampere-turns. The shunt magnetizing force is, therefore: ^^h = 5216 + 605 + 1387 -f 1662 = 8870 ampere-turns. 2. Series Magnetizing Force. E' = 125 + 1.25 x 400 X .0256 = 137 volts. = 6 x '37 X io 9 Air gaps: maxwells . 414 X 200 0,030,000 = -3133 X 2 ~ X 75 = .3133 X 24,300 X .75 = 5710 ampere-turns. Armature core: , 9,9"? o oo i. (B a = - - = 82,100 lines per square inch; 121 9,930,000 (B . = - ~ = 37,400 lines per square inch. 266 35 + 7 . af & = ^* X 39 = 820 ampere-turns. 562 DYNAMO-ELECTRIC MACHINES. [137 Magnet cores: I. 24 X QiQ"?O,OOO (K)098 Qh at c 918,340 r'te = 1-078 X .00098 = .00106 ohm, at 34.5 C. and the total weight: wt^ = 2 x 14 X 3 ' 4 X 22 X .1264 = 238 Ibs., bare wire; 12 //' M = 1.029 X 238 = 245 Ibs., covered, or 122| Ibs. per magnet. 2. Shunt Winding. The two shunt coils to be connected in parallel. By (318), p. 385: A 8h = - X X 1.35 X (i + .004 x 19) = 397 ft. per ohm. 564 DYNAMO-ELECTRIC MACHINES. [% 137 The nearest gauge wire is No. 14 B. and S. (.064" -f- .007") with a specific length of 398 feet per ohm. By (346), P. 400: /> 8h 12- x 860 400' X ' 2 10 = 218 85 = 133 watts. / By (312), p. 383: ^' S h = 133 x 1.35 = l8 watts - By (314), p. 384: ^ 8h = 887 i ^ o 125 = 6170 turns per magnet. By (315). P- 384: Zgh = 6170 X = 24,200 feet per core. 12 Total weight: wtsk 2 X 24,200 x .01243 604 Ibs., bare wire. wffr = 1.0325 x 604 = 624 Ibs., covered, or 312 Ibs. per magnet. Shunt resistance per core: >* = ^ = 60.8 ohms, at 15.5 C. r'^ = 60.8 x 1.076 = 65.5 ohms, at 34.5 C. '"sn = 65.5 X 1.35 = 88.4 ohms, each shunt circuit. Exciting current: I 2? Ah = OQ 142 amperes, at normal load. 00.4 3. Arrangement of Magnet Winding on Cores. Number of series wires per layer: Number of layers of series wire: 14 X 22 = 4. 78 Height of series winding: 4 x .216 = .864 inch. 137] EXAMPLES OF GENERATOR CALCULATION. 565 Number of shunt wires per layer: = 240. .071 Number of layers of shunt wire : = 26. 24O Height of shunt winding: 26 X .071 = 1.846 inch. Allowing .1 inch for core covering and insulation between layers, the actual total depth of magnet winding is: h m = .864 + 1.846 + .1 = 2|f inches. Actual magnetizing force at full load: AMPERE- TURNS. Series magnetizing force, AT ee = 14 X 4 = 5600 Shunt magnetizing force, AT^ = 26 X 240 X 1.42 = 8850 Total magnetizing force, .... A T= 14,450 /. CALCULATION OF EFFICIENCIES. i. Electrical Efficiency, By (353), p. 406: 125 X 400 __ A 125 X 400 + (400 + 2 X 1.42)" X .0314 + 400' X .00106 + (2 X 1.42)* X -jp = .98, or 89.8*. _ ve 2. Commercial Efficiency. Allowing 2500 watts for commuta- tor- and friction-losses, we have by (361), p. 408: 50,000 50,000 - ~ , % = 55.630 + 33. + .500 = 58^= - 8 5 6 ' OT 85 -*' 3. Weight Efficiency. The estimated weights of the different parts of our dynamo are : Armature : Core, 3.56 cubic feet of wrought iron, . 1710 Ibs. Winding, insulation, binding, etc., . . 640 " Shaft, commutator, spiders, etc., . . 500 " Armature complete, .... 2850 Ibs. 566 DYNAMO-ELECTRIC MACHINES [138 Frame : Magnet cores, 2 x 45 X 10 X 6| = 6075 cubic inches of wrought iron, . . 1700 Ibs. Polepieces, [45 X 45 - (39 2 X |+ 2 X 18 X 3l + 2 x 15 X i J)] X 10 = 6700 cubic inches of cast iron, ....... 1750 " Field-winding and insulation, 250 -J- 650 = 900 " Dynamo portion of bed, bearings, etc., . 800 " Frame, complete, .... 5 I 5 I DS - Fittings: Brushes, holders, and brush-rocker, . . 100 Ibs. Switches, series field regulator, cables, etc., 100 " Fittings, complete, . . . . 200 Ibs. Total net weight of dynamo, . . . 8200 Ibs. The specific output, therefore, is: 4H - = 6.1 watts per pound. 8200 138. Calculation of a Multipolar, Multiple Magnet, Smooth Ring, High-Speed Shunt Dynamo : 1200 Kilowatts. Radial Innerpole Type. 10 Poles. Cast Steel Frame. 150 Yolts. 8000 Amps. 232 Revs, per min. a. CALCULATION OF ARMATURE. i. Length of Armature Conductor. Assuming A=s . 78 we find, from Table IV., p. 50: e = 60 X iQ- 8 volt per foot. Table V., p. 520:, gives an average conductor speed of 90 ft. p. sec. for a looo-KW high-speed ring armature; we will take in the present case: v = 96 feet per second; 138] EXAMPLES OF GENERATOR CALCULATION. 567 From Table VIII., p. 56, we obtain: E' = 1.02 x 150 = 153 volts. This machine being of comparatively low voltage and high current strength, the field-density obtained from Table VI. is reduced according to the rule given on page 54, thus: JC" = f X 60,000 = 40,000 lines per square inch. Consequently, by (26), p. 55: = 5 X .53 X IP' = 332 feet oo X 96 X 40,000 2. Area and Shape of Armature Conductor. By 20: oV = 600 x ^^= 961,000 circular mils. In this case we will employ a wedge-shaped conductor, the external surface of the armature being used as a commutator. The height of the winding space, by Table XVIII., p. 75, is h& -75 inch, from which is to be deducted .100 inch for core insulation (column a, Table XIX., p. 82), and .025 inch for thickness of bar covering (half of the .050 inch insulation be- tween two bars, column e, Table XIX.), leaving .625 inch for the height of the armature conductor, whose mean width on the internal periphery, therefore, is: 71 960,000 X ~- = 1.2 inch. .625 x io 6 Since this would make too massive a single conductor, we divide it into 4 bars of .3 inch average width. 3. Diameter of Armature Core, Number of Conductors. By (30), P. 58: <4 = 230 x = 96 inches, 232 being rounded off to the next higher even dimension, since in this case d & is the internal diameter of the armature. The mean winding diameter, therefore: d'* = 9 6 2 X . 125 .625 = 95^ inches, 568 DYNAMO-ELECTRIC MACHINES. and the number of armature conductors: X * [138 o 4X(.3+-5) 4. Length of Armature Core. By (40), p. 76: / a = I2 X 332 = 20 inches. 200 5. Radial Depth, Minimum and Maximum Cross- Section, and Average Magnetic Density of Armature Core. By (137), P- 201: g _ 6 x 5 X 153 X TO' _ 99 OQO ooo maxwells. 200 X 232 By (48), p. 92, and Table XXII.: A. = 99, 000,000 = 8 inches. 10 X 70,000 X 20 External diameter of armature core, Fig. 354, Fig. 354. Dimensions of Armature Core, I2OO-KW lo-Pole Radial Innerpole-Type Generator. d' & = 964-2 X 8 = 112 inches. Mean diameter of armature core, d'"^ = 96 -|- 8 = 104 inches. The width of one-half field space is 95 X 2 X 10 .78= 12 inches, 138] EXAMPLES OF GENERATOR CALCULATION. 569 hence, by Fig. 354: ' a = \A2 a + 8* = 14^ inches. By (232), p. 34i : Sa, = i X 20 x 8 X .9 = 14,400 square inches. B Y (233), P- 34i : S^ = 10 X 20 x 14^ X -9 = 28,100 square inches. Hence: 000 , 000 _ 58, 800 lines per square inch; 14,400 99,000,000 (B . = - -- 34,000 lines per square inch. 20, IOO By (231), p. 34 i: *tf*a = -^, = 12.5 ampere-turns per inch. Corresponding average density: <$>"*. = 58,750 lines per square inch. 7. Size of Armature Conductor; Weight and Resistance of Armature Winding. From Fig. 355 the exact size of the armature bars is ob- tained as follows: \ I i Fig- 355- Dimensions of Armature Conductor, I2OO-KW lo-Pole Radial Innerpole-Type Generator. Minimum thickness of bar on inner circumference: 57 DYNAMO-ELECTRIC MACHINES. [138 Maximum thickness of bar on inner circumference: 95 ^ X n - .050" = .3260 inch. 4 X 200 Minimum thickness of bar on outer circumference: ___ _ _ ^ inch> 4 X 200 Maximum thickness of bar on outer circumference: " 3 ^ X n - .050* = .3957 inch. 4 X 200 Area of conductor on inner circumference: (*.)' = 4 X 625 x 32I-I + 326 ' = 808,875 square mils. Area of conductor on outer circumference: . ( P- II2: 104 XTT X 20 X 8 X .9 . . , M - - = 27.2 cubic feet. 1728 232 NI = -~ x 5 = 19.33 cycles per second. From Table XXIX., p. 113, (for &" a = 58,750): rj = 21.35. From Table XXXI., p. 116, (for 6, = .015*): c = .0258 X 1.5' = .058. By (73), P- 112: A = 21.35 X 19-33 X 27.2 = 11,220 watts. By (76), P. 120: P e = .058 x 19. 33 s X 27.2 = 580 watts. By (65), p. 107: PL = 7000 + 11,220 + 580 = 18,800 watts. By (79), P- 125: S A = 2 X 104 x 7t X (20 + 8 + 4 X I) = 20,250 sq. ins. Ratio of pole area to radiating surface: 94 X n X 20 X .78 20,250 From Table XXXVL, p. 127: 6' a = 40^ C. By (81), p. 127: .227. 20,250 Armature resistance, warm: r\ = .000091 X (i + .004 X 37i) = .000105 ohm, at 53 C. 9. Circumferential Current Density, Safe Capacity and Running Value of Armature; Relative Efficiency of Magnetic Field. By (84), p. 131: 8000 200 X - / c = - = 490 amperes per inch circumference. 104 X n 572 DYNAMO-ELECTRIC MACHINES. [138 By (88), p. 134: P 1 = 96' X 20 X .85 X 232 X 40,000 X io-' = 1,510,000 watts. By (90), p. 135 : />' = '53 X 8000 _ ^^ watt per Ib. of copper, at unit 3440 X 40,000 density. #'P = 99 000 > 000 x 6 _ 7770 maxwells per watt at unit 153 X 8000 velocity. b. DIMENSIONING OF MAGNET FRAME. 1. Total Magnetic flux, and Sectional Area of frame. By (156), p. 214, and Table LXVIII. : #' = 1. 1 2 X 99,000,000 = 111,000,000 maxwells. By (218), p. 314: = 111,000,000 = 181Q einches> 85,000 2. Magnet Cores. There being io magnetic circuits through the io cores, each circuit containing two of the magnets in series, the sectional area of one core must be one-fifth of the total frame area obtained; making the breadth of the cores 19 inches, that is, inch narrower than armature and polepieces, their thickness is found: r j 10 t = 13J inches. 5 X i9i The length of the cores is obtained from Table LXXXIIL, p. 321, the nearest cross-section being 12 x 24 inches, for which 4, = 16 inches. 3. Polepieces. External diameter of field frame, by Table LXI., p. 209: d v = 9 6 - 2 X ( f + |) = 93f inches. 138] EXAMPLES OF GENERATOR CALCULATION. 573 Distance between pole-corners: ^ P = 93i X sin 4 = 6$ inches. This is not as large as given by Table LX., p. 208, but is sufficient for the radial innerpole type. Taking 2^ inches for the centre thickness of the polepieces, their dimensions are derived as follows: Width of plane face: 2 x ( ~ - 2 1 ) X tan 14 = 22 inches. Width of curved face: 9 3f x sin 14 = 22| inches. Thickness of pole-tips: 2 COS 14 4. Yoke. Making the width of the yoke 1 9\ + 2 X i = 20^ inches, its radial thickness must be: '3 10 , = 61 inches. 10 X 2o From Fig. 356, the diameter across flats is: 93f 2 X (2^ + 16) = 56 inches. Diameter across corners: = 59 inches. cos 18 Length of side of decagon: 56 x sin 18 = 17J inches. C. CALCULATION OF MAGNETIC LEAKAGE. i. Permeance of Gap Spaces. OC* X v c = 40,000 x 96 = 3,840,000- by Table LXVL, p. 225, k n 1.25; hence, by (167), p. 226: ^ i (931 + 96) X 7t x .85 X 20 __ 2540 _ 1.25 X (96 - 93 J) 2.8 ' 574 DYNAMO-ELECTRIC MACHINES. [138 2. Permeance of Stray Paths. Distance apart of cores, at yoke-end: c l = (17^ 13^) X cos 18 = 3.6 inches. Distance apart of cores, at pole-end: 3- 6 X = 13.6 inches. tan i8 c SCALE, 1 :40. 12 9 i 30 I ft, Fig- 356. Dimensions of Field-Magnet Frame, taoo-KW lo-Pole Radial Innerpole-Type Generator. Projecting area of polepiece: S, = 22 x 20 19^ x 13^ = 177 square inches. Projecting area of yoke: S", = 20^ x 17 J 194- X 13^ = 91 square inches. Total stray permeance, from Fig. 356 : o X = 10 x (18.1 + 4.6 + 4.2) = 269. 16 138/ EXAMPLES OF GENERATOR CALCULATION. 575 3. Leakage Factor, and Total Flux. By (^T), P- 218: A = 907 + 269 = 76 = 907 907 This is considerably higher than the value taken from Table LXVIII. and employed in the calculation of the frame area (see p. 572). The corrected total flux of <' = 1.295 X 99,000,000 = 128,000,000 maxwells brings the density in the frame up to 128,000,000 ooo>ooo _ Q lines per square inch. 5 X 22f X 20 hence by (250), p. 352, and Table XCI. : 200 X 8000 4 - . ..f. at. = 1.25 X X - - = *4oO ampere-turns. 10 180 5. TV/a/ Magnetizing Force Required. By (227), p. 339: A T 34, 200 + 350 + 4650 -f- 4450 = 43,650 ampere-turns. C. CALCULATION OF MAGNET WINDING. In the present machine the winding space is limited by the shape of the frame, the height available at the pole end of the core being 4 inches, and at the yoke end only if inch, see Fig. 356. The larger depth can be employed until the distance between two adjoining coils becomes the same as that allowed at the yoke end; leaving inch for the bobbin flanges, and for insulation and clearance, it is thus found that 8f inches of the available length of each core can be wound 4 inches deep, and that for the remaining 7 inches the winding depth tapers from 4 inches to if inch. This gives a mean winding depth of 4 X 8f + - (4 -f if ) X 7 ^ m = = 3 J inches. Mean length of one turn: 4 = 2(19^ + 13^) -f 3 X it 77 inches. Radiating surface of each magnet: S* = 2 (19^ + 13^+ 3 X 7t) X i5f = 1585 square inches. By means of formula (328), p. 390, we can now determine the minimum temperature increase that can be obtained with the present design (by entirely filling the given winding space). The weight of bare copper wire filling one bobbin is, by (330), p. 390: Wp = 77 X i5f X 3i X .21 = 890 pounds. 138] EXAMPLES OF GENERATOR CALCULATION. 577 hence by (329), p. 390: l\i 7 x ( 43 ' 65 X 11 Y X -1S-1 L 31 ' 3 X V 2 12 / X i 3 8 5 J 6 m - - -=r- ^r^ - 44 C. 890 .004 x |_3i-3 X 140' X Although this is rather high, especially for so large a machine, it is yet within practical limits, and we therefore base the winding calculation on the above dimensions of the winding space. Connecting the 10 coils in 5 groups of 2 each, the terminal voltage of 150 volts will correspond to the total magnetizing force of one circuit, and formula (318), p. 385, gives the specific length of the wire required, for 20 per cent, extra-resistance: A ^ = 4^0 x 11 x x . 20 x (, _j_ . 004 x 44) = 2635 feet per ohm. No. 8 B. W. G. wire (165* + .010*) has a specific length of 2637 feet per ohm. By 312, P- 383: P'fr = - t - x 2 x 1480 x 1.20 = 2080 watts per magnetic * 3 circuit. B 7 (3*4), P- 384: 43,650 x 150 turns per 2080 By (315), P- 384: 3150 X 2080 . Ah : - = 20,200 feet, per pair of magnets. 20,200 _, __. . .... ^ ' r sh = ft - = 7.67 ohms, 2 coils in series, at 15.5 C. J / By (318), P . 385: r'pii = 7- 6 7 X (i + .004 X 44) = 9.0 ohms, one group, at 59-5 C < 578 DYNAMO-ELECTRIC MACHINES. [138 By (Si?) P- 3 8 4: r'^ = 9.0 X 1.20 = 10.8 ohms, one shunt branch, at normal load. 150 . . = 13.9 amperes, current in each branch. 10. 8 There being 5 magnetic circuits with their magnetizing coils in parallel, the total exciting current is: 13.9 X 5 = 69.5 amperes, while the joint shunt resistance of the 10 coils is: = 1.8 ohm, at 59.5 C. Total weight: wt*. = 5 X 7 " 7 = 8330 pounds, bare wire. .0046 wt'^ = 8330 x 1.0221 = 8530 pounds, covered wire, or 853 pounds of No. 8 B. W. G. wire per core. Actual magnetizing force at full load: AT 3150 x 13.9 = 43,800 ampere-turns. Since in this example the dimensioning of the winding space was the starting point of the winding calculation, no checking of the result with reference to the length of mean turn, radi- ating surfaces, etc., is necessary. /. CALCULATION OF EFFICIENCIES. 1. Electrical Efficiency. By (35 2 ), P- 4o6: _ 150 X 8000 " 150 X 8000 + 8069.5' X .000105 + 5 X J 3-9 S X 10 - 8 1,200,000 = - - = .987, or 98.7 %. 1,217,200 2. Commercial Efficiency. Taking the commutation- and fric- tion-losses at 40,000 watts, we obtain by (360), p. 407: _ 1,200,000 _ 1,200,000 _ 1,217,200+ 1 1, 800 + 40, ooo 1,269,000 or 94.7 %. 138] EXAMPLES OF GENERATOR CALCULATION. 579 3. Weight. Efficiency. The weight of the machine is obtained as follows: Armature: Core, 27.2 cu. ft. of wrought iron, 13,000 Ibs. Winding and insulation, etc., . 4,000 " Armature spider, shaft, etc., . 8,000 " Armature, complete, Frame: Magnet cores, 10 x 19^ X 13^ X 16 = 42,100 cu. ins. of cast steel, n>5oo Ibs. Polepieces, 10 X 22| X 20 X 2^ = 10,050 cu. ins. of cast steel, 2,800 " -)X20| Yoke, (.735X59'-43'j) = 20,500 cu. ins. of cast steel, 5,700 Field winding, spools, and insula- tion), ..... 10,000 Flange for fastening yoke to en- gine frame, outboard bearing, etc., ..... 12,000 Frame, complete, .... Fittings: Brush shifting and raising de- vices, brushes, studs, etc., . 3,000 Ibs. Switches, cables, etc., . . 1,000 " Fittings, complete, .... Total net weight of dynamo, Weight efficiency: 1,200,000 71,000 16.9 watts per Ib. 25,000 Ibs. 42,000 Ibs. 4,000 Ibs. 71,000 Ibs. 580 DYNAMO-ELECTRIC MACHINES. [139 139. Calculation of a Multipolar, Single Magnet, Smooth Ring, Moderate Speed Series Dynamo : 30 KW. Single Magnet Innerpole Type. 6 Poles. Wrought-Iron Core. Cast Steel Polepieces. 600 Volts. 50 Amps. 400 Revs, per Min. a. CALCULATION OF ARMATURE. 1. Length of Armature Conductor. A = .75; = I8 (' 6 ~ -75) = 7t o ; , = 57 5 x I0 _. y p ft z/ c = 60 feet per second; 3C" = 15,000 lines per square inch; E = 1. 10 X 600 = 660 volts. By (26), p. 55: = 3 X 660 X io g = 387() feet 57.5 X 60 X 15,000 2. Sectional Area of Armature Conductor. By (27). P- 57: a. Mean Winding Diameter of Armature. By (3) P- 5 8: <*' = 2 3 X ^- = 140f inches. 3. Area and Shape of Armature Conductor; Size and Number of Slots. By 20: or > say, 336 slots, 2 x it this being the nearest number divisible by 16. 140] EXAMPLES OF GENERATOR CALCULATION. 4. Length of Armature Core. By (48), p. 92: 589 33 6 X 6 5. Arrangement of Armature Winding. y (45), P- 89: One commutator-division per slot making the number of commutator-bars smaller than this minimum, we have to take Fig. 358. Dimensions of Slot and Armature Conductors, 2OOO-KW i6-Pole, Radial Outerpole Type, Low-Speed Generator. two per slot, and the winding must be arranged in 772 coils of 3 turns each. 6. Radial Depth, Minimum and Maximum Cross-Section, and Average Magnetic Density of Armature Core. By (i3 8 )> P- 20I: AA 336 X 6 X 70 = 188,000,000 maxwells. By (48), P. 92: b. = ' - - 16X65, ooox(32 .90 = 61 inches, 596 DYNAMO-ELECTRIC MACHINES. f 146 allowance being made for 6 air-ducts of \ inch width, and for 2 phosphor-bronze end-frames of inch thickness, thus: 6X^ + 2X|=2| inches. Total radial depth of armature core: 6J -f 3^ = 10 inches. Maximum depth of armature core: in -^ ) + io j Vio" 4 7 144 X sin - ) + io j Vio" + 10* = 14 inches. Minimum and maximum cross-sections: S" &i = 16 X 29^ X 6^ X .9 = 2920 square inches. S'^ = 1 6 X 29^ X 14 X .9 = 5950 square inches. Maximum and minimum flux densities: 188,000,000 188,000,000 ' = 64.400 ;= = Mean specific magnetizing force and corresponding average density: 115.0 4- c.8 m\ = -2- - = 10.4 ampere-turns per inch. (B" a = 53,000 lines per square inch. 7. Weight and Resistance of Armature Winding. % (57), P- ioo : A = ( i + -293 X ) X 5350 = 12,400 feet. V 3/ B y (58)> P- 101: wti = .0000303 x 278,000 x 12,400 = 10,425 Ibs. By (61), p. 105: r * = ~ x I2 ' 4 x ' = 00183ohm ' at ^-s c. 8. Energy Losses in Armature, and Temperature Increase. By (72), p. 112: 134 X JT X 10 - 336 X 3 X -H- X 29^ X .9 M= - - 1728 = 55 cubic feet. . 140] EXAMPLES OF GENERATOR CALCULATION. 59 1 In this the depth of the slot is taken 3 inches only, in order to allow for the volume of the lateral projections of the teeth. Frequency : N l = jr- X 8 = 9.33 cycles per second. By (68), p. 109: P & = 1.2 x 3700' X 00183 = 30,000 watts. By (73). P- " 2: A = 18.1 X 9.33 X 55 = 9300 watts. B 7 (76), p. 120: P e = .081 X 9.33' X 55 = 100 watts. By (65). P- 107 : P* = 30,000 + 9300 + 400 = 39,700 watts. By (79). P- i 2 5: St = 134 x n X 2 X (36 + 10) 38,700 sq. inches. Ratio of pole area to radiating surface : X 7f X 32 X .70 _ 10,200 38,700 3 8 >7 hence by (81), with the use of Table XXXVI., p. 127: and by (63), p. 106: r' a = (i -f .004 X 45) X .00183 = .00216 ohm, at 6oJ C. [NoTE. For the calculation of the hysteresis loss in toothed armatures, Dr. Max Breslauer 1 gives a more accurate expres- sion, consisting of two terms, P' h -\- P" h ; the former, P' b , rep- resenting the loss in the solid portion of the core, and the latter, P' b , the loss in the teeth only. While P' h is obtained from (73) by inserting for M the weight of the solid portion, the second term, P" b , is the hysteresis loss in the teeth, due to 1 " On the Calculation of the Energy Loss in Toothed Armatures," by Dr. Max Breslauer, Elektrotechn. Zeitschr , vol. xviii. p. 80 (February II, 1897); Electrical World, vol. xxix. p. 325 (March 6, 1897). 59 2 D YNAMO-ELECTRIC MA CHINES. [ 140 the smallest density (in the largest section, at the periphery of the armature) multiplied by a factor, a, which depends upon the ratio, of minimum to maximum width of tooth, and upon the shape of the slot, ranging as follows: TABLE CVI. FACTOR OF HYSTERESIS Loss IN ARMATURE TEETH. RATIO OF MINIMUM TO FACTOR d OF HYSTERESIS Loss IN ARMATURE TEETH. MAXIMUM WIDTH OF TOOTH, Rectangular Circular ** Slot. Slot. 5.00 21.00 0.05 3.75 13.00 .1 3.04 8.75 .2 2.47 5.34 .3 2.10 3.77 .4 1.83 2.90 .5 1.61 2.25 .6 1.44 1.81 .7 1.30 1.51 .8 1.19 1.30 .9 1.09 1.14 1.0 1.00 1.00 The hysteresis loss in the mass of the teeth, however, ordi- narily is only a small fraction of the total hysteresis loss, P^ y of the armature, and the total hysteresis loss in well-designed machines is so small compared with the C^-loss that the dif- ference in the total energy loss due to the use of the above method amounts to but a few per cent., and that, therefore, in the majority of practical cases such a refinement in the calc| lation is unnecessary. Thus, in the present example, which is chosen to illustrate the above statement, because in it the difference between the approximate and the exact methods, on account of the great 140] EXAMPLES OF GENERATOR CALCULATION. 593 mass of the teeth about n cubic feet is near its maximum amount, the hysteresis loss in the solid portion of the arma- ture core is: P\ = 18.1 x 9-33 X (65 n) = 7450 watts. Minimum density in teeth: 188,000,000 188,000,000 / 33 6\ 3425 2 X .70 X I 144 * ~ ~ ) X 29^ X .9 = 55,000 lines per square inch; Hysteresis factor for this density: rf = 19.21 watts per cubic foot. Ratio of minimum to maximum width of tooth: i37| X 7t _ *'t 336 rt _ .^ = .545. b t 144 X n 336 Tooth-factor, by interpolation from the above table: a = 1.53; hence, hysteresis loss in teeth: .'. P\ = 19.21 X 9-33 X ii X 1-53 = 3000 watts. The total hysteresis loss, therefore, theoretically accurate, is A = 745 + 3 = I0 >45 watts. This is about 12^ per cent, greater than the value found on p. 591 (/* h = 9300 watts), while the increase in the value of P due to this difference amounts to about 3 per cent, only.] b. DIMENSIONING OF MAGNET FRAME. i. Total Magnetic Flux and Sectional Area of Frame. B Y C^ 6 ). P- 214: #' = 1.15 X 188,000,000 = 216,000,000 maxwells. By (218), p. 339: 216,000,000 . , S = - - - = 2540 square inches, 85,000 594 D YN A MO-ELECTRIC MACHINES. [140 2. Cores. The length of the polepieces being 32 inches (equal to length of armature core), and their circumferential width being ieJL 144$ X sin - - = 20 inches, the core section must be so dimensioned that the projecting strip of the polepiece has the same width both in the lateral Fig. 359. Dimensions of Armature and Field Magnet Frame, 2000 KW, i6-Pole, Radial Outerpole Type, Low-Speed Generator. and in the circumferential directions; making this uniform width of the polepiece-shoulder 3^ inches, see Fig. 359, the total actual cross-section of the cores becomes: S" OA = 8 X 25 x 13 = 2600 square inches. Length of cores, by Table LXXXIIL, p. 321: / m = 16 inches. 3. Polepieces. Bore: 4. X 144 + 2 X ~ = 144 inches. Distance between pole-corners: /' p = 144$ x sin 3 | = 8J inches. 140] EXAMPLES Of GENERATOR CALCULATION. 595 Radial thickness, in centre, If inch; at ends, \\ + (72^ - V75iV - Io3 ) = ty inches. 4. Yoke. Making the yoke of same width as the armature core, its radial thickness is: _ 2540 _ g j nc j, es 16 X 32 In order to secure a straight seat for the cores and to allow room for the flanges of the magnet-coils, bosses of |^ inch ra- dial height must be provided at the internal periphery of the yoke, making the external diameter of the frame, Fig. 359, i 4 4l + 2 X (i| + 16 + H + 5) = 191 inches. C. CALCULATION OF MAGNETIC LEAKAGE. i. Permeance of Gap -Spaces. I>3S ~" ' 25 = Ratio of radial clearance to pitch: Product of field-density and conductor-velocity: 35,000 x 42.8 = 1,500,000. By Table LXVIL, p. 230: k^ = i. 60. From Table LXVI., p. 225, for a corresponding perforated armature, j2 = 1.20. Average factor of field deflection: i. 60 + i. 20 -= 1.40. 59 6 DYNAMO-ELECTRIC MACHINES. [140 B y (175), p. 230: <% = j (M4| X n X .70 + 1.29 X 336 X .76) X j (32 + 31) 1.40 X (144$ - 144) -3190. 2. Permeance of Stray Paths. By (181), p. 233: = 8 x 19 X 3 x J -248. From Fig. 359: 2 3 = 16 X ^-^ = 16 X 9 = I** i From Fig. 359: s< = 8 x (3* X .0) - ( 5 X .3) = 3. Leakage Factor; Total Flux. B 7 (i57), P- 218: , 3190 + 248 + 144+ '5 8 3740 A. ! - = 1. 17. 3190 3190 By (158), p. 218: A/ = 1.025 x 1.17 = 1.20. .-. $' = 1.20 x 188,000,000 = 260,000,000 maxwells. d. CALCULATION OF MAGNETIZING FORCES. i. Shunt Magnetizing Force. No-load flux: 6 * 8 40 3 6 X 6 Air gap ampere-turns: = 1^,000,000 maxwells. f 184,000,000 v at- = .3133 X - - X 2.55 = 28,800 ampere-turns. 5100 140] EXAMPLES OF GENERATOR CALCULATION. 597 Armature ampere-turns: 9 , -g -f at l\ = 1303 X n X h 63 + 2 x 3| = 30 inches. J * 184,000,000 184,000,000 B % " 2920 63 ' ooo; " % ~ 5950 = 31,000; . . at &o = -^ ^ x 30 = 300 ampere-turns. Magnet core ampere-turns: _ i. 20 X 184,000,000 .. (B m = - - = 85,000 lines per square inch; 2OOO .'.at m = 44 X 16 X 2 = 1410 ampere-turns. Polepiece ampere-turns: (B" Pi = (B m = 85,000 lines per square inch; 184,000,000 ,. (B Do = = 18,000 lines per square inch; P2 o 10,200 44 H~ 4-7 .'.af Po = -i-t- x 2| X 2 = 130 ampere-turns. Yoke ampere-turns: Maximum depth = V'sH* + 6? 2 = 8.7 inches (see Fig. 359); = 86,300 lines per square inch; = 49,600 lines per square inch. 16 X 5 X 3 2 1.20 X 184,000,000 y 2 i68.7 X 32 Length of magnetic circuit in yoke (Fig. 359): l' y ^ 6J + 5-B- = 36 inches; 47 + ii. 8 .-. afy o = - x 36 = 1060 ampere-turns. Total shunt magnetizing force: AT eh = 28,800 -(- 300 -}- 1410 -f- 130 -}- 1060 = 31,700 ampere-turns. 2. Series Magnetizing Force. Full-load flux: $ = 188,000,000 maxwells. Air gap ampere-turns: , 188,000,000 af e -3 J 33 X X 2.55 = 29,600 ampere-turns. 5100 59 8 DYNAMO-ELECTRIC MACHINES. [ 140 Armature ampere-turns, see pp. 590 and 597: at^ = 10.4 x 30 = 310 ampere-turns. Magnet core ampere-turns: i. 20 X 188,000,000 o .. (B m = - -- = 87,000 lines per square inch; 2600 .-. af m = 49 x 32 = 1570 ampere-turns. Polepiece ampere-turns: _, 1.20 X 188,000,000 _ .. ($> = - = 87,000 lines per square inch; 2OOO 1.20 X 188,000,000 .. (B p = - - - - = 22,100 lines per square inch; 10,200 .. at p = 49 ~l~ 5-4 x ^ __ 2 y 2 x ^ _ I ^ Q am p ere .t u rns. Yoke ampere-turns: 1.20 X 188,000,000 00 ,. (B yi = -- - = 88,200 lines per square inch; 10 X 5 X 3 2 _ 1.20 X l88.000.OOO (B yg = !6 x 8.7 x 32 = 50)7 llnes per S( l uare mch ? 52 -|- 12 ' ' afy ~ 2 -- x 3 6 = 3 2 X 36 = 1150 ampere-turns. Compensating ampere-turns: For " p = 75,000 (porresponding to w'p = 27.2), Table XCL, p. 352, gives u = 1-25. Maximum density in teeth: f _ 188,000.000 * ~ i X .70 X (i37f X n - 136 X H) X 2 9 x .9 188,000,000 = - gg = 100,000 lines per square inch. For this density, the brush-lead coefficient is found, from Table XC., p. 350: *is= -55 the value being taken near the upper limit, on account of the low conductor velocity. By (250), p. 352, therefore: < = ,., s X " 6 X ^ X " x -55^X31 = 6ooo arap .. turns . Total magnetizing force required at full load: AT 29,600 + 310 + 1570 -f 150 + 1150 -f 6000 = 38,780 ampere-turns. 140] EXAMPLES OF GENERATOR CALCULATION. 599 And the required series excitation: AT K = 38,780 31,700 = 7080 ampere-turns. f. CALCULATION OF MAGNET WINDING. Rise of temperature, m = 37^ C. Percentage of Regulating Resistance, r x = 20$. i. Series Winding. / T = 2 x (25 + 13) -f 3^ x n = 87 inches. .S- M = 2 X (25 X + 13 + 3i X n) X (16 - $) = 1460 square inches per core. Connecting all the 16 series coils in parallel, the current flow- ing in each will be: o = 231.25 amperes, se and the number of series turns required on each core, two magnets being in series in each magnetic circuit, l - X 7080 N K = - = 16 turns. 231-25 By (343), P- 400: l - x 3 8 ,78o X 231.25 x 87 ______ x (I + . 004 x 3H) = 532,000 circular mils. Using a ig-wire cable, the area of the wire required is : = .875 x l6 X 87 = .00235 ohm per core. 19 x 27,225 Joint resistance of all series coils: = .000147 ohm at 15.5 C. Total weight, bare: 8*7 wt K = 16 X 16 X -- X 19 X .0824 = 2910 pounds, or 182 pounds per core. 2. Shunt Winding. Grouping all the 16 shunt coils in series, the gauge of the shunt wire must be: 2 (3i,7oo) A* = -- X X 1.20 X (i + .004 X 37i) ~ X540 = 4690 feet per ohm. No. 5 B. W. G. wire (.220* + .012") has 4688 feet per ohm, and therefore gives the required resistance. By (346), p. 400: ^Bh = Tf X J 46o - 231.25' X .00235 X (i + .004 X 37$) / = 730 143 = 587 watts. By (312), p. 383: f"*b = 5 8 7 X 1.20 = 705 watts per magnet. 140] EXAMPLES OF GENERATOR CALCULATION. 6oi By (314), p. 383: (31,700) x x 540 705 Number of turns in one layer: 12 = 760 turns per core. .232 Number of layers required: = 61; - 15. 51 Winding space taken up: 15 x .232 = 3 inches. By (315), P- 384: An = 5 1 X 15 X - 5540 feet per core. 12 Total weight, bare : wt^ = 16 X 5540 X .1465 = 13,000 Ibs., or 812 Ibs. per core, Total resistance: r^ = 16 X 5540 X .0002128 = 18.9 ohms, at 15.5 C. By (318), P- 385: r'& = 18.9 X (1.004 X 37i) = 21.7 ohms, at 53 C. By (317), P- 384: r" ab =21.7 X 1.20 = 26 ohms, entire shunt circuit. . . /^ = =~ = 20.8 amperes, shunt current, at normal load Actual magnetizing foi'ce: = 2 x 16 X 231.25 = 7,500 ampere-turns. ^ = 2 X 51 X 15 X 20.8 = 31,800 " Total exciting power: AT = 39,300 ampere-turns. 6o2 DYNAMO-ELECTRIC MACHINES. [140 . CALCULATION OF EFFICIENCIES. 1. Electrical Efficiency. fi y (353), P- 4o6: 540 X 3700 540 X 3700 + (3720.8) 2 X .00216 + 3700 2 X .000147 + 20.8* X 26 2,000,000 .. , = - = .978, or 97.8 #. 2,043,3 2. Commercial Efficiency. By (361), p. 408: 2,000,000 2,000,000 f.. 7? c = r : = J = -947, or 94.7$. 2,043,300 -j- 9700 -f- 60,000 2,113,000 3. Weight- Efficiency. The weight of this machine is estimated as follows: Armature: Core, 55 cubic feet of wrought iron, . 26,500 Ibs. Winding and insulation, connections, etc., . . . . . . 12,000 " Commutator, ..... 15,000 " Skeleton pulley, spider frames, shaft, etc., 16,500 " Armature, complete, .... 70,000 Ibs. Frame : Magnet-cores, 16 x 13 X 25 X 16 = 83,200 cubic inches of cast steel, . 23,000 Ibs. Yoke 186 X it X 32 X 5 = 93,500 cubic inches of cast steel, .... 26,000 " Polepieces, 16 X 20 x 32 X if = 18,000 cubic inches of cast steel, . . . 5,000 " Field-winding, spools, and insulation, . 20,000 " Supporting lugs, flanges and bosses on frame, outboard bearing, etc., . . 16,000 " Frame, complete, 90,000 Ibs. [ 141 EXAMPLES OF GENERATOR CALCULATION, 603 Fittings: Brush-shifting and raising devices, brushes and holders, etc., .... 4,000 Ibs. Switches, connections, cables, etc., . 1,000 " Fittings, complete, S,ooo Ibs. Total net weight of dynamo, . . 165,000 Ibs. Weight efficiency: 2,000,000 m * j ^2 = 12.1 watts per pound. 165,000 141. Calculation of a Multipolar, Consequent Pole, Perforated Ring, High-Speed Shunt Dynamo: 100 KW. Fourpolar Iron Clad Type. Wrought-Iron Cores, Cast-Steel Yoke and Polepieces. 200 Tolts. 500 Amps. 600 Revs, per Min. (Calculation in Metric Units.) a. CALCULATION OF ARMATURE. i. Length of Armature Conductor. From 15: fit = .70, 180 X (i .70) a - *- 'i ' - i 3 p ; From Table IV., p. 50: e l = 3.8 x lo" 5 volt per metre per bifurcation. From Table V., p. 52: z/e = 24 metres per second; From Table VII. , p. 54: OC = 3850 gausses; From Table VIII., p. 56: E = 1.04 X 200 = 208 volts. By (26), p. 55: 2 x 208 X io~ 6 A = o -3 =118 metres. 3.8 X 24 X 3850 604 DYNAMO-ELECTRIC MACHINES. [141 2. Sectional Area of Armature Conductor. By (28), p. 57: Wmin = .2 X 5 -^ = 50 mm. 2 , or by (29) p. 57: = -5 X / 5 = 8 mm. 3. Mean Winding Diameter of Armature, and Number of Per- forations. By (31), p- 58: = 14,000 = 10,500,000 13,000 2. Magnet Cores. Each of the two magnet cores carries two IF ,- i 1370 m /, >! SCALE, li Fig. 361. Dimensions of Field-Magnet Frame, loo-KW Fourpolar Iron- Clad Generator. of the four magnetic circuits, Fig. 361, hence the magnet diameter: For a flux of 5,250,000 maxwells passing through each core, Table LXXXIL, p. 320, gives. 75 as the ratio of length to diameter, consequently 4i = -75 X 22 = 16.5 cm. 3. Polepieces.'Yhe radial clearance, from Table LXL, p. 209, being about 5 mm., the bore is: d 9 - 810 + 2 X 5 = 820 mm. Pole distance: / P = 820 x sin 13^ = 190 mm. 141] EXAMPLES OF GENERATOR CALCULATION. 609 Pole chord: h v = 820 x sin 31^ = 425 mm. Thickness in centre, 22 mm. ; at ends, 4. Yoke. Only one magnetic circuit passes through the yoke-section; for a breadth of 23 cm., equal to length of armature core, therefore, the thickness of the yoke is: 810 h, = - = 9 cm. 4 X 23 Length over all (Fig. 361): 820 + 2 x (20 + 165 -f- 90) = 1370 mm. Height of frame: 820 + 2 X 90 = 1000 mm. C. CALCULATION OF MAGNETIC LEAKAGE. i. Permeance of Gap- Spaces. For z> c X 3C = 24 x 3 8 5 = 9 2 >5, Table LXVL, p. 225, gives u = 1.22; therefore, by (176), p. 230: ^(82 X.7 + 8i X .8)X 2 3_ 2200 _ = == 180 - i. 95 x (82 - so r 2. Permeance of Stray Paths. By (165), p. 223, and (185), p. 237: 5 ._ (16.5 + 38.5) X (22 n + 23 + 2 X 9) _ 30 + .3 X 22 By (196), p. 243: 42.5 X (8+ 2.2) _ *3 Z A ~ ~ 1 1 i? + 42-5 X - 6l DYNAMO-ELECTRIC MACHINES, [ 141 P- 247 : 4X(8X2 3 ) 2 X (42-5 X 23 22 27 M 19-75 l6 -5 3. Probable Leakage Coefficient, and Total Flux. B y (157), p- 218: _ 1800 + 166 -f 17 +110 2093 ~~ = 78oo = IM ' By (158) p. 218, and Table LXV.: A' = 1.04 x 1.16 = 1.20, . . $' = 1.20 X 8,120,000 = 9,750,000 maxwells. d. CALCULATION OF MAGNETIZING FORCES. 1. Air Gaps. Actual density: 8,120,000 ~ 2200 = 3 6 9 gausses. Magnetizing force: at g = .8 x 3690 x 1.22 = 3600 ampere-turns. 2. Armature Core. By (237), P. 343, ? + 'SI' '' = 6l X n X - -^ --- h 10 -f- 2 X 5 = 51 cm. Magnetizing force: at & = 4. i x 51 = 210 ampere-turns. 3. Magnet Cores. 9,750,000 w.i. = - - = 12,800 gausses. 2 X 22 2 4 Magnetizing force: Av.i. = 13-8 X 21 = 290 ampere-turns. 141] EXAMPLES OF GENERATOR CALCULATION. 61 1 4. Polepieces. Density at junction with cores: - = 12,800 gausses; 2 X 22 3 - 4 Density at poleface: v _ _ 8,120,000 - = 3940 gausses, -X 81.6 X n X 23 X .70 By (241), p. 34 6, and Table LXXXIX. : 15.2 -j- 2.34 WP = - = 8.77 ampere-turns per cm. Corresponding average density: (B p = 10,750 gausses. Length of circuit in polepieces, see Fig. 361 : / p = 10 cm. Magnetizing force: at v 8.77 x 10 = 90 ampere-turns. 5. Yoke. m c. s . = n.i ampere-turns per cm. ; 4.8. = 9 cm- (Fig. 361). Magnetizing force: .-. at c& = 1 1. 1 x 90 = 1000 ampere-turns. 6. Armature Reaction. For& p = 10,750 gausses, Table XCL, p. 352, gives 14 = 1.25 Maximum density in iron projections: 8,120,000 - X .70 X (72.2 X it 128 X 1.2) X 23 X.i = 15, 700 gausses, for which Table XC., p. 350, gives an average coefficient of brush lead of J3 = .4. 6l2 DYNAMO-ELECTRIC MACHINES. [ 141 Hence by (250), p. 352: atr = !. 2S X 5 ' 2 X 5 X --4134 = 2400 ampere-turns. 4 i oo 7. T0/0/ Magnetizing Force Required. Summing up we have : AT = 3600 + 210 -f- 2 9 H~ 9 + 1000 -f- 2400 = 7590 ampere-turns. e. CALCULATION OF MAGNET WINDING. Temperature increase desired, m = 40 C. ; percentage of regulating resistance, at normal load, r x = 50 per cent, of magnet resistance. Table LXXX., p. 317, gives for a 20 cm. multipolar type magnet core a ratio of winding height to core diameter of .36, which makes the winding depth for the present case: h m = .36 X 22 = 8 cm., and therefore the mean length of one turn: / T = (22 + 8) X 7t = 94.25 cm. Hence by (318), p. 385, if the two coils are connected in series, each taking 100 volts, i 759 94-2<; A ' h =: 1^ X ^ X r -5 X (i + .004 X 40) = 124.5 metres per ohm. According to the common millimetre wire gauge, a wire of a specific length of 122 metres per ohm has a diameter of 6 m = r.6 mm., bare, or 6' m = 1.6 -f .25 = 1.85 mm., covered. This wire will give the required temperature increase with 50 X 122 x I24 . 5 = 49 per cent. extra-resistance in circuit. Radiating surface: S* = (22 + 2 x 8) x 7f X (16.5 - .5) = 1910 cm 8 . 40 = - x _ x 1<49 _ 236 watts 141] EXAMPLES OF GENERATOR CALCULATION, 613 By (314), p. 384: ^ = 7590 X ioo = 236 Number of turns possible per layer: Number of layers required: Net winding depth needed: ti m = 38 x 1.85 = 70 mm. By (315), p- 384: Z^ = 86 x 38 X 2 f^ = 2980 m. 2980 .-. r^ = = 24:. 5 ohms, per coil, at 15.5 C. By (318), P . 385: ''sh = 2 4-5 X (i + .004 X 40) = 28.5 ohms, at 55.5 C. By (317), P- 384: r \M = 2 X 28.5 x 1.49 = 85 ohms, total resistance of shunt circuit. , 200 rt _ ' Ah = -g = 2.35 amperes. Actual magnetizing force: AT = 86 x 38 X 2.35 = 7670 ampere-turns. Weight per coil, bare: x I7 ' 8 = 17.8 being the weight, in kilogrammes, of 1000 metres of cop- per wire, of 1.6 mm diameter. CHAPTER XXX. EXAMPLES OF LEAKAGE CALCULATIONS, ELECTRIC MOTOR DESIGN, ETC. 142. Leakage Calculation for a Smooth Ring, One- Material Frame, Inverted Horseshoe Type Dynamo : 9.5 KW " Phoenix " Dynamo. 1 105 Volts. 90 Amps. 1420 Revs, per Min. a. PROBABLE LEAKAGE FACTOR (FROM DIMENSIONS OF MACHINE). i. Permeance of Air Gaps. From Fig. 362, which shows the principal dimensions of this machine, its gap area is obtained: I /I04 X 71 , II2\ ^ g = -(- - + nf x TT X r- \ X 9 125 square ins. 2 \ 2 3 6 / The useful flux (see below, 142, b., i, p. 616): > = 2,600,000 maxwells, therefore the field density: _ nn 2,600,000 . 5C = - = 20,800 lines per square inch. The conductor velocity being ii X n 1420 . z'c = - X ~r = 68 feet per second, 12 60 the product of density and speed is OC" X z> c = 20,800 X 68 = 1,415,000, for which Table LXVI., p. 225, gives a factor of field deflec- tion: ia = 1.30. 1 Silvanus P. Thompson, " Dynamo-Electric Machinery," fourth edition, p. 416 and Plate V. 614 142] EXAMPLES OF LEAKAGE CALCULATION. Hence, by (167), p. 226: t s i-3 X (nf - io|) .975 2. Stray Permeances. By (177), P- 232: = 128 . i-\ mm Fig. 362. 9.5 KW Phoenix Dynamo. By (192), p. 241: 3 __ IPX 9 2 X *< Tt 10 X 2 X 7T The projecting area of the yoke, at each core is: / 6 i \ S = I + 2 I X 9 47.25 square inches, hence, by (202), p. 246, cp _ 47-25 9 X 4| = 5.4 + 2.5 = 616 DYNAMO-ELECTRIC MACHINES. [142 3. Probable Leakage Factor. B y ('57), p- 218: i _ 128 + 9.6 + 10.6 + 7.9 rS 6 - 1 _ t - - - - 128 128 A ACTUAL LEAKAGE FACTOR (FROM MACHINE TEST). 1. Total Magnetizing Force of Machine. The dynamo is compound-wound, having a series resistance of .021 ohm, and a shunt resistance of 39.76 ohms: its armature resistance is .04 ohm. Therefore, the total current generated: 1 = 9 + 3*7*5" = 92 ' 65 am P eres > and the total E. M. F. : E' 105 + 92.65 X .04 -}- 90 X .021 = 1 10.6 volts. There are 180 conductors on the periphery of the armature, hence by (138), p. 202: - 6 X 110.6 X io 9

37-7 Inserting the above values into (209), p. 259, we obtain: m" m = - - = no ampere-turns per inch. 37-7 According to Table LXXXVIII., p. 336, this specific mag. netizing force corresponds to a magnetic density in highly permeable cast iron, of (B" m = 50,000 lines per square inch, 6:8 DYNAMO-ELECTRIC MACHINES. [143 from which, by formula (210), p. 259, follows the total mag- netic flux: <' = 66 x 50,000 = 3,300,000 maxwells. The actual leakage coefficient, consequently, from (214), p. 262, is: 2,600,000 The probable leakage factor computed from the dimensions of the frame has, on page 616, been found \ = 1.22, which is 4 per cent, below the actual value. 143. Leakage Calculation for a Smooth Ring, One- Material Frame, Double Magnet Type Dynamo s 40 KW " Immisch " Dynamo. 1 690 Yolts. 59 Amps. 480 Revs, per Min. a. Probable Leakage Factor. (From Fig. 363). ^ Fig. 363. 4O-KW " Immisch " Dynamo. By (167), p. 226: X - 24) i-95 1 For data of this machine see Gisbert Kapp's " Transmission of Energy, third edition, p. 272. 143] EXAMPLES OF LEAKAGE CALCULATION. 619 By (194). P- 242; ep r(54 + 16) X 10 + 4 X 16 16 X ?i , 2JO61 g *- 'L TT" f 9i+7^ 9* J Hence, by formula (157), p. 218, in which for the present type ft?!, %,, and $ 4 are zero, i= '.67 + 8^35.. 2O7 2O7 b. Actual Leakage Factor. The armature is wound with 760 turns of No. 9 B. &S. wire, resistance .36 ohm; the field winding consists of 984 series turns (No. 4 S. W. G.) per core, two coils in parallel, joint resistance .25 ohm. By (9), P- 37 : E' = 690 -|- 59 (.36 + .25) = 690 -)- 36 = 726 volts. By (138), p. 202: , 6 x 726 X io 9 7 6o x 480 = 12,000,000 maxwells. By (139)' P- 202: 12,000,000 ,. X : = 23,100 lines per square inch. By (228), p. 339: at g = .3133 X 23,100 X 1.95 = 14, 100 ampere-turns. By (232), p. 341: 5" a , = 2X(i6 2)X4^X .865 = 109 square inches By ( 2 33), P- 34i: .S" a , = 2 X (16 - 2) X 4k X y ^ ~ i X .865 = 230 square inches. By (231), P. 341: 290 -f- 10.2 m a - - 150 ampere-turns per inch. 620 DYNAMO-ELECTRIC MACHINES. [143 By (236), P. 343: l\ i9i X 7t X 9 6 + 4i = 22f inches. B y (23), p- 340: at & = 150 X 22f = 3400 ampere-turns. The angle of lead was measured to be about 20, therefore by (250), p. 352: So 20 at r 1.40 X 760 x - X -^ = 35 ampere-turns. The total magnetizing force of the machine is: trn AT = 984 x -- 29,000 ampere-turns. The frame is all wrought iron, having a uniform cross-sec- tion of S m = 10 x 16 = 160 square inches, and the length of each circuit in the frame is: /" m = 75 inches. Hence we have: 75 X m" m 29,000 (14,100 + 3400 + 3500) = 8000 ampere-turns. from which: 8000 . . m :" m = = 106.7 ampere-turns per inch. / Consulting Table LXXXVIIL, p. 336, we find: #' (B" m ==--. = 102,000 lines per square inch; 1 60 or, the total flux: $' = 160 x 102,000 = 16,400,000 maxwells. .-. A = l6 ' 4 ' 000 =1.86. 12,000,000 The probable leakage factor found, In this case, is about 3 per cent, smaller than the actual one. 144] EXAMPLES OF LEAKAGE CALCULATION. 621 144. Leakage Calculation for a Smooth Drum, Com- bination Frame, Upright Horseshoe Type Dynamo: 200 KW " Edison " Bipolar Railway Generator. 1 500 Volts. 400 Amps. 450 Revs, per Min. a. Probable Leakage Factor. (From Fig. 364). __ ^AREA OFIBEDPLATE' OPPOSITE FIEtflS = 625 SO. INS. Fig. 364. 200-KW " Edison" Bipolar Railway Generator. By (167), p. 226: X X n x X 1-3 X ' (178), P. 232: = 25X 7TX3' 2 X I2| + 1.5 X 25 ~ 23!) = 38.7. "35 2.52 1 For description see Electrical Engineer, vol. xiii. p. 321 (March 23, 1891); Electrical World, vol. xix. p. 220 (March 26, 1892). 622 DYNAMO-ELECTRIC MACHINES. [144 By (188), p. 239: |T34iX (aoj+Ix 26) +625"! s - = - r*fi J = 6 - By (199), P- 245: 9 _ 345 , 34} X 26 *4 ~ = I 6. 5. 2 X3i + (26 + 2i)x - 2 B y (157), p- 218: x _ 45 1 + 3 8 -7 + 60.9 + 16.5 567.1 _ 45i 45^ " b. Actual Leakage Factor. The total E. M. F. generated, by considering the losses in armature and series field windings, is found: E' = 520 volts; and there are 228 conductors on the armature periphery; there- fore by (138), p. 202: , 6 X 520 X io 9 22 8 x 450 = 30,500,000 maxwells. n 3>S OO ) OO ." 3C : ^ = 27,000 lines per square inch. By (228), P . 339: af g -3 T 33 X 27,000 X 2.52 = 21,300 ampere-turns. By (232) and (233), p. 341: S"*! = 2 x 34^ X 8f x .85 = 502 square inches. S \ = 2 X 34* X 8f X A/ ~*j - i X .85 = 665 sq. ins. Therefore: (U" 3>5 OO > OO _ f 30,500,000 ' ai " S2 ** ~ 665 ~ 45 ' 7 o; and by (231), p. 34 i : _ 13. 2 + 8.6 n - - = 10.9 ampere-turns per inch. By (236), p. 343: '". = i Si X TT x - "t + 8| = 23.9 inches. 144] EXAMPLES OF LEAKAGE CALCULATION. 623 , P- 34: at & = 10.9 x 23.9 = 260 ampere-turns. By (250), p. 352: 4OO 4- *. 6 2^4; at r = 2.15 X 114 X T 3 X^ = 7000 ampere-turns. The magnet winding consists of about 8000 shunt turns and of 46 series turns. The shunt-circuit has a resistance of 139 ohms, making the shunt field current at normal load 500 7 gh = - - 3.6 amperes; J 39 hence, the total magnetizing force actually exciting this machine at full load: AT = 8000 x 3.6 4- 46 X 400 = 47,200 ampere-turns; and by (207), p. 258: a/ m = 47,200 (21,300 -f- 260 -f- 7000) = 18,640 ampere-turns. The section of the cores is: S" m = 25* x - = 490.9 square inches; 4 and that of the yoke : S" y = 25 x 21 = 525 square inches; the resultant area in wrought iron, therefore, can be taken at about *$* w .i. = 500 square inches. The cross-section at centre of polepieces is: x i if = 405 square inches, and the vertical cross-section is: 34^ X 26 = 885 square inches. Increasing the minimal area by one-third of the difference between the maximum and minimum area, we obtain: c" i ^85 - 405 . , o ^ = 405 -j -^ = 565 square inches, 624 DYNAMO-ELECTRIC MACHINES. [g 145 which we will take as the resultant area of the circuit in cast iron. The lengths of the magnetic circuit are: in wrought iron, /" w i. = 120 inches; in cast iron, /* cl =36 inches By (213), p. 261, we consequently have the equation: 120 X w" w .i. + 36 X w" c4 . = 18,640, which is satisfied by = 37>5> 000 ' for, by employing this value of 4>, we obtain: <&' 37,500,000 & w.i. = -^7T =- = 75 000 ' m w.i. = 24.7; w,i. 5 ,, C.I. = 077- = %/ ~ = 66,300; " ci = 436; ca. 55 therefore, the left member of the above equation becomes: 120 X 24.7 + 36 X 436 = 2960 + 15,700 = 18,600, which is practically identical with the actual number of ampere- turns. Hence, the actual leakage factor: A= 37,5oo,ooo = L88< 30,500,000 In this instance, the probable value obtained is about 2^ per cent, in excess of the actual value. 145. Leakage Calculation for a Toothed Ring, One- Material Frame, Multipolar Dynamo : 360 KW "Thomson-Houston" Fourpolar Railway Generator. 1 600 Yolts. 600 Amps. 375 Revs, per Min. a. Probable Leakage Factor. (From Figs. 365 and 366). Effective total length of armature conductor: Z e = 90 x 4 X ^ X 2 X Q 82 = 683 feet. 12 IOO 1 This machine, but bored for a 48-inch armature, is used in the power station of the West-End Railway Company of Boston, Mass.; for 'description see Electrical Engineer, vol. xii. p. 456 (October 21, 1891). 145] EXAMPLES OF LEAKAGE CALCULATION Conductor velocity: X * 625 = 12 The total E. M. F. is ?--*- ' 60 E' = 620, Figs. 365 and 366. 36o-KW Thomson-Houston Fourpolar Railway Generator, hence, by (144), p. 205: 2 X 620 X io 8 3C = 36,000 lines per square inch. 72 X 683 X 7 . . v e X 3C" = 70 X 36,000 = 2,520,000. Ratio of radial clearance between armature and field to pitch of slots: 1-553 therefore, by Table LXVI., p. 225: k n = 1.4, and by Table LXVIL, p. 230: 12 = 2.2; average: k a = 1.8. Hence, by (175), p. 230: -[45 X it + (1.24 + .094) X 90] X 2 X g 82 X 25 6 4 100 1.8 X (45 - 44|) = 1656. 626 DYNAMO-ELECTRIC MACHINES. [145 By (181), p. 233: , , x ii x-j+ 14X12$ 1 4 \ W O V ITT -I- T2A-I V IN X 4 = 69.5 + 43 = II2 -5- B 7 (!97), P- 243: _ T + 7X 3+I3X = 132.5. . A _ 1656 + "2.5 + 132-5 _ i9i 1656 1656 Ratio of width of slot to pitch : U 1-553 = -523- for which Table LXV., p. 219, gives a factor of armature leakage of Aj= 1.05; hence, the total probable leakage coefficient: A' = 1.05 X 1.15 = 1.21. b. Actual Leakage Factor. The machine is compound-wound, having 16,600 shunt am- pere-turns and 5500 series ampere-turns on each magnet; the total exciting power per circuit, two coils being magnetically in series, therefore, is: AT 2 X (16,600 -j- 5500) = 44,200 ampere-turns. By (228), p. 339: af g = .3133 X 36,000 x .9 = 10, 140 ampere-turns. fi y (232), P. 341: ''*, = 4 X 9f X 25 X .85 = 828 square inches 146] EXAMPLES OF LEAKAGE CALCULATION. 627 5C.OOO.OOO ,, ,. . ' . ($>\ = JJ = 66,500 lines per square inch. O2o By (233), P. 341: ", 4 X X 25 X .85 = 1252 square inches. CC, 000. 000 .. . , . . (B* = = 44,000 lines per square inch. 1252 By (231)* P. 341: , 18.6 + 8.4 m a = - J z 13.5 ampere-turns per inch. 2 By (236), p. 343: l\ = 3'i- X 7t X ^ 1- 9f + 2 X if = 26J inches. By (230), p. 340: 0/ a = 13.5 x 26 1 = 360 ampere-turns. The shunt current is 16 amperes, and the angle of brush lead, by measurement, about 5, hence by (250), p. 352: 616 5 a/ r = 2 x 360 x X 4- = 3 100 ampere-turns. 4 iso The magnetizing force left for the magnet frame, con- sequently, is: dr/ m = 44,200 (10,140 -j- 360 -j- 3100) = 30,600 ampere-turns. The magnet frame is of cast iron; each circuit has a length of /* m = 90 inches; the total cross-section of the cores is: a X 22 X 25 = i ioo square inches, and that of the yokes: 4 x i2| x 25 = 1250 square inches. Taking S' m =1125 square inches as the resultant sectional area, the value of #' is found as follows: 90 X m" m = 30,600; 628 DYNAMO-ELECTRIC MACHINES. [146 30,600 nt m = *-r- - = 340 ampere-turns per inch; 90 $' (R" m = -- = 62,500 lines per square inch; & = 1125 x 62,500 = 70,500,000 maxwells. The useful flux is: 2 X 6 X 620 X io 9 = w 000,000 maxwells, 360 X 375 consequently, the actual leakage factor: % _ 7>5 00 > 000 _ 1^8. 55,000,000 The formula for the probable leakage factor, for this ma- chine, gave a value of 5^ per cent, below this actual figure. 146. Calculation of a Series Motor for Constant Power Work: Inverted Horseshoe Type. Toothed-Drum Armature. Wrought-Iron Cores and Polepieces, Cast-Iron Yoke. 25 HP. 210 Volts, 850 Revs, per Min. a. Conversion, into Generator of Equal Electrical Activity. Assuming a gross efficiency of 93 per cent, and an electrical efficiency of 95 per cent, (see Table XCIX., p. 422), the elec- trical energy active in the armature of the motor is, by (382), p. 420: f, = 746 X 25 _ 2Q 00Q watts> 93 and the E. M. F. active, by (383), p. 421: E' = 210 X .95 = 200 volts; hence, by (384), p. 421, the current capacity: , 20,000 (K) which, in the present case of a series motor, is also the current intensity to be supplied to the motor terminals. 146] EXAMPLES OF MOTOR CALCULATION. 629 Intake of motor, by (381), p. 420: _ 20,000 _ 21 Ann wa tts .95 b. Calculation of Armature. According to 146, a, the armature has to be designed to give a total E. M. F. of 200 volts and a total current of 100 amperes, at a speed of 850 revolutions. For the reason ad- vanced on p. 63, a toothed armature with its projections highly saturated at full load is chosen. In order to obtain high efficiencies at small loads, the armature, as explained in 116, must overpower the field, and therefore a low conductor velocity and a small field density must be taken: A -755 c = 40 feet per second, Table XXXVI., p. 127, gives: O' a = 440 C., hence 6 a = 44 X = 61 C. 9 J 3 .. r' & = .092 X (i + .004 x 61) = .115 ohm, at 76.5 C. d. Dimensioning of Magnet Frame. In order to secure a small excitation, the density in the wrought iron is taken : (BVi. = 75,000 lines per square inch; Fig. 369. Dimensions of Magnet Frame, 25 HP Inverted Horseshoe Type Series Motor. and that in the cast iron: "c.i. 30,000 lines per square inch. >' = 1.20 x 3,180,000 = 3,820,000 maxwells. ?, 820.000 . . S' , = - = 51 square inches. 75,000 146] EXAMPLES OF MOTOR CALCULATION. 633 3,820,000 . S c , = =127 square inches. 30,000 Cross-section of cores, rectangle, 5^" X 5^", between two semi-circles of 5^-" diameter; (Figs. 369 and 370) : 5 1 X Si + 5i" X = 50.5 square inches. k i _ Fig. 370. Joint of Magnet Core and Yoke, 25 HP Inverted Horseshoe Type Series Motor. Length of cores, by Table LXXXIIL, p. 321: / m =: 7J inches. Cross-section of yoke: 15" X 8|" (= 127.5 square inches). Core projection, rectangular: lof X 2-| X 8. Area of contact of same with yoke, Fig. 370: (lof -f 2 x 2|) X 8 + ' ^ = 160 square inches. Polepieces: ^ p =ii|-f-2X-| = 12 inches. /' p = 12 x sin 22^ = 4J inches. e. Calculation of Magnetic Leakage. Width of tooth: u X n 0\ - -^ fi = -5 -328 = .172 inch. Ratio of radial clearance to pitch: . Product of field density and conductor velocity: 3C" X z> c 20,000 x 40 = 800,000. 634 DYNAMO-ELECTRIC MACHINES. [146 B y ( l6 9)> P- 22 7: y _ I (12 X n X .75 + i-5 X .172 X 74 X .88) x iof 1.7 X (12 n|) 1 20 = = 257. 45 By (170), p. 228: (9| X 7T-74 Xfi) T6" By (171)1 P- 228: V" = 74 X. 75X1^1 = 209 ft By (168), p. 227: 257 X (1370 + 209) _ 257 + 1370 + 209 ' By (179) p. 232: ' 2 x 6 2x6 + 1.5 X By (192), p. 241: .X.. , X n X 7^ , , 6 _ q Q h ~ 3>5H t + 3 X - 4}+ 6| X j By (202), p. 246: 7i + (8 + H) X J , _ 221 + 9.8 + 8.3 + 7.3 246.4 A. - - - - = 1. 12. 221 221 \' = 1.05 x 1. 12 = 1.18. f. Calculation of Magnetizing Forces. t g = .3133 X 20,000 x -45 = 2820 ampere-turns. ' =7-5 X 12 = 90 ampere-turns. 146] EXAMPLES OF MOTOR CALCULATION. 635 a/ w j = 24. 7 X 40 = 990 ampere-turns. af e.i. = 50 X n = 590 ampere-turns. at r = ,. 25 x 74 X 6 2 X I0 X ' ? = 2530ampere-t U rn S . AT = 2820 -f- 9 + 990 + 590 + 2530 = 7000 ampere-turns. g. Calculation of Magnet Winding. The total magnetizing force being kept exceedingly low, a very small winding depth will be sufficient to accommodate the winding. Taking h m =. i inch, formula (291), p. 374, will give the mean length of one turn: 4 = 2 X 5i + (5i -f X 7t = 31 inches. = 135 turns, total, or 68 turns per core. 52 68 x 3I =176 feet per core. 1 ) SM = 2 X 7i x_5i X -+ 1 x7r = 253sq. in. p. magnet. For a rise of 20 C, we find: 2O 2 *\ "Z I r se = X ~ X : - = .0231 ohm per core. 75 52" i +.004 X 20 = 7620 feet per ohm. .0231 The nearest gauge wire is No. 2 B. W. G. (.284* -\- .020"), with a specific length of 7813 feet per ohm. The number of turns of this wire filling one layer on the cores is: 7j ~ j _ 7 _ 23 . .284-}-. 020 .304 therefore, the number of layers required: fi-.-fc 2 3 Actual winding depth: ^m = 3 X .304 = .912 inch. Actual excitation: ^7^=2X23X3X52 = 7176 ampere-turns, 636 DYNAMO-ELECTRIC MACHINES. [146 Joint series resistance, warm: r' K = '-^ X (i + .004 x 20) = .0125 ohm, at 35.5 C. Total weight of wire, bare: wt K = 2 x 23 x 3 X |^ X .244 = 87 Ibs. h. Speed Calculations. E. M. F. lost in armature and series winding: 100 X (. 115 + .0125) = 12.75 volts. Actual E. M. F. active in armature: E = 210 - 12.75 = 198.25 volts. Torque, by (93), p. 138: r = ^ir X ioo X 444 X 3,180,000 = 166 foot-lbs. Specific generating power: 198.25 x 60 = ^- - = 14 volts at i revolution per second; 050 hence, by (389), p. 426, the speed at any supply voltage, E: N, = 60 X (* - 8.52 X C"S + .' t '5)X.66\ \ 1 4 J 4 / = 4.3 E - 53. For E = 210 volts: N^ = 903 53 = 850 revs, per min. " E - 200 volts: IV, = 860 - 53 = 807 revs, per min., etc; /. Calculation of Efficiencies. Electrical efficiency, at normal load: = *ooX.o -(... 5 +.o.2 5 )X.oo- = 200 X IOO Commercial efficiency at normal load: __ 200 x ioo (ioo 2 X .1275 -f" 74 + I 5) 200 X ioo* _ 20,000 - (1275 + 1574) 17,151 ~ = = .oo 20,000 20,000 147] EXAMPLES OF MOTOR CALCULATION. 637 Commercial efficiency, at | load (the energy loss in arma- ture and series-field windings varying practically as the square of the load, and hysteresis and friction losses being independ- ent of the load): _ f X 20,000 - [(|) 8 X 1275 + 1574] _ 12,709 _ g 5 X 20,000 15,000 Commercial efficiency, at \ load: _ X 20,000 - [(|) 2 X 1275 + 1574] _ 8107 _ j 7/ c - - - - -- O 1 X 20,000 10,000 Commercial efficiency at load: _ X 20,000 - [q) 2 X 1275 + 1574] _ 3346 fi7 \ X 20,000 5000 Commercial efficiency, at 50 per cent, overload: _ ij X 20,000 - [(ilY X 1275 + 1574] _ 25,556 _ 1$ X 20,000 30,000 The latter is lower than the efficiency at normal load. 147. Calculation of a Shunt Motor for Intermittent Work: Bipolar Iron Clad Type. Smooth Ring Armature. Cast-Iron Frame. 15 HP. 125 Volts. 1400 Revs, per Min. a. Conversion into Generator of Equal Electrical Activity. Assuming an efficiency of 89$, the electrical activity is: F> = 746 ^ I5 = 12,600 watts. From Table VIII., p. 56: ' = 125 - .06 x 125 = 117,5 volts. 638 DYNAMO-ELECTRIC MACHINES, [147 Current in armature, at full load, by (384), p. 421: r . I2,6OO -trim I' = - = 107 amperes. Intake, by (381), p. 420: 12.600 /* = - - = 14,000 watts. 9 b. Calculation of Armature. In this case we want a weak armature of few ampere-turns and a strong field with large exciting power. Hence the con- ductor velocity and the field density must both be taken very high: /?, = .80; e 65 X io~" volt p. ft.; v c =92.5 feet p. second; 5C" = 26,000 lines per square inch. L _ 117.5 x io 8 . _ feet 65 X9 2 -5 X 26,000 5>oo . = 3 ' . X .07,500 X 6| X .85 147] EXAMPLES OF MOTOR CALCULATION. 639 = I07 ' 3 'a = 3 X /4 -1=6 inches. a i 2 X HX3X .85 <*" = T^ixTx .85 = 53 ' 7 lines per square inch; m " & l86 "* I0 ' 7 = 98.4 ampere-turns per inch. Average density: (B" a = 101,000 lines per square inch. = X(6| + 3) + iX x 6 = 2 fect . 0/4 = 233 X 2 x .0436 = 20J Ibs. r a = ^ X 233 X .00072 = .021 ohm, at 15.5 C. 4X2 c. Energy Losses in Armature, and Temperature Increase. M = ..X.TX6JX3X.8S = 355 cubic foQt NI = ^4 2 3-33 cycles per second. 60 P^ 1.2 X 107" X .021 = 290 watts. P b = 50.8 X 23.33 X .355 = 363 watts. ^e = -295 X 23.33' X -355 = 57 watts. / A = 290 + 363 + 57 = 710 watts. S= 2 X 12 x 7t X (6| -f 3 + 4 X i) = 780 sq. inches. r' & = .021 X (i + .004 X 38) = .024 ohm, at 53.5 C. d. Dimensioning of Magnet Frame. <' =1.15 X 3,500,000 = 4,025,000 maxwells. = 4,025,000 = 95 e 42,500 Breadth of cores: ||- = 15 inches. 64 DYNAMO-ELECTRIC MACHINES. [147 Breadth of polepieces: 15! X sin 72 = 15 inches. These two dimensions being equal, no separate polepieces are required, and the frame may be cast in one piece, as shown in Fig. 37 1. Fig- 37 1 - Dimensions of Armature Core and Field-Magnet Frame. I5-HP Bipolar Iron-Clad Type Shunt Motor. e. Calculation of Magnetizing Forces. af g = -3133 X 26,008 x T.2 X | = 7320 ampere-turns. at & = 98.4 X 14 = 1380 ampere-turns. af m = 101 X 83 = 8300 ampere-turns. X j ^ = 1400 ampere-turns. AT = at, = i. 80 X 7320 + 1380 + 8300 + 1400 = 18,400 ampere-turns. f. Calculation of Magnet Winding. Since the motor is not intended for continuous work, a high increase, 6, n = 40 C., is permitted. Regulating resistance, at full load, r x = 23 per cent. Height of winding space, estimated: 2^ inches. / T = 2 (6| + 15) + 2 x it = 50 inches. 147] EXAMPLES OF MOTOR CALCULATION. 641 18,400 50 A* = - X ^ X 1.23 X (i + .004 X 40) = 874 feet per ohm, corresponding to No. 13 B. W. G. (.095* -{- .010*). S* = 2 X (6| + 15 + a TT) X 2 X 8 = 1000 sq. inches. f A = X 1000 X 1.23 = 655 watts. 75 18,400 ;ci25 gh D Number of turns per layer: =80; .095 +.010 Number of layers required: '7SQ _ oo 80 ' *** Depth of magnet winding: h' m = 22 x (.095 + .010) = 2.32 inches. Z* = aX8oX*aX= 14,650 feet. r sh = -Q = 16 75 ohms, shunt resistance, at 15.5 C. 074 r\ = 16.75 X (i + .004 x 40) = 19.45 ohms, shunt resistance, at 55.5 C. r" Bb = ip-45 X 1.23 = 23.9 ohms, res. of entire shunt-circuit, at full load. I 2 actual slot for 36 No. n B. W. G. wires, see Fig. 372, is 1-J-J- inch deep and \\ inch wide. . Fig. 372. Dimensions of Armature-Slot, 75 HP Fourpolar Compound Motor. Number of slots: , = X = 112. = 785 X 12 = 112 X 6 X 2 x 420 X io 9 = - - - = 10,000,000 maxwells. 112 x 9 X 500 10,000,000 rt _ . , = - - = 21 inches. 4 X 105,000 X 9i X .875 = 105,000 lines; (B" a2 4 ,5o lines; = I37 = 72.3 ampere-turns per inch, 646 DYNAMO-ELECTRIC MACHINES. ' [14.8 Average density: (B* a = 96,000 lines per square inch. 2 X (qi + 23) 4- i44 x TT Z t = W x 112 X 9 = 2540 feet. 12 w/ a = 2540 X 4 X .0436 = 442 Ibs. bare wire. r a = - X 2540 X .000717 = .114 ohm at 15.5 C. 4X4 c. Energy Losses in Armature, and Temperature Increase. M _ (27 X TT X 4^ - *H X H X 112) X 9i X .875 1728 = 1.44 cubic foot. W t = -^ X 2 = 16.67 cycles per second. P A = 1.2 x 143' X .114 = 2800 watts. P h = 46.85 X 16.67 X 1.44 = 1120 watts. /> e -^= .0665 x 1 6.6 7 a x 1-44 = 30 watts. /> A = 2800 + 1 1 20 -j- 30 = 3950 watts. S = 27 X 7f X 2 X (9^ + z| + ifj- X 7t 3000 square inches. fl a = 41 x = 54 C. 3000 r\ = .114 X (i + .004 X 54) = .139 ohm, at 69^ C. d. Dimensioning of Magnet Frame. (Fig. 373.) $' = 1.20 X 10,000,000 12,000,000 maxwells. Width of frame (equal to length of armature core) : 9f inches. Breadth of cores: 12,000,000 -r = 8 inches. 2 X 80,000 X 9i Thickness of yoke: 12,000,000 =4 inches. 4 X 80,000 x Length of cores: 4i = 7 inches. Breadth of polepieces: ^P = 3 2 iV X sin 31^ = 16J inches. 148J EXAMPLES OF MOTOR CALCULATION. 647 Distance between pole-corners: /p = 32^ X sin 13! = 7| inches. e. Calculation of Magnetizing Forces. The E. M. F. at no load being, E 440 volts, and that at full load being E' = 440 143 X .139 X 1.25 = 415 volts, the shunt winding is to be calculated to supply the total mag- netizing force necessary to produce 440 volts, and the series Fig. 373. Dimensions of Magnet Frame, 75 HP Fourpolar Compound Motor. winding, in order to regulate for constant speed at all loads, must provide the difference between the magnetizing forces required for 440 and 415 volts, respectively, and must be con- nected so as to act in opposition to the shunt winding. (Dif- ferential winding. ) Magnetizing Force Required at No Load : ~ 6 X 2 x 440 X 10* # = d-ZZ 10,500,000 maxwells. 112 x 9 X 500 2 X 44 X io 8 . 3C = = 20, 500 lines p. sq. in 112 X 9 X 9i 72 X - '- X.8o x 65 3C"o X f' c = 29,500 X 65 = 1,920,000. 648 DYNAMO-ELECTRIC MACHINES. [ 148 Ratio of clearance to pitch : _ 3lAA^ = . 28 . 112 From Table. LXVII., p. 230: u = 1.90; .-. at go = .3133 X 29,500 X X 1.90 = 9000 ampere-turns. _ 10,500,000 % 4 X 9 \ X 2^ X .875 10,500,000 ffi <%= iirsTxinrsTs = 42 ' 5 lmes per 290 + 8 .'. a/ a = - - X 20 = 3000 ampere-turns. 1.2 X 10,500,000 -}- 7. .*. a/ a = - * - * X 20= 1300 ampere-turns. (B" m = 78,300 lines per square inch; .-. af m = 29.3 X 60 = 1750 ampere-turns. 14.3 .40 X Tti / P = 1.25 X 112 X 9 X X - Q 6J = i35oamp.-turns. 4 loo .'. AT = 8200 -f 1300 + 1750 + 1350 = 12,600 amp. -turns. Magnetizing Force for Series Differential Winding. AT AT - 12,600 14,200 = 1600 amp. -turns, 148] EXAMPLES OF MOTOR CALCULATION. 649 As seen from the above, the armature reaction, by increas- ing the excitation needed for full load, in a motor reduces the difference between full load and no load magnetomotive force; and by properly adjusting the magnetizing forces required for the various portions of the magnetic circuit, the difference be- tween the ampere-turns required to overcome the reluctances of the circuit at no load and full load, respectively, can, indeed, be brought within the amount of the armature reactive ampere-turns, so that no series winding at all is needed for regulation, the armature-reaction (which may have to be made extra large for this purpose, either by widening the polepieces or in giving the brushes a greater backward lead) taking its place. In the present machine, this can be achieved by increas- ing the radial depth of the armature core from z\ n to 3^", whereby the average specific magnetizing force is reduced to m\ o = 29.5 ampere-turns per inch at no load and to m\ = 23.5 ampere-turns per inch at full load, making the corresponding magnetizing forces at^ =590 ampere-turns and at & = 470 ampere-turns, respectively. Substituting these figures for those in the above calculation, the total exciting power at no load is found A T = 11,790 ampere-turns, and at full load AT = 11,770 ampere-turns. The remaining small difference of 20 ampere-turns is negligible, and we have then a self- regulating shunt-motor of practically constant speed for all variations of load. /. Calculation of Magnet Winding. Series Winding. 1600 i m = - - = 12 turns per magnetic circuit, J 43 or 6 turns per core. Allowing 1000 circular mils per ampere, and taking 2 cables of 7 wires each, the size of each wire is: , 1000 x M3 , ., o ai = = 10,200 circular mils, 2X7 or No. 10 B. & S. (. 102"). 65 DYNAMO-ELECTRIC MACHINES. [ 14$ Assuming // m = 4 inches, twelve cables of 3 X (.102" -(- .008") = .33 inch diameter will just fill the winding space, and but one layer, axially, is therefore required. / T 2 X (8 + 9^) + 4 X 7t - 47! inches, a^ = 12 x 14 X ^^- X .0315 = 21 Ibs. per pair of cores, or 42 Ibs. total. fee I2 X X '- -- = .0034 ohm per pair of magnets, at 12 14 15-5 C. Shunt Winding. For 6 m = 25 C, and r x = 45^. Connecting all four shunt coils in series, the potential across a pair of coils is 220 volts, and the size of the wire required: ^ = X X -.45 X (. + .004 X ,5) 2 2 O 12 = 408 feet per ohm, which is the specific length of No. 16 B. W. G. wire (.065" -f- .007'). Allowing ^ of the length of the core for width of bobbin flanges, the radiating surface of one pair of shunt coils is: S K = 2 X (8 + 9^ + 4 X TT) X 2 X (?i -- i) = 870 square inches. P * = ~ X 8 7 - 143 s X .0034 X (i + -o4 X .25) = 290 77 = 213 watts. P' 8h = 213 x 1.45 = 309 watts. ^ = I^?2^JL = 10 ,100 turns. 39 Allowing inch for the series winding and its insulation, the length available for the shunt winding is 6J inches, which holds : .072 = 94 No. 1 6 B. W. G. wires: 148 J EXAMPLES OF MOTOR CALCULATION. 651 hence, the height actually occupied by the shunt winding: /i' m = ^-^ - x .072 = 54 X .072 3.89 inches. 2 X 94 wt& = 2 x 94 X 54 X X .0128 = 512 Ibs. per pair of mag- nets, or 1024 Ibs., total. r _ 4 X 94 X 54 X 47j _ 1% ohm total at c 12 X 49 r' sh 196 X (i + .004 X 25) = 215.5 ohms, at 40.5 C. r" sh = 215.5 x I -45 =312 ohms, entire shunt-circuit, at full load. 7 gh = - = 1.41 ampere, shunt current, full load. o Actual magnetizing force at full load: AT = 2 x 94 X 54 X 1.41 12 X 143 = 14,300 - 1720 = 12,580 ampere-turns. g. Speed Calculations. Actual counter E. M. F. of motor at full load : E 1 = 440 143 X (.139 + -004) = 44o 2o = 419| volts. Useful flux at full load: i 8 105 68 18J 9A 68$ 25 100 250 8 37 10| | 156 67 17 75 68 24 125 250 8 45 13 7 208 76f 18 7| 80 26 150 200 130 100 200 250 175 125 250 300 150 8 8 50 57 164 19 12 15 108 168 90 107 25* 14 99 29j 128 32 300 100 13 77 144 198 1183 23" 12 350 88 400 100 500 125 12 87 153 160 135 | 254 138 600 100 12 95 152 151 284 15i TABLES OF DIMENSIONS OF MODERN DYNAMOS. 669 H Fig. 381. General Electric Multipolar Generator. TABLE CXIL DIMENSIONS OP GENERAL ELECTRIC MULTIPOLAB LOW-SPEED RING-ARMATORE GENERATORS. (See Fig. 381 ) Armature. Approximate Weight. 1 KW. R p.m. No. of Poles. A B C D No. of Slots. Armature and Commutator. Generator Complete. 1 150 200 6 46 12i 26A IT". 130 6400 29000 2 300 150 8 68 14 45" HA 272 17000 55000 3 400 120 8 72 18J 48 240 22000 79000 4 500 120 10 84 17J 62 1? 280 25000 81000 5 800 80 14 K'0 19* 98 1? 364 50000 135000 6 1600 75 22 164 19 144 1J 440 74000 180000 Magnet Frame. General Dimensions. . i E P H I J E L H N \ 99 25 8tt 13? 23 114 35 121 19} 32 9 2 125 27 10 151 32 141 41 I'll 293 49 11} 3 135 32* 11 18 41 150 48 18H 35/8 49 15 4 5 144} 187 30 32 a 16j 18 44 53 154 201 45 48 ISA 31 60 84 16 19 6 230 24 12$ HJjf 63 245 48 181 37i 120 24 > YNAMO-ELECTklC MA CHINES. TABLE CXIII. RING- ARMATURE DIMENSIONS. High Speed. Medium Speed. Low Speed. KW. R. p. m. Diam. Length. KW. R. p. m. Diam. Length. KW. R. p. m. Diam. Length. .1 1300 3 2 .15 1600 3JS IB .25 1400 4} IB .5 1200 5S 2i 1 1000 7 2ft 1.5 975 7 3ft 2.25 950 4 3ft 2 500 12 3} 2.5 1200 7ft 34 3.5 1600 7ft y s 4 925 9ft 41 4 425 15 32 4.5 1150 B) 34 5.75 1400 84 W 6.5 1050 9i 6.5 950 9i 6 6.5 875 H>4 *B 7 400 19 4} 8.25 1300 9J 8.5 850 II 6} 9 1450 51 6 9 950 11 5 9 350 21 5 11.5 1300 11 5 13 900 HI CB 17.5 1300 us 6| 13.5 850 13 64 15 325 224 64 17.5 1175 13 64 18 875 13 23 1150 13 7 20 700 16 7 20 300 20} 6J 27 1125 14 74 23 5 850 14 74 30 1050 16 7 30 775 15 8 30 300 22} 8} 40 1050 15 8 30 675 18 8J 45 975 18 8| 45 700 16J 9 50 275 24 9i 55 930 16J 9 50 600 20} 8f 60 275 28 11 65 875 20} 8J 65 625 19 104 75 250 324 124 80 750 19 104 75 550 22 9} 100 250 37 101 &5 750 22 9i 90 560 24 9J 125 250 45 13 110 720 24 9| 130 500 324 124 150 200 46 J2g 150 550 324 18 150 130 50 16J 200 450 324 13J 200 175 f.O 164 250 225 50 164 200 100 57 19 250 125 57 19 300 150 57 19 300 150 68 14 300 100 77 144 350 88 87 15; 400 120 72 18; 400 100 87 15 500 125 87 15; 500 120 84 17; 600 100 95 17; 800 80 120 19 1600 75 164 19 It will be noted in Tables CXIII. and CXIV. , where machines of different manufacturers are placed .side by side, that the armature dimensions of dynamos for similar output and speed in some instances vary greatly from one another, which goes to show that a wide range is given to the judgment of the de- signer in assuming the variable quantities, such as peripheral speed, shape-ratio, etc. For instance, in Table CXIII. two 3oo-KW i5o-revolution armatures are given, the first having a diameter of 57 inches and a length of 19 inches, while the TABLES OF DIMENSIONS OF MODERN DYNAMOS. 671 TABLE CXIV. DRUM- ARMATURE DIMENSIONS. High Speed. Medium Speed. Low Speed. KW. R. p. m. Diam. Length . KW. R. p. m. Diam. Length. KW. R. p. m. Diam. Length. .5 2100 2 T B 8 4 ' .56 1300 5J 2g .75 1.5 2400 2100 2g 35 5 6J .75 1.875 1900 1700 if n 3i 1.5 2.63 1200 1050 ?! 31 4 3 1900 4 8 3.75 1600 7f 4 3.75 950 81 51 6 '1800 5M 91 5.62 1350 84 5* 5.62 850 9* 5J 8.5 1700 61 10 7.5 1250 9J 5i 7.5 750 10J- 6 12 1600 6J 12 11.25 1150 lOi 6 1125 650 llf 6J 15 1500 13J 15 1050 HI 6J 15 POO 13 8 20 1400 7j 15 22.5 975 13 8 22.5 575 15 8i 25 1300 8f 16^ 30 950 13J 8i 30 550 15J 8J 30 1200 9A 18 375 9CO 15 8 37.5 550 16J 9 45 1000 n^ 20J 45 850 15J H GO 700 12J m 56.25 800 16J 9 100 650 16i 25 150 200 450 450 23J 23J 3 second has a diameter of 68 inches and a length of 14 inches. The peripheral velocity in the first machine is X it , X -r- =37-3 feet per sec., DO = while in the second it is _ 68 X Tt 12 The length is ^, or , of the diameter in the first armature, and fa or about 4-, of the diameter in the second armature. X -f = 44.6 feet per sec. oo APPENDIX II. WIRE TABLES AND WINDING DATA. WIRE TABLES AND WINDING DATA. THE tables here compiled will be found useful in connection with dynamo calculation. Table CXV., on pages 676 and 677, gives the resistance per foot and per pound, the weight per ohm, and the length per ohm of pure copper wire at 20 C. (68 F. ), 60 C. (140 F.), and 100 C. (212 F.). The figures are substantially those adopted by the American Institute of Electrical Engineers upon the recommendation of the Committee on Standards, in 1893. The table is based on Matthiesson's standard of resis- tivity for soft copper, which is 1.5939 microhms per cu. cm. (i cm. length, i sq. cm. cross-section), corresponding to 10.32 ohms per mil-foot (i ft. length, ~ mil diameter, or i circular mil area), at o C. (32 F.). Specific gravity of copper wire, 8.90. The temperature coefficient of copper is taken as (i -f- .00388 /), in which / is the elevation of temperature in degrees C. The data are given for all sizes of the American, or Browne & Sharpe (B. c^ S. ) gauge as well as of the Birming- ham wire gauge (B. W. G.). The wires are arranged accord- ing to size, so that the nearest standard gauge wire corre- sponding to any given resistance, weight, or length, can be obtained by referring to but one table. Table CXVL, page 678, gives the winding data for B. & S. and B. W. G. wires, when insulated for use as armature wires. In the first five columns the gauge numbers, diameters, sec- tional areas, and resistances of the sizes commonly employed are repeated for convenience; the sixth column, headed "Di- ameter of Insulated Wire," gives the diameter of the respec- tive wire when insulated with a double cotton covering (D. C. C.) which is the usual insulation on armature wires. The figures given in this column are in each case the maximum diameter of three samples of insulated wires furnished by dif- ferent manufacturers. The next two columns, Nos. 7 and 8, 675 676 TABLE CXV. RESISTANCE, WEIGHT, AND LENGTH COOL SIZE or WIRE. at 20 C. (68 Fahr.) Gange Number. Diameter. Area. Resistance. Weight. Length. B AS. B.W.G. Inches. Cir. Mils. Ohms p. Ib. Ohms p. ft. Ibs. p. ohm. Ibs. p. ft ft. p. ohm. feet p. Ib. 0000 .460 211,600 .0000764 .0000488 13,140 .6412 20,495 1.560 0000 .454 206,116 .0000802 .0000501 12,470 .6246 19,970 1.601 000 .425 180,625 .0001045 .0000571 9,570 .5472 17,500 1.827 000 .4096 167,772 .0001215 .0000615 8,260 .5084 16,250 1.967 00 .380 144,400 .0001634 .0000715 6,120 .4376 13,990 2.285 00 .365 133,225 .000193 .0000776 5,190 .4033 12,890 2.480 .340 115,600 .000255 .0000*93 3,920 .3503 11,200 2.885 .325 105,625 .000307 .0000980 3,260 .3199 10,230 3.126 1 .300 90,000 .000421 .0001147 2,377 .2727 8,718 3.667 1 .289 83,521 .00048S .0001234 2,055 .2536 8,106 3.943 2 .284 80,656 .000524 .0001280 1,909 .2444 7,812 4.092 3 .259 67.081 .000757 .000154 1,320 .2033 6,497 4.919 2 .258 66,564 .000776 .000156 1,290 .2011 6.428 4.973 4 .238 56,644 .001062 .000182 940 .1717 5,487 5.824 3 .229 52,441 .001235 .000196 813 .1595 5,098 6.270 5 .220 48,400 .001455 .000213 688 .1467 4.688 6.817 4 .204 41,616 .001960 .000247 510 .1265 4.043 7.905 6 .203 41,209 .00301 .000251 498 .1249 3,992 8.006 5 .182 33.124 .00312 .000312 320 .1003 3,205 9.970 7 .180 32,400 .00325 .000319 308 .0982 3,138 10.135 8 .165 27,225 .00400 .000379 21S .0825 2,637 12.12 6 .162 26,244 .00496 .000393 202 .0795 2,542 12.57 9 .148 21,904 .00710 .000471 141 .0664 2,122 15.06 7 .1443 20,822 .00789 .000496 127 .063' 2,017 15.85 10 .134 17,956 .01060 .0005 75 95 .0544 1,739 18.38 8 .1285 16,512 .01255 .000625 80 .0500 1,600 19.98 11 .120 14,400 .0164 .000717 61.0 .0436 1,395 22.91 9 .1144 13,087 .0200 .000730 503 .0397 1,268 25.21 12 .109 11,881 .0242 .000869 41 4 .0360 1,151 27.78 10 .1019 10,384 .0316 .000994 31.6 .0315 1.006 31.78 13 .095 9,025 .0418 .001144 23.9 0274 874 36.56 11 .0907 8,226 .0505 .001255 19.9 .0249 797 40.11 14 .083 6,889 .0718 .00150 13.9 .0209 667 47.89 12 .0808 6,529 .0802 .00158 12.5 .0198 633 50.53 13 15 .072 5.184 .1275 .00200 7.9 .0157 502 63.65 16 .065 4,225 .191 .00244 5.24 .0128 409 78.13 14 .0641 4.109 .203 .00251 4.95 .0125 398 80.32 17 .058 3,364 .301 .00307 3.32 .0102 326 98.04 15 .0571 3,260 .323 .00317 3.12 .00988 316 101.2 16 .0508 2.581 .513 .00400 1.96 .00782 250 127.8 18 .049 2,401 .591 .00430 1.69 .00728 233 137.4 17 .0453 2,052 .815 .00505 1.24 .00622 199 160.8 19 .042 ,764 1.095 .00585 .91 .00535 171 187.0 18 .0403 ,624 1.296 .00636 .77 .00492 157 203.0 19 .0359 ,289 2.05 .00801 .49 .00391 125 256 20 .035 ,225 2.27 .00343 .44 .00371 119 269 20 21 .032 ,024 3.25 .01010 .31 .00310 99.2 322 21 .0285 812 5.17 .0127 .19 .00246 78.7 406 22 .028 784 5.54 .0132 .18 .00238 75.9 421 22 .0233 640 8.32 .0161 .12 .00194 62.0 516 23 .025 625 8.73 .0165 .115 .00189 60.5 528 23 .0226 511 13.06 .0202 .077 .00155 49.5 646 24 .022 484 14.54 .0213 .069 .00147 46.9 682 24 25 .020 400 21.30 .0258 .047 .00121 38.8 825 25 26 .018 324 32.45 .0319 .0308 .000982 31.4 1.019 26 27 .016 256 52.00 .0403 .0192 .000776 248 1,239 27 28 .014 196 KS.7 .0527 .0113 .000594 19.0 1.684 29 .013 169 119.3 .0611 .0084 .000512 16.4 1,952 26 .0126 159 135.1 .0650 .0074 .000481 15.4 2,078 30 .012 144 164.3 .0717 .0061 .000436 14.00 2,291 29 .0113 128 209.0 .0808 .0048 .000387 12.40 2,584 30 31 .010 100 341.0 .1032 .00293 .000303 9.69 3,300 31 32 .009 81 520 .1275 .00193 .000246 7.85 4,073 32 33 .008 64 832 .1613 .00120 .000194 6.20 5,155 33 34 .007 49 1419 .2111 .000705 .000149 4.74 6,734 34 .0063 40 2164 .260 .000462 .000120 3.85 8,313 35 .0056 31 3465 .329 .000289 .000095 3.04 10,530 36 35 .005 25 5453 .413 .0001S3 .0000758 2.42 13,200 OP COOL, WARM, AND HOT COPPER WIRE. 677 WARM HOT SIZE or WIRE. at 60 C. (140 Fahr.) at 100 C. (212 Fahr.) Gauge Number. Resistance. Weight. Length. Resistance. Weight. Length. B AS. B.W.G. Ohms p. Ib. Ohms p. ft Ibs. p. ohm. ft p. ohm. ohms p. Ib. ohms p. ft. Ibs. p. ohm. ft p. ohm. 0000 0000 .0000871 .0000917 .0000558 .0000573 11,480 17,920 10,900 1 17,460 .0000980 .0001033 .0000629 .0000645 10.200 9.681 15,910 15,500 000 .0001195 .0000654 8,368 15,300 .0001346 .0000736 7,429 13,580 000 .0001385 .0000704 7,220 14,200 .0001560 .0000793 6,410 12,610 00 .000187 .0000818 5,350 12,230 0002105 .0000921 4,750 10,860 00 .000890 .0000887 4,539 11,250 .0002481 .0001000 4,031 10.004 .000292 .0001021 3,427 9,797 .0003287 .0001151 3,042 8,688 .000350 .0001118 2,857 8,945 .0003942 .0001259 2,537 7,943 1 .000481 .0001312 2,078 7,622 .000542 .0001478 1,845 6,766 1 .000557 .0001411 1,797 7,087 .000627 .000159 1,595 6,289- 2 .000599 .0001464 1,669 6,831 .000675 .000165 1,482 6,064 3 .000866 .0001761 1,155 5,679 .000975 .000198 1,025 5.043 2 .OOOKS5 .0001780 1,129 5,618 .000997 .000200 1,003 4,990 4 .001215 .0002084 823 4,798 .001368 .000235 731 4,261 3 .001408 .0002244 710 4,456 .001586 .000253 631 3,956 5 .001664 .000244 i 610 4,098 .001874 .000275 534 3,639 4 .002237 .000283 447 3,536 .002520 .000319 397 3,139 6 .00230 .000287 436 3.490 .002586 .000323 387 3,099 5 .00356 .000357 281 2,802 .004010 .000402 249 2,488 1 .00371 .000365 269 2,743 .004160 .000411 239 2,435 8 .00526 .000434 190 2,306 .00592 .000489 169 2,047 6 .00566 .000450 177 2,222 .00638 .000507 159 1,974 9 .00812 .000539 123 1,855 .00915 .000607 109 1,647 7 .00899 .000567 111 1,763 .01013 .000639 98.7 1,565 10 .0121 .000658 83 1,521 .01362 .000741 73.4 1,350 8 .0143 .000715 70 1,399 .01611 .000805 62.1 1,242 11 .0188 .000820 53.2 1,220 .02117 .000923 47.2 1,083 9 .0228 .000902 44.0 1,101 .02563 .001016 39.0 984 12 .0276 .000994 36.2 1,006 .03111 .001119 32.1 894 10 .0362 .001 137 27.7 880 .04074 .001281 24.6 781 13 .0479 .001809 20.9 764 .05391 .001474 18.6 678 11 .0576 .001436 17.4 696 .06487 .001617 15.4 618 14 .0821 .001713 12.2 584 .0925 .00193 10.80 518 12 .0914 .00181 10.9 553 .1030 .00204 9.71 491 13 15 .1450 .00228 6.9 439 .1634 .00257 6.12 390 16 .218 .00280 4.58 358 .246 .00315 4.07 318 . 14 .231 MOM 4.33 348 .260 .00324 3.85 309 17 .344 .00351 2.91 285 .388 .00395 2.68 253 15 .367 .00362 2.73 276 .413 .00408 2.42 245 16 .585 .00458 1.71 219 .659 .00515 1.52 194 18 .676 .00492 1.48 203 .761 .00554 1.31 181 17 .926 .00575 1.080 174 1.043 .00 48 .959 154 19 1.253 .00669 .790 149 1.411 .00754 .709 133 18 1.478 .00727 .676 138 1.665 .00819 .601 122 19 2.35 .00916 .426 1090 2.64 .01031 .379 97 20 2.60 .00904 .385 104.0 2.93 .01086 .342 92 20 21 3.72 .01153 .269 86.7 4.19 .0130 .239 77 21 5.91 .01454 .169 68.8 6.66 .0164 .150 61 22 6.34 .01506 .158 664 7.14 .0170 .140 59 22 9.52 .01845 .105 54.2 10.72 .0208 .093 48 33 9.9S .0189 .100 52.9 11.24 .0213 .0890 47 23 14.94 .0231 .067 432 16.83 .0260 .0594 38.4 24 16.63 .0244 .060 40.9 18.73 .0275 .0534 364 24 25 24.4 .0295 .041 33.9 27.44 .0333 .0364 30.1 25 26 37.1 .0365 .0269 27.4 41.81 .0411 .0239 24.4 26 27 59.5 .0461 .0168 21.7 67.00 .0519 .0149 19.3 27 28 101.4 .0603 .0099 16.6 114 .0679 .00876 14.7 29 136.5 .0699 .0073 14.3 154 .0787 .00651 12.7 28 154.5 .0744 .0065 13.4 174 .0838 .00574 11.9 30 188 .0820 .00530 12.20 212 .0923 .00472 10.80 29 239 .0925 .00420 10.80 269 .1042 .00372 9.60 30 31 390 .1181 .00257 8.47 439 .1330 .00228 7.52 31 32 594 .1458 .001680 6.86 669 .1643 .00149 6.09 32 33 952 .1845 .001050 5-42 1,072 .2078 .000933 1 4.81 33 34 1623 .2415 .000616 4.14 1.828 .2719 .000547 3.68 34 24'.'5 .2975 .000404 3-36 UM .3*5 .000359 2.98 35 3964 .3766 .000252 2.66 4.4ti4 .424 .000224 2.36 36 35 6237 .4723 .000160 2.12 7,026 .532 .000142 1.88 678 DYNAMO-ELECTRIC MACHINES. TABLE CXVI. DATA OF ARMATURE WIRE. (D.C.C.) a d S a ,-s d . d O d o SIZE OF WIBB. 'o d-g o O fbi o "2 ^ j^ M ^ ' c S s.1 ft ^ w d . rS 8 s^l *o u <4- ^ HH O m cj * S g d | QJ P. W 2 Gange Number. Diameter. Area. o f" A III b . a .2 2 ""* |l a; $_, ~ 3 "ti . c o ^ O 2> S C3 ii l*i 2 '5 QO -g B & S. B.W.G. Inches. Cir. Mils. K 5 * ^ S h- 1 1 .300 90.000 '.0001147 .320 3.1 9.8 .279 .000094 I .289 83,521 .0 101234 .309 3.25 10.5 .200 .000107 2 .284 80.656 .0001280 .304 3.3 10.8 .250 .000116 3 .259 67,0*1 .000154 279 3.6 12.9 .208 .000107 2 .258 06,504 .000156 JSKB 3.6 13.0 .206 .000109 4 .238 50,044 .000182 .258 3.9 15.1 .176 .000230 3 .229 52,441 .000196 .249 4.0 16.2 .164 .000267 5 .220 48,400 .000213 .240 4.2 17.4 .150 .000310 4 .204 41,616 .000247 .224 4.45 30.0 .130. .000415 6 .203 41,209 .000251 .323 4.5 20.2 .1285 .000423 5 .182 33,124 .000312 .200 5.0 25.0 .1030 .000651 7 .180 32,400 .000319 .198 5.1 25.5 .1010 .000080 8 .165 27,2'.'5 .000379 .183 5.5 30.0 .0852 .00095 6 .163 20,244 .000393 .180 5.6 31.0 .0821 .00106 9 .148 21,904 .000471 .164 6.1 37.2 .0085 .00147 7 .1443 20,822 .000496 .160 6.3 39.0 .0652 .00162 10 .134 17,956 .000575 .150 6.7 44.6 .0503 .00215 8 .1285 16,512 .000625 .145 6.9 47.5 .0518 .00249 11 .120 14,400 .000717 .136 7.4 54.2 .0454 .00325 9 .1144 13,087 .000789 .130 7.7 58.3 .0415 .00442 12 .109 11,881 .000809 .125 8.0 64.0 .0376 .00465 10 .1019 10,384 .000994 .117 8.5 73.0 .0331 .00007 13 .095 9.025 .001144 .110 9.1 82.8 .0289 .00792 11 .0907 8,226 .001255 .106 9.4 89.0 .0264 .00934 14 .083 6,889 .00150 .095 10.5 110.5 .0220 .01383 12 .0808 6,529 .00158 .093 10.8 1156 .0208 .01526 13 15 .072 5,184 .00199 .084 12.0 145.2 .0106 .02410 16 .065 4,225 .00244 .077 13.0 169.0 .0136 .0345 14 .0041 4,109 .00251 .075 13.3 177.8 .0133 .0373 17 .058 3,364 .00307 .068 14.7 216.0 .0108 .0553 15 .0571 3,260 .00317 .067 14.9 222.8 .01050 .0590 16 .0508 2,581 .00400 .061 16.4 2687 .00835 .0896 18 .049 2,401 .00430 .059 17.0 2890 .00780 .1038 17 .0453 2,052 .00503 .055 18.2 330.6 .00672 .1392 19 .042 1,764 .00585 .052 19.3 371.0 .00580 .1815 13 .0403 1,624 .00036 .050 20.0 400.0 .00533 .2124 19 .0359 1,289 .00801 .046 21.7 473.5 .00426 .3172 20 .035 1,225 .00843 .045 22.2 495.0 .00407 .3480 20 21 .032 1,024 .01010 .042 23.8 566.9 .00343 .4790 21 .0285 812 .0127 .039 25.7 660.0 .00276 .7375 22 .028 784 .0132 .038 26.3 692.5 .00266 .7620 22 .0253 640 .0161 .035 28.6 876.3 .00221 1.0963 23 .025 625 .0165 .035 28.6 870.3 .00215 1.210 23 .0226 511 .0202 .033 30.3 918.3 .00179 1.555 24 .022 484 .0213 .032 31.3 980.0 .00170 1.746 24 25 .020 400 .0258 .030 33.3 1111.1 .00142 2.373 25 26 .018 324 .0319 .028 35.7 1276.4 .00117 3.436 26 27 .016 256 .0403 .026 88.5 1479.3 .00094 5.022 TABLE CXVII. DATA OP MAGNET WIRE. (S.C.C.) 679 1 2 1 ?" ~ < ^ ^^ *o *o SIZE or WIRE. 2 o S.C.C. WIKB IN COILS. WEIGHT. & t> tir u ^ 's ^3 Q . Q ^> - CB 1- tt ^ ^ p;O W R W O^M Number of Wires in Concentric Layers. - Sn CT CT d OS -5 -3 QC X tO tO O ti CT - O Ol O CT O 8-' O CT O CT O CT O CT O CT O CT O CT O CT O ~< O i' O O O O O O O O O pp pp p p p p p p p p p p p p p p PPP ^_i i_i L. Li io io io io io to io co cc ic ic ic c: co cc 4- 4>. CT CT CT ci --3 -3 tO4-s;xo. J&- CT CT CT to 4* CT -7 00 CD O 7- tO OS 4- CT CT CS -^ X GC IO OT X Q O ~ O O ^ ' ' k- 1 "- 1 ' t- 1 >- k i- 1 *-' ' -* tO tO tO tO tO IO IO CC CO CC CC hf^ (U - * v: *w -: c,i cs -7 -7 x co co o < c/ tc. c;i x o b b i- 1 ' i ' ' !-i i-i l-i U^ 'i i-i - "^ 't-i i-* I-i t-> io to to io cc cc os co -} X tO O ' JO tO CC *>- 4- CT Ci Ci -7 -7 GC X CO 1C CT -7 O CC OS OO C,rC;C5C;i4--lC.tOC:lCtOC,l^ -3 IO 3CCOOCCCTCTCTtO4*-CCOCT oobbbo 1 '-*' 1 -''-*'- 1 '- 'ii-'i-'i-ii-i^i-iioioioioioosco CT Ci -7 X tO tO O tC; 10 1C 1C 4- 4- CT CT Ci Ci OC O -' CC 31 OO O IO ~. ~. H < 1 IS ir ^ -J - 3 I ' 4*- OC O O O b p p o b b O b b b b '*-' ^ >-i >-' i-* i- 1 i- 1 i- 1 -* i- 1 i- i* i* io to nf^r-^fio^rixxxtrtoooo^^^to^CTcsoco^cc D O O C4 -3 3 o b o o o c _ CT iri Ci C: S; -7 -7 -7 X X X X to tO CO O ^- IO CC CT C6 QC O *^.&i5.CTC;75;c;5ct-7^7- 7 ~>occoie>tOif.-3otO4>-c:coco o "r 1 to cc CT Ci r? tpCCCC4^4>4-CTCTCTCiCiaiC;^7^7 7^)O ? xSoO^ J CC4^ "c ^ ic i: r- i"' I- ^ ~ ~ ~ ~ ^; ~> ~, ^> ^r -2 ~ o ' :. i: i- ^O4^OCtOCiCOt04---3Ot04--3O>->O5CT-7C:*>.lOC>tOCC4^4>' CC OO IO Ci O CC Ci CC S 4^ Ci OC O CC CT ^7 CO b IO I OC CT tO 4^- CT CT 'c- /c. i; ic ;c -^- -i IT i' I;T c,r i"i * ct ci c^ ci ^' 'X to c^ o *-* >OCJO4^-3OOSCiOOOCOCT-JCO^t04-CiOCCiCOOC1^3O0^3C SS2SS8CTclsS-^SoQ to CO CO CO TT CO rj to CO - Q X H V OB Si o o H4 w Q 688 D YNA MO-ELECTRIC MA CHINES. ill armature winding calculations. The size of the single wire required to carry the given current having been found, this table gives directly, without further calculation, the size of wire for a subdivided armature conductor. The scope of this table, including all sizes from No. oooo to No. 20 B. & S., and from No. oooo to No. 21 B. W. G., and giving subdivisions from 2 to 24, is such that it will answer for all the usual cases occurring in practice. TABLE CXXIV. SIZE AND WEIGHT OF CABLES. SIZE OF CABLE, B. & S. GAUGE. AREA OP CABLE, ClKCULARMlLS. MAXIMUM DIAMETER OF COPPER STRAND, INCHES. OUTSIDE DIAMETER OF CABLE, INCHES. WEIGHT PER FOOT OF CABLE, POUNDS. 1,000,000 11 11 3.7 900,000 If If 3.0 800,000 1 lit 2.9 .... 750,000 1* 1 2.8 700,000 1* 1 6 X tf 2.5 .... 650,000 1* -| 1 9 1 5'2" 2.4 .... 600,000 1* ly 9 * 2.1 .... 550,000 H it 2.0 .... 500,000 1A i* 1.9 .... 450,000 if 1.6 .... 400,000 if 1.5 .... 350,000 1 T 1.3 .... 300,000 it A 1.2 .... 250,000 i* 1.0 OOOO 211,600 - it i*. .82 000 168,100 1 i .65 00 133,225 & if .55 105,625 I .46 1 83,521 A if .38 2 66,564 1 .30 3 52,441 H if .27 4 41,616 S if .22 5 33,124 S " .20 6 26,244 T .18 Tables CXXIL, CXXIIL, and CXXIV. give the data of flexible copper wire cables, such as are used for dynamo con- nections. In Table CXXIL, page 686, the diameter of the copper strand of cables containing from 3 to 427 wires is given, and the arrangement of the various stranded cables is shown. The unit of the diameter in each case is the diame- ter of the wire employed in making up the cable, so that the diameter in inches is found by multiplying the given figure by the diameter of the wire. For instance, the diameter of the WIRE TABLES AND WINDING DATA. 689 copper strand of a cable consisting of 133 No. 13 B. & S. wires is 15 X .072 = 1.08 inches. From the last column it will be seen that cables are made up in either of two ways: (i) one single wire forms the center layer, 6 wires the second layer, 12 wires the third layer, etc.; or (2) the center layer consists of 3 wires, the second layer of 9 wires, the third of 15 wires, etc. Up to 9 concentric layers are used in this manner; cables requiring a larger number of wires are made TABLE CXXV. IRON WIRE FOR RHEOSTATS AND STARTING BOXES. FOR RHEOSTATS. SIZE FOR OF WIRE. OTAKTINO WOOD FRAME. IRON FRAME. . g d T3 _" a _. a pi *rf o.2 ^ ^ of = I jS He" i 00 o> ffi || 3 -> 03 33 S " ||| If 8|l 2o| tie. / t- || '* 00 a- =. a ai-H -< .| .-no .|~-O 53 .2 ^ ^, O o 5 g v o a K.t!0 s " o jj leg BO O '5 OQ o 8 .1285 17.4 6.32 20.3 5.42 436 2.52 .00398 250. .040 9 .1144 14.6 7.53 17.1 6.43 36.6 3.01 .00578 173. .033 10 .1019 12.3 8.94 14.3 7.69 30.8 3.57 .00728 137. .0275 11 .0907 10.3 10.68 12.0 9.17 25.8 4.26 .00918 108. .0218 12 .0808 8.7 12.64 10.1 10.89 21.7 5.07 .01157 86.4 .0173 13 .072 7.3 15.07 85 12.94 18.3 6.01 .01459 68.5 .0137 14 .0641 6.1 18.03 7.1 15.49 15.3 7.19 .01840 54.3 .0109 15 .0571 5.1 21.57 6.0 18.33 12.9 8.53 .02320 43.1 .0063 16 .0508 4.3 25.58 5.0 22.00 10.8 10.19 .02925 34.1 .00685 17 .0453 3.6 30.56 4.2 26.19 9.1 12.09 .03688 27.1 .00543 18 .0404 3.0 36.67 3.5 31.43 76 14.47 .04652 21.4 .00430 19 .0359 2.52 43.65 2.9 37.93 6.3 17.46 .06032 16.5 .00341 20 .032 2.17 50.69 2.5 4400 5.4 20.37 .07396 13.5 .00271 21 .0285 1.82 60.44 2.1 52.38 45 2444 .09332 10.7 .00231 22 .0253 1.53 71.90 1.77 62.15 3.8 2895 .11769 8.49 .001838 23 .0226 1.28 85.94 1.5 73.33 3.2 3438 .14843 6.73 .0014V7 24 .020 1.08 101.85 1.2 91.67 23 47.83 .18717 5.34 .001155 up by stranding together 7 individual cables, each composed of the proper number of concentric layers. In the 343-wire cable, each of the 7 cables so stranded is again subdivided into 7 cables, each of the small cables consisting of 7 wires in two concentric layers. The figures given in Table CXXIII., page 687, are the diameters of the wire required to produce a given sectional area when used for making up a cable of a given number of wires. Thus, the size of wire for a 690 DYNAMO-ELECTRIC MACHINES. i47-wire cable of 400,000 circular mils sectional area is given, as .052 inch. The nearest gauge sizes are No. 15 and No. 16 B. & S. ; the former is to be taken if it is not desirable to go below the specified area, and the latter may be used if a TABLE CXXVI. CARRYING CAPACITY OP GERMAN SILVER RHEOSTAT COILS. (18$ Commercial German Silver.) 05 B PERMISSIBLE CURRENT fc ~ f-i 03 E a c- 5 2 fc s IN A {[-INCH SPIRAL, 3J INCHE* LONG, STRETCHED HORIZONTALLY TO 7 INCHES, FOR A RISE IN TEMPERATURE OF: " ^ o ^ ^ 2 p* |-| *-j K H W B 2 U * > 05 5 K KJH < 0. M O Q S* WCC M a a ts Ed g 50 C. (90 F.) 75 C. (135 F.) 100 C. (180 F.) 125 C. (225 F.) 150 C. (270 F.) ---- O P* X O 10 923 12.03 14.04 16.15 17.03 1.100 11 7.75 1007 11.79 13.46 14.29 .964 12 6.52 8.47 9.88 11.31 12.03 .812 13 5.48 7.15 8.32 9.50 10.11 .703 14 4.50 6.00 7.00 8.00 8.50 .600 15 389 5.03 5.86 6.71 7.15 .481 16 3.22 4.21 4.90 5.62 5.99 .406 17 2.73 3.59 4.13 4.71 5.04 .311 18 2.28 2.98 3.47 3.95 4.22 .287 19 1.89 2.46 2.90 3.30 3.48 .236 20 1.62 2.12 2.46 2.76 2.98 .203 21 1.36 1.78 2.10 2.35 2.50 .170 22 1.14 1.50 1.76 2.00 2.11 .149 23 .96 1.25 1.47 1 61 1.78 .126 24 .81 1.04 1.23 1.39 1.48 .105 25 .68 .88 1.03 1.19 1.24 .089 26 .57 .74 .87 .99 1.05 .074 27 .48 .63 .73 .83 .885 .063 28 .40 .52 .61 .70 .74 .052 29 .34 .44 .51 .59 .625 .039 30 .29 .37 .43 .50 .52 .037 31 .24 .31 .36 .41 .44 .031 32 .20 .26 .31 .35 .37 .027 33 .17 .22 .25 .29 .31 .022 34 .14 .19 .21 .245 .256 .019 35 .12 .16 .18 .205 .215 .016 36 .10 .13 .15 .174 .185 .013 37 .084 .11 .13 .144 .156 .011 38 .071 .092 .11 .121 .130 .009 39 .060 .077 .090 .100 .110 .008 40 .050 .065 .077 .088 .092 .007 slight shortcoming of the cross-section is immaterial. Table CXXIV., page 688, gives the maximum bare and outside diameters and the weights of flexible cables from 1,000,000 circular mils down to 26,244 circular mils area, the latter being WIRE TABLES AND WINDING DATA. ' 691 equivalent to a 6 No. B. & S. wire. The figures in the third column are based on the data given in Table CXXIII. for 343- wire cables; to obtain the diameter given in the fourth column, | of an inch is added to the former dimensions, the thickness of insulation on flexible dynamo and power cables being usu- ally about ^ of an inch. Table CXX1V. will be found useful for designing the cable-lugs of brush holders and the cable-re- ceiving parts of switches, etc. Tables CXXV. and CXXVL, finally, contain all the data necessary for selecting the proper size of wire for resistance coils. Table CXXV., page 689, gives the safe current-carry- ing capacities, the resistance required, the specific resistance, the specific length, and the specific weight of tinned iron wires from No. 8 to No. 24 B. & S. gauge for wooden and iron rheo- stats as well as for starting boxes. The resistance of the shunt circuit corresponding to each current strength is calculated for the case of no volts; this resistance must be multiplied by Tf 2 for 220 volts, by 5 for 550 volts, and by where E is the no E. M. F. at shunt terminals, for any other voltage E. The resist- ance so obtained is the minimum resistance that should be pro- vided for the voltage in question. Table CXXVI., page 690, gives the current capacities for temperature increases of 50, 75, 100, 125, and 150 C., respectively, of German Silver rheostat coils from No. 10 to No. 40 B. & S. wire. The figures are the results of tests made with spirals wound to a solid length of $\ inches on a f-inch mandrel, and afterwards stretched to a length of 7 inches; thus making the space between the turns equal to the diameter of the wire. The last column of this table serves to correct the values given for the 7-inch spiral in the case that its length, that is to say, its number of turns, is increased; twice the current strengths given in this column are to be deducted from the respective table-value for every additional inch length of spiral above 7 inches. Thus, for in- stance, the current capacity of an 8^-inch spiral of No. 12 Ger- man Silver wire for a temperature increase of 125 C. is 11.31 2 X (8| 7) X .812 = 11.31 2.44 = 8.87 amperes. Table CXXVI. refers to the so-called 18 per cent. German Silver, containing 18 per cent, of nickel, this alloy being usu- 692 DYNAMO-ELECTRIC MACHINES. ally employed for resistance coils. From a great number of tests it has been found that the average resistance of this ma- terial is a trifle over eighteen times the resistance of copper at 75 F. German Silver is also made with 30 per cent, of nickel, but in this composition it is now but rarely used for electrical purposes. The resistance of the 30 per cent, alloy is about twenty-eight times that of copper. APPENDIX III. LOCALIZATION AND REMEDY OF TROUBLES IN DYNAMOS AND MOTORS IN OPERATION. LOCALIZATION AND REMEDY OF TROUBLES IN DYNAMOS AND MOTORS IN OPERATION.* Classification of Dynamo Troubles. The constructive expedients to be employed when designing a dynamo having been treated in the text, the following pages are intended for the consideration of the attendant in whose care the machine is placed, and upon whose competency depends, in no small measure, its efficiency and 'even its life. While general pre- cautions and preventive measures do not always insure free- dom from trouble, neglect and carelessness with any ma- chinery are usually followed by accidents of some sort. The success of an electric plant depends to a very great extent upon the promptness with which the attendant is able to remedy such difficulties. The usual troubles in dynamo-electric machinery may be clas- sified as follows: 1. Sparking at commutator. 2. Heating of armature and field magnets. 3. Heating of commutator and brushes. 4. Heating of bearings. 5. Noises. 6. Abnormal speed. 7. Dynamo fails to generate. 8. Motor stops or fails to start. 1. Sparking at Commutator. The most common trouble met with in running continuous-current dynamos and mo- tors is the sparking at the commutator. Since excessive sparking wears, and eventually even destroys, the commu- * Compiled from " Practical Management of Dynamos and Motors," by Crocker and Wheeler. 695 696 DYNAMO-ELECTRIC MACHINES. tator and brushes, and produces heat which may become in- jurious to the armature and bearings, it is of the greatest importance that sparking, upon its discovery, should be promptly checked. CAUSES OF SPARKING. Sparking may be due to any of the fol- lowing causes: (i) Brushes not set at neutral points. (2) Brushes make poor contact with commutator. (3) Vibra- tion, or chattering, of brushes. (4) Short-circuited or reversed coil in armature. (5) Weak field. (6) Unequal distribution of magnetism. (7) High resistance brush. (8) Vibration of machine. (9) Commutator rough, eccentric, or having " high " or " flat " bars. (10) Broken circuit in armature. (n) Ground in armature. (12) Armature overloaded. PREVENTION OF SPARKING. It is seen from the preceding that sparking at the commutator may be due to one, or more, of many causes. The first step in the speedy prevention of sparking, therefore, is the detection of the trouble that causes it. If due to any one cause, the finding of the trouble is comparatively easy, since in each case the symptoms are different and quite well pronounced; but when two or more causes combine in effecting excessive sparking, it requires more care to locate the faulty conditions. FAULTY ADJUSTMENT. Causes (i) to (3) are due to faulty ad- justment of the brushes, and sparking in consequence of these causes can be easily prevented by resetting the brushes. In the first case, when the brushes are not at neutral points, they must be set exactly opposite each- other, if the machine is bi- polar; po apart, if it is fourpolar; 60, if it has six poles, etc. The proper points of contact for so setting the brushes are best determined by counting the commutator bars. To find the opposite bar to No. i, add i to half ihe. number of bars; to find the po bar, add i to one-quarter the number of bars; to find the 60 bar, add i to one-sixth the number of bars, etc. For instance, if the commutator has ^c?bars, one- half the number is 24, and 24 -{- i = 25, hence bar No. 25 is opposite bar No. i; since one-quarter of 48 is 12, bar No. 13 is the one 90 from No. i; and i added to one-sixth of 48, LOCALIZATION AND REMEDY OF TROUBLES. 697 or 8, gives No. 9 as the bar 60 from No. i. Mark bars Nos. i and 25 in case of a bipolar machine, bars i and 13 in case of a four-pole machine, or i and 9 in case of a six-pole machine, and adjust the brushes so that each set rests on one of the marked bars, taking care that all the brushes of one set are exactly in line with each other, so that none is ahead or behind the others. This being done, the rocker- arm or brush-yoke, as the movable bracket is called to which the brush-holders are attached, is shifted backward or for- ward until sparking is reduced to a minimum, or disappears. If the sparking is due to the second cause, poor contact, an ex- amination of the brushes will show that they touch only at one corner, or only at one edge, or that there is dirt or oil between them and the commutator. In case of metallic brushes, they should then be filed or bent until they rest evenly on the commutator. Carbon brushes are fitted- by pasting a band of sandpaper around the commutator and revolving the armature while the brushes are firmly pressed in their proper positions. In this manner, the tips of the brushes are hollowed out to the exact shape of the commu- tator, and after removal of the sandpaper, the brush-contact is found to be perfect. The third cause, vibration of brushes, is frequently met with carbon brushes which are set radially to the commutator. Such brushes, when the commutator has become sticky, are thrown into rapid vibration by the running of the machine, and create a chattering noise. The ensuing spark is easily stopped by cleaning and slightly lubricating the commutator. In applying the lubricant, which may consist of ordinary machinery-oil, vaseline, or specially prepared commutator- compound, care should be exercised in using it very sparingly, preferably by rubbing it over the commutator with the finger. For, since all oils are non-conductors of electricity, too much lubrication will insulate the brushes from the com- mutator, and will thus prevent the machine from operating. FAULTY CONSTRUCTION AND WRONG CONSTRUCTION. Causes (4) to (8) are a consequence either of faulty construction of, or wrong connections in, the machine, and can be properly eliminated only by repairing the machine. 698 bVNAMO-ELECT&lC MACHINES. If a coil in the armature has been accidentally short-circuited of reversed while connecting up the armature, it will, when ro- tated in the magnetic field, generate local currents which give rise to sparking. Short-circuits in the coils are frequently caused by solder dropping between two commutator bars when fastening the wires to the commutator. Defects of this kind can be readily detected by careful inspection, and are easily remedied by removal of the obstruction. Re- versals are due to mistaking the terminals of the armature coils, so that the end of a coil is connected to a bar where the beginning of the coil should be, or vice versa. In this case the faulty coils must be disconnected and properly re- attached to the commutator. A weak field may be due to a break, or to a short-circuit, or to a ground in the field coils. These faults can be easily repaired if they are external or accessible. When internal, the only remedy is to partially, or wholly, rewind and replace the faulty coil. Unequal distribution of magnetism, which is usually traced to weak- ness of one of the pole-tips, causes one brush to spark more than the other. In this case the polepieces must be re-shaped so as to weaken the strong tip or to strengthen the weak tip. The brushes of a machine must be of sufficient conductivity to carry the current generated by the armature without undue heating. Their material as well as their cross-section must therefore be suitably selected. Brushes of abnormally high resistance become very hot, cause sparking, and reduce the output of the machine. By using new brushes of proper material and thickness, the sparking due to this cause is immediately stopped. Vibration of machine is usually due to an imperfectly balanced armature or pulley, to a bad belt, or to an unsteady founda- tion, or sometimes to poor design of the field frame. In the two former cases, re-balancing of the rotating parts, or re- lacing the belt, respectively, will remove the vibration; in the two latter cases, the weak parts must be strengthened or rebuilt. WEAR AND TEAR. Causes (9) to (i i) are consequent upon wear and tear, and are therefore the most usual. LOCALIZATION AND REMEDY OF TROUBLES. 699 A commutator, after seme time, shows grooves and ridges, wears more or less eccentric, and develops projections and flats. To avoid sparking from these causes, the commutator should from time to time be smoothed by means of a fine file or sandpaper, but never by means of emery-paper. Emery, con- taining the metal particles taken from the commutator, would lodge in the insulation between the bars, and would thus cause short-circuits, which would give rise to worse sparking than the unevenness of the commutator did before smoothing. A broken circuit in the armature is either located in the com- mutator connection or in the coil itself. If the commutator connection has worked loose, the break can easily be re- paired; but if the wire inside the coil has broken, the coil must be removed and the armature rewound. Grounds in the armature are due to breakdown of the insula- tion between two wires or between a wire and the armature core. To repair a ground, the defective insulation must be replaced. EXCESSIVE CURRENT. If a machine is overloaded, cause (12), the winding is forced to carry too much current, which causes excessive heating of the armature. Sparking due to ex- cessive current can be reduced by decreasing the load upon the machine, or by decreasing the strength of the magnetic field in the case of a dynamo, or increasing it in the case of a motor. 2. Heating of Armature and Field Magnets. Injurious heating in a dynamo or motor can be detected by placing the hand on the various parts. If any part so examined feels so hot that the hand cannot remain in touch without discomfort, the safe limit of temperature has been passed, and the trouble should be remedied. If the heat has become so great as to produce odor or smoke, the current should be shut off and the machine stopped immediately. The above sim- ple method of testing for heat should be applied shortly after the machine has been started up, because after the machine has run for some time, any abnormal heating effect will spread until all parts are nearly equal in temperature, and it will be almost impossible to locate the trouble. 700 DYNAMO-ELECTRIC MACHINES. Abnormal heating of the armature or field magnets may be due to excessive current, to short-circuits, to moisture in the coils, or to excessive generation of eddy currents in the armature core or polepieces. Excessive current in the armature is remedied by reducing the load, or eliminating whatever other cause is responsible for it, which may be either a short-circuit, or a leak, or a ground on the line. To decrease the current in the field circuit, in- crease the field resistance by inserting rheostat, in case of a shunt machine, or by shunting, in case of a series machine, or by both of these methods in a compound machine. If heating is caused by a short-circuit in the winding, the faulty coil must be located, and repaired or replaced by a new one. The presence of moisture is revealed by the formation of steam when the machine becomes hot. A moist machine should be stopped and the moisture expelled by baking the affected part in a moderately warm oven for 4 or 5 hours, or by pass- ing a current through it which should be regulated to main- tain a temperature of about 75 Centrigrade. Heating due to eddy currents in the iron is indicated by the fact that, after a short trial run, the iron parts will feel warmer than the windings; it is always the result of some construc- tional fault of the machine, such as insufficient lamination of the armature core, misproportioning of the armature teeth, improper arrangement of the polepieces, etc. 3. Heating of Commutator and Brushes. Heating of the commutator and brushes may be due to sparking at the brushes, arcing in the commutator, or to excessive resistance. Sparking always heats both the commutator and the brushes. Heating from this cause is checked by shifting the rocker arm, or by applying the proper remedies for the sparking. Frequently heating of the commutator is produced by the causes which induce sparking without being accompanied by the visible manifestation of the latter. Arcing within the commutator, either between one bar and the next, or between the bars and the commutator shell, is due to defective or punctured insulation; if the heating is traced to this cause, the commutator must be taken apart and re- paired. LOCALIZATION AND REMEDY OF TROUBLES. 701 Heating of commutator and brushes is often due to insufficient contact area, the cross-section of the brushes being too small to carry the current without overheating. In this case, either thicker brushes of the same material as the old ones, or new brushes of a higher-conductivity material, should be substituted. Sometimes connections or joints in the brush-holder or cable terminal become loose by the vibration of the machine, and cause heating of the joints due to increased contact resistance. By tightening all contacts before every run, however, this trouble can always be prevented. 4. Heating of Bearings. Heating of the bearings may arise from lack of lubrication, presence of grit, or from fric- tion due to roughness or tight fit of shaft, faulty alignment of bearings, excessive belt pull, or to end-thrust or side- thrust of armature. The first two causes, and also excessive belt tension, can be easily detected and remedied, while a rough, sprung, bent, or tight shaft has to be turned or filed down true in the lathe. When the bearings are out of line, they must be un- screwed and properly adjusted, by filing out the bolt holes if necessary, so that they will stay in line, with the armature central to the polepieces, when the screws are tightened. Friction due to end-thrust may be relieved by lining up the belt, shifting armature collar or pulley, turning off shoulder on shaft, or filing off bearing until a sufficient clearance be- tween the two is obtained. In case of side-thrust, the arma- ture must be re-centered by adjusting the bearings or the polepieces. Water or ice cooling of the bearings should only be used in cases of extreme necessity, and should never be attempted if there is the slightest danger of wetting the commutator or the armature. 5. Causes and Prevention of Noises in Dynamos. The humming noise often issued by an electric machine is pro- duced by vibration due to armature or pulley being out of balance. The armature and pulley should always be bal- anced separately by slowly rolling the armature, first without ?62 DYNAMO-ELECTRIC MACHINES. and then with pulley, upon a knife-edge track and attaching weights to the places which show a tendency to remain on top. An excess of weight on one side of the armature and an equal excess on the opposite side of the pulley will not produce a balance when running, though it does when standing still; on the contrary, it will give the shaft a strong tendency to wobble. A perfect balance is only obtained when the weights are directly opposite in the same line per- pendicular to the shaft. Rattling noises are sometimes caused by striking of the arma- ture against one or more of the polepieces, by scraping of the shaft collar or pulley hub against the bearing, or by looseness of screws or other parts. In these cases, the machine should be immediately stopped and the parts properly adjusted. Singing or hissing of the brushes is usually occasioned by rough or sticky commutator or by unevenness of the brushes, especially when the commutator or the brushes are new, and have not yet worn smooth. A sparing application of oil or vaseline to the commutator, with a rag or the finger, will in most cases stop the noise. If not, shortening or lengthening of the brushes may be resorted to, and, if hissing still contin- ues, it will be necessary to sandpaper, file, or turn down the commutator. A humming sound is often heard in toothed-armature machines, due to the sudden changes of magnetic conditions as each tooth passes the edge of the polepieces. This sound is reduced or stopped by filing away the ends of the polepieces, so that the armature teeth pass each pole-edge gradually. Slipping of the belt causes an intermittent squeaking noise, which can be stopped by tightening the belt. If the belt is poorly laced, so that the joint is rough, a pounding is emitted every time the joint passes over the pulleys. A properly made joint will immediately obviate this difficulty. 6. Adjustment of Speed. Too high or too low speed is generally a serious matter in either dynamo or motor, and it is always desirable and often imperative to shut off immedi- ately, and make a careful investigation of the trouble. Low speed in a motor may be caused by overloading, or short-cir- cuits, or grounds in armature, or by excessive friction in the LOCALIZATION AND REMEDY OF TROUBLES. 703 bearings. Accidental weakness of the field due to a break, short-circuit, or ground in the field coils, or to weakness of the field current, has the effect, on a constant-potential circuit, of making a motor run too fast if lightly loaded, or too slow if heavily loaded, or even to stop or to run backward if the overload is excessive. A series motor on a constant-potential circuit, or any motor on a constant-current circuit, is liable to run too fast if the load is very much reduced. Constant- current motors, except when directly coupled, must, there- fore, be provided with automatic governors or cut-outs, which act to reduce the power if the speed becomes too great. 7. Failure of Self-Excitation. The inability of a gener- ator to excite or build up its field magnetism is in most cases due to weakness or absence of the residual magnetism, caused either by vibration or jar, or by counter-magnetization effected by the proximity of another dynamo or by the earth's mag- netism, or by accidentally reversed current through the fields. Residual magnetism can be restored by sending a current from any dynamo or battery through the field coil ; if, upon starting the machine, it fails to generate, apply the battery current in the opposite direction, since the magnets may have enough polarity to prevent the battery from building them up in the direction first tried. By shifting the brushes backward from the neutral point, the armature magnetization can be made to assist the field. Other causes for dynamo failing to generate are reversed con- nections, reversed direction of rotation, short-circuit in machine or external circuit, connection of field coils in opposition, open circuit, and faulty position of brushes. Any of these troubles can be detected by carefully inspecting and testing the ma- chine, and, when found, can readily be eliminated. A break, poor contact, or excessive resistance in the field circuit or regulator of a shunt dynamo will make the magnetization weak, and prevent its building up. This may be detected and overcome by cutting out the rheostat for a moment, taking care not to make a short-circuit. An abnormally high resistance anywhere in the circuit of a series machine will prevent it from generating, since the field coil is in the main circuit. The magnetization in this case 704 DYNAMO-ELECTRIC MACHINES. can be started up by short-circuiting the machine for an in- stant. Either of the above two expedients should be applied very carefully, and not until the polepieces have been tested with a piece of iron to make sure that the magnetization is weak. 8. Failure Of Motor. The stopping of a motor, or its re- fusal to start, may be due to excessive overload, to open circuit, or to a wrong connection. While a moderate overload causes the motor to run below its normal speed, an excessive overload 'will stop it entirely. The abnormal load is not 'always exterior to the motor, but may be due to unusual friction in the motor itself, occasioned by jamming of the shaft, bearings, or other parts, or by arma- ture touching polepieces. In either case, the current should be turned off instantly, the load or the friction reduced, and the current supplied again for a moment, just long enough to see if trouble still exists. If the motor comes promptly up to speed, it may then be left in circuit. If the stopping of the motor is caused by open circuit, a melted fuse or broken wire will be found upon examination of the motor, provided its brushes are in contact and the external circuit is in proper order. If there is no visible break, the armature and field coils must be tested for continuity by means of a battery (or magneto) and electric bell. On a constant-potential circuit, if current is excessive, it indicates a short-circuit. If the field is at fault, the polepieces will be found non-magnetic, or but very weakly magnetized. The possible complications of wrong connections art so great that a very careful and systematic examination and comparison of the connections with the diagram furnished by the manu- facturer is necessary to locate the trouble. INDEX. (Numbers indicate pages.) Absolute units, 7, 47, 199, 332, 333 Accessibility of parts in dynamos, 287, 432 Accumulator charging dynamos, 91, 92, 461, 462 Act of commutation, 29 Active wire in armature. 49, 55 Activity, electrical, in armature, 405, 407, 420, 422, 628, 637, 644 Addenbrooke, on insulation-re- sistance of wood, 85 Addition of E. M. Fs. in closed coil, 12 Adjustment of brushes, 29 Advantages of combination mag- net-frames, 294 of drum-wound ring arma- tures, 35 of iron clad types, 286 of multipolar dynamos, 33, 34, 285 of open coil armatures, 144 of oxide coating of armature laminae, 93 of stranded armature con- ductor, 528, 553 of toothed and perforated armatures, 61, 62, 63 of unipolar dynamos, 25, 26 Air-ducts in armature, 94, 590 Air-friction, 407, 526 Air-gaps, ampere-turns required for, 339, 340 graduation of, 295 - influence of change of, 483,484 length of, 62, 208, 433, 469, 470-472, 483 permeance of, 217, 224-231 Alignment of bearings, 304, 409 Allowance for armature-binding, 75, 507, 536 for clearance, 209, 210, 518, 536, 543. 558, 576, 583, 6o4 for flanges on magnet-cores, 523, 542, 576, 595, 650 Allowance for height of commu- tator-lugs, 514 for spaces between armature- coils, 73, 506, 638 for spread of magnetic field, 529 for stranding of armature- conductor, 530 Alternating current, production of, 12 rectification of, 13 Alternators, unipolar, 24 Aluminum, in cast iron, in, 293, 312, 313, 314, 315, 316, 336, 337, 338 Aluminum-bronze, 189 "American Giant " dynamo, 272, 281 Amperage, permissible, 56, 57, 132, 133, 183 Ampere-turn, the unit of exciting power, 333 Ampere-turns, calculation of, 339- 356, 520, 537, 547, 560, 575, 585, 605, 638, 645, 657 Analogy between magnetic and electric circuit, 354 Angle of belt-contact, 193 of field-distortion, greatest permissible, for various num- bers of poles, 340 of lag or lead, 30, 349, 350, 421 of pole-space, 210, 211 Application of connecting for- mula, 152-155 of generator formulae to motor calculation, 419 Arc of belt-contact, 193 of polar embrace, 49 Arcing in commutator, 700 Arc-lighting dynamos, designing of, 455-459, 4620 flux density in armature of, 9i regulation of, 458, 459 series-excitation of, 37 7s 706 INDEX. Area, see Sectional Area, Surface. Armature, calculation of, 45-195, 413-416, 505, 527, 552, 566, 580, 587, 603, 629, 638, 644, 652, 656 circumflux of. 131 closed coil- and open coil-, 143 cylinder-, or drum-, see Drum- Armature. definition of, 4 disc-, 4 energy-losses in, 107-122 load limit and maximum safe capacity of, 132-135 perforated, or pierced, or tunnel-armature, see Perfor- ated Armature. pole-, or star-, 4 principles of current-genera- tion in, 3 ring-, see Ring-Armature, running-value of, 135, 136 smooth core-, see Smooth Core Armature. toothed, or slotted, see Toothed Core Armature. Armature-calculation, formulae for, 45-195 practical examples of, 505, 527, 552, 566, 580, 587, 603, 629, 638, 644, 652, 656 simplified method of, 413-416 Armature-coils, formulae for con- necting of, 152-155 grouping of, 147-151 Armature-conductor, active and effective, 49 length of, 55, 94 size of, 56 Armature- conductors, number of, 76, 11 peripheral force of, 138-140 Armature-core, diameter of, 58 insulation of, 78-82 length of, 72, 76 magnetic density in, 90, 91 magnetizing force for, 340- 343 radial depth of, 92 Armature-current, total, in shunt and compound dynamos, 109 volume of, 131 Armature-divisions, number of, 90 Armature-induction, specific, 51 unit, 47-50 Armature-insulations, selection of material for, 83-86 thickness of, 82 Armature-reaction, compounding motor by, 649 Armature-reaction, magnetizing force for compensating, 348- 352 Armature-reaction, prevention of, 463-470 regulating for constant cur- rent by, 456 Armature-thrust, 140-142, 513, 534 Armature-torque, 63, 137, 138, 513, 534 Armature-winding, arrangement of, 87, 507, 529, 554, 581, 589, 604, 657 circumferential current-den- sity in, 130-132 connecting-formulae for, 152- 155 energy dissipated in, 108 fundamental calculations for, 47 grouping of, 147-151 mechanical effects of, 137-142 qualification of number of conductors for, 155-167 temperature rise in, 126-130 types of, 143-147 weight of, 101, 102 Armature wire (D.C.C), data of, 678 Arnold, Professor E., on arma- ture-winding, 152 on unipolar dynamos, 25 Arrangement of armature-wind- ing, 87, 507, 529, 554, 581, 589, 604, 657 of field-poles around ring- armature, 98 of magnet-winding on cores, 387, 401, 551, 564, 576, 599, 613, 635, 641, 655, 660 Asbestos, for armature-insulation, 78, 79, 85, 93, 94 " Atlantic " fan-motor, 282 Attracting force of magnetic field, 140, 141 Auxiliary pole method, 469 Available height of armature- winding, 74 of magnet-winding, 377 Average efficiencies of electric motors, 422 E. M. F., 8, 9, 19, 20, 21 magnet density in armature- core, III, I2O pitch of armature-winding, 158-167 relative permeance between magnet-cores, 231, 238 traction-resistance, 440 INDEX. 707 Average turn, length of, on mag- nets, 374 useful flux of dynamos, 212- 214 values of hysteretic resistance, no volts between commutator sections, 88, 151 weight and cost of dynamos, 412 Axial multipolar type, 270, 282 BackE.M.F.,or Counter E.M.F., 421, 423, 434, 438, 453, 461 pitch of armature-winding, 159-167 Backward lead, see Angle of Lag. Bacon, George W.,on magnetism of iron, 335 Bar armatures, 101, 567, "569, 588 Base, or bedplate, of dynamo, 299, 300 Battery-motors, 54, 91, 92 Baumgardt, L., on dimensioning of toothed armatures, 67 Baxter, William, on seat of elec- tro-dynamic force in iron clad armatures, 64 Bearings, 184, 186, 187, 190, 191, 192, 303-305, 516 Belt-velocity, 193 Belt-driven dynamos, 520, 60, 132, 193, 194 Belts, calculation of, 193-195, 517 losses in, 409 Bifurcation of current in arma- ture, 48, 49, 51, 104 Binding-posts, contact area for, 183 Binding wires, for armatures, 75 Bipolar dynamos, act of commu- tation in, 29 classification of, 269, 270-278, 286 connecting formula for, 153 field densities for, 54 generation of current in, 27 running value of, 136 Bipolar iron clad type, 234, 235, 247, 255, 263, 637 Bipolar types, comparison of, 249- 256 practical forms of, 270-278 Blank poles, 469 Bobbin, formulae for winding of, 359-363 Bolted contact, 182, 183 Booster, 452 Bore of polepieces, 209, 210 Bottom-insulation of commutator, i?i Brass, current-densities for, 183 for brushes, 173, 176 for commutators, 169 for dynamo-base, 300 safe working load of, 189 Breadth of armature section, 92 of armature-spokes, 189, 516 of beltand pulley, 193-195, 517 of brush-contact, 175, 514 Breslauer, Dr. Max, on hysteresis- loss in toothed armatures, 591 Bristol-board, for armature-insu- lation, 85 Brunswick, on variation of air- gaps, 483 Brush, multi-circuit arc dynamo, 4620 Brushes, adjustment of, 696 arrangement of, on commuta- tor, 169, 170, 174 best tension for, 176-180, 515 dimensioning of, 175, 176, 515 displacement of, 30 material and kinds of, 171-174 number of, for multipolar dynamos, 34 Brush-holders, 181 Buck, H. W., on commutator- brushes, 177 Bullock Electric Mig. Co.'s teaser system of motor control, 452^ Burke, James, on insulating ma- terials, 86 Butt-joints in magnet-frame, 306 Cables, stranding of, 686, 687 size and weight of, Table, 688 Calculation of armature, 45~ 1 95, 413-416, 505,527, 552, 566, 580, 587, 603, 629, 638, 644, 652, 656 of dynamotors, 452, 655 of efficiencies, 405-410, 526, 546, 565, 578, 602, 636, 643 of field magnet frame, 313- 327, 517, 534, 557, 572. 583, 593, 607, 632, 639, 646, 657 of generators for special pur- poses, 455-463 of leakage-factor, 217-203, 519, 536, 559. 573, 584, 595,609, 614-628, 633 of magnetic flux, 200-216, 708 INDEX. 517, 531, 554, 568, 581, 589, 605, 638, 645, 657 Calculation of magnetizing forces, 339-356, 520, 537, 547, 560, 575, 585, 596, 610, 634, 640, 647, 654, 658 of magnet-winding, 359-401, 486-497, 522, 540, 549, 562, 576, 599, 612, 635, 640, 649, 654. 659 of motors, 419-442, 628, 652 of railway motors, 431-442, 500-502 of unipolar dynamos, 443- 451, 652 Canfield, M. C., on disruptive strength of insulating mate- rials, 86 Canvas, for armature-insulation, 78, 79 Capacity, maximum safe, of arma- ture, 132-135 of railway motor equipment, 440-442 Carbon-brushes, 171-180, 183 Card-board (press-board) for arma- ture-insulation, 78, 79, 80, 85 Carrying capacity of circular cop- per rods. Table, 682 of copper wires, Table, 681 Cast iron, in, 178, 189, 288, 312, 313, 448 Cast steel, in, 189, 288, 293, 448 Cast-wrought iron, or mitis metal, in, 294, 312, 313 Causes of sparking, see Sparking. C.-G.-S. units, 7, 47, 199, 332, 333 Characteristic curves, 476-483 Charging accumulators, dynamos for, 91, 92, 461, 462 Checks on armature calculation, .130, 132, 135 Cheese-cloth, varnished, for arma- ture-insulation, 85 Chord-winding, or surface ring winding, 35, 89, 99, 165 Circuit, closed electric, 6, 317 magnetic, 317, 331 Circumflux of armature, 131 Clamped contact, 182, 183 Classification of armatures, 4 of armature-windings, 143, 144 of dynamos, 35, 269, 270 of field-magnet frames, 269, 270 of inductions, 23 Clearance between armature and pole-face, 209, 210 Clearance between pole-corners, 207, 208 Closed coil winding, 143, 144, 458 Coefficient, see Factor. Coil, closed, moving in magnetic field, n, 12 Coils, number of, in armature, 87-89 short-circuited, in armature, 28, 30, 149, 174, 175, 298 Coil-winding calculation, 359-373 Collection of- current, by means of collector rings, 12 by means of commutator, 13 energy-loss in, 176-180 sparkless, see Sparking. Collection of large currents, 174 Collector, see Commutator. Combination brushes, 173, 174 Combination-frames, advantages of, 294 calculation of flux in, 260, 261, 621 joints in, 306-309 Combination-method of speed con- trol for railway motors, 436 Combination of shunt-coils for series field regulation, 378- 382, 523-526 Commercial or net efficiency, 406- 409, 422, 526, 546, 578, 602 copper, specific resistence of, 104, 105 wrought iron, permeability of, 311 Commutation, act of, 29 effect of, in generator and motor, 30 sparkless, in toothed and per- forated armature, 62 sparkless, promotion of, 30, 62, 172, 173, 297, 298, 299, 459, 463-470, 471, 472 Commutator, construction and di- mensioning of, 168-170, 514 principle of, 13 14 thickness of insulation for, 171 trueing of, 699 Commutator-divisions, difference of potential between, 88, 151 number of, 87, 88 Compactness of railway motors, 432 Comparison of bipolar and multi- polar types, 487*5 of efficiency-curves of motors, 431 INDEX. 709 Comparison of various types of dynamos, 248-256 Compensating ampere-turns, 348 Compound-dynamo, constant po- tential of, 43 efficiency of. 42, 43, 406, 408 E. M. F. allowed for inter- nal resistance of, 56 Compound-dynamo, fundamental equations of, 41, 42, 43 over-compounding of, 43, 396 total armature current in, 109 Compound-motor, 406, 408, 426, 428, 644 Compound-winding, calculation of, 395-401, 456, 549, 503, 599, 649 principle of, 41-43 Conductivity, electrical, of copper and iron, 119 Conductor, armature-, see Arma- ture-Conductor. describing circle in magnetic field, 8 motion of, in uniform mag- netic field, 5 Conductor-velocities, 52 Connecting-formula for armature- winding, 152-155 Consequent poles, 275, 286, 327, 603 Constant current dynamos, see Arc-Lighting dynamos. excitation in compound dy- namo, 43 potential dynamos, 43 power work, motors for, 429, 431, 628 speed motors, 63, 426, 427 Construction-rules for field-frame, 288-309 Contact-area of commutator- brushes, 169, 174-176 Contact-resistance of commutator- brushes, 177-180 Contacts, various forms of, 181- 183 Continuous current, production of, 13, 14, 22 Conversion, efficiency of, see Effi- ciency, Gross. of motor into generator, 419, 628, 637, 644 Conveying parts, 181-183 Cooling surface, see Radiating Surface. Copper, current-densities for, 183 physical properties of, 101, 104, 113, 362 Core, see Armature Core or Mag- net Core, respectively. Corsepius, on magnetic leakage, 262 Cost of dynamos, 288, 289, 300, 411, 412 Cotton, for armature-insulation, 78,85 Cotton covering on wires, insulat- ing properties of, 85 weight of, 103, 367 Counter Electro-Motive Force, 421, 423. 434, 438, 453, 461 Magneto-Motive Force, see Armature-Reaction. Cox, E. V., on Commutator- brushes, 177 Critical brush-tension, 176-179, 5'5 Crocker, Professor F. B., on high- potential dynamos, 462 on unipolar dynamos. 25, 26 Crocker Wheeler bipolar motors, dimensions of, 664 multipolar dynamos, dimen- sions of, 668 Cross-connection of commutato- bars, 35, 155 Cross-Induction, see Armature Re- action. Cross-Magnetization, see Arma- ture Reaction. Cross-Section, see Sectional Area. Crowding of magnetic lines in polepieces, 295 Current, alternating, 12, 13 collection of, from armature coil, 12 commutated, fluctuations of, 14-21 constant, see Constant Cur- rent. direction of, in closed coil, 12 in electric motors, 427-429, 642 in single inductor, 10 Current- density, circumferential, of armature, 130-132 in armature-conductor, 56, 57 in magnet-core, 364, 365 permissible, in materials* 183 Currents, eddy, or Foucault, see Eddy Currents. Curve of average E. M. F. in- duced in armature, 19 of E. M. Fs., rectified, 14 of induced current, 13 of induced E. M. F., 13 Curves, characteristic, 476-483 7 io INDEX. Curves of contact-resistance and friction of commutator- brushes, 177, 178 of eddy current factors, 121 of hysteresis factors, 114 of potentials around arma- ture, 32, 33 of relative hysteresis-heat in armature-teeth, 68 of specific temperature-in- crease in armature, 128 of temperature-effect upon hysteresis, 117 Cutting of magnetic lines, 3, 5, 6, 8, 9, 12, 22, 27, 47, 48, 52, 200, 20 1 Cycle of magnetization, 109, no, in, 113, 115, 119, 121 Cylinder armature, see Drum Ar- mature. Cylindrical magnets, 232, 234, 291, 318, 319, 320, 323, 369, 374, 375 Data for winding armatures, 155- 167, 678 for winding magnets, 679 general, of railway motors, 435 Dead wire on armature, 94 Deflection of lines of force in gap- space, 225, 230, 349, 456 Definition of armature, 4 of closed and open coil wind- ing, 143 of dynamo-electric machine, 3 of generator, 3 of magnetic units, 199 of motor, 3 of unipolar, bipolar, and mul- tipolar induction, 23 of unit induction, 47 Demagnetizing action of arma- ture, see Armature-Reaction. Density of current, 56, 57, 132, 133, 183 of magnetic lines, 54, 91, 313 Depth of armature-core, 92, 341, 342 of armature-winding, 70, 71, 74. 75 of magnet-winding, 317, 361, 371, 375, 377, 386, 387 Design of current conveying parts, 181-183 of generators for special pur- poses, 455-463 Design of magnet-frames, 270- 309 of motors for different pur- poses, 429, 430 of railway motors, 432 Developed winding diagrams, 146, 147 Diagram of closed coil armature- winding, 144 of doubly re-entrant winding, .150 of duplex winding, 149 of drum-wound ring arma- ture, 101 of lap-winding, 145, 146 of long shunt compound- wound dynamo, 42 of mixed winding, 147 of open coil armature wind- ing, 144 of ordinary compound-wound dynamo, 41 of parallel armature winding, 165, 1 66 of series armature winding, 157 of series winding with shunt- coil regulation, 378 of series-wound dynamo, 36 of shunt-wound dynamo, 38 of simplex winding, 149 of singly re-entrant winding, 150 of spiral winding, 145 of wave winding, 146, 147 Diamagnetic materials, permea- bility of, 311 Diameter of armature-core, 58,60, 61 of armature-shaft, 184-187, 516 of armature-wire, 57 of commutator brush-surface, 168, 514 of heads in drum armatures, 124 of magnet wire, 361, 362, 365 of pulley, 191, 517 Dielectrics, properties of, 83-86 Difference of potential, see Elec- tro-Motive Force. Differentially wound motor, 647, 648 Dimensions of armature-bearings, 184, 191, 516 of armature-core, 58-86 of belts, 194, 517 of driving-spokes, 188-190, 5i6 of magnet-cores, 319-324 INDEX. Tit Dimensions of toothed and per- forated armatures, 65-72 of unipolar dynamos, 443- 446, 652 see also Length, Breadth, Diameter, Sectional Area, etc. Direct-driven machines, 52, 61, 91, 132, 134, 136, 185, 187, 192 Direction of current, 10, 30 of K. M. F., 9 of rotation, 10, 12, 422 Disadvantages of laminated pole- pieces, 292 of multiple magnetic circuits, 286, 290 of multipolar frames for small dynamos, 285 of paper -insulation between armature-laminae, 93 of toothed and perforated ar- matures, 61, 62 Disc-armature, definition of, 4 Disruptive strength of insulating materials, 83, 84, 85 Dissipation of energy in armature core, i 10-122 in armature winding, 108, 109 in magnet winding, 370, 372 Distance between magnet-cores, 320-324 between pole-corners, 207, 208 Distortion of magnetic field, 225, 230, 349, 456 Distribution of flux in dynamo, 397-399 of potential around armature, 3i, 33 Division-strips in drum armatures, 73 Dobrowolsky's pole-ring, 49, 296 Double-current generators, 462^ Double horseshoe type, classifica- tion of, 269, 276 magnetic leakage in, 242, 252, 253, 263 Double magnet multipolar type, 270, 283 Double magnet type, classification of, 269, 275, 276 leakage factor of, 252, 254, 263 permeance across polepieces, in, 240. 242 permeance between magnet cores in, 237, 238 permeance between pole- pieces and yoke in, 246, 247 Doubly re-entrant armature-wind- ing, 150, 156, 160, 161 Drag, magnetic, see electro-dy- namic force, 63, 64 Draw-bar pull of railway motors, 440-442 Driving-horns for drum arma- tures, 73, 140 Driving-power for generator, 408, 420 Driving-spokes for ring armatures, 186, 188-190, 516 Drop of voltage, 37, 39, 43 Drum armature dimensions, Table of, 671 armatures, allowance for di- vision-strips in, 60 bearings for, 191 core densities for, 91 definition of, 4 diameters of shafts for, 186 heating of, 129, 130 height of winding in, 75 insulation of, 78, 79 radiating surface of, 123-125 size of heads in, 123, 124 speeds and diameters of, 60 total length of wire on, 95 Drum-wound ring armatures, 35, 89, 99- 165 Duplex, or double, armature wind- ing, 149, 151, 156, 160, 166, 167 Dynamo-electric machines, defini- tion of, 3 Dynamo-graphics, 476-502 Dynamo speeds, high, medium and low, Table of, 52^. Dynamos, bipolar, see Bipolar Dynamos. constant current, see Arc- Lighting Dynamos. Electro-plating, Electro-typ- ing, etc., see Electro- Metal- lurgical Dynamos. for charging accumulators, 91, 92, 461, 462 list of, considered in prepara- tion of Tables, see Preface iii-v. multipolar, see Multipolar Dynamos. unipolar, or homopolar, see Unipolar Dynamos. Dynamos of various Manufactur- ers: Aachen Electrical Works, 277 Actien-Gesellschaft Elektrici- tatswerke, 273, 274, 278, 281 712 INDEX. Dynamos of various Manufactur- ers Con ttnued. Adams, A. D., see Commercial Electric Co. Adams Electric Co., 270 Akron Electric Manufacturing Co., 275 Alioth, R., & Co., 281 Allgemeine Electric Co., 49, 281 Alsacian Electric Construction Co., 281 Atkinson, see Goolden & Trot- ter Aurora Electric Co., 272 Bain, Force, see Great Western Electric Co. Baxter Electrical Manufactur- ing Co., 276, 281 Belknap Motor Co., 272, 280 Berliner Maschinenbau Actien- Gesellschaft, 273, 281 Bernard Co., 271 Bernstein Electric Co., 274 Boston Fan Motor Co., 274 Brown, C. E. L., see Oerlikon Machine Works. Brush Electrical Engineering Co., 278, 282, 283 Brush Electric Co., 276, 459 "C. & C." (Curtis & Crocker) Electric Co., 270, 276, 282, 283 Card Electric Motor and Dy- namo Co., 272, 274, 278 Chicago Electric Motor Co., 274 Clarke, Muirhead & Co., 272 Claus Electric Co., 280 Columbia Electric Co., 271, 280 Commercial Electric Co., 275 Crocker-Wheeler Electric Co., 272, 280, 398, 664, 668 Crompton & Co., 276, 277 Cuenot, Sauter & Co., 282 Dahl Electric Motor Co., 281 "D. & D." Electric Co., 274 De Mott Motor and Battery Co., 275 Desrozier, M. E., 282 Detroit Electrical Works, 271, 27? Detroit Motor Co., 272 Deutsche Elektricitatswerke, 278, 281 Dobrowolsky, M. von Dolivo-, see Allgemeine Electric Co. Donaldson-Macrae Electric Co., 273 Duplex Electric Co., 275, 285 Eddy Electric Manufacturing Co., 280 Dynamos of various Manufactur- ers Contin ued. Edison General Electric Co.,i68, 270, 284, 305, 398, 435, 458, 621, 665 Edison Manufacturing Co., 275, 278 Eickemeyer Co., 277 Elbridge Electric Manufactur- ing Co., 274 Electrical Piano Co., 275 Electro-Chemical and Specialty Co., 282 Electro-Dynamic Co., 276 Electron Manufacturing Co., 170, 271, 274, 284 Elektricitats-A c t i e n-G e s e 1 1- schaft, 281 Elliot-Lincoln Electric Co,, 284 Elphinstone & Vincent, 284 Elwell-ParkerElectricConstruc- tion Corporation, 277, 284 Erie Machinery Supply Co., 278 Esson, W. B., see Patterson & Cooper. Esslinger Works, 283 Excelsior Electric Co., 272, 273, 459 Fein & Co., 275, 276, 277, 281 Fontaine Crossing and Electric Co., 276 Ford-Washburn Storelectric Co., 276 Fort Wayne Electric Corpora- tion, 170, 274, 277, 280, 283, 458 Fritsche & Pischon, 282 Fuller, see Fontaine Crossing and Electric Co. Garbe, Lahmeyer & Co., see Deutsche Elektricitatswerke. Ganz & Co., 273, 281 General Electric Co., 270, 277, 278, 280, 282, 284, 435, 667, 669 General Electric Traction Co., 275 Goolden & Trotter, 274 Granite State Electric Co., 277 Great Western Electric Manu- facturing Co., 273, 280, 458 Greenwood & Batley, 274 Giilcher Co., 170 Helios Electric Co., 276, 282 Henrion, Fabius, 282 Hochhausen, see Excelsior Elec- tric Co, Holtzer-Cabot Electric Co., 272, 274 Hopkinson, Dr. J., see Mather and Platt. INDEX. 7'3 Dynamos of various Manufactur- ers Continued. Immisch & Co., 276, 618 India Rubber, Guttapercha and Telegraph Works Co., 272 Interior Conduit and Insulation Co , 277, 283 Jenney Electric Co., 273 ^[enney Electric Motor Co., 274 [[ohnson & Phillips, 273 Johnson Electric Service Co., 278 Kapp, Gisbert, see Johnson & Phillips. Kennedy, Rankine, see Wood- side Electric Works. Keystone Electric Co., 272, 275 Knapp Electric and Novelty Co., 272 Kummer, O. L. & Co., see Ac- tien-Gesellschaft Elektrici- tatswerke. Lahmeyer, W., see Aachen Electrical Works. Lahmeyer, W. & Co., see Elek- tricitats-Actien-Gesellschaft. Lafayette Engineering and Electric Works, 278 La Roche Electrical Works, 272, 277 Lawrence, Paris & Scott, 276 Lundell, Robert, see Interior Conduit and Insulation Co. Mather & Platt, 272, 276 Mather Electric Co., 275, 280, 281 Mordey, W. H., see Brush Elec- trical Engineering Co. Muncie Electrical Works, 278 Naglo Brothers. 274, 275, 276, 281 National Electric Manufactur- ing Co., 272 Novelty Electric Co., 271 Oerlikon Machine Works, 276, 278, 281, 435 Onondaga Dynamo Co., 277 Packard Electric Co., 274 Patterson & Cooper, 170, 273, 614 Ferret, see Electron Manufac- turing Co. Porter Standard Motor Co., 274 Preimer Electric Co., 274 Riker Electric Motor Co., 274, 280, 281 Royal Electric Co., 170 Schorcb, 276 Schuckert & Co., 49, 276, 278, 281, 282 Schuyler Electric Co., 459 Dynamos of various Manufactur- e r s Con tin ued. Schwartzkopff, L., see Berliner Maschinenbau Actien-Gesell- schaft. Shawhan-Thresher Electric Co., 278, 280 Short Electric Railway Co., 282, 283, 435 Siemens & Halske Electric Co., 168, 170, 273, 275, 281 Siemens Brothers, 272 Simpson Electric Manufactur- ing Co., 274 Snell, Albion, see General Elec- tric Traction Co. Sperry Electric Co., 458 Sprague Electric Co., 398 Stafford & Eaves, 278 Standard Electric Co., 280, 458 Stanley Electric Manufacturing Co., 280 Storey Motor and Tool Co., 170, 284 Thomson-Houston Electric Co., 277. 458, 624 Thury, see Cuenod, Sauter & Co. Triumph Electric Co., 170, 278 United States Electric Co., 274, 276 Waddell-Entz Co., 283 Walker Electric Manufacturing Co., 170, 280, 435 Wenstrom Electric Co., 278, 284 Western Electric Co., 276, 458 Westinghouse Electric and Man- ufacturing Co., 280, 435, 666 Weston, see United States Elec- tric Co. Wood, see Fort Wayne Electric Corporation. Woodside Electric Works, 274 Zucker & Levitt & Loeb Co., 281 Zucker & Levitt Chemical Co., 271 Zurich Telephone Co., 273, 278, 281,285 Dynamotors, 452-454, 655 Ebonite, see Hard Rubber. Ecentricity of polefaces, 298 Economic coefficient, 406-409 Eddy Co., Equalizing system, 4520 Eddy currents in armature con- ductors, 107, 119 INDEX. Eddy currents in armature core, 107, 119-122 in polepieces, 295 Edge-insulation of armature, 79, 82 Edison bipolar dynamos, dimen- sions of, 665 Edser, Edwin, on magnetic leak- age, 262 Effective height of armature wind- ing, 74 of magnet winding, 377 Effective length of armature con- ductor, 49 Effects, mechanical, of armature winding, 137-142 Efficiencies, average, of electric motors, 422 Efficiency, commercial, or net, 406-409, 422, 526, 546, 565, 578, 602 electrical, 37, 38, 39, 40, 42, 43. 405, 406, 422, 526, 546, 565, 578, 602 gross, 409, 410, 422, 526, 546 of armature as an inductor, 135 relative, of magnetic field, 211-214, 512, 533, 557, 572 space-, of various railway motors, 435 weight-, 33, 410-412, 527, 546, 565, 578, 602 Effort, horizontal, of railway mo- tors, 440-442 Electro-dynamic force, seat of, in toothed armatures, 63, 64 Electro-magnet, see Magnet. Electro- metallurgical dynamos, designing of, 459-461 field-density for, 54 magnetic density in armature of, 91, 92 unipolar forms of, 25, 652 Electro-motive Force, addition of, in closed coil, 12 allowed for internal resist- ances, 56 at various grouping of con- ductors, 151 average, 8, 9, 19, 20, 21 direction of, 9 fluctuation of, 19 magnitude of, 6 production of, 4 Elliptical bore of field, 296 magnet-cores, 289, 291 Embedding of armature-conduc- tors, see Perforated Armature. Emission of heat from armature, 126, 127 Empirical formula for heating of drum armatures, 129 Enamel, for armature-insulation, ?8, 94 End-insulation of commutator, 171 End-rings for armature, 188, 590 Energy-dissipation, see Dissipa- tion of Energy. Energy-loss, specific, in armature, 126-128 in magnets, 368, 371, 372 Energy-losses in armature, 107- 122 in collecting armature cur- rent, 176-180, 515 in magnets, 366, 368, 372, 375, 383, 399. 400, 577 Equalizing dynamo, 452^ Equations, fundamental, for dif- ferent dynamos, 36-43 Equivalents of wires, Table of, 684-685 Esson, W. B., on capacity of ar- matures, 131 on magnetic leakage, 262 Evenness, degree of, of number of conductors for series wind- ings, 159-163 Ewing, Professor J. A., on hys- teresis, no, 115 on magnetism of iron, 335 on permeability of cast-steel, 289 Examples, 158, 162, 167, 249-256, 481, 488, 492, 495, 501. 505^-660 Excitation of field-magnetism, methods of, 35 Exploration of magnetic field, 31 of magnetic flux, 397, 398 Exponent, hysteretic, 116 of output-ratio, 416, 417 External characteristic, 476 Extra-resistance, 383, 384, 385, 393, 540 Face-connection of drum-wound ring armature, 101 Face-insulation of armature-core, 79, 82 Face-type commutator, 168 Factor of armature ampere-turns, 480 of armature reaction, 352 of brush-lead in toothed and perforated armatures, 350 INDEX. 715 Factor of core-leakage in toothed and perforated armatures, 219 of eddy-current loss, 120-122 of field-deflection, 225, 230 of hysteresis-loss, 112, 113, 115 of magnetic leakage, 215, 217- 265 of safety, 189, 190 Faults, remedy of, in dynamos and motors, 695-704 Fay, Thomas J., on constant speed motors, 427 Feather-keys, 309 Feldkamp motor, 275 Fibre, vulcanized, for armature- insulation, 79, 84, 85 Field-area, effective, 204, 207 Field-bore, diameter of, 209, 210 Field-density, actual, of dynamo, 202, 204, 205, 206 definition and unit of, 199 practical values of, 54 Field-distortion, 225, 230, 349, 456 Field-efficiency, 211-213 Field-excitation, methods of, 35-43 Field-magnet frame, see Magnet- Frame. Field, magnetic, see Magnetic Field. unsymmetrical, effect of, on armature, 140-142, 513, 534 Finger-rule for direction of cur- rent and motion, 10 Firms, see Dynamos of various Manufacturers. Fischer-Hinnen, J., on dynamo- graphics, 487, 497, 500 on prevention of armature- reaction, 464 Fitted contact, 182, 183 Fittings (brush holders, conveying parts, switches, etc.), 181-183 Flanges for magnet-cores, 308, 523, 542, 576, 595, 650 on field-frames, 287 Flat-ring armatures, 93 Fleming, Professor J. A., on eddy current loss. 121 on rule for direction of cur- rent, 10 Flow of magnetic lines, see Flux. Fluctuations of E. M. F. of corn- mutated currents, 14-21 Flux-density, magnetic, in air- gaps, 54 in armature-core, 91 in magnet-frame, 313 Flux, distribution of, in dynamo, 397-399 Flux, magnetic, 199, 331 total, of dynamo, 214, 257- 261 useful, of dynamo, 92, 133, 2tx>-202, 211-214 Foppl, A., on hollow magnet- cores, 292 Forbes, Professor George, on leakage formulae, 216 on prevention of armature- reaction, 465 Force, attractive, of magnetic field, 140, 141, 513, 534 electro-dynamic, in toothed armatures, 63, 64 Electro-Motive, see Electro- motive Force. horizontal, exerted by railway motor, 440-442 magnetizing, see Magnetiz- ing Force. peripheral, of armature-con- ductors, 138-140, 188, 513, 534 thrusting, on armature, 140- 142, 513, 534 tangential, at pulley-circum- ference, 193, 287 due to brush -friction, 179, 515 Ford, Bruce, on unipolar dyna- mos, 25 Forged steel, 448, 450 Forms of cross-section for magnet- cores, 289-291 of dynamo-brushes, 172-174 of field magnet frames, 269- 287 of fields around ring arma- ture, 98 of polepieces, 30, 295-299 of slot-insulation for toothed and perforated armatures, 81 of unsymmetrical bipolar fields, 142 Formulae for dimensions, wind- ing data, etc., see Dimensions, Diameter, Length, Breadth, Sectional Area, Number, etc. fundamental. 7, 8, 9, 36-43, 55, 57. 200, 201, 219, 314, 334, 377, 385 Foucault currents, see Eddy Cur- ents. Four-coil armature, 17, 18 Fourpolar double magnet type, 240, 270, 285 iron-clad type, 236, 255, 263, 270, 284, 603 Frame, see Magnet Frame. Frequency, no, in, 119, 287^: 716 INDEX. Friction, losses by, 406-409, 526, 546, 565, 578, 602, 636, 643, 651 of commutator-brushes, 176- 180 Fringe of magnetic field, 29, 30 Frisbee, Harry D., on distribution of magnetic flux, 397 Front-pitch of magnetic-winding, 159-167 Fundamental calculations for ar- mature winding, 47-57 equations for different excita- tions, 36-43 permeance formula, 219 Gap, see Air Gap. Gap-circumference, effective, 135 Gauges of wire, 103, 367 Gauss, the unit of magnetic den- sity, 199 Gauze brushes, 171, 173 Gearing of railway motors, 433 Gearless railway motors, 434 General Electric Co 's generators, dimensions of, 667, 669 Generation of E. M. F., 4, 22, 47 Generator, electric, definition of, 3 German Silver rheostat coils, Table of, 690 " Giant " dynamo, 272 Gilbert, the unit of magnetomo- tive force, 333 Grade of railway track, 440, 441 Graphic methods of dynamo-cal- culation, 476-502 Grawinkel & Strecker, on forms of field-magnets, 273, 274, 275, 276, 278, 281, 282 Griscom motor, 276 Gross Efficiency, 409, 410, 422, 526 Grotrian, Professor, on hollow magnet-cores, 291 Grouping of armature-coils, 147 of magnetic circuits, 353-356 Gun-metal, 169 H Hard rubber, 85 Hardness, magnetic, no Head in drum-armatures, 123, 124 Heat, effect of, on hysteresis, 117 on insulation-resistance, 85 Heating of armatures, 127, 129, 130, 132, 699 of bearings, 701 Heating of commutator and brushes, 700 of magnet-coils, 368-371. 699 Height of armature winding, 70, 7i, 74, 75 of magnet winding, 317, 361, 371, 375, 377, 386, 387 of polepieces, 326 of zinc blocks, 301-303, 536 Hering, Carl, on unipolar dyna- mos, 25 Herrick, Albert B., on insulating materials, 86 Heteropolar induction, 23, 26 High-potential dynamos, 462, 463 High-speed dynamos, 52^, 60, 91, 132, 134, 136, 185, 187, 192, 193 Hill, Claude W., on strength of reversing field, 471 Hobart, H. M., on armature wind- ing, 156 Holes in core-discs, see Perforated Armature. Hollow magnet-cores, 290-292 Homopolar dynamos, see Unipolar Dynamos. Hopkinson, Dr. J., on hysteresis, no Hopkinson, J. & E., on magnetic leakage, 262 Horizontal effort of railway mo- tors, 438-442 magnet types, 238, 239, 245, 246, 251, 253, 254, 263, 269, 270, 273, 275, 276, 277, 284, 285 Horns for driving drum armatures, 73, 140 of polepieces, see Pole-Tips. Horsepower, the unit of work, 137 Horseshoe types, leakage factors of, 249-251, 252-254, 263 permeance across polepieces in, 238, 242 permeance between magnet cores in, 231-233 permeance between pole- pieces and yoke in, 245, 246 Huhn, George P. , on distribution of potential, 32 Hysteresis, definition of, no variation of, with density of magnetization, 116 variation of, with tempera- ture, 118 Hysteresis-heat.specific, in toothed armatures, 69 Hysteresis-loss in armature, cal- culation of, 107, 109-118, 591 INDEX. 7'7 Hysteretic exponent, 116 resistance, no, in Ideal position of brushes, 29 Impurities in cast steel, 288, 289 Incandescent generators, large, field-densities for, 54 magnetic density in armature of. 91 shunt-excitation of, 39 Inclined magnet types, 232, 269, 276 Induction, electro-magnetic, 3, 5, 22, 23, 47, 48, 405, 423 Inductor, see Armature Conduc- tor. Ineconomy of small dynamos, 472 Innerpole types. 131, 168,263,264, 269, 270. 281, 282, 287, 566, 580 Insulating materials, properties of, 83-86 Insulation, between laminae of armature core, 93, 94 of armature, resistance of, 86, 510 of armature, thickness of, 82 of commutator-bars, 171 of magnet-cores, thickness of, 543, 565, 576 weight of, on round gauge wire. 103 Intake of motor, 405, 420 Integrated curve of potentials, 32, 33 Intensity, see Density. Intermittent work, motors for, 429-431,637 Internal characteristic. 476 Inventors, see Dynamos of various Manufacturers. Inverted horseshoe type, 240, 241, 246, 250, 263, 264, 269, 272, 286, 299, 614 Iron-clad types, classification of, 269, 270, 277, 278, 284 leakage-factor for, 255, 256, 263 permeance across polepieces in, 243 permeance between magnet cores in, 234-237 permeance between pole- pieces and yoke in, 247 Iron, for armature-cores, 93, 94, 1 10. 113, 115, 118, 119, 120, 121, 122 for magnet-frame, 30. 288, 289, 293, 294, 300, 305-309 Iron, hysteretic resistance for va- rious kinds of, in permeabil ity of different kinds of, 310-313 projections, effect of, in mag- netic field, 64 specific magnetizing forces for different kinds of, 336-338 wire, for armature-, and mag- net winding, 472-475 wire, for armature-cores, 93, 94, no, 113. 115 wire, for rheostats, 689 Ives, Arthur Stanley, on magnetic leakage, 262 Jackson, Professor Dugald C., on ratio, cross-section, 292, 293 Japan (enamel) for armature-insu- lation, 78, 94 Joints in magnetic circuit, 305-309 Journals, calculation of, 184, 186, 187, 190, 191, 192, 303-305, 5i6 friction in, 406-409. 526, 546, 565, 578, 602, 636, 643, 651 K Kapp, Gisbert, on diametral cxir- rent density of armature, 133 on magnetic leakage, 216 on permeability of cast steel, 289 Kelvin, Lord, see Thomson, Sir William. Kennedy, Rankine, on shape of polepieces, 299 Kennelly, A. E., on magnetism of iron, 335 on seat of electro-dynamic force in iron-clad armatures, 64 "King" dynamo, 271 Kittler, Professor Dr. E., on forms of field magnets, 273, 275, 276, 277, 281. 282. 283, 285 Klaasen, Miss Helen G., on hys- teresis, 115 Knee of saturation curve, 312 Knight, Percy H., on magnetism of iron, 335 Kolben, Emil, on railway motor construction, 431 on worm-gearing for electric motors. 434 Kunz, Dr. W., on hysteresis, 116 7 i8 INDEX. Lag, angle of, 30, 421 Lahmeyer, W., on magnetic leak- age, 262 Laminated joint, 182 Lamination of armature core, 93, 94, 119-122 of polepieces, 297 Lap-, or loop-, winding. 144, 145, 152 Law of armature-induction, 47, 48, 49 of conductance, 219 of cutting lines of force, 47, 200 of hysteresis, no of magnetic circuit, 331 Ohm's, 36, 41, 384, 393 Layers, number of, of armature wire, 74, 508 Lead of brushes, 30, 349, 350, 421 Leads for current, 181-183, 379, 524 Leakage, magnetic, calculation of, from dimensions of frame, 217-256 calculation of, from machine- test, 257-265 in toothed armatures, 53, 218, 219 Leakage factors, Tables of, 263,265 Leather, safe working strength of, 193 Leatheroid for armature-insula- tion, 79, 85 Lecher, Professor, on unipolar dynamos, 25 Length of armature-conductor, 55, 95- roo of armature-bearings, 190-192 of armature-core, 76 of armature-shaft, 184 of commutator brush-surface, 168, 176, 515 of heads in drum armatures, 123, 124 of magnet-cores, 316-319 of magnetic circuit, 224, 230, 243, 347, 348 of magnet-wire, 360 of mean turn on magnets, 374 Liberation of heat from armature, 126, 127 Limit of armature capacity, 132 of magnetization, 313 Limiting currents for copper wires, 680 Line, neutral, of magnetic field, 225, 459 Line-potential for railway motor, 442 Lines of force, cutting of, 3, 5, 6, 8, 9, 12, 22, 27, 47, 48, 52, 200 definition and unit of, 199 Linseed oil ; for armature insula- tion, 83, 85 Load-limit of armature, 132-135 Localization and remedy of trou- bles in dynamos and motors, 695-704 Long connection type of series armature winding, 157, 158 Long shunt compound winding, 41 Loop winding, 144, 145, 152 Losses in armature, 107-126 in bearings, 406-409, 526, 546, 565, 578, 602, 636, 643, 651 in belting, 409 in commutator-brush-contact, 175, 176-180 Low-speed dynamos, 52, 61, 91, 132, 134, 136, 185, 187, 192 Lubrication of bearings, 305 of commutator, 177, 179 Lugs for connecting cables, 181, 182 M Magnet-cores, dimensioning of, 316-324 general construction rules for. 288-293 relative average permeance between, 231-238 Magnet-frame, classification of types of, 269, 270 dimensioning of , 313-327 general design of, 288-309 magnetizing force for, 344- 348 Magnetic circuit, air-gap in, see Air-Gaps. joints in, 305-309 law of, 331 reluctance of. 331 Magnetic field, definition and unit of, 199 exploration of, 31 fringe of, 29, 30 motion of conductor in, 5 relative efficiency of, 211 Magnetic flux, see Flux. intensity, or magnetic den- sity, 54, 91, 313 INDEX. 719 Magnetic leakage, see Leakage, Magnetic. permeability, 310-312 potential, 224 pull on armature, or arma- ture-thrust, 140-142, 513, 534 reluctance, 331 units, definition of, 199 Magnetization, absolute and prac- tical limits of, 313 influence of, on brush-lead in iron-clad armatures, 350 influence of, on hysteretic ex- ponent, 1 16 influence of, on magnetizing force, 336, 337 Magnetizing force for air-gaps, 339. 340 for any portion of a circuit, 333-338 for armature-core, 340-343 for compensating armature- reaction, 348-352 for field-frame, 344-348 Magnetomotive force, 331 Magnet-poles, number of, for va- rious speeds, Table, 287^ Magnet-winding, calculation of, 359-401, 450, 451, 486-497, 522, 540, 549, 562, 576, 599, 612, 635, 640, 649, 654, 659 methods of excitation of. 35 Magnet-wire (S.C.C.), data of. 679 " Manchester" dynamo, 276 Manganese, in cast steel, 288, 289 Martin & Wetzler, on electric motors, 270 Mass of iron in armature core, no, in, 112, 114, 119, 120 Materials for armature core, 93 for armature insulation, 83-86 for commutator, 169 for dynamo-base, 299, 300 for magnet-cores, 288 for polepieces. 53, 296 Mavor, on magnetic leakage, 264 Maximum efficiency, current for, of motors, 428, 429, 642 electrical efficiency, of shunt- dynamo, 39, 40 safe capacity of armature, 132-135 Maxwell, the unit of magnetic flux, 199, 200 Mean E. M. F., 21 Mechanical calculations about ar- mature, 184-195, 516, 517 effects of armature-winding, 137-142, 513, 534 Merrill, E. A., on capacity of rail- way motors, 438 Metallurgical dynamos, see Elec- tro-Metallurgical Dynamos. Mho, unit of electrical conductiv- ity, 119 Mica, for armature-insulation, 78, 79. 83, 85 for commutator-insulation, 170-171 Micanite, for armature-insulation, 80, 81, 84, 85 Mitis iron, in, 294, 312, 313 Mixed armature winding, 144, 147 Monell, A., on effect of tempera- ture on insulating materials, 86 Mordey, W. H., on prevention of armature-reaction, 465 Motion, relative, between conduct- ors and magnetic fields, 3-12 Motor, electric, calculation of, 419-442, 628-652 definition of, 3 failure of, 704 Motor-generators, 452 Multi-circuit arc dynamos, 4620 Multiple circuit winding, 148, 151, 152, 154 Multiplex, or multiple, winding, 149, 150, 151, 160, 165 Multipolar dynamos, classification of, 269, 270, 279-285, 287 connecting formula for, 154, 155 economy of, 33 field-densities for, 54 kinds of series windings pos- sible for, 156 number of brushes for, 34, 102 permeance across polepieces in, 243, 244 permeance between magnet cores in, 233, 234 permeance between pole- pieces and yoke in, 247, 248 Multipolar types, practical forms of, 279-285 Monroe and Jamieson, on insula- tion-resistance of wood, 85 Muslin, for armature-insulation, 79.85 N Negbauer, Walter, on magnetism of iron, 335 Net- efficiency, 406-409 Neutral points, 148, 459 726 IfrDEX. Noises in dynamos, causes and prevention of, 701 Normal load, calculation of mag- netizing force for, 396 Number of ampere-turns, 333-352 of armature circuits in multi- polar dynamos, 49, 104 of armature conductors, 76, 77, i59-i 6 3 of armature divisions, 90 of brushes in multipolar ma- chines, 34, 102 of coils in armature, 15-21, 87, 90, 153-155, 158-163 of commutator divisions, 87 of convolutions per commu- tator division, 89 of cycles of magnetization, IIO, III, 112, Iig, 121 of layers of wire on arma- ture, 74, 508 of lines of force per square inch, 54, 91 of pairs of magnet poles, 48, 51, 53, 287^ of reversals of E. M. F. in one revolution of conductor, 22, 23 of revolutions of armature, 58, 60, 61 of slots in toothed and per- forated armatures, 65, 66, 70, 71 of useful lines of force, 7, 9, 92, 133, 200-202, 211-214 of wires per layer on arma- ture, 72, 73, 74 Oersted, the unit of magnetic re- luctance, 333 Ohm's law, 36, 41, 384, 393 Oiled fabrics (paper, cloth, silk) for armature insulation, 78, 85 One-coil armature, 15, 20 One-material magnet frame, cal- culation of flux in, 259, 614, 618, 624 joints in, 305, 306, 307 Open circuit, calculation of mag- netizing forces for, 395 Open-coil winding, 143, 144, 458 Ordinary compound dynamo, 41 Outer inner-pole type, 270, 283 Outerpole types, 269, 270, 280, 281, 287, 304 Output, formulae for, 405, 420, 438 maximum, of armature, 132- 135 Output of dynamo as a function of size, 416-418 Oval magnet cores, 232, 234, 289, 291, 318, 322, 374 Over-compounding, 43, 396 Over-type, 272, 278, 304 Owens, Professor R. B., on closed coil arc dynamo, 455 Oxide coating for insulating ar- mature-laminae, 93, 94 Paper, for armature insulation, 78, 85, 94 Paraffined materials, for armature insulation, 83, 85 Parallel, or multiple circuit, arma- ture winding, 148, 151, 152, 154 Parchment, for armature insula- tion, 85 Parmly, C. H., on unipolar dyna- mos, 25 Parshall, H. F., on armature windings, 156 on use of steel in dynamos, 288 Pedestals for dynamos, 142, 303 Perforated armatures, advantages and disadvantages of, 61, 62, 63 core-leakage in, 53, 218, 219 definition of, 4 dimensioning of, 71, 72 effective field area of, 207 insulation of, 81 percentage of effective gap, circumference for, 135 percentage of polar arc for, 50 Peripheral force on armature-con- ductors, 138, 139 on pulley, 193 Peripheral speed of armature, 52, 53 of pulley, 193 Permeability of iron, 310-312 Permeance, law of, 219 relative, across polepieces, 238-244 relative average, between magnet cores, 231-238 relative, between polepieces and yoke, 244-248 relative, general formulae for, 220-223 relative, of air-gaps, 224-230 Permissible current densities, 180 energy-dissipation, in arma- ture, 127 INDEX. 721 Permissible energy-dissipation, in magnets, 372 Perry, C. L., on effect of tempera- ture on insulating materials, 86 " Phoenix " dynamo, 614 Phosphor-bronze, 169, 189, 434 Phosphorus, in cast steel, 288 Physical principles of dynamo- electric machines, 3-43 Picou, on E. M. F. of shunt dy- namo, 485 Pierced core-discs, see Perforated Armatures. Pitch of armature-conductors, 414, 4i5 of armature-winding, 152- 167 of slots in toothed armatures, 65, 7i Plating dynamos, see Electro- Metallurgical Dynamos. Plugs, for switch connections, 182, 183 Points, neutral, on commutator, 148 Polar arc, 49, 203, 207, 210 Pole-armature, 4 Pole-bridges, 296 Pole-bushing, 49, 296 Pole-corners, 207, 208, 298 Pole-faces, eccentricity of, 298 Pole-number for multipolar field- magnets, 287^ Pole-pieces, bore of, 209, 210 dimensioning of, 325-327 magnetic circuit in, 346, 348 material and shape of, 293- 299 Pole-strength, unit of. 199 Pole-surface, 127, 128, 204 Pole-tips, 296, 298 Poole, Cecil P., on simplified method of calculation, 413 Position of brushes, 29, 697 Potential, distribution of, around armature, 31-33 magnetic, 224 Power for driving generator, 420 for propelling car, 440-442 Power-losses, see Energy-losses. Power-transmission, dynamos for, 9 1 - 497 Practical field densities, 54 limit of magnetization, 313 values of armature induction, 50 working densities in magnet frame, 313 Press-board, for armature insula- tion, 78, 79, 80, 85 Pressure, best, of commutator brushes, 176-179, 515 effect of, on joints, 306, 307 electric, see Electro-Motive Force. Prevention of armature-reaction, 463-470 of armature-thrust, 298 of crowding of lines in pole- pieces, 295, 296 of eddy currents in pole- pieces, 297 of sparking, 30, 62, 172, 173, 297, 298, 299, 459, 465, 471, 472 of vibration, 287, 299, 431 Principles, physical, of dynamo- electric machines, 3-43 Production of continuous current, 13, 14, 22 of E. M. F., 4, 5, 47, 48 Projecting teeth, 76, 134, 219, 228, 229 Projections of magnet-frame, 294 Puffer, Professor, on magnetic leakage, 262 Pull, see Force. Pulley, calculation of, 191, 195 O Quadruple magnet type, 270, 285, 299 Quadruplex armature winding, 150 Quadruply re-entrant armature- winding, 150 Qualification of number of con- ductors for various windings, 157-167 R Radial clearance of armature, 209 depth of armature core, 92 multipolar type, 243, 248, 269, 280, 281, 566, 587, 624. 644 Radiating surface of armature, 52, 122-126 of magnets, 369 Radiation of heat from armature, 126, 127 Radi-tangent multipolar type, 270, 282 Railway-generators, adjustment of carbon brushes in, 172 magnetic dens' ty in armature of, 91 722 INDEX. . Railway-generators, toothed arm- atures for, 62 Railway-motors, calculation of, 438-442, 500-502 general data of, 435 magnetic density in armature of, 91 Randolph, A., on unipolar dyna- mos, 25 Ratio of armature- to field ampere- turns, 340, 349 of clearance to pitch in slotted armatures, 230 of core diameter to winding diameter of small armatures, 59 of height of zinc-blocks to length of gaps, 301, 302 of length to diameter of drum armatures, 96, 97 of length to diameter of mag- net-cores, 320-322 of magnet-, to armature cross- section, 292, 293 of mean turn to core diameter of cylindrical magnets, 375 of minimum to maximum width of tooth in iron clad armatures, 592 of net iron section to total cross-section of armature- core, 94 of pole area to armature radi- ating surface, 127 of pole-distance to length of gaps, 208 of radiating surface to core surface of magnets, 371 of shunt-, to armature-resist- ance, 40 of speed-reduction, of rail- way motors, 433, 435 of transformation, of motor- generators, 454, 656 of width of slots to their pitch on armature circumference, 219, 230 of winding-height to diame- ter of magnet core, 317, 371 Reaction of armature, see Arma- ture-Reaction. Rectangular magnet-cores, 233, 289, 291, 318, 321, 369, 374 Rectification of alternating cur- rents, 13, 14 Re-entrancy of armature-wind- ing, 150 Regenerative armatures, reversi- ble, 467 Regulation of arc lighting dyna- mos, 458, 459 of railway motors, 436, 437 of series dynamos, 377-382, 523-526 of shunt dynamos, 390-394, 487-497 Reid, Thorburn, on railway mo- tor calculation, 438 Relation between brush-lead and density of lines in armature- teeth, 350 - between core-leakage and shape of slots in toothed ar- matures, 219 between effective gap circum- ference and polar embrace, 135 between electrical efficiency and ratio of shunt- to armature resistance, 40 between fluctuation of E. M. F. and number of commuta- tor divisions, 19 between horizontal effort and grade, 441 between size and output of dynamos, 416-418 between temperature in- crease and peripheral velocity of armature, 127, 128 between temperature in- crease and winding depth of magnets, 371 between total length of ar- mature wire and ratio of length to diameter of core, 96 Reluctance, 331 Reluctivity, 331 Resistance, hysteretic, of various kinds of iron, in insulation-, of various mate- rials, 85 internal, of dynamo, E. M. F. allowed for, 56 of armature-winding, 102-106 of copper wire, Table, 676- 677 of magnet- winding, 375, 376, 384, 388, 399, 400, 679 Resistance-method of speed-con- trol for railwaj' motors, 436 Reversing field, strength of, 471 Rheostat for regulating series dy- namos, 377-382, 523-526 for regulating shunt dyna- mos, 390-394, 487-497, 543-546 for starting motors, 424 wire for, 689, 690 INDEX. 723 Ribbon armature-cores, 93 copper-, for series field wind- ing, 36, 3?6 Ring-armature dimensions, Table of, 670 Ring-armatures, bearings for, 192 core-densities for, 91 definition of, 4 diameters of shafts for, 187 drum-wound, 35, 89, 99, 165 height of winding space in, 75 insulation of, 80, 81 radiating surface of, 125, 126 speeds and diameters of, 60, 61 total length of conductor on, 98, 99 Ring-winding, 144, 152, 154, 189 Robinson, F. Gge., on disruptive strength of insulating mate- rials, 86 Rockers, 527 Rotary converters, 452^ Rotation, direction of, in genera- tor, 10 in motor, 422, 423 Round magnet cores, 232, 234, 291, 319, 320, 323, 369, 374, 375 Rubber, for armature-insulation, 73, 83, 85 Rule for direction of current, 10 for direction of motion, 10 Running value of armature, 135, 136 Rushmore multi-circuit arc dy- namo, 462^ Ryan, Professor Harris J., on shape of polepieces, 298 on prevention of armature- reaction, 464 Safe capacity of armature, 132-135 peripheral velocities of uni- polar armatures, 448 working strain of materials, 189, 193 Safety, factor of, 189, 190 Salient poles, 275 Saturation, magnetic, 312, 313, 338 Sayers, W. B., on driving force in toothed armatures, 63 on prevention of armature- reaction, 467 Schulz, Ernst, on cast steel mag- net frames, 289 on heating of armatures, 129 Schulz, Ernst, on hollow magnet cores, 292 on lamination of armature core, 93 Screwed contact, 182, 183 Screw-stud, 308 Secondary generators, 452 Sectional area of armature-con- ductor, 57 of armature-core, 92 of magnet-frame, 313-316 of magnetic circuit, 204, 230, 34i, 345, 346 of magnet-wire, 363 of slots in toothed and per- forated armatures, 71 Selection of insulating material, 83 of magnet-type, 285-287, 437 of wire for armature con- ductor, 57, 506, 528, 567, 588, 638, 645 of wire for magnet-winding, 376, 386, 400, 523, 541, 549, 587, 599- 6 49 Self-excitation, failure of, 703 Self-induction, 29, 62, 172, 297,465 Self-oiling bearings, 305 Series dynamo, efficiency of, 37, 405, 407 E. M. F. allowed for internal resistance of, 56 fundamental equations of, 36 Series motor, 406, 408, 428, 429, 436, 628 Series, or two-circuit, armature- winding, 148, 151, 153, 155-164 Series parallel armature-winding, 148, 153 control of railway motors, 437 Series-winding, calculation of, 374-382, 522, 586, 635 principle of, 36, 37 Sever, George P., on effect of temperature on insulating materials, 86 Shaft, calculation of, 184-186, 516 insulation of, 79, 82 Shape, see Form. Sheet iron, for armature cores, 93, 94, no, 113, 115, 120, 121, 122 Shellacked materials, for arma- ture insulation, 85 Short-circuiting of armature-coils, 28, 30, 149. 174, 175, 298 Short-connection type of series winding, 157, 158 Short, Professor Sidney H., on gearless railway motors, 434 724 Shunt-coil regulator for series winding, 377-382, 523-526 Shunt-dynamo, efficiency of, 38, 39, 40, 406, 407, 408 E. M. F. allowed for internal resistance of, 56 fundamental equations of, 38, 39. 40 total armature current in, 109 Shunt, magnetic, across pole- pieces, 296 Shunt-motor, 406, 408, 426, 427, 428, 429, 637 Shunt-resistance, ratio of, to ar- mature-resistance for differ- ent efficiencies, 40 Shunt-winding, calculation of 383-394, 54i, 576, 612, 640, 654, 659 principle of, 37-40 Side-insulation of commutator, 171 Silicon, in cast steel, 288, 289 Silk-covering of wires, weight of, 103 Silk for armature insulation, 78, 85 Simplex, or single, armature- winding, 149, 150, 151, 156, 157, 159, 164, 165 Simplified method of armature- calculation, 413-416 process of constructing mag- netic characteristic, 480 Sine curve, 13, 20 Single horseshoe type, classifica- tion of, 269, 270-273 magnetic leakage in, 231, 232, 239, 240, 241, 245, 246, 249, 250, 251, 263 Single magnet iron-clad type, 237, 263, 269, 278 multipolar types, 263, 270, 283. 580 ring type, 269, 275 type, classification of, 269, 273-275 type, magnetic leakage in, 241, 242, 251, 252, 263 Singly re-entrant armature-wind- ing, 150, 156, 160, 161, 162, 163, 164, 167 Sinusoid, 13 Size, see Dimensions. Skeleton pulleys, for driving ring armatures, 186, 188-190 Skinner, C. A., on closed coil arc dynamo, 455 Slanting pole-corners, 296, 460 Sliding contact, current density for, 183 Slotted armatures, see Toothed Core Armatures. Slotting of polepieces, 297 Smooth core armatures, definition of, 4 effective field area of, 204 factor of field-deflection for, 225 gap-permeance of, 224-227 height of binding-bands on, 75 . height of winding space in, 75 percentage of effective gap circumference for, 135 percentage of polar arc for, 49 Sources of energy-dissipation in armature, 107 of magnetomotive force, grouping of, 353, 354 of sparking, see Sparking. Space-efficiency of railway mo- tors, 435 Spacing of armature-connections, see Pitch of Armature-Wind- ing, 152-167 Span, polar, 49, 203, 207, 210 Sparking, 29, 30, 62, 172, 173, 297, 298, 299, 459, 696 Specific armature induction, 51 energy-loss in armature, 126 energy-loss in magnets, 372 generating power of motor, 425, 636, 642, 651 magnetizing force, 334-338 resistance of insulating ma- terials, 85 temperature increase in ar- mature, 127 temperature increase in mag- net-coils, 371 weight and cost of dynamos, 412 Speed, see Velocity. Speed-calculation of electric mo- tors, 424-427, 636, 642, 651 Speed regulation of railway mo- tors, 436, 437 Speeds, table of, for armatures, 60, 61 Spherical bearings, 304 Spiders for ring armatures, 140, 186, 188-190 Spiral winding, or ring winding, 144, 152, 154, 189 Spokes for ring armatures, 186, 188-190, 516 Spools for magnet-cores, 359-363, 543, 55i INDEX. 725 Sprague motor, 398 1, of : 529 Spread, lateral, of magnetic field, Spring contact, 181, 183 Spur gearing, 433, 435 Square wire, for armature-core, 94 Stansfield, Herbert, on magnetic leakage, 262 Star armature, definition of, 4 " Star " dynamo, 273 Starting resistance, 424 Stationary motor, see Motor. Steel, for armature-shafts, 184-186 for magnet-frame, 288, 293 safe working load of, 189 Steinmetz, Charles P., on arc lighting dynamos, 455 on disruptive strength of dielectrics, 86 on hysteresis, no, 116 on magnetism of iron, 335 Strain, greatest, in belt, 193 permissible specific, in mate- rials, 189, 193 Stranded wire conductors, 36, 105, 181, 183, 376, 528, 549 Stranding of standard cables, Tables, 686, 687 Stratton, Alex., on distribution of magnetic flux, 397 Stray paths of magnetic flux, 218, 300, 398 Street car motors, see Railway Motors. Strength, disruptive, of insulating materials, 83, 84, 85 tensile, of materials, 189, 193 Sulphur, in cast steel, 288 Surface of armature, 122-126 of brush contact, 168, 174- 176, 5M of magnet-coils, 369 Switches, design of, 181-183 Symbols for armature windings, 150 used in formulae, see List of Symbols, xxv-xxxvi. Symmetry of magnetic field, 140, 304 Tables, list of, see Contents ix- xxiv. Tangential multipolar type, 244, 270, 281, 282 pull, see Force, peripheral and tangential. Tape, for armature-insulation, 78 Taper-plugs, 182, 183 Teaser system of motor control, 45 zc Temperature-increase in arma- ture, 126-130 in magnet-coils, 368-371 Temperature, influence of, on hysteresis, 117, 118 on insulation-resistance, 85 Tension, best, for brush-contact, 176-179, 515 safe, in materials, 189, 193 Thickness of armature-insula- tions, 78-82 of armature-laminae, 94, in, 119-122 of armature-spokes, 189, 516 of belts, 194 of commutator-brushes, 174 of commutator-insulations, 171 Thompson, Milton E., on magnet- ism of iron, 335 Thompson, Professor Silvanus P., on circumflux of armature, 131 on diametral current density of armature, 133 on eddy current-loss in arma- ture, 121 on forms of field-magnets, 272, 273, 274, 276, 277, 278, 282, 283 on homopolar and hetero- polar induction, 23 on leakage formulae, 216 on prevention of armature- reaction, 465 on ratio of magnet-, to arma- ture-cross-section, 292, 293 on test of Westinghouse No. 3 railway motor, 435 Thomson, Professor Elihu, on prevention of armature-reac- tion, 469 Thomson, Sir William (Lord Kel- vin), on efficiency of shunt dynamo, 39 Thrusting force, acting on arma- ture, 140-142, 513, 534 . Timmermann, A. H. and C. E., on armature-radiation, 126 Tool-steel, hysteretic resistance of, in Toothed core armatures, advan- tages and disadvantages of, 61, 62, 63 core-leakage in, 53, 218, 219 definition of, 4 726 INDEX. Toothed core armatures, dimen- sioning of, 65-72 effective field-area of, 207 factor of field-deflection for, 230, 231 gap-permeance of, 227-231 height of winding-space in, 75 hysteresis heat in, 67, 68, 69, 591 insulation of, 81 number of slots for, 66 percentage of effective gap circumference for, 135 percentage of polar arc for, 50 seat of electro-dynamic force in, 63, 64 various types of slots for, 66 Torque, calculation of, 137, 138, 513, 534 of toothed and perforated ar- matures, 63 Traction-resistance, 440 Transformation-ratio, in dyna- motors, 454, 656 Transformer, rotary or rotary con- verter, 452C Transmission of power, at con- stant speed, 497 Trapezoidal armature-bars, 78, 101, 567 Triplex, or triple, armature- wind- ing, 149, 150, 151, 156, 162, 163, 166, 167 Triply re-entrant armature-wind- ing, 150, 156, 162, 164, 167 Troughs, micanite, for insulating armature-slots, 81, 82 Trueing of commutator, 699 Tubes, insulating, for armature slots, 80, 82 Tunnel Armature, see Perforated Armature. Turn, mean, length of, on mag- nets, 374 Turning moment, see Torque. Two-circuit winding, see Series Armature-Winding. Two-coil armature, 15, 16, 20 Type, selection of, 285, 437 Types of armature-winding, 143 of field-magnets, 269-285 of polepieces, 296 of series-windings, 157, 158 of slots for armatures, 66 U Under-type, 270, 278, 287 Unequal distribution of magnet- ism, 698 Unipolar dynamos, calculation of, 443-451, 652 principle of, 23-26 Unipolar induction, 22, 23 Unit armature-induction, 47-50 Units, electric, 7, 47 electro-magnetic, 200, 332, 333 magnetic, 199, 200 Unsymmetrical magnetic field, ef- fect of, on armature, 140-142, 5i3, 534 Unwound poles, 470 Upright horseshoe type, 239, 245, 249, 263, 269, 270, 527, 547, 621 Useful magnetic flux, 92, 133, 200- 202, 211-214 Utilization of copper, specific, see efficiency of Magnetic Field. Variable resistance, see Rheostat. shunt method of regulation, 459 Varnish, for armature-insulation, 85, 94 Varying cross-section in magnetic circuit, 345, 346, 348 Velocity of armature-conductors, 6, 7, 52, 448 of belt, 193 of commutator, 179, 180, 515 Velocity of railway-cars, 433, 440- 442, 500-502 of unipolar armatures, 448 Ventilation of armature, 53, 94, 528, 590 Vertical magnet types, 252, 253, 263, 269, 270, 273, 274, 276, 278, 284, 285, 299, 304 Vibration of dynamo, 287, 300, 43i " Victoria " dynamo, 282 Volume of armature current, 131 Voltage, see Electromotive Force. Vulcabeston, 80, 84, 85 Vulcanized fibre, 79, 84, 85 W Warburg, on hysteresis, no Warner, G. M., on unipolar dy- namos, 25 Wave winding, or zigzag winding, 144, 146, 147, 153. 154 Weaver, W. D., on shunt motors, 428 Weber, the unit of magnetic flux, 199, 200 INDEX. 727 Webster, A. G., on unipolar dy- namos, 25 Wedding, W., on magnetic leak- age, 262 Wedge-shaped armature-conduct- ors, 78, loi, 567 Weight-efficiency of dynamos, 33, 410-412, 527, 546, 565, 578, 602 Weight of armature winding, IOO of insulation on round copper wire, 103 of magnet winding, 366-368, 388-390 of parts of dynamos, 527, 546, 565, 579, 602 Westing house four-pole drum-ar- mature dynamos, dimensions of, 666 Width, see Breadth. Wiener, Alfred E., on calculation of electric motors, 419 on commutator-brushes, 171 on dynamo-calculation, see Preface, iii-viii. on efficiency of dynamo-elec- tric machinery, 405 on magnetic leakage, 216 on ratio of output and size of dynamos, 416 Wilson, Ernest, on heating of drum armatures, 130 Winding of armatures, see Arma- ture-Winding. Winding of magnets, see Magnet- Winding. Winding-space, height of, in ar- matures, 70, 71, 74, 75 height of, in magnets, 317, 36i, 3?i, 375. 377, 386, 387 Wire, copper, 101, 104, 119, 676- 681 Wire for armature-binding, 75 gauges, 103, 367 iron, for armature and mag- net winding, 472, 475 iron, for armature-cores, 93, 94, no, 113, 115 Wolcott, Townsend, on seat of electro-dynamic force in iron- clad armatures, 64 Wood, for armature-insulation, 85 for dynamo-base, 300 Wood, Harrison H,, on curves for winding magnets, 365 Work done by armature, 137 Working-stress, safe, of different metals, 189 of leather, 193 Worm gearing, 434, 435 Wrought iron, for armature-cores, 90-94, 109-122 for armature-shafts, 186 for magnet cores, 288 for polepieces, 293 for unipolar armatures, 448 , magnetic properties of, in, 3". 313 safe working load of, 189 Yokes, dimensioning of, 325 length of magnetic circuit in, 347 Zigzag winding, or Wave-Wind- ing, 144, 146, 147, 153, 154 Zinc blocks, 300-303 A 000 663 594 o