GIFT or Daughter of m Stuart Smith N PRACTICAL CALCULATION OF DYNAMO-ELECIRIC MACHINES ^ A MANUAL FOR ELECTRICAL AND MECHANICAL ENGINEERS AND A TEXT-BOOK FOR STUDENTS OF ELECTRO-TECHNICS BY ALFRED E. WIENER, E. E., M. E. M. A, I. E. E. NEW YORK THE W. J. JOHNSTON COMPANY 253 BROADWAY 1898 COPYRIGHT, 1897, BY THE W. J. JOHNSTON COMPANY 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 " 11 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 " iii IV 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, . . . . a " 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, . . size. Kennedy Single Magnet Type, " Leeds " Single Magnet Type, . Immisch Double Magnet Type, . "Silvertown" Single Horseshoe Type, Elwell-Parker Single Horseshoe Type, . Sayers Double Magnet Type, . . 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 " 41 Iron-clad Type, . -. . ' . . ' 2 " " Inward Pole Horseshoe Type, : . . 2 '* Guelcher Multipolar Type, . t . . . 2 " Schorch Inward Pole Type, . . . i size. Kummer & Co. Radial Multipolar Type, . i * Bollmann Multipolar Disc Type, . . i " 30 PREFACE. French Machines. Gramme Bipolar Type, Marcel Deprez Multipolar Type, . . Desrozier Multipolar Disc Type, Alsacian Electric Construction Co. Innerpole Type, . . . . . . . Swiss Machines. Oerlikon Multipolar Type, .... 4 sizes. Bipolar Iron-clad Type, . . . 2 " " Bipolar Double Magnet Type, . 2 " Brown Double Magnet Type (Brown, Boveri & Co.), . . . . .' . . 2 " Thury Multipolar Type, . . . . i size. Alioth & Co. Radial Outerpole Type ("Helvetia"), V ' . . . i " 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 for 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 VI 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 formulae 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 for a 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. Vll 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. CONTENTS. LIST OF SYMBOLS, xxiii 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 11. Unipolar Dynamos, . . . . . . . . -23 12. Bipolar Dynamos, . . . ' . . . . . . 26 13. Multipolar Dynamos, . ... . . ... . 33 14. Methods of Exciting Field Magnetism, ... . '. - 35 a. Series Dynamo, . . . . . r ... 36 b. Shunt Dynamo, . . . . . ... . 37 Table II. Ratio of Shunt Resistance to Armature Resistance for Different Efficiencies, . . 40 c. Compound Dynamo, . . . . . . . . 41 Part II. 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. Mean Conductor Velocities, ... 52 18. Field Density, 53 Table VI. Practical Field Densities, in English Measure, ........ 54 Table VII. Practical 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, .. . v . . . , . . . 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 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 for Dynamos of Various Sizes and Voltages, . . 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, .." 9 1 Table XXIII. Ratio of Net Iron Section to Total Cross-section of Armature Core, . . . 94 27. Total Length of Armature Conductor, i . . . . 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, . . . . . . . m 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. xiii PAGE b. Application of Connecting Formula to the Various Prac- tical Cases, . . . . . .->< . . . .. . 153 46. Armature Winding Data, . . , v ;.* . . . 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 XL VI. 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. PAGE Table LI. Diameters of Shafts for Drum Arma- tures, 186 Table LII. Diameters of Shafts for High-Speed Ring Armatures, 187 Table LIII. Diameters of Shafts for Low-Speed Ring Armatures, . . . . . . .187 52. Driving Spokes, 186 53. Armature Bearings, ......... 190 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, . . . . . . .... 192 Table LVII. Bearings for Low-Speed Ring Arma- tures, . . ' : .' . . .,..'. . . 192 54. Pulley and Belt, . . . 191 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 LXI II. 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, 2^7 - a. Smooth Armatures, . . . . . . . .217 b. Toothed and Perforated Armatures, . . . . .218 Table LXV. Core Leakage in Toothed and Per- forated Armatures, . . . . . . 219 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. PAGE CHAPTER XIII. CALCULATION OF LEAKAGE FACTOR, FROM MACHINE TEST. 69. Calculation of Total Flux, 257 a. Calculation of Total Flux when Magnet Frame Consists of but One Material, ........ 259 b. Calculation of Total Flux when Magnet Frame Consists of Two Different Materials, 260 70. Actual Leakage Factor of Machine 261 Table LXVIII. Leakage Factors for Various Types and Sizes of Dynamos, .... 263 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 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-Core Drum Arma- tures, ..." . 301 Table LXXI. Height of Zinc Blocks for High- Speed Dynamos with Smooth Core Ring Arma- tures . . , . .302 ' Table LXXII. Height of Zinc Blocks for Low- Speed Dynamos with Toothed and Perforated 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. xvii 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 xvin CONTENTS. PAGE 88. Magnetizing Force Required for any Portion of a Magnetic Circuit, 333 Table LXXXVIII. Specific Magnetizing Forces for Various Materials at Different Densities, in English Measure, ...... 336 Table LXXXIX. Specific Magnetizing Forces for Various Materials, at Different Densities, in Metric Measure, 337 CHAPTER XVIII. MAGNETIZING FORCES. Sg. Total Magnetizing Force of Machine, . . '.,,.... 339 90. Ampere-Turns for Air Gaps, ....... 339 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, i . . . . 359 96. Size of Wire Producing Given Magnetizing Force at Given Voltage between Field Terminals. Current Density in Mag- net Wire, . . . . . . * . . . 363 Table XGII. 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, . 375 100. Series Winding with Shunt-Coil Regulation 375 CONTENTS. xix 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^ jj88_ 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 Cost of Dy- namos, . . . . . ., . . . 412 CHAPTER XXIV. DESIGNING OF A NUMBER OF DYNAMOS OF SAME TYPE. no. Simplified Method of Armature Calculation, . . . 413 in. Output as a Function of Size, . . . . . . 416 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, . i - . . . 424 Table C. Tests on Speed Variation of Shunt Motors, 427 xx CONTENTS. PAGE 115. Calculation of Current for Electric Motors, .... 427 a. Current for any Given Load, 427 b. Current for Maximum Commercial and Electrical Effi- ciency, . . . . . . . . . 428 116. Designing of Motors for Different Purposes, .... 429 Table CI. Comparison of Efficiencies of Two Mo- tors Built for Different Purposes, . . . 430 117. Railway Motors, 431 a. Railway Motor Construction, 431 (1) Compact Design and Accessibility, .... 432 (2) Maximum Output with Minimum Weight, . . 432 (3) Speed, and Reduction-Gearing, .... 433 Table CII. General Data of Most Common Rail- way 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 Energy Output of Motor, 438 (2) Speed of Motor for Given Car Velocity, . . . 439 (3) Horizontal Effort and Capacity of Motor Equipment for Given Conditions, 44O Table CIII. Specific Propelling Power Required for Different Grades and Speeds, . . . 441 Table CIV. Horizontal Effort of Motors of Vari- ous Capacities at Different Speeds, . . 442 (4) Line Potential for Given Speed of Car and Grade of Track, 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 . .. 446 120. Formulae for Unipolar Double Dynamo, 449 121. Calculation for Magnet Winding for Unipolar Cylinder Dy- namos, . . . . . - . ... 450 CHAPTER XXVII. CALCULATION OF MOTOR-GENERATORS ; GENERATORS FOR SPECIAL PURPOSES, ETC. 122. Calculation of Motor-Generators, ; 452 123. Designing of Generators for Special Purposes, . . -455 a. Arc Light Machines (Constant-Current Generators), . 455 b. Dynamos for Electro-Metallurgy, ..... 459 c. Generators for Charging Accumulators 461 d. Machines for Very High Potentials, 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, . . ... . ' i, . . 493 Practical Example, . .... . . 495 d. Regulators for Varying the Potential of Shunt Dynamos, 496 132. Transmission of Power at Constant Speed by Means of 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.), I . 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. 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.), . 587 141. 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. "Phoenix" 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.), . . . * H . .... 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 Motor-Generator (Bipolar Double Horseshoe Type, si KW. 1450 Revs. Primary: 500 V. n Amp. Secondary: noV. 44 Amp.), . . . ... 655 INDEX, . . . . 661 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. A T' total magnetizing force required for maximum output of machine. AT" = total magnetizing force required for minimum output of machine. ^ = total magnetizing force required for maximum speed of machine. = 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. 0/ 0 "ai = maximum density of magnetic lines in armature core. (B aa , (B"a 2 minimum density of magnetic lines in armature core. (B c>i ., (B" c .i. = mean density of magnetic lines in cast iron portion of frame. i , (&" w .i. magnetic density in wrought iron portion of mag- netic circuit. b breadth, width. b & = breadth of armature cross-section, or radial depth of armature core. b\ = maximum depth of armature core. LIST OF SYMBOLS. XXV b b width of commutator brush. 6 E = breadth of belt. ^ k = circumferential breadth of brush contact. b s = width of armature slot. b' s == available width of armature slot. b" s width of armature slot for minimum tooth-density. ^ s = smallest breadth of armature spoke (parallel to shaft). b t = width, at top, of armature tooth. b\ = radial depth to which armature tooth is exposed to mag- netic field. b\ width, at root, of armature tooth. b y = breadth of yoke. fj angle embraced by each pole. /?j = percentage of polar arc. /3\ = percentage of effective arc, or effective field circum- ference. Y = electrical conductivity, in mhos. Z>, d, 6 = diameter. Z> m = external diameter of magnet coil. Z) p = diameter of armature pulley. d & = diameter of armature core. d' & = mean diameter of armature winding. d 1 \ = external diameter of armature (over winding). d'" & mean diameter of armature core. */ b = diameter of armature bearings. d c diameter of core-portion of armature shaft. d t mean diameter of magnetic field. d h diameter of front head of (drum) armature. d' h diameter of back head of (drum) armature. / ((B" a ) = specific magnetizing force of armature core. / ((B t ..i.), / ((B" c .i.) = specific magnetizing force of cast iron por- tion of magnetic circuit. /((B c .s.)> /("c. s .) = specific magnetizing force of cast steel por- tion of magnetic circuit. f (P)> f ("P) specific magnetizing force of polepieces. / (t)> / ("t) = specific magnetizing force of armature teeth. / (w.i.)> / (" w .i.) = specific magnetizing force of wrought iron portion of magnetizing circuit. / ((By), / ( r iii resistances of coils I, II, ... of series field regulator. LIST OF SYMBOLS. xxxill p = resistivity of brush-contact, in ohms per square inch of surface. Pm = resistivity of magnet-wire, in ohms per foot. S = surface, sectional area. S A = radiating surface of armature. S & sectional area (corresponding to average specific mag- netizing force) of magnetic circuit in armature core. S Al minimum cross-section of armature core. S &z maximum cross-section of armature core. So. i. sectional area of magnetic circuit in cast iron portion of field frame. S c 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. 5 M = radiating surface of magnets. S ' M = surface of magnet-cores. S m = sectional area of magnet-frame, consisting of but one material. Sp = area of magnet circuit in polepieces of uniform cross- section. vSpj = minimum cross-section of polepieces. S V9 maximum area of magnetic circuit in polepieces. ^ =: sectional area of armature slot, in metric units. S" s = 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. r torque, or torsional moment. a = rise of temperature in armature, in degrees Centigrade. 6' a = specific temperature increase in armature, in degrees Centigrade. Q m = rise of temperature in magnets, in degrees Centigrade. 6' m = specific temperature increase in magnets, in degrees Centigrade. xxxi v LIST OF SYMBOLS. v velocity, linear speed. V B = belt velocity, in feet per minute. v' E =z 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. v m velocity of railway car, in miles per hour. M\, wt weight. W t total weight to be propelled by railway motor, in tons. wt & =. weight of armature winding, bare wire, in pounds. wt' & weight of armature winding, covered wire. wt m = weight of magnet winding, bare wire. wt' m = weight of magnet winding, covered wire. wt se = weight of series winding, bare wire. wt' se weight of series winding, covered wire. // gll = weight of shunt winding, bare wire. o//' sh = weight of shunt winding, covered wire. X a , .x a = 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. y^ = back- pitch; /. e. 9 connecting-distance on back of arma- ture. y t =2 front-pitch; /. , and the time taken by this half-revolution is E = X io~ 8 2 $ N' x io~ 8 seconds; consequently the average E. M. F. for this case is: (6) xio-=.I- 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 YNAMO-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 5C), and the middle finger in the direction of the /motion, 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 middle finger will point to the direction in which the motion 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 other, and thereby a system of CURRENT GENERATION IN ARMATURE. 1 1 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. AT CONDUCTOR MAGNET POLE Fig. 7. Ring Armature Coil. . 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. [7 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 induced 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 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 decrease in 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 CURRENT GENERA TION IN ARMATURE. 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^ at any moment is expressed by the product of the maximum value and the sine of the angle through which the coil has moved, o

a : + , Figs. 15 and 16. Commutation of Armature Current. of rectification of the currents generated in the drum armature coil of Figs. 12 and 13 by means of a two-division commutator is shown in Figs. 15 and 16, of which the former refers to the first and the latter to the second half-revolution of the coil. The corresponding curve of the induced E. M. Fs. is repre- sented in- Fig. 17, which shows that the current issuing from a Fig. 17. Rectified Curve of E. M. Fs. single coil is of a pulsating character, its value periodically increasing from zero to a maximum, and decreasing again to zero. 9. Fluctuations of Commutated Currents. The instantaneous E. M. Fs. induced in a single coil vary- ing between the values e min = o and ^ max = E' , the mean E. M. F. is (o 9] CURRENT GENERATION IN ARMATURE. and the amount of fluctuation, with a two-division commuta- tor, is E' E' : = .5, or 50$. In order to obtain a less fluctuating current it is necessary to employ more than one armature coil, the current growing 360 Fig. 18. One-Coil Armature. the steadier the greater the number of the coils. If a coil of, say, 16 turns, Fig. 18, generating a maximum E. M. P\ of 'ma* = E' volts, is split up into'two coils of half the number of turns each, which are set at right angles to each other, Fig. 19, each will only generate half the maximum E. M. F. 90 Fig. 19. Two-Coil Armature. of the original coil, viz. : - E - \ max o max ^ i6 D YNAMO-ELECTRIC MA CHINES. [e but each of them will have this maximum value while the other one passes through the position of zero induction, as is shown in Fig. 20. Hence, if the E. M. Fs. of the two coils are X Fig. 20. Fluctuation of E. M. F. in Two-Coil Armature. added by means of a four-division commutator, the minimum joint E. M. F. in this case is ^ m\n while the total maximum E. M. F., the maximum inductions in the two coils not occurring at the same time, does not reach the maximum valued" of the undivided coil, but, being the JBSI- A Iftaf 180 Fig. 21. E. M. Fs. in Two-Coil Armature at one-eighth Revolution. sum of the E. M. Fs. induced at one-eighth revolution, when both partial E. M. Fs. are equal, is, with reference to Fig. 21, = (',) .) = ~- ( Sln 45 + COS 4 5) The mean E. M. F., therefore, is (^u, + '~J = l ~ (-5 + .707") E' = .60356 ', 9] CURRENT GENERATION IN ARMATURE. and the fluctuation of the E. M. F., with a four-division com- mutator, amounts to .60356)^' ^'max .707II..' imln^Lmean _ (-5 ~ -6o35 6 ) E< ^'max .70711 E' or 14. If each of the two coils i and 2, Fig. 19, is again subdivided into two coils of half the number of turns, four coils, i', 2', 3', 315; 45 370-- Fig. 22. Four-Coil Armature. and 4', are obtained which make angles of 45 with each other, Fig. 22. Plotting the curves of E. M. Fs., therefore, we get T" 45 90 180 270 Fig. 23. Fluctuations of E. M. F. in Four-Coil Armature. _i_^_ four waves, */, ^', ^ s ' and + ( e *') 22 y 2 = 2 X -- (sin 22^ -f- COS 22^) .38268 -4- .02388 -^ -E :=. 65328^. From this follows the mean E. M. F. obtained with an eight-division commutator: '"'mean = \ (-60356 + .65328) E' = .62842 E', giving a fluctuation of the maximum E. M. F. in the amount of (.65328 .62842) E' 1 max - mean '"'max .65328^' "I .02486_ ''"min ~ ^ mean _ (- 6o 35 6 -. 62842) ^ ^ f ' .653^8 '"'max .65328.S' J = .0386, or 3.86^. The above calculations show that the percentage of fluctua- tion rapidly diminishes as the number of armature coils increases, and in continuing the process of subdividing the coils into sections symmetrically spaced at equal angles, we will get for resultants curves which more and more resemble a straight line, and thus indicate the approaching entire dis- appearance of fluctuations and, therefore, continuity of the E. M. F. In the following Table I. the numerical results of such continued subdivision of the armature coils are given, the original maximum E. M. F. E' being for convenience taken as unity: ] CURRENT GENERATION IN ARMATURE. 19 TABLE I. FLUCTUATION OF E. M. F. OF COMMUTATED CURRENTS. NUMBER OP ANGLE AMOUNT FLUCTUA- COMMUTA- TOR EMBRACED BY MAXIMUM E. M. F. MINIMUM E. M. F. MEAN E. M. F. OP FLUCTUA- TION IN P. CENT. DIVISIONS. EACH COIL. TION. OP MAX. E. M. FT 2 180 1. 0. .5 .5 50$ 4 90 .70711 .5 .60356 .10356 14.65 8 45 .65328 .60356 .62842 .02456 3.86 12 30 .64395 .62201 .63298 .01097 1.70 18 20 .63987 .63014 .63500 .00487 .76 24 15 .63844 .63298 .63571 .00273 .43 36 10 .63743 .63501 .63622 .00121 .19 48 n .63708 .63571 .636395 .000685 .107 60 6 .63691 .63604 .636475 .000435 .068 90 4 .63675 .63637 .63656 .000190 .030 180 2 .63665 .63656 .636605 .000045 .007 360 1 .63664 .63660 .63662 .000020 .003 The average E. M. F., that is, the geometrical mean of all the sums of instantaneous E. M. Fs. induced in the various 45 U 90 180 270 360 Fig. 24. Average E. M. F. Induced in Rotating Armature. subdivisions of the coil, must be the same in every case, for, the total number of turns, the speed, and the field-strength remain the same for any number of commutator divisions. Fig. 25. Average E. M. F. of One-Coil Armature. Numerically, the average E. M. F. is the height of a rectangle having an area equal to the surface extending between the axis of abscissae, the two end-ordinates, and the curve of 2O D YNAMO-ELECTRIC MA CHINES. E. M. F., as shown in Fig. 24. In case of the one-coil armature the average E. M. F., in considering one-half of a revolution, is the height of a rectangle equal to the area of a single wave having.fi 1 ' as its amplitude. The area S inclosed by a sinusoid of amplitude E' and length /, Fig. 25, is: / f 77 F' I S = - E ' sin X d X = - (- cos 180 - (- cos o)) therefore the average E. M. F. = ^ = - X ' = .63662 E 1 . (7) Fig. 26. Average E. M. F. of Two-Coil Armature. For the two-coil armature the area S lt Fig. 26, of one-quarter of a revolution is the sum of a rectangle of length and height E' and of a wave of amplitude - | (sin 45 + cos 45) i and length or: 9] CURRENT GENERATION IN ARMATURE. 21 The average E. M. F. in this case is: = = *-Bl< = 2 ' = . 63*6,*', 7T 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 L, for increasing number of commutator divisions, approach the figure .63662 for the average E. M. F. as a limit. CHAPTER II. THE MAGNETIC FIELD OF 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 uni- directed or continuous E. M. F. In the second case, however, the inductor #, 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 #, 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, it 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. 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 (homo^alike) for unipolar, and heleropolar (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 D YNAMO-ELECTRIC MA CHINES. [H M. F. current, but which do not increase the amount of E 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, tht armature having no winding and no 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, rol. 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. Zeilschr., March 7, 1895, Electrical World, vol. xxv. p. 427 /April 6, 1895). 2 " Unipolar Dynamos for Electric Light and Power," by F. B. Crocker and C. H. Parmly, Trans. A. I. E. E., vol. 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 D YNA MO- EL E C TRIG MA CHINES. [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. 2^ 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 5-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 \sfrom 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 l 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 ami 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 3 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, DYNAMO-ELECTRIC MACHINES. [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 90 180 270" 360 Fig- 36. Curves of Potentials around Armature at No Load. 90 180 270 3GO 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, w-hen 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. 1 86 (February 15, 1893). 13] and **-a THE MAGNETIC FIELD. i cos a 33 X sm a X 2H , ,, sin a TC X a X r Ttrr f - X i cos a 2 n 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. 38. Distribu- tion of Potential around Commu- tator at No Load. . 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 tern- 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- folar 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 a_n 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; (ti) 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 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; I m = current in series field; r se = resistance of series-field coil; 7; e = electrical efficiency; the following equations exist, by virtue of Ohm's law of the electric circuit, for the series dynamo: E' (8) = I-.-.r 14] THE MAGNETIC FIELD. 37 = E useful energy ^ e " " total energy - / 2 -# /"' 2 / >P i ./ ( -/t j T 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 YNA MO- ELE C TRIG MA CHINES. 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, Fig. 42. Diagram of Shunt-Wound Dynamo. the following fundamental equations for the shunt dynamo can be derived: / = / + /* = /+ ^Sh R I - E ~' ' = ,..(11) > (12) El & + - + 2 - a - + H 1 si. 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 Inserting this value in (13) we obtain the equation for the max- imum electrical efficiency of a shunt dynamo: 1 Sir W. Thomson (Lord Kelvin), La Lumiire Electr., iv., p. 385 (1881). 40 DYNAMO-ELECTRIC MACHINES. [14 Now, since the armature resistance is usually very small com- pared with the shunt-field resistance, the sum r & -\- r Bh may be replaced by r sh , and the quotient sh may be neglected, when the following very simple approximate value of the efficiency is obtained: (16) 1 + 2 and this, by transformation, furnishes 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 7/ e = .995, or from 80 to 99.5 per cent. : TABLE II. RATIO OF SHUNT TO ARMATURE RESISTANCE FOR DIFFERENT EFFICIENCIES. PERCENTAGE OF ELECTRICAL EFFICIENCY. RATIO OF SHUNT TO ARMATURE RESISTANCE. PERCENTAGE OF ELECTRICAL EFFICIENCY. RATIO OF SHUNT TO ARMATURE RESISTANCE. 100 r;e ra 100 r, e rsh ra 80$ 64 95.5$ 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 L JL_L-R / 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). 7 8h = 7 se + 7, sh /sh = = - --* = J X Ss-? 1 Sh > ....(18) 42 DYNAMO-ELECTRIC MACHINES. [14 El r R ET - r v a (2) Z...(20) L E_J__R J Fig. 44. Diagram of Long Shunt Compound- Wound Dynamo. E _ R - I X (21) ' = E + I' (r. + (22) 14] THE MAGNETIC FIELD. 43 r R 1 + r * t r * e + 2 ra . + rse + ^_^- e - sh (23)- 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~* volt" and " Every metre of inductor 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 D YNAMO-ELECTRIC MA CHINES. [15 The derivation of these two laws from the fundamental defi- nition is given in the following Table III. : TABLE III. UNIT INDUCTIONS. LENGTH OP INDUCTOR. CUTTING VELOCITY. DENSITY OF FIELD. E. M. F. 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 144X10- 8 Volt 1 cm. 1 metre 1 metre 1 metre 1 cm. per second 1 m. per second 1 m. per second 1 m. 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~ b volt of the output E. M. F. In multipolar armatures the number of the electrically paral- lel portions of the winding generally is 2;z' 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 volt ; that is, 72 X io~* 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~ 5 volt, or 5 X fO~ b 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 Shuckert, 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 " All- gemeine Elektricitaets Gesellschaft" dynamos, in which the poles are united by a common cast-iron ring (Dobrowolsky's pole bushing. See 76, Chap. XV.). In fixing a preliminary value of this percentage, ft lt in case of a new design, take 67 to 80 per cent., or (3^ = .67 to .80, for smooth drum armatures; /? t = .75 to .85 for smooth rings, and D YNA MO-ELE C TRIG MA CHINES. [16 /?! = .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. F. PER PAIR OF ARMATURE CIRCUITS. PERCENTAGE ENGLISH UNITS. METRIC UNITS. OF Volt per Foot. Volt per Metre. POLAR ARC. BIPOLAR MULTIPOLAR BIPOLAR MULTIPOLAR DYNAMOS. DYNAMOS. DYNAMOS. DYNAMOS. ft e e ei ei 1.00 72 X 10- 8 72 X 10- 8 5 X 10- 5 5 X 10-' .95 71 68 4.9 4.8 .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 c x oe", (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. ; #'p = number of bifurcations of current in armature, or number of pairs of parallel armature circuits; ' p has the following values, to be multiplied by the number of independent windings in case of multiplex grouping ( 44): #'p i for bipolar dynamos and for multipolar ma- chines having ordinary series grouping, #'p = ;z p for multipolar dynamos with parallel group- ing, n p being the number of pairs of mag- net poles, n' p = - for multipolar dynamo with series-parallel 3 grouping, n s 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 iecM PoIepi.cM Pol.pl.cn Toothed Armature Core Cut Wr't Irou Iron or Steel .1 .2E .5 1 2.5 5 7.5 10 100 800 aoo 500 1000 8000 10000 12000 14000 15000 30000 15000 16000 17000 25000 26000 19000 20000 22000 04000 27000 80000 80000 86000 45000 8000 10000 12000 13000 14000 15000 16000 17000 18000 20000 22000 24000 27000 12000 15000 18000 19000 27000 30000 40000 10000 12000 13000 14000 18000 12000 14000 15000 16000 18000 22000 14000 18000 19000 20000 21000 24000 26000 28000 30000 32000 35000 38000 41000 45000 20000 24000 27000 30000 35000 41000 44000 47000 56000 12000 14000 16000 17000 18000 19000 20000 21000 22000 23000 25000 27000 29000 31000 33000 35000 18000 21000 24000 30000 35000 40000 42000 44000 46000 48000 50000- 10000 11000 12000 13000 14000 15000 16000 17000 18000 19000 24000 15000 16000 18000 20000 21000 23000 24000 28000 .1 .25 .5 1 2.5 5 7.5 10 100 200 1000 2000 TABLE VII. PRACTICAL FIKLD DENSITIES, IN METRIC MEASURE. Field Densities, in Lines of Force per sqmvre Centimetre . Bipolar-Dynamos Toothed Armature Core BtnJght Teeth Projecting Teeth as PoUpltcM PobpUcM Multipolar Dy Smooth Armature Core Toothed Armature Core EC 3 .2! .6 1 2.5 5 7.5 10 25 50 100 900 300 500 1000 8000 1550 1850 2150 2500 3100 8400 8700 4700 2300 2800 8100 4000 4700 5100 6600 7000 1250 1550 1850 2000 2150 8100 8400 8700 1850 8100 3400 3700 4700 5100 5600 1400 1550 1700 1850 2000 2150 2800 8100 2150 2300 2500 3100 3700 4700 2150 2500 3100 3250 3400 8700 4000 4350 4700 5000 5400 5900 6400 7000 3100 3700 4200 4350 4500 4700 5000 5400 5900 6400 6800 7300 7750 8200 8700 1850 2150 2500 2650 3100 4200 4500 4800 5100 5400 3700 8850 4000 4350 4700 5000 5400 6500 6800 7200 7500 7800 1700 1850 2150 2300 2500 3100 8400 8700 2500 2800 8100 3500 3700 4000 4700 5000 .1 ,26 .5 *1 2.5 5 7.5 10 100 500 1000 2000 19] FUNDAMENTAL CALCULATIONS FOR WINDING. 55 19, Length of Armature Conductor. By means of the specific armature induction obtained from formula (24), the total length of active wire to be wound upon the pole-facing surface of any armature can be readily deter- mined. If E' denotes the total E. M. F. generated in an armature, and Z a the total length of active wire wound on it, then E 1 divided by Z a will give the specific armature induction, e'. The length of active conductor for any armature can therefore be obtained from the formula in which Z a = total length of active conductor (on whole cir- cumference opposite polepieces), in feet, or in metres; E ! = total E. M. F. to be generated in armature, i. c expressed in metres per second, and if oc" is replaced by 5C in lines per square centimetre. To find the total electromotive force, E', 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 DYNAMO-ELECTRIC MACHINES. [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 FOR INTERNAL RESISTANCES. ADDITIONAL E. M. F. 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 3i 8 6 6 5 200 3| 3 6 5 5 4 500 3 2i 5 4 4 3 1,000 3i 2 4 3 3 2i 2,000 2 H 3 8* 2* 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 ...... (37) where # a 2 = sectional area of armature conductor, in circular mils; 6 & = diameter of armature wire, in mils; /' = total current generated in armature, in amperes; and ' p = number of pairs of parallel armature circuits. In the metric system, taking .4 square millimetre per am- pere (= 2.$ amperes per square millimetre) as the average current density in the armature conductor, the sectional area of the inductor, in square millimetres, is obtained : from which, in case of a circular conductor, the diameter can be derived : 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 JV 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 . . N 12 from which follows: (30) In the metric system the mean diameter of the armature winding, in centimetres, is given by 100 X 60 v v f d\ = ~ ~- - X ^ = 1,900 X ^, . . .(31) in which v c is to be expressed in metres per second. 58 21] DIMENSIONS OF ARMATURE CORE. 59 From this mean winding diameter, 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 ARMATURE 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 (a^ X A S s ) the symbol A standing for the expression: 7 It _ ..f . x (32) a 7T~ f* e '> w ii 2' c X tan ^ 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' = number of slots; b s = width of slots (in millimetres); S a sectional area of slot = b s X h & (in 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 s = .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. 2 (= .14 square inch) to d" & = 5,000 mm. ( =197^*), 'c 320, S a = 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 F 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 y^.Vn % 3 /i6 M h % % \ 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- 322] 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. RELATIVE SPECIFIC HYSTERESIS HEAT IN TEETH. WIDTH OF SLOT. 4" to 10" 10 to 40" 40" to 120" 120" to 200" (100 to 250 (250 to 1,000 (1,000 to 3,000 (3,000 to 5,000 mm.) mm.) mm.) mm.) Inch. Millimetres. Armature. Armature. Armature. Armature. A 0.75 H to 3 li to 2i li to 2i Iito2 A 1.5 1 ' li li 2 H 2 li' If i * l ' li 1 H 1 H li' H A 4.5 li ' 2 1 H l H 1 ' li 6 li ' 3 li 2 H if 1 ' li -1 9.25 2i ' 10 li 3i li 2* H' H 12.5 4 ' 20 2i 6i If 3 li' 2 f 16 6 ' 25 3f 12 2i 4 If 2i f 18.5 4f 18 2f 5 li' 3 1 22 6 22 3f 7 If 4 i 25 5 12 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% inch (3 mm.) slot for which, in that group, it is a mini- mum. The value of b m for which the magnetic density in the teeth becomes a minimum, is found by making the circumferential width at the bottom of the teeth, n =7t ( =7t d" - - n ' c X a maximum; and the value of b B which does the latter is v = . /?_ x s \ (33) DYNAMO-ELECTRIC MACHINES. [22 where b\ = width of slot for minimum tooth density, in inches or in centimetres; S" s = 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 *.= X it 2 X TABLE XV. DIMENSIONS OP TOOTHED ARMATURES, IN ENGLISH MEASURE. DIAMETER DIMENSIONS OP SLOTS. NUMBER OP CORE WIDTH AT OP SLOTS. DIAMETER, BOTTOM OF ARMATURE, IN INCHES. Depth, in inches. Width, in inches. Ratio of Depth to v= IN INCHES. TOOTH, IN INCHES. Width. to a t t*a *i j^ d\ ft. b a 26 8 d\-2h & n' c 5 f j 2.50 30 84 .14 6 2.59 36 4f .14 8 3 2.66 44 H .18 10 7 it 2.95 52 .20 12 1 A 3.20 60 10 .21 15 1 3.43 72 12f .23 18 li 11 3.64 80 .26 21 1 1 3.66 88 m -.28 25 li 3.69 98 22 .30 30 1 3.71 108 27| .37 40 If 15 3.73 136 36^ .38 50 IT ^ 3.75 160 46-1 .41 60 2 17 3.76 180 56 .45 70 $1 A 3.78 196 65f .51 80 2J 9 3.79 212 75-|- .52 90 24 4 228 85 .55 100 2f it 4 232 94^ .59 125 3 i 4 264 119 .67 150 34 7 4 272 143 .78 200 4 1 4 320 192 .89 22] DIMENSIONS OF ARMATURE CORE. that is to say, to make the width of the slots equal to half their pitch on the outer circumference, for the special case of a straight-tooth core, then the width of the slots is equal to the top width of the teeth. The proper sectional area S\ of the slots to accommodate a~ sufficient amount of armature winding is obtained by making the depth of the slot from 2^ to 4 times its width, according to the size of the armature, the minimum value referring to very small and the maximum value to the largest machines. Applying these rules to armatures of various sizes, the ac- companying Tables XV. (see page 70) and XVI. have been calculated, giving the dimensions of toothed armatures, the former in English and the latter in metric measure: TABLE XVI. DIMENSIONS OF TOOTHED ARMATURES, IN METRIC MEASURE. I DIAMETER OF DIMENSIONS OF SLOTS. NUMBER OP SLOTS. CORE DIAMETER, WIDTH AT BOTTOM op ARMATURE, Depth, Width, Ratio n' c = IN CM. TOOTH, IN CM. IN CM. in cm. in cm. of Depth to Width d!" a 7r d & = d & TT d\ Aa *s 7*a : l>* 2& s d\ - 2h & n' c ** 10 1.5 .6 2.50 24 7 .32 15 1.75 .65 2.69 36 11.5 .36 20 2 .7 2.86 44 16 .44 25 2.25 .75 3.00 52 20.5 .49 30 2.5 .8 3.13 60 25 .51 40 3 .9 3.34 70 36 .72 50 3.5 1.0 3.50 78 43 .75 60 4 1.1 3.64 86 52 .80 75 4.5 1.2 3.75 98 66 .92 100 5 1.3 3.85 120 90 1.06 150 5.5 1.4 3.95 168 139 1.20 200 6 1.5 4.0 210 188 1.32 250 7 1.75 4.0 224 236 1.56 300 8 2.0 4.0 236 286 1.81 400 9 2.25 4.0 288 382 1.92 500 10 2.5 4.0 320 480 2.21 b. Perforated Armatures. The same considerations that prevailed in determining the number and the width of the slots in toothed armatures are also decisive for the dimensioning of perforated cores. The DYNAMO-ELECTRIC MACHINES. [23 number of perforations, for this reason, can be taken in the same limits as the number of slots for toothed cores. See Table XIII. In case of round holes, Fig. 51, the thickness of the iron between two adjacent perforations should be taken between 0.4 and 0.75 times the diameter of the hole. For rectangular holes, Fig. 52, the thickness of the iron 0.56 g T00.9& s Figs. 51 and 52. Dimensions of Perforated-Core Discs. between them is to be taken somewhat greater than for round holes, namely, from 0.5 to 0.9 times the width of the channel. The distance of the holes from the outer periphery is to be made as small as possible, and may vary between 1/32 and 1/8 inch, according to the size of the armature. 23. Length of Armature Core. The number of wires that can be placed in one layer around the armature circumference, and the depth of the winding space, determine the total number of conductors on the arma- ture, and the latter, together with the length of active wire, gives the length of the armature core. a. Number of Wires per Layer. For smooth armatures the number of wires per layer is ob- tained in dividing the available core circumference by the thickness of the insulated armature wire. If the whole circum- ference is to be filled by the winding, then X (35) 23] DIMENSIONS OF ARM A TURE CORE 73 where /z w = number of armature wires per layer; d & = diameter of armature core, in inches; d' & = width of insulated armature conductor, in inches. See 24. If, in the metric system, d & is given in cm. and d' & in mm., the above formula becomes: 10 X X 7t .(36) In case the winding is to consist in separated coils, the sum of the separating spaces is to be deducted from the armature circumference. The value of n w is to be rounded off to the nearest lower even and easily divisible number, and, in the case of a drum armature, allowance for division strips or driving horns is to be made according to Table XVII. This table gives the average circumferential space occupied by the division strips in drum armatures of different sizes and various voltages, in per cent, of the core circumference. After fixing the number of armature divisions, which will be shown in 25, this table may also be used to determine the thickness of the driving horns, which are usually made of hard wood, or fibre, and sometimes of iron: TABLE XVII. ALLOWANCE FOB DIVISION STRIPS IN DRUM ARMATURES. DIAMETER OF ARMATURE CORE. PERCENTAGE OP CORE CIRCUMFERENCE OCCUPIED BY DIVISION STRIPS. Inches. Centimetres. Up to 300 Volts. 400 to 750 Volts. 800to2000Volts. Up to 3 Up to 7.5 12 % 15 % " 6 " 15 10 12 15 % " 12 " 30 8 10 12 " 20 " 50 7 9 10 " 30 " 75 6 8 9 Denoting one-hundredth of these percentages by k^ the core circumference being unity, the formula for the number of wires per layer in a drum armature in English measure becomes : 9 a (37) 74 DYNAMO-ELECTRIC MACHINES. [23 In metric measure the same value of # w is obtained by multi- plying the numerator of (37) by 10, thus deriving the metric formula similarly as (36) is derived from (35). In toothed armatures the number of wires in one layer is found from the number, ' c , and the available width, b' m of the slots by the equation: (38) In this formula the value of b' m is to be derived from the actual width, b m of the armature slots ( 22), by deducting the thickness of insulation used for lining their sides, data for the latter being given in 24. For calculation in metric system the factor 10 is -to be em- ployed, as before. b. Height of Winding Space. Number of Layers. In dividing the available height, h' M of the winding space by the height d" M of the insulated armature conductor, the number of layers of wire on the armature is found: ! = number of layers of armature wire; h\ available height of winding space, in inches; d" a = height of insulated armature conductor, in inch. The height of the insulated armature conductor, tf" a , in the case of round or square wire, is identical with its width, $' a . If h & is expressed in cm. and d" & in mm., the right-hand side of (39) must be multiplied by 10 in order to correct the for- mula for the metric system. The available height, 7z' a , of the winding space is obtained from its total height, h M averages for which are given in Table XVIII. (page 75) by deducting from 1/32 to 1/4 inch (see 24), according to size and voltage of machine, for the insulation of the -armature core, insulation between the layers, thickness of binding wires, etc. The nearest whole number is to be substituted for the value of n v 23] DIMENSIONS OF ARMATURE CORE. 75 TABLE XVIII. HEIGHT OF WINDING SPACE IN ARMATURES. ENGLISH MEASURE. METRIC MEASURE. Height of Winding Space, in inches. Height of Winding Space, in centimetres. Diameter of Smooth Armature Diameter of Smooth Armature Armature, in inches. Core. Toothed Armature Armature, in cm. Core. Toothed Armature Drum Ring Core. Drum Ring Core. Armature. Armature. Armature. Armature. Up to 2 .25 Up to 5 .7 3 .3 . . 7.5 .8 4 .35 .20 10 .9 .5 1.5 6 .4 .225 H 15 .55 1.75 8 .45 .25 I 20 : .1 .6 2 10 .5 .275 25 .2 .65 2.25 12 .55 .3 i 30 .35 .7 2.5 15 .6 .325 H 40 .5 .8 3 18 .65 .35 li 50 .65 .9 3.5 21 .7 .375 if 60 .8 1 4 25 .75 .4 i* 75 2 1.2 4.5 30 .8 .45 if 100 1.4 5 40 .5 if 150 1.6 5.5 50 .55 l| 200 1.8 6 60 .6 2 250 2 7 70 .65 2i 300 2.2 8 80 . . .7 2i 400 2.5 9 90 .75 2i 500 3 10 100 . .8 2f 125 .85 3 150 .9 3i 200 1.0 The radial height taken up by the armature-binding in smooth armatures averages as follows : Up to i KW 5 10 200 500 1,000 2,000 .030 inch 035 " . 040 ' l .050 " .060 " .070 " .085 " .100 " (No. 24 ( " 22 B. & S.) ( " 21 n \ ( " 17 ( " 16 n \ ( " 14 tt \ ( " 12 11 ) These figures, besides allowing for the binding wires, which range from No. 24 B. & S. (.020") to No. 12 B. & S. gauge (.080") respectively, as indicated, include the insulation of. the 7 6 DYNAMO-ELECTRIC MACHINES. [23 bands, the thickness of which, therefore, varies from .010 to .020 inch, according to the size of the armature. The bands usually consist of from 12 to 25 convolutions of phosphor bronze or steel wire, their width varying from * inch to 2 inches. They are insulated from the winding by strips of mica from j^$ to i inch wider than themselves, and are placed at distances apart equal to about twice the width of a band. In straight-tooth armatures recesses are usually turned to receive a few light bands, while armatures with projecting teeth and with perforated cores need, of course, no binding at all. c. Total Number of Armature Conductors. Length of Armature Core. The product of the number of layers and the number of conductors per layer gives the total number of conductors on the armature; and this, divided into the total length of active armature conductor, furnishes the active length of one con- ductor, that is, the length of the armature body: l _ 12 X - a _ 12 X n& X ^ ? (4o\ where / a = length of armature core parallel to pole faces, in inches; Z a = length of active armature conductor, in feet, from formula (26); n w = number of wires per layer, from formula (35), (36), or (37), respectively; ! = number of layers of armature wire, from formula (38); n$ = number of wires stranded in parallel to make up one armature conductor of area tf a 2 , formula (30); - - = total number of conductors on armature. i In the metric system, Z a being expressed in metres, the length / a is found in centimetres by replacing the factor 12 in (40) by 100. For preliminary calculations an approximate value of the 23J DIMENSIONS OF ARMATURE CORE. 77 number of conductors, N & all around the polefacing circum- ference of the armature, may be obtained by dividing the con- ductor area found from formula (27) into the net area of the winding space. Taking .6 of the total area of the winding space as an average for its net area in smooth armatures witFi winding filling the entire circumference, we obtain: # w X i _ ,,. _ 1,000,000 X .6 X d & X n X h & ~~ ~~~ = 1,885,000 x ^-* (41) This result is to be correspondingly reduced for windings filling only part of circumference, or to be multiplied by (i ^), see formula (36), in case of a drum armature, re- spectively. In toothed armatures the average net height of the winding space is about three-fourths of the total depth of the slot, hence the approximate number of armature conductors: w X i _ jy _ 1,000,000 X n' c X &' s X 24^ a n& Fig. 54. Core Insulation of High-Voltage Drum Armature. Table XIX. In modern high-voltage drum armatures mica is used exclusively for insulating the core, the edge- and face- insulations being united into the form of flanged micanite discs, and micanite cylinders or tubes being used around the circumference and over the shaft, see Fig. 54. In this case of all-mica insulation the thicknesses of the coatings at the various parts of the core can all be made alike and equal in amount to that of the circumferential covering, columns a, Table XIX. D YNA MO-ELE C TRIG MA CHINE S. [24 In ring armatures the core insulation, a, is extended so as to include also the inner circumference and the faces of the body as well. To prevent grounding of the winding at the edges, their insulation is thickened by coatings inserted beneath the circumferential covering. In small rings, Fig. 55, the insula- Fig. 55- Core Insulations on Small Ring Armature. tion, #, usually is applied in form of a narrow band, and is simply wrapped around the core, the reinforcements at the edges being laid upon the core, as the enwrapping proceeds, in the shape of short strips of oiled material or mica of such gauge as to make the total thickness of insulation at the edges equal to the edge-insulation given in columns b of Table XIX. In large ring machines, Fig. 56, the core faces are often insu- Fig. 56. Core Insulations on Large Ring Armature. lated by means of curved vulcabeston, pressboard, or micanite discs, b^ fitting over the end rings; these discs are pressed or molded in special forms, and are of a thickness ranging from .060 to .250 inch (1.5 to 6.4 mm.), see columns b, Table XIX. For toothed and perforated armatures, Fig. 57, the core-cir- cumference insulation is carried out in form of channels or tubes of paper, or cardboard, or vulcanized fibre, fitted into the grooves, or, especially in large toothed-core machines, by 24] DIMENSIONS OF ARMATURE CORE. 81 means of micanite troughs lining the bottom and the sides of the slots. The thickness of this lining ranges from .010 to . 125 inch (0.25 to 3 mm.), proportional to the size of the slots, Fig. 57- Various Forms of Slot Insulation. and according to the voltage of the dynamo, columns e, Table XIX. The core faces of toothed armatures are insulated in a similar manner as those of a smooth armature. Fig. 58 shows Fig. 58. Core Insulation of Large Toothed-Ring Armature. a well-insulated armature core of a large toothed-ring machine, micanite troughs being used in the slots and micanite caps over the end rings. 82 D YNA MO- ELE C TRIG MA CHINES. [24 gjg 5' on C rt ET}S B-.E-3 2,g.'f? t/i rt A 3 U C n O tn r*3 B-E.- > oo o o in ^ g a Core Circum- ference. Core Edges. : : : liiSsi! Core Faces. Shaft Insula- tion. OOOOOOO n in 8iS Risllii Slot Lining. Insulation between Layers. Core Circum- ference. ;^-* O ( oo< Core Edges. EEBiSi Core Faces. Shaft Insula- tion. Slot Lining. OOOOOO< I Insulation between Layers. Core Circum- ference. S> O' O O I Core Edges. Core Faces. Shaft Insula- tion. OOOOOO = I Slot Lining. Insulation between Layers. Core Circum- ference. * Core Edges. Core Faces. Shaft Insula- tion. Sisilii i-- 1 Slot Lining. 1222- S Insulation between Layers. 24] DIMENSIONS OF ARM A TURE CORE. 83 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 34 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 .015-.040 .001-. 125 .012-.016 .008-.020 .005-.012 .010-.025 .010-.075 .010-.015 .010-.020 .005-.030 .004-.006 .006-.010 .003-.006 004 .008 .1-.5 .2-.6 .2S-.75 .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 .3-.4 .2-.5 .125-3 .25-.G .25-.2 .25-.4 .25-.S .125-.75 .1-.15 .15-.25 .075-. 15 .1-.2 .125-.25 .05-.2 .2S-.5 .6-2.0 .35-1.5 .15-.3 .025-.065 .04-.! .04-. 125 .05-.175 .15-.3 1.0-2.5 3.0-100 3.0-100 3.0-100 7 680* 850* 120 10 25 11,800,000 10 25 470 600 6 10,000 33,000 310,000 t 440,000 t 490,000 500,000 t 980,000 620,000 t 320,000 ** 650 tt 1,850 it 1,600 6 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 79.000.0UO 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 75 150 100-180 225-490 330-500 150-250 260-340 340-370 380-480 210-240 250-300 150-325 900-1,300 '150-250 750-900 2,000-^.000 1 240-490 175-310 390-510 280-390 940-1,120 830-1,040 575-790 450-650 550-700 600-960 200-275 190-250 160-200 800-1,000 830-950 100-420 350-600 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 2UO 1,000 175 800 3,000 300 200 425 300 1,000 900 600 500 600 700 225 200 175 900 850 150 400 40 475 525 375 450 250 75 15 10 20 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 " oiled and Muslin, oiled Bristol Board Cotton, Single Covering (on Cotton, Single Covering, shel- lacked Cotton, Single Covering, boiled Cotton, Doable Covering Cotton, Double Covering, shel- lacked Hard Rubber Linseed Oil, pure, oxidized .... Micanite Cloth " flexible Paper " flexible Plate " flexible, " A " il " "B"f Oiled Cloth (Cotton, Linen, or Muslin) Oiled Paper, single coat double " Paper white writing " yellow .005-.010 .002-. 008 .010-. 020 .025-.075 .015-.060 .006-.012 .001-.0025 .0015-.004 .0015-.005 .002-.007 .006-.012 .040-. 100 Paraffined Paper Parchment oiled Press Board Rubber Sheet Shellacked Cloth Silk, Single Covering (on wires) " shellacked. " Double " " shellacked. Varnished Cheese Cloth Vulcabeston Wood, Mahogany Pine " Walnut * Insulation resistance at 50 C. is about , at 70 C. about &, and at 100 C. about & of^that at 30 C. t :; ;; :; ;: :: li Mica Laminae, put together by solution of guttapercha (Mica Insulator Co.). IT " " " " 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 C. is about %, at 70 C. about J, and at 100 C about ^ f tnat at 3 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 of the various insulating materials commonly used, and is aver- aged from information contained in writings by Steinmetz, 1 and by Canfield and Robinson, 2 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). 2 " 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). 3 " 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 n, 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. generator; 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 YZ of i per cent. ; for 36 coils, embracing an angle of 10 each, f of i percent.; for 48 divisions of 7^ each, T V of i per cent. ; for 90 divisions with coil-angle of 4, T f 5 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 T^ O 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 YNA MO- RLE C TRIG 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 " " 21 " 20 " " 23 " 10 " " 25 " 5 " " 30 " 2 " " 40 " 1 " " 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. DIFFERENCES OF POTENTIAL BETWEEN COMMUTATOR DIVISIONS. CURRENT INTENSITY PER ARMATURE CIRCUIT. DIFFERENCE OF POTENTIAL BETWEEN COMMUTATOR DIVISIONS. Over 100 amp 100 to 50 eres lot 12 3 20 vc 21 .Its 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. " 100 to 50 A. " 50 to 20 A. " 20 to 10 A. " 10 to 5 A. " 5 to 2 A. " 2 to i A. circuit : ( c ) min (^c)min " (^c)min " (c)min " (o)mln " (c)mln (c)min E X 2 ' p X p 1 - (45) 20 IO E X 2 n' v EX 'p 21 10.5 ^ X 2 n'^ _ E X n' p 23 ii-5 _ Ex *n'v _Exn' v 25 I2 -5 ^' X 2 ' p E x * p 3 T 5 ^ X 2 ' p ^ x 'p 40 20 ^ X 2 ' p ^ X ' p ^o 2q Having thus determined the minimum number of divisions that can be used in the commutator without excessive spark- ing, the actual number, n s , 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 Divisions. 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: c x V and for .'+ Af- IV.: A = ,L&*) + ^ n X L & ........ (56) In these formulae / a , a , and Z a are known by virtue of equa- tions (40), (48) and (26), respectively, and h & can be taken 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 Ring 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 DYNAMO-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 in bending of the connection strips the Eickemeyer method is applied. 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, o O 00 "~ ^ e= C) 5n C O 02 *> "te c5 i 02 10AJMB/I IS . ts s a IP sill Sill S +3 ? fl|i **" o~ t> fl> *-*^ ||| 3 aj.2 ojjts Ctf-^oly ||13* S i N" CQ inch mm *o 3, is| & i 'o K jll *s| ^ 1 .300 7.62 .020 15 2.28 1.0228 'i .289 7.34 1 .020 14.45 2.32 1.0232 '2 .284 7.21 .020 14.2 2.33 1.0233 3 .259 6.58 .020 12.95 2.40 1.024 '2 .258 6.55 .020 12.9 2.40 1.024 'i .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 0-20 11 2.65 1.0265 '4 .204 5.18 .012 17 2.20 1.022 .020 10.2 2.85 1.0285 'e .203 5.16 .012 16.9 2.20 1.022 .020 10.15 2.86 1.0286 . . *5 .182 4.62 .012 15.15 2.27 10227 .018 10.1 2.87 1.0287 7 .180 4.57 .012 15 2.28 1.0228 .018 10 2.90 1.029 8 .165 4.19 .012 13.75 2.33 1.0233 .018 9.17 3.20 1.032 'e .162 4.12 .010 16.2 2.24 1.0224 .018 9 3.25 1.0325 *9 .148 3.76 .010 14.8 2.30 1.023 .016 9.25 3.15 1.0315 '7 .144 3.66 .010 14.4 232 1.0232 .016 9 3.25 1.0325 io .134 3.40 .010 13.4 2.36 1.0236 .016 8.4 3.55 1.0355 *8 .1285 3.27 .010 12.85 2.40 1.024 .016 8 3.75 1.0375 ii .120 3.05 .010 12 2.50 1.025 .016 7.5 4.10 1.041 9 .1144 2.91 .010 11.4 2.55 1.0255 .016 7.1 4.35 1.0435 i2 .109 2.77 .010 10.9 2.66 1.0266 .016 6.8 4.60 1.046 io .102 2.59 .010 10.2 2.85 1.0285 .016 6.4 5.00 1.05 is .095 2.41 .010 9.5 3.10 1.031 .016 5.9 5.55 1. Oi355 ii .091 2.31 .010 9.1 3.25 1.0325 .016 5.7 5.85 1.0585 i4 .083 2.11 .007 12 2.50 1.025 .016 5.2 6.60 1.066 12 .081 2.06 .007 11.6 2.54 1.0254 .016 5.1 6.80 1.068 15 13 .072 1.83 .007 10.3 2.80 1.028 .016 4.5 7.80 1.078 16 .065 :.65 .007 9.3 3.15 1.0315 i .016 4.1 8.60 1.086 ii .064 .63 .007 9.1 3.25 1.0325 .016 4 8.80 1.088 if .058 1.47 .007 8.3 3.60 1.036 .014 4.1 8.60 1.086 is .057 .45 .007 8.1 3.70 1.037 .014 4.1 8.60 1.086 16 .051 1.30 .007 7.3 4.20 1.042 .014 3.6 9.60 1.096 is .049 1.25 .007 7 4.40 1.044 .014 3.5 9.80 1.098 i7 .045 .15 .005 9 3.25 1.0325 .012 3.75 9.30 1.093 i9 .042 1.07 .005 8.4 3.55 1.0355 .012 3.5 9.80 1.098 is .040 1.02 .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 0.89 .005 7 4.40 1.044 .005* 6.00 1.06 21 20 .032 0.81 .005 6.4 5.00 1.05 I .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 i .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 8.80 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 .104 .004* 4 10.40 1.104 28 27 .014 0.36 .005 2.8 11.25 .1125 .004* 3.5 11.25 1.1125 29 28 .013 0.33 .005 26 11.65 .1165 .004* 3.25 11.65 1.1165 30 .012 0.31 .005 2.4 ! 12.05 .1205 .004* 3 12.05 1.1205 29 .011 0.28 .005 2.2 ! 12.45 .1245 .004* 2.75 12.45 1.1245 1 * Double silk : i mil of silk insulation taken equal in weight to 1.25 mil of cotton covering. 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 n p , and the resistance of each branch becomes p p . see Fig. 68, page 102. The joint resistance of these 2 n' p circuits, that is, the actual armature resistance, will consequently be ~ 4 X (n f p )* ' The total resistance, & , of all the armature wire in series can be calculated from the total length, Z t , and the sectional area, # a 2 , of the conductor by the formula 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 for commercial copper, or iQ-3 2 "- If the temperatures are measured by the Fahrenheit scale, i per cent, is to be added to the resistance for every 4^ over 60 Fahr., and the formula becomes: F. = 450 (64) In both (63) and (64), r & is the resistance at 15.5 C. ( = 60' Fahr.) found from formula (61) or (62), respectively. CHAPTER VI. ENERGY LOSSES IN ARMATURE. RISE OF ARMATURE- TEMPERATURE. 30. Total Energy Loss in Armature, There are three sources of energy-dissipation in the arma- ture which cause a portion of the energy generated to be wasted, and which give rise to injurious heating of the armature. These sources are (i) overcoming of electrical resistance of armature winding, (2) overcoming of magnetic resistance of iron, and (3) generation of electric currents in the armature core. The energy spent for the first cause, that is, the energy spent by the current in overcoming the ohmic resistance of the conductors, is often called the C*R loss (C = current, R resistance), for reasons evident from 31. The energy consumed from the second cause, or spent in continually reversing the magnetism of the iron core, as the armature revolves in the field, is called the hysteresis loss (see 32), and the energy spent from the third cause, in setting up useless currents in the iron and, in a small degree, also in the armature conductors, is styled the eddy current loss, or Foucault current loss (see 33). The total energy transformed into heat in the armature of a dynamo-electric machine is the sum of the C*R loss, of the hysteresis loss, and of the eddy current loss, and can be expressed by the formula: A - A+ A + A, (65) in which P A = total watts absorbed in armature; P & = watts consumed by armature winding, form- ula (68) ; P h = watts consumed by hysteresis, formula (73); PI watts consumed by eddy currents, formula (75)- 107 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: P a = (/')" X r' a , (66) where P & = energy dissipated in armature winding, in watts; /' = total current generated in armature, in amperes; r' a 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 a , at 15.5 C. (= 60 Fahr.), multiplied by ( 1+ _*s r -_!o ] = 1 . 2 . The energy dissipated in overcoming the resistance of the armature winding, consequently, for shunt- and compound- dynamos can be obtained from the formula: P & = 1.2 X (l + E\ X r & ..(67) I = current-output of dynamo, in amperes; E E. M. F. output of dynamo, in volts; r & = resistance of armature, at 15.5 C. (= 60 Fahr.), in ohms; 32] ENERGY LOSSES IN AXMATUKE. 109 r m = resistance of shunt-circuit (magnet resistance -j- re g- ulating resistance) at 15.5 C. (for series dynamos 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 = 1.2 X (k & X /) 2 X r a ........ (68) and in this the coefficient k 6 for series dynamos is k 6 = 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 OF CURRENT OUTPUT. #6 .1 15* .15 .25 12 .12 .5 10 .10 1 8 .08 2.5 7 .07 5 6 .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. Energy 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 no D YNA MO- RLE C TRIG MA CHINES. [32 of the magnetization. The name of "Hysteresis" (from the Greek vGrepico, 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, 3 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 proportioned 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\ = i h x &a 6 x jv; x M\ 9 where P\ = energy consumed by hysteresis, in ergs; rf l = constant depending upon magnetic hardness of material (" Hysteretic Resistance"); (B a = density of lines per square centimetre of iron; N^ 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 XXVIII., 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 : tj l .0035, Iron wire : rf l .040. '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 ; Philos. 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. m TABLE XXVIII. HYSTERETIC RESISTANCE FOR VARIOUS KINDS OF IRON. KIND or IRON. HYSTERETIC RESISTANCE. Sheet Iron, magnetized lengthwise 0025 to 005 0165" thick ( 42 mm ) 0035 .015" " ( .38 " ) 004 .006" " ( .15 " ) 005 magnetized across Lamination 007 Iron Wire length-magnetization 0035 cross- ... 040 Wrought Iron, Norway Iron 0023 " ordinary mean . . 0033 Cast Iron ordinary mean 013 containing -- % Aluminium. 0137 0146 Mitis Metal . 0043 Tool Steel glass hard 070 ' ' oil hardened 027 annealed 0165 Cast Steel hardened 012 to 028 " annealed 003 to 009 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 : P h = io- 7 X .0035 X j X ^ X 28,316 X M = 5 x io- 7 x Y- 6 x N! x M, ......... (69) and in any armature with core of iron wire : P h = 5.7 x io- 6 X respectively, into one factor, 77, the factor of hysteresis; that is, the energy absorbed by hysteresis in one cubic foot of iron, when subjected to magnetization and demagnetization at the rate of one complete cycle (two reversals) per second. For convenience, the author, in Table XXIX., has calcu- lated the numerical values of these hysteresis factors, 77, for all core densities from 10,000 to 125,000 lines per square inch, thus simplifying the equation for the hysteresis loss into the formula: P h = 77 x NI X M ............ (73) In Table XXIX., columns headed 77 -s- 480, are added for the case the hysteresis loss is to be calculated for an arma- ture, of which the weight, in pounds, of the iron core is known: 32] ENERGY LOSSES IN ARMATURE. TABLE XXIX. HYSTERESIS FACTORS FOR DIFFERENT CORE DENSITIES, IN ENGLISH MEASURE. WATTS DISSIPATED WATTS DISSIPATED MAGNETIC DENSITY AT A FREQUENCY OF ONE COMPLETE MAGNETIC CYCLE PER SECOND. MAGNETIC DENSITY AT A FREQUENCY OF ONE COMPLETE MAGNETIC CYCLE PER SECOND. IN IN ARMATURE CORE. Sheet Iron. Iron Wire. ARMATURE CORE. Sheet Iron. Iron Wire. LINES OF LINES OF FORCE FORCE PER SQ. IN. fry II a per cu. ft. per Ib. per cu. ft. per Ib. PER SQ. IN. &"a per cu. ft. per Ib. per cu. ft. per Ib. >? rj-f-480 n Tj+480 17 r?-*-480 n ij+480 10,000 1.25 .0026 14.3 .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 .0(503 330.1 .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 .0673 368.5 .768 37,000 10.20 .0213 116.5 .242 77,000 32.91 .0687 376.3 .784 38,000 10.65 .0222 121.6 .253 78,000 33.60 .0701 384.2 .800 39,000 11.10 .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 .834 41,000 12.01 .0250 137.2 .286 81,000 3569 .0745 408.0 .851 42,000 12.48 .0260 142.5 .297 82,000 36.40 .0760 416.0 .868 43,000 12.96 .0270 148.0 .308 as,ooo 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 449.2 | .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 ! .972 49,000 15.96 .0333 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 .008 51,000 17.01 .0355 194.3 .405 91,000 43.00 .0897 491 5 .023 52,000 17.55 .0366 2006 .418 92,000 4376 .0913 500.0 .042 53,000 18.10 .0377 206.9 .431 93,000 44.53 .0929 509.0 .064 54,000 18.65 .0388 213.2 .444 94,000 45.30 .0945 518.0 .0*0 55,000 19.21 .0400 2195 .457 95,000 46.07 .0961 527.0 .098 56,000 19.78 .0412 226.0 .470 96.000 46.85 .0977 536.0 .116 57,000 20.35 .0424 232.6 .484 97,000 47.63 .0993 545.0 .135 58,000 20.92 .0436 239.2 .498 98,000 48.41 .1009 554.0 .154 59,000 21.50 .0448 245.8 .512 99000 49.20 .1025 5630 .173 60,000 22.09 .0460 252.5 .526 100,000 50.00 .1041 572.0 .192 61,000 22.69 .0472 259.4 .530 105,000 54.06 .1127 618.0 .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 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 7; 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-ELECTRIC MA CHINES. [32 in cubic metres, from the n c X *-> s X 4, X #2 c*^ a ), for toothed armatures; / a =r length of armature core, in centimetres; b & = radial depth of armature core, in centimetres; n' c = number of slots; 6*8 = slot-area, in square centimetres; k 9 = ratio of magnetic to total length of armature core, Table XXI., 26. Then, formula (73) will give the hysteresis loss in watts, if the factor of hysteresis ;; is replaced by rf from the following Table XXX., rf being calculated from 3.5 X io~ 4 X (B a 1>6 , in case of sheet-iron, and from 4 x io~ 3 X ($>&'*, in case of iron wire: 32] ENERGY LOSSES IN ARMATURE. TABLE XXX. HYSTERESIS FACTORS FOR DIFFERENT CORE DENSITIES, IN METRIC MEASURE. 1 ; WATTS DISSIPATED WATTS DISSIPATED MAGNETIC DENSITY IN AT A FREQUENCY OP ONE COMPLETE MAGNETIC CYCLE PER SECOND. MAGNETIC DENSITY IN AT A FREQUENCY op ONE COMPLETE MAGNETIC CYCLE PER SECOND. ARMATURE ARMATURE CORE. CORE. LINES OF FORCE PER CM ^ Sheet Iron. Iron Wire. LINES OF FORCE Sheet Iron. Iron Wire. (GAUSSES) per cu. m. per kg. per cu. m. per kg. PER CM. (GAUSSES) per cu. m. per kg. per cu. m. per kg. v V-i-7,700 V v+r,ro> v V-i-7,700 * Vn-7,700 2,000 67.0 .0087 765.1 .0994 12,000 1,177.0 .1529 13,451.0 1.7469 3,000 128.1 .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 1,296.9 .1685 14,821.0 1.9248 4,500 245.0 .0318 2,800.2 .3637 13,000 1,337.8 .1737 15,288.7 1.9855 5,000 290.0 .0377 3,314.6 .4305 13,250 1,379.2 .1791 15,7C1.7 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 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 7,385.5 .9592 16,500 1,959.0 .2544 22,389.0 2.9076 8,500 677.9 .0880 7,747.0 1.0061 16,750 2,006.7 .2606 22,934.0 2.9785 8,750 710.1 .0922 8,114.8 1.0539 17,000 2,054.9 .2669 23,484.5 3.0499 9,000 742.8 .0965 8,488.6 1.1024 17,250 2,103.5 .2732 24,039.5 3.1220 9,250 776.1 .1101 8,869.2 1.1152 17,500 2,152.5 .2795 24,599.0 3.1947 9,500 809.9 .1105 9,255.6 1.1202 17,750 2,201.9 .2860 25,164.0 3.2681 9,750 844.2 .1110 9,649.0 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 10,250 914.6 .1188 10,452.2 1.3574 18,500 2,352.6 .3055 26,886.0 3.4918 10,500 10,750 950.5 987.0 .1234 10,863.2 .1282 111,284.0 1.4108 1.4650 18,750 19,000 2,403.7 2,455.1 .3122 .3189 27,470.0 28,058.6 3.5676 3.6440 11,000 1,024.0 .1330 11,702.5 1.5198 19,250 2,507.1 .3256 28,652.0 3.7210 11,250 11,500 1,061.5 1,099.5 .1379 12,131.0 .1428 12,565.3 1.5755 1.6319 19,500 19,750 2,559.3 2,636.2 .3324 .3424 29,248.6 29,844.6 3.7986 3.8760 11,750 1,138.0 .1478 13,005.3 1.6890 20,000 2,665.1 .3461 30,458.7 3.9556 With regard to the exponent of (&" 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). n6 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. HYSTEUETIC EXPONENT. Lines of Force per Square Inch. &"a Linos per cm. 2 (.Gausses.) &a 1,300 to 3,000 3,000 " 6,500 6,500 " 13,000 13,000 " 50,000 50,000 " 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 to I -7> the 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' h = 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. 194 (April 5, 1894); Electrical World, vol. xxiii. p. 647 (May 12, 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, #, 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 10O ,2OO 3OO 4OO 5OO 6OO 7OO 8OO 9OO 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 DYNAMO-ELECTRIC MACHINES. [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. OF HYSTERESIS 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 axiF^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: />', = ' X (V X -AT' XM'^ P' e energy dissipated by eddy currents, in ergs; (B t = density of lines of force, per square centimetre of iron; N TV, =. frequency, in cycles per second, = -^ x # p ; M\ = mass of iron, in cubic centimetres; f' eddy current constant, depending upon the thickness and the specific electric conductivity of the mate- rial; for the numerical value of this constant Stein- metz gives the formula: ~ 9 e' -- X 6* X y X 10 - 9 = 1.645 X & X y X io 6 = thickness of material, in centimetres. Y electrical conductivity, in mhos; for iron : y = 100,000 mhos; for copper: y = 700,000 mhos. Inserting the value of e f with reference to iron, into the above equation expressing the Eddy Current Law, and trans- forming into practical units, the eddy current loss in an arma- ture, in watts, is obtained: io- 7 X 1.645 X(2. 5 4i) 2 X I0 ~ 4 x 5 X-tf/X 28,316 X M= 7.22 X io- 8 X 3? X (BY X N? X M. ..(75) i = thickness of iron laminae in armature core, inch; 120 DYNAMO-ELECTRIC MACHINES. [33 (B" a =: density, in lines per square inch, corresponding to average specific magnetizing force of armature core, see 91; N^ -- frequency, in cycles per second; M = mass of iron, in cubic feet. Uniting again 7.22 x io~ 8 X $? X (BV into one factor, in this case the Eddy Current Factor, e, we have the simplified formula: P e = e X ^ 2 XM. (76) TABLE XXXIII. EDDY CURRENT FACTORS FOR DIFFERENT CORE DENSITIES AND FOR VARIOUS LAMINATIONS, ENGLISH MEASURE. MAGNETIC WATTS DISSIPATED MAGNETIC WATTS DISSIPATED DENSITY PER CUBIC FOOT OF IRON DENSITY PER CUBIC FOOT or IRON IN AT A FREQUENCY OP 1 CYCLE IN AT A FREQUENCY OP 1 CYCLE ARMATURE PER SECOND, e. ARMATURE PER SECOND, e. CORE. CORE. LINES OP LINES OP FORCE Thickness of Lamination, Si. FORCE Thickness of Lamination, Si PER SQ. IN. PER SQ. IN. '. .010" .020' .040" .080" &"a .010" .020" .040" .080" 10,000 .0007 .003 .012 .046 66,000 .0315 .126 .503 2.013 15.000 .0016 .007 .026 .104 67,000 .0325 .130 .519 2.075 20,000 .0029 .012 .046 .185 68,000 .0335 .134 .534 2.137 25,000 .0045 .018 .072 .288 69.000 .0345 .138 .550 2.200 30,000 .0065 .026 .104 .416 70,000 .0355 .142 .566 2.265 31,000 .0070 .028 .111 .444 71,000 .0365 .146 .582 2.330 32,000 .0074 .030 .118 .472 72,000 .0375 .150 .599 2.396 33,000 .0079 .032 .126 .503 73.000 .0385 .154 .616 2.463 34,000 .0084 .034 .134 .534 74^000 .0396 .158 .633 2530 35,000 .0089 .036 .142 .567 75,000 .0407 .163 .650 2.600 36,000 .0094 .038 .150 .600 76,000 .0418 .167 .668 2.670 37,000 .0099 .040 .158 .633 77.000 .0429 .171 .685 2.740 38,000 .0104 .042 .167 .667 78,000 .0440 .176 .703 2.810 39,000 .0110 .044 .176 .703 79,000 .0451 .180 .721 2.883 40,000 .0116 .046 .185 .740 80,000 .0462 .185 .740 2.958 41,000 .0122 .049 .194 .777 81,000 .0474 .190 .758 3.033 42,000 .0128 .051 .204 .815 82,000 .0486 .194 .777 3.108 43,000 .0134 .054 .214 .855 83,000 .0498 .199 .796 3.184 44.000 .0140 .056 .224 .896 84,000 .0510 .204 .815 3.260 45,000 .0146 .059 .234 .937 85,000 .0523 .209 .835 3.340 46,000 .0153 .061 .245 .979 80,000 .0535 .214 .855 3.420 47,000 .0160 .064 .256 1.022 87,000 .0548 .219 .875 3.500 48.000 .0167 .067 .267 1.066 88,000 .0560 .224 .895 3.580 49,000 .0174 .070 .278 1.110 89,000 .0573 .229 .916 3.662 50,000 .0181 .072 .289 1.155 90,000 .0586 .234 .937 3.745 51,000 .0188 .075 .300 1.200 91,000 .0599 .240 .958 3.830 52000 .0195 .078 .312 1.248 92000 .0612 .245 .979 3.915 53,000 .0202 .081 .324 1.297 93,000 .0625 .250 1.000 4.000 54,000 .0210 .084 .337 1.346 94,000 .0638 .255 1.021 4.085 55,000 .0218 .087 .349 1.397 95,000 .0651 .261 1.043 4.170 56,000 .0226 .091 .362 1.448 96,000 .0665 .266 1.064 4.257 57,000 .0234 .094 .375 1.500 97,000 .0679 .272 1.086 4.345 58.000 .0242 .097 .389 1.555 98,000 .0693 .277 1.109 4.436 59,000 .0251 .101 .403 1.610 99,000 .0707 .283 1.132 4.528 60,000 .0260 .104 .416 1.665 100,000 .0722 .289 1.156 4.622 61,000 .0269 .108 .430 1.720 105,000 .0797 .319 1.274 5.095 62,000 .0278 .111 .444 1.776 110,000 .0875 .350 1.398 5.593 63,000 .0287 .115 .458 1.833 115,000 .0955 .382 1.528 6.113 64,000 .0296 .118 .473 1.891 120,000 .1040 .416 1.664 6.655 65,000 .0305 .122 .486 1.951 125,000 .1128 .451 1.806 7.222 1 1 1 33] ENERGY LOSSES IN ARMATURE. 121 The values of e for core-densities from 10,000 to 125,000 lines per square inch, and for laminations of thickness tfj = .010", .020", .040", and .080", are given in the foregoing Table XXXIII., page 120. Curves corresponding to the value of in the above table are plotted in Fig. 71. CORE DENSITY, IN LINES OF FORCE P. SQ< INCH. Fig. 71. Eddy Current Factors for Various Densities and Different Laminations. The eddy current factors ' for the metric system, in watts per cubic metre of iron, as calculated from 1.645 X io~ 7 X 6'* X (B a 2 , for densities from (B a = 2,000 to 20,000 gausses, and for laminations of d' { = 0.25 mm., 0.5 mm., i mm., and 2 mm. thickness, are given in Table XXXIV., page 122. Prof. Thompson 1 gives for the calculation of the eddy cur- rent loss the following formula by Fleming which is much used by English engineers: P e = & x & a 2 X N? X M\ X io- 16 , where P e = eddy current loss, in watts; tf'j = thickness of iron laminae, in mils; (^ = magnetic density, in lines per square centimetre; N l frequency, in cycles per second; M\ = mass of iron, in cubic centimetres. 144 Dynamo Electric Machinery," 5th edition, p. 137. 122 DYNAMO-ELECTRIC MACHINES. [34 TABLE XXXIV. EDDY CURRENT FACTORS FOR DIFFERENT CORE DENSITIES AND FOR VARIOUS LAMINATIONS, METRIC MEASURE. MAGNETIC WATTS DISSIPATED MAGNETIC WATTS DISSIPATED DENSITY PER CUBIC METRE OF IRON, DENSITY PER CUBIC METRE OF IRON, IN ATA FREQUENCY OF 1 CYCLE IN AT A FREQUENCY OF 1 CICLE ARMATURE PER SECOND, e'. ARMATURE PER SECOND, e'. CORE. CORE. LINES OF FORCE Thickness of Lamination, S'i- LINES OF FORCE Thickness of Lamination, 6'i. PER CM. a PER CM. 3 CQAUSSES) ( GAUSSES') &a 0.25mm 0.5 mm 1 mm 2 mm <&a 0.25 mm 0.5 mm 1 mm 2 mm 2,000 .041 .165 .658 2.632 12,000 1.481 5.922 23.688 94.752 3,000 .093 .370 1.481 5.922 12,250 1.543 6.172 24.687 98.746 3,500 .126 .504 2.015 8.061 12,500 1.607 6.426 25.704 102.815 4,000 .165 .658 2.632 10.528 12,750 1.671 6.685 26.741 106.965 4,500 .208 .833 3.331 13.325 13,000 1.738 6.950 27.801 111.203 5,000 .257 1.028 4.113 16.450 13,250 1.805 7.220 28.880 115.520 5,250 .283 1.134 4.534 18.136 13,500 1.874 7.495 29.980 119.921 5,500 .311 1.244 4.976 19.904 13,750 1.944 7.775 31.100 124.401 5,750 .340 1.360 5.441 21.766 14,000 2.015 8.061 32.242 128.968 6,000 .370 1.481 5.922 23.689 14,250 2.088 8.351 33.404 133.615 6,250 .402 1.607 6.426 25.704 14,500 2.162 8.647 34.586 138.345 6,500 .434 1.738 6.950 27.801 14,750 2.237 8.947 35.789 143.156 6,750 .468 1.874 7.495 29.980 15,000 2.313 9.253 37.013 148.050 7,000 .504 2.015 8.061 32.242 15,250 2.391 9.564 38.257 153.026 7,250 .542 2.167 8.667 34.666 15,500 2.470 9.880 39.521 158.085 7,500 .578 2.313 9.253 37.013 15,750 2.550 10.202 40.806 163.225 7,750 .619 2.476 9.903 39.613 16,000 2.632 10.528 42.112 168.448 8,000 .658 2.632 10.528 42.112 16,250 2.715 10.860 43.438 173.753. 8!250 .700 2.799 11.196 44.785 16,500 2.799 11.196 44.785 179.141 8,500 .743 2.971 11.885 47.545 16,750 2.885 11.538 46.153 184.610 8,750 .787 3.149 12.595 50.379 17,000 2.971 11.885 47.541 190.162 9,000 .833 3.331 13.325 53.298 17,250 3.059 12.237 48.949 195.796 9,250 .880 3.519 14.075 56.300 17,500 3.149 12.595 50.378 201.512 9,500 .930 3.712 14.846 59.384 17,750 3.239 12.957 51.828 207.311 9,750 .977 3.909 15.638 62.550 18,000 3.331 13.325 53.298 213.192 10.000 1.028 4.113 16.450 65.800 18,250 3.424 13.697 54.789 219.155 10,250 1.080 4.321 17.283 69.130 18,500 3.519 14.075 56.300 225.201 10.500 1.134 4.534 18.136 72.545 18,750 3.615 14.458 57.832 231.328 10,750 1.188 4.753 19.011 76.042 19,000 3.712 14.846 59.385 237.538 11,000 1.244 '4.976 19.905 79.618 19,250 3.810 15.240 60.958 243.830 11,250 1.301 5.205 20.820 83.278 19,500 3.910 15.638 62.551 250.205 11,500 1.360 5.440 21.756 87.022 19,750 4.010 16.041 64.165 256.661 11J50 1.420 5.678 22.712 90.846 20,000 4.113 16.450 65.800 263.200 Transforming this formula into English units, we obtain: *' X 28 ' 6 X " X = 6.81 X io~ 8 X 7 in this formula varies with the slope of the head, and this, in turn, depends upon the ratio between the diameter of the armature and the thickness of the shaft. For, in large machines the shaft bears a smaller proportion to the armature diameter than in small ones, and therefore in large armatures there is comparatively much more room between the shaft circumference and the core periphery than in small armatures, and since the diameter of the head must never exceed that of the armature itself, it is evident that the slope of the head is smaller, and consequently its relative length is larger in the smaller armatures. The following Table XXXV. gives the values of this coefficient for the various sizes of drum armatures: TABLE XXXV. LENGTH OP HEADS IN DRUM ARMATURES. EXTERNAL DIAMETER OF ARMATURE. d" & VALUE OF AVERAGE LENGTH k, OF HEADS. Inches. Cm. Up to 6 Up to 15 .60 to .50 l h = .55 Xrf"a+27* a " 12 " 30 .55 to .45 = .50 X d\+%h & " 18 " 45 .50 to .40 . 45 " 24 " 60 .45 to .35 = .40 X d\-\- 27i a " 30 " 75 .40 to .30 = .35 X d\+ 2 7> a As to the diameters at the ends of the heads, that of the front head, <4, at commutator end of armature, is generally made from 0.75 d\ to i.o a" ^ while the diameter of the end washer of the back head, ^' h , ranges in size from 0.5 d" & to -75 d"v Taking d h 0.9 d\ as the average diameter of the front head, and d\ =0.6 a" & as that on the back head (Figs. 73 and 74, page 125), we obtain the following formula for the radiating surface of a drum armature: S A = d\ x X 34] ENERGY LOSSES IN ARMATURE. 125 or approximately: S A = d\ x n x (4 + 1.8 X 4); (78) S A radiating surface of armature, in square inches^ or^in square centimetres; d\ =. external diameter of armature, in inches, or in centi- metres, = A in which a = rise of armature temperature, in degrees Centi- grade; 6 = factor of magnetic saturation in smallest cross- section of armature core, -4- 18,000 = (B a -+- 18,000. 2 n p X b & X / a X , (?> = useful flux through armature, in webers; 2 #p = number of poles; ^ a X / a X <& 2 = 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; 6" A = surface of armature-core, in square centimetres, , <4* 7T , = c/ a TT X 4 H~ i r smooth armatures, = d" & n X /a + , for 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. 1 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: 00045 a = rise of armature temperature, in degrees Centigrade; (B" a = density of magnetization, in lines per square inch; n p = number of pairs of poles; JV = number of revolutions per minute; M = mass of iron, in cubic feet; 6" 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 (October 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: I' ;" - - ^=i? ; ^ i 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 n' p = number of electrically parallel armature portions, eventually equal to the number of poles; = current flowing through each conductor, in amperes; 2 n f N c X r total number of amperes all around armature; 2 n p this quantity is called "volume of the armature cur- rent" by W. B. Esson, and "circumflux of the arma- ture" by Silvanus P. Thompson; <4 = 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'" M should be substituted for d & . By comparing the values of / 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 I 3 2 D YNAMO-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 OF ARMATURE TEMPERATURE, CORRESPONDING TO VARIOUS CIRCUMFERENTIAL CURRENT DENSITIES. CIRCUMFERENTIAL RISE OP ARMATURE TEMPERATURE, a . High Speed (Belt-Driven) Dynamos. Low Speed (Direct-Driven) Dynamos. 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. ., vol. xx. p. 142. (1890.) 38] 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: N X = W x <* and since for the total electrical energy of the armature we can write, see formula (136), 56, AT y v /' _ - LV c A ^ A ^v ,-, /ftA\ - ^X io 8 X 60 X I ' ~ in which P' total electrical energy generated in dynamo, in watts; E l 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; N = speed, in revolutions per minute; #'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): *JL^ = 6 3 x to- x <4x N x 9. (87) But the useful flux, $, is, the product of gap area and field density, or, approximately, Kapp, S. P. Thompson's "Dynamo-Electric Machinery," 4th edition, p. 439. 134 DYNAMO-ELECTRIC MACHINES. [38 and consequently the safe capacity of a high-speed dynamo : p' = 6 3 x 10 - 8 x d & x N x d ^^- x ft\ x 4 x oe" = lo- 6 x <4' x 4 x /?', x ^ x oe" ......... (88) For low-speed machines, 2,500 amperes per inch diameter, or 800 amperes per inch circumference, can safely be allowed, hence, in order to obtain the safe capacity of a direct-driven machine, the factor i.jj must be adjoined to formula (88). In (88), P' = maximum safe capacity of armature, in watts; d & =: diameter of armature core, in inches; / a = length of armature core, in inches; fi 1 ' x = percentage of useful gap circumference; to be taken somewhat higher than the percentage of polar arc, to allow for circumferential spread of the lines of force, see Table XXXVIII. ; 3C" = field density, in lines of force per square inch; N = speed, in revolutions per minute. Inserting into (85) the equivalent limit current density in metric units, of 240 amperes per centimetre circumference (= 765 amperes per centimetre diameter), the maximum safe capacity, in watts, of a high-speed armature given in metric measure is obtained : P' = 765 X d & x W X $ io 8 X 3 = 4 X io- 7 X d; X / a X ft\ 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 /3\, 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. TABLE XXXVIII. PERCENTAGE OP EFFECTIVE GAP CIRCUMFERENCE FOR VARIOUS RATIOS OF POLAR ARC. PERCENTAGE OF EFFECTIVE GAP CIRCUMFERENCE. PERCENTAGE OF 2 Poles. 4 to 6 Poles. 8 to 12 Poles. 14 to 20 Poles. POLAR ARC. fc *g * 1 fc * /? o ^ o ^2 O ^ c5 02 O <, 4> r^ Q> A ^"S _s ,s"H 5 -c-2 .elS-H ' -a 2 agS ,- = pi if |s w is s -1 *jj p OJ t; 1 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 .815 .775 .80 .775 .70 .85 .735 .80 .73 .78 .725 .76 .725 .65 .82 .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 Yalue 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: ' x r >4 x JC" (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); JC" = field density, in lines of force per square inch, or per square centimetre, respectively. 136 D YNAMO-ELECTRIC MA CHINES. [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 OF VARIOUS KINDS OF ARMATURES. TYPE OF MACHINE. KIND OF 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. 2 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 I .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. 4:0. 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 1 = ' X /' watts; and mechanically, as the product of circumferential speed and turning moment, or torque, P' = 27txNxrx 74 - - = . 142 x N 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; t 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 : ' X /' E' X I 1 r = .142 X N = 7 ' 42 X ~^~W~~ foot -P unds - -.(91) Or, in metric system, i kilogramme-metre being = 7.233 foot- pounds, ' (92) Inserting into (91) and (92) the expression for the E. M. F. from 56, viz.: 7\T N/ (ft V A7^ T"l f C ^* r\ * W L, "== n'X io 8 X 60' p 137 I3 8 DYNAMO-ELECTRIC MACHINES. [41 the equation for the torque becomes: N e x $ X N I' ^ 42 x .7x 10* x 60 > 7y = ~ if- X - X ^ c X $ foot-pounds ^ 10 n p J- ...... (93) I 62? /' = -jj? X ^- X ^ c X ^ kg. -metres J 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: P unds x ^v c x p\ Inserting into this equation the value of t from formula (91), we obtain : E' x I' ft 24 x 7-042 X ft- 2 X 7-042 X n E' x /' /\ 60 ... ...... X N c X ft\, 60 12 \ or, ; -...(95) 41] EFFECTS OF ARMATURE WINDING. 139 / a = peripheral force per armature conductor, in pounds; E' x /' = total output of armature, in watts; v c mean conductor velocfty, in feet per second; N c = total number of armature conductors; fi\ = 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: f - 2 4x 11.74 _/; ^c x * < ; x N C x ft\ x <*'* 2.82 /' X # Replacing in this the useful flux $ by its equivalent, the product of gap area and field density, we find a third formula for the peripheral force: 2 .82 r X *'> X ~ X ?> X *' X *' /a ~Ts~ I0 X a X ___ T" ^"O \/ v/ 7 \/ *i/"> ^ v\/\ t * ^ rl e / O ^ \ ^- A r A *a A wt> pUUIlUb , V.t''/ IO n p = total current flowing in each armature conductor, in amperes; 4 = length of armature core, in inches; JC" = field density, in lines of force per square inch. If the dimensions of the armature are given in centimetres, the conductor velocity in metres per second, and the field density in gausses, the peripheral force is obtained in kilo- grammes from the following formulae: /a = ' I02 X v c x j X p\ kil S rammes ' /a = X ' ' p X X ft' and /a = ^4 X -r X / a X 5C kilogrammes, . ..(100) n P which correspond to (95), (96) and (97), respectively. 14 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: / = 2 it X ^L X ( V = .0199 X S g X 5C 2 dynes, \ 47r / or, since 981,000 dynes = i kilogramme, / = T X S g X 3C 2 = 2.03 x io~ 8 X S g X 3C 2 kilogrammes; Sg = gap area, in square centimetres; 3C = field density, in lines of force per square centimetre. 42] EFFECTS OF ARMATURE WINDING. I4 1 Expressing the gap area by the dimensions of the armature, we obtain: / = 2.03 X io- 8 x ^~ x 4 x ft\ x oe 2 = 32 x io- 9 x <4 X 4 X /?', X OC 2 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 < X 4 X ft\ X OC; kilogrammes, and / 2 = 32 x io- 9 X <4 X 4 X /?'i X 3C 2 2 kilogrammes, and will be drawn toward the stronger side by the amount of the difference of their attractive forces. The armature thrust, therefore, is: / t =/ 1 -/ 2 ^ 3 2xio- 9 x^x/ a x^ 1 x(ae 1 2 -ae 2 2 )kg.; ...(102) / t = thrusting force acting on armature, due to unsym- metrical field, in kilogrammes; d & = diameter of armature, in centimetres; 4 = length of armature, in centimetres; '/.. /3\ = percentage of effect. 'ye gap-circumference, see Table XXXVI. ; 5d = density of field, on stronger side, lines per square centimetre; 3C 2 = density of field, on weaker side, lines per square centi- metre. In English measure, i pound being = .4536 kilogrammes, and i square inch = 6.4515 square centimetres, the formula for the armature thrust becomes: X 4 X ^', X = ii Xio- 9 X^aX4X/^X(rcY-3e'' 2 2 ) pounds, ....(103) in which d & and / a are to be expressed in inches, and 3C", and 3e" 2 in lines per square inch. In such types, where the attractive force of the field mani- fests itself as a downward thrust, as in those shown in Figs. 142 D YNAMO-ELECTRIC MA CHINES. [42 78, 80, 82 and 85, the value obtained by (102) or (103), re- spectively, is to be added to the dead weight of the armature, in order to obtain the total down thrust upon the bearings. If, however, / t is an -upward thrust, as is indicated in Figs. 77, Fig. 77- Fig. 78. Fig. 79- Fig. 80. Fig 81. Fig. 82. Fig. 83. Fig. 84. Fig. 85. Figs. 77 to 85. Unsymmetrical Bipolar Fields. 81 and 84, the down thrust upon the bearings is the weight of the armature, diminished by the amount of f t . In the cases illustrated by Figs. 79 and 83 the action of the field causes a sideward thrust, which has to be taken care of by a proper design of the bearing pedestals, or of the journal brackets. CHAPTER VIII. ARMATURE WINDING OF DYNAMO-ELECTRIC MACHINES. 4:3. Types of Armature Winding. a. Closed Coil Winding and Open Coil Winding. If, in a continuous current dynamo, the reversal of the cur- rent would take place in all the conductors at once, consider- able fluctuation of the E. M. F. would be the result. In order to obtain a steady current, the armature conductors are, there- fore, to be so arranged relative to the poles, that a portion of them is in the strongest part of the field, while others are exposed to a weaker field, and some even are in the neutral position. After having thus arranged the conductors, their connecting can be effected by one of the following two methods : (I.) All conductors are connected among each other so as to form an endless winding, closed in itself, and consisting of two or more parallel branches, in each of which all the single E. M. Fs. induced have the same direction, and in which the reversal of the current occurs in such conductors only that at the time are in the neutral position. An armature with such connections is called a closed coil armature (Fig. 86). (II.) The conductors are joined into groups, each group con- taining all such conductors in series which, relative to the field, have exactly the sam position; and the current is taken off from such groups only which at the time have the maximum, or nearly the maximum, E. M. F., all other groups being at that time cut out altogether. An armature wound in this manner is styled an open coil armature (Fig. 87). Although in a closed coil armature the sum of all the E. M. Fs. of the single coils is collected by the brushes (see 9), while in an open coil armature the E. M. F. of one group of coils only is delivered to the external circuit, and although, therefore, the total E. M. F. output of an armature is smaller when connected up in the open coil fashion than it would be if 144 DYNAMO-ELECTRIC MACHINES. [43 the same armature were run at the same speed but connected by the closed coil method, yet an open coil armature offers great advantages in case of high potential machines, as there is no difference of potential between adjoining commutator bars belonging to different groups of coils and only a small Fig. 86. Closed Coil Winding. Fig. 87. Open Coil Winding. number of segments is required to bring the fluctuation of the E. M. F. within practical limits. Open coil armatures are therefore preferable to closed coil ones in case of machines for series arc lighting, where, if closed coil windings are em- ployed, a great number of commutator segments is required on account of the high total potential around the commutator. (See Table XXL, 25.) b. Spiral Winding, Lap Winding, and Wave Winding. According to the manner in which the connecting of the conductors by the above two methods is performed, the fol- lowing types of armature windings can be distinguished: (1) Spiral Winding, or Ring Winding, Figs. 88 and 89; (2) Lap Winding, or Loop Winding, Figs. 90 and 91; (3) Wave Winding or Zigzag Winding, Figs. 92 and 93. In the spiral winding, Figs. 88 and 89, which can be applied in the case of ring armatures only, the connecting conductors are carried through the interior of the ring core, and the wind- ing thus constitutes either one continuous spiral, Fig. 88, from which, at equal intervals, branch connections are led to the commutator, or a set of independent spirals, Fig. 89, which are separately connected to the commutator. 43] ARMATURE WINDING. 145 The lap winding, as well as the wave winding, is executed en- tirely exterior to the core, and can be applied to both drum and ring armatures. In the lap winding, Figs. 90 and 91, the end of each "Coil, Figs. 88 and 89. Spiral Windings. consisting of two or more conductors situated in fields of opposite polarity, is connected through a commutator segment to the beginning of a coil lying within the arc embraced by the former. With reference to the direction of connecting, Fig. 90. Lap Winding. therefore, the beginning of every following coil lies back of the end of the foregoing, and the winding, consequently, forms a series of loops, which overlap each other. Fig. 90 represents such a lap winding for a four-pole drum armature, the development of which, Fig. 91, more clearly shows the forming of the loops and the manner of their overlapping. 146 DYNAMO-ELECTRIC MACHINES. [43 In the wave winding, Figs. 92 and 93, the connecting contin- ually advances in one direction, the end of each coil being connected to the beginning of the one having a corresponding position under the next magnet pole; and the winding, in con- ^ 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 ' p > i and ;z' 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 ' p parallel branches. The latter is the case N if y and - are prime to each other; the former if they have a ^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 7i & = i, if in the connecting formula the number of conductors, JV C , is replaced by the number of coils, n c . For ordinary bipolar armatures, therefore : n - i= i, n & = i, ' p = i ; y = n c q= i (107) 154 D YNAMO-ELECTRIC MA CHINES. [ 45 (2) If the number of commutator segments is half the num- ber of armature coils, /. & 16 Simplex Duplex GD GD Triplex Singly reentrant Simplex Winding " Duplex = Doubly .. = Triply " Triplex < 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 p y i), for drum armatures, and n c = n p y i , for ring armatures; in which: IS 8 DYNAMO-ELECTRIC MACHINES. [46 N Q = 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 i P It is preferable to have the pitchy the same at both end's, 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 folio wing Table XLIIL, 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, 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 _ 1.25 x io 10 "5.X 3> X 27,000 and Table XLIII. shows that the number of conductors in this 46] ARMATURE WINDING. 159 TABLE XLIIL NUMBER OF CONDUCTORS AND CONNECTING PITCHES FOR SIMPLEX SERIES DRUM WINDINGS. I QUALIFICATION OF NUMBER OP CONDUCTORS, JV" C . -i- M- w Jjf B ' i g & S Equation Degree of Description. t3 1 for J\/ c Evenness. 2 < i ^ y'+i 8 jUt.*i f odd Any singly even num- ber. ^(f* 1 ) *-! / + l Any even number, having either 2 or 10 y.=i to8 N c even 3 as remainder when divided by 5, i. e., any number -l(f-) /-I y'+i having a 2 or an 8 as the unit digit. 12 *.u.*. ^ c odd Any singly even num- ber not divisible by 3. H(f^) y y' \ y y'+i Any even number 14 *.=i te9 ^TC even having either 2 or 5 as remainder when divided by 7. ^-Kf* 1 ) y'-\ y y'+i Any singly even num- 16 *=lte S ^odd ber having either 2 or 14 as remain- der when divided y =i(fi) y'l y y'+i by 16. * General formula: N c = -2 n x 2 ; zn- = number of poles, x = any integer. t For ring armatures replace ' by n c (number of coils). t 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. 1 60 DYNAMO-ELECTRIC MACHINES. [46 case must fulfill the condition JV C = 6 x 2, which, for # z= 5, and for the + sign makes ^"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 ^c = 2 (p y m ) , TABLE XLIV. NUMBER OP CONDUCTORS AND CONNECTING PITCHES FOR DUPLEX SERIES DRUM WINDINGS. NUMBER OP POLES 2np KIND OF SERIES WINDING.* QUALIFICATION OF NUMBER OF CONDUCTORS, _ZVc AVERAGE PITCH. % FRONT PITCH. eoe Equation Degree of Evenness. Description. 2 iV c =4 x 2 **- odd Any singly even num- ber. ^=-2 y y' y (5>C5> iV c =4 x 4 ^even Any multiple of 4. =ir 2 l r -\ y+i 4 O O N c =Sx ~T e Any multiple of 8. y f c -[- 2 ) y y' y 1 (2) 2V C =8 x 4 WL odd 4 Any quadruple of an odd integer. H(4-*> I--* y ~T"1 y'-j-l 6 ^c=12 z 2 ^.odd Any singly even num- ber, not divisible by 3. -l(f-) , w I \ cs^ iV c =12 a; 4 f- Any multiply even number (even multi- ple of 2) not divisi- ble by 3. 8 -ZVc=16 a; 4 ^- odd 4 Any quadruple of an odd integer. r=i(f^ /-i y' ~~ 1 46] ARMATURE WINDING. 161 TABLE XLIV. NUMBER OF CONDUCTORS AND CONNECTING PITCHES FOR DUPLEX SERIES DRUM WINDINGS. Continued. NUMBER OP POLES. . 2n p . KIND OF SERIES WINDING.* QUALIFICATION OF NUMBER OF CONDUCTORS, JV C AVERAGE PiTCH.J FRONT PITCH. an Equation for.V c .t Degree of Evenness. Description. 10 ^=30 * 6 T dd Any singly even num- ber having a 4 or a 6 as its unit digit. y 1(** 2 \ y y (2) (5) \N C =2Q x 4 ^.even Any multiply even number having a 4 or a 6 as its unit digit. y 5 1 2 ( V y'-iL/'+i 12 Lar=S4 xs ^even Any multiple of 8, not divisible by 3. 1 ( Nc +2\ y y <><) JV C =24 x 4 ^ odd Any quadruple of an odd integer, not di- visible by 3. y Q\ 2 2 J y'-i '+i 14 O O <> N c =2Sx 10 JV C =28 * 4 JV c =32z 12 %" Any singly even num- ber having 3 or 4 as remainder when di- vided by 7. y- l ( Nc 2} y y ^even Any multiply even number having 3 or 4 as remainder when divided by 7. y 7 | k 2 &) y' 7 i y'+i y 16 ^Lodd Any quadruple of an odd integer of the form 8 x 3. v 1 ( Nc +2\ y (5) (5) ^.=32 * 4 T odd Any quadruple of an odd integer of the form 8 x 1. y s( 2 2 J y'-i y'+i * O O ~ singly re-entrant duplex winding "Q) (J) ^ doubly re-entrant duplex winding. t General formula for O O : N c = 4 p -*" (2 p 4; ( 2 p = number of poles. General formula for(5}(jLX -We = 4 p * 4- ) x = any integer. ^. In case of ring windings replace - by c (number of coils). If y is odd both pitches are = y; \iy is / N c = 6 x 6 N c even Any multiple of 6. y ~ 2 : /-i /+! 4 ooo ^T c =12 x 2 t- Any singly even num- ber, not a multiple of 3. '4(4+) y ,'+1 aM ^ c =12 x 6 f-" Any odd multiple of 6. H(f + 3 ) I J+l 6 ooo JTe=18* N c even Any multiple of 18. '=-s(j+ 8 ) y'-l ^+1 ooo -ZVc=18 x 6 K even Any even multiple of 3, /-I /+! -8 OOO N c =24: x 1Q * odd Any singly even num- ber, not a multiple of 3. 1 p y'-\ ,4! eM N c =24 x 6 f odd Any odd multiple of 6. 4\ 2 / y A* 10 000 14 Nc even Any even number not divisible by 3, and having either a 4 or a 6 as unit digit. ^ . y A fflffl JV C =30 x 6 N c even Any odd multiple of 6, having either a 4 or a 6 as unit digit. y /-i A 46] ARMATURE WINDING. 163 TABLE XLV. NUMBER OF CONDUCTORS AND CONNECTING PITCHES FOR TRIPLEX SERIES DRUM WINDINGS. Continued. QUALIFICATION o g OF NUMBER OF CONDUCTORS, JV C . i too ft AVERAGE g P PITCH4 PH 9 p Equation for Ac.t Degree of Evenness. Description. 1 I 02 12 000 jVc=36 # 18 IT odd Any odd multiple of 18. H(lT+ 3 ) f-i 3/'+l o o o JV C =36 a? 6 -j=r- odd Any odd multiple of 6, not divisible by 9. y =1(^-3) /-i Al Any even number, not , Q a multiple of 3, hav- y y 14 000 ' l 22 j>T c even ing either 1 or 6 as remainder when di- vided by 7. y=if^. 8 ) y'-i y'-M Any multiple of 6, hav- TV / y V (5) N c =42 x 6 Nc even ing either 1 or 6 as remainder when di- vided by 7. Any singly even num- , JQ ^"c ber, not a multiple of y y ooo _ZVJ.=48 # gg -3 Odd 3, having either 6 or 10 as remainder y' 1 At' \ _"| 16 when divided by 16. 1 (N c , o\ Any odd multiple of 6, y ~ 8\ IT j ! (0^65)0 AT" /1Q N c having either 6 or 10 y y UiiU Q- odd as remainder when divided by 16. y'-i y+i *0 O O = singly re-entrant triplex winding :(&XSxS> = triply re-entrant triplex winding, t General formula for O O O : NG = 6 * p x & p - 6), or ' N c = 6 J x ( 4 p - 6)'; V 2 P = "umber of poles. General formula for(2x) (u = number of brushes per set, b = width of brush) ; I total current output of dynamo, in amperes; n\ = number of pairs of brush sets (usually either n" v = i, or equal to the number of bifurcations of the armature current, n\ = n' p ). For the purpose of securing a good contact, the length / k should be subdivided into a set of b individual brushes, of a width ^ 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. 177 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 5 1 1'5 2 2-5 3 3-5 BRUSH PRESSURE, IN POUNDS PER SQUARE INCH. Fig. 114. 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). i 7 8 DYNAMO-ELECTRIC MACHINES. [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 0'51 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 XLVIL CONTACT RESISTANCE AND FRICTION FOR DIFFERENT BRUSH TENSIONS. CONTACT RESISTANCE TANGENTIAL PULL DUE TO BRUSH FRICTION PER SQUARE INCH OF BRUSH SURFACE, PER SQUARE INCH OF CONTACT AT PERIPHERAL SPEED OF 1,000 FEET PER MINUTE. p k) IN OHM. y k , IN POUNDS. BRUSH i IN POUNDS 4 Commutator Dry. Commutator Oiled. PER 3 -g .3 SQUARE INCH. ! P 31 E s Is a J *3 afl jj 11 fi ll il in ' -g al 3 ;_ PH > H W | Is BO Ij || &s 58 1 a Q 9 & l S St 1 H| J .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 1.7 .95 1.5 .48 .30 .45 2 .007 .12 .10 2.25 1.25 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 3.5 1.12 .70 1.05 4 .005 .08 .07 4.5 2.5 4 1.30 .80 1.20 The specific pull, y 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, z- k , can be found from the formula ...... (.19) 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 1 80 D YNA MO-ELECTRIC MA CHINES. [ 49 quotient by the number of sets of brushes and by the square of the current passing through each set, thus: * = 2 x = .00268 X ft* x /2 horse power, ..... (120) ^k X #k X 72 p where ./\ = energy absorbed by contact resistance of brushes; p k = resistivity of brush contact, ohm per square inch surface, from Table XLVIL; 4 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 n "p x 4 x ^ x p k 33,000 = 6 x io- 5 X /' k X 4 X ^ k X n\ X z> k , ........ (121) in which P t = energy absorbed by brush friction, in HP; /'k = specific tangential pull due to friction, at ve- locity z> k , in pounds, see formula (119); 2 #" p X /k X <^k total area of brush contact surfaces, in square inches; v k = peripheral velocity of commutator, in feet per minute, _ <4 X 7t X N 12 By calculating the amounts of /\ and ./^ , from (120) and (121) respectively, for different brush tensions, the best tension giving a minimum value of the total brush-loss, /> k -f- P t , can readily be found. 50] 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-ELECTRIC 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. 119. -LAMINATED JOINT. FIG. 121. -LUG HELD BETWEEN NUTS ON A STUD. F(G . 122 . - LUG ' CLA MPED BETWEEN WASHERS. FIG. f24. -TAPER PLUG INSERTED BETWEEN TWO SURFACES. ,FIG. 125. -TAPER PLUG GROUND TO SEAT AND BOLTED. Figs. 119 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 XLVIII., 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 OF 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. 2 mm. 2 per ampere. Sliding Contact (Brushes) Copper Brush 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 Spring 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 fo 13.5 Brass on Brass 40 to 50 20,000 to 25,000 5.000 to 6,700 6 to 8 12.5 to 16.5 Screwed Contact Copper to Copper 150 to 200 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 10,000 to 13,000 15 to 20 5 to 6.5 Composition to Copper 75 to 100 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 5 to 7 Composition to Copper 100 to 125 8,000 to 10,000 15 to 20 Composition to Composition 75 to 100 10,000 to 13,000 12 to 16 6 to 8.5 Pitted and Screwed Contact Copper to Copper 200 to 250 175 to 200 4,000 to 5,000 30 to 40 2.5 to 3.5 Composition to Copper 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 300 150 to 250 .35 to .55 Copper Wire Cable 1,000 to 1,600 600 to 1,000 .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 &//////A -Si __ .* "~"9 " , ^^,1.7.3"" y////////// 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: 4, = k, x V^ x yffi, (122) where lbs - P er square inch. 11 brass ........... = 6,000 " " 4< phosphor-bronze = 7,000 il " " wrought iron. ... = 10,000 " " aluminum bronze = 12,000 " " " cast steel ....... =15,000 *' " For spiral windings, now, s , as stated above, is given by making it as large as possible, and from (125) we therefore obtain: I 9 DYNAMO-ELECTRIC MACHINES. [53 For windings external to the core, h* may be fixed and then calculated from: 4 >8 = l8x ^r x ^,x>i%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 to 36, 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; r' B = belt speed, in feet per minute, see Table LVIII. ; JV = speed of dynamo, in revolutions per minute. The belt speed in modern dynamos ranges between 2,000 I 9 2 DYNAMO-ELECTRIC MACHINES. [53 TABLE LVI. BEARINGS FOR HIGH-SPEED RING ARMATURES. SIZE OF BEARING. SPEED CAPACITY, IN KILO- VALUE OP CONSTANT IN REVS. PER Mm. (FROM Diameter Length. Ratio. WATTS. 10. TABLE XI.) N. (from Table LII.) <*b i b = & 10 x d b x VN. b : <*b .1 .1 2,600 i li 5.0 .25 .1 2,400 11 5.0 .5 .1 2,200 J si 4.75 1 .1 2,000 I 2f 4.4 2.5 .1 1,700 4i 4.1 5 .1 1,500 If 5f 3.9 10 .11 1,250 If 6f 3.85 25 .12 1,000 2f 10 3.8 50 .13 800 3i 13 3.7 100 .15 600 4f 17i 3.7 200 .16 500 6f 23 3.6 300 .17 450 7i 27 3.6 400 .175 400 8i 30 8.5 600 .18 350 10 33i 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 LVIL BEARINGS FOR LOW-SPEED RING ARMATURES. SIZE OP BEARING. SPEED CAPACITY, VALUE IN REVS. IN KILO- WATTS. OP CONSTANT &10. PER MIN. (FROM TABLE XII.) N. Dimeter (from Table LIII.) <*b Length. i b = &io x d b x VN. Ratio. *b : ^b 2.5 .15 400 H 3f 3.0 5 .16 350 H 4i 3.0 10 .17 300 2 51 2.9 25 .18 250 3i 8f 28 50 .19 200 4i IH 2.7 100 .20 175 H 15i 265 200 .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 13i 32i 2.4 1,000 .28 75 15 36^ 2.4 1,500 .29 70 18 43i 2.4 2,000 .30 65 20 48 2.4 54] MECHANICAL CALCULATIONS. and 6,000 feet per minute (= 600 and 1,800 metres per minute), as follows: TABLE LVIII. BELT VELOCITIES FOB HIGH-SPEED DYNAMOS OP VARIOUS CAPACITIES. BELT SPEED, # B CAPACITY Feet per Minute. Metres per Minute. Up 2.5 to 5 " 25 2,000 3,000 to 3,000 " 4,000 600 to 900 900 " 1,200 10 " 100 4,000 " 5,000 1,200 " 1,500 50 " 500 5,000 11 6,000 1,500 " 1,800 The pull at the pulley circumference, in pounds, is: p - 33>QQQ X HP = 33,ooo X HP ' ~ 12 Watts For an arc of belt contact of 180, which can safely be as- sumed for dynamo pulleys, the pull F v , 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 - z/ Allowing 300 pounds per square inch as the safe working strain of leather, the necessary sectional area of the belt can be found from -- ' X --; .(130) B = width of belt, in inches; / = thickness of belt, in inches; F B = greatest strain in belt, /. > 7 I 48.5 43 38.7 35.2 32.2 500 CO i-^^y 60 53.5 48 44 40 54] MECHANICAL CALCULATIONS. *S Heavy double belt. . A = \\ x ^ = .6 X ^ (133) Three-ply belt 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 XL 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; \\\\* direction, therefore, indicates tint 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 gattss. 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 the name of i weber has been given. 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 200 DYNAMO-ELECTRIC MACHINES. [56 directions; /. e., radii of a sphere. The surface of a sphere of i centimetre radius is 4 n square centimetres; a pole of unit strength, therefore, has a magnetic flux of 4 it absolute or C. G. S. lines of magnetic force, or of 4 TC webers. The number of C. G. S. lines of force, or the number of webers expressing the strength of a certain magnetic field, must consequently be divided by 4 TT, or by 12.5664, in order to give that same field strength in absolute units of magnetism, *". ., in unit-poles. A magnetic field of unit intensity also exists at the center of curvature of an arc of a circle whose radius is i centimetre and whose length is i centimetre, when a current of i absolute electromagnetic unft of intensity, or of 10 practical electromagnetic units, that is, of 10 amperes, flows through this arc. Therefore, the unit of magnetic flux, i. 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; ft^ = percentage of polar arc, see 58; Z a = length of active armature conductor, in feet, for- mula (26) or (148); v e = conductor speed, in feet per second. The field density in metric units is obtained from if Z a is expressed in metres and v c 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 a from the data of the finished armature : L^N C x =x -, ...... (148) 12 12 where N c total number of conductors on armature; / a = length of armature core, in inches; n w number of wires per layer; \ , = number of layers of armature wire; > see 23. j = 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 the application to smooth armatures, however, the polar embrace, ft l , in formula (146) and (147), is to be replaced by the corresponding value of the effective field circumference,-/^-, 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 X v c X ae ' Xio 8 ..(U9) 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 makingthat distance from 1.25 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~Ax K-4J (150) where / p = mean distance between pole-corners; d v = diameter of polepieces; d & = diameter of armature core; for toothed and per- forated armatures, d & is the diameter at the bot- tom of the slots. The value of k^ for various cases may be chosen within the following limits: TABLE LX. RATIO OF DISTANCE BETWEEN POLE-CORNERS TO LENGTH OF GAP-SPACES, FOR VARIOUS KINDS AND SIZES OF ARMATURES. VALUE OF RATIO ku. CAPACITY IN KILO- Smooth Armature. Toothed or WATTS. Bipolar. Multipolar. Perforated Armature. Drum. Ring. Drum. Ring. Bipolar. Multipolar. .1 1.5 2.5 1.5 2.5 1.25 1.25 .25 1.75 3 1.75 2.75 1.5 1.3 .5 2 3.5 2 3 1.75 1.4 1 2.25 4 2.25 3.25 2 1.5 2.5 2.5 4.5 2.75 3.5 2.25 1.6 5 3 5 3 3.75 2.5 1.7 10 3.5 5.5 3.25 4 2.75 1.8 25 4 6 3.5 4.25 3 1.9 50 4.5 6.5 3.75 4.5 3.25 2 100 5 7 4 4.75 3.5 2.1 200 5.5 7.5 4.25 5 3.75 2.2 300 6 8 4.5 5.25 4 2.3 400 .... .... 4.75 5.5 .... 2.4 600 .... 5 5.75 .... 2.5 800 .... 6 .... 2.6 1,000 .... . 6.5 .... 2.7 1,200 .... ... 7 .... 2.8 1,500 7.5 .... 2.9 2,000 ... 8 3 Whenever n can be made larger than given in the above table without reducing the percentage of the polar embrace below its practical limit, it is advisable to do so, and in fact this ratio in some modern machines has values as high as n = 12. 58] USEFUL AND TOTAL MAGNETIC FLUX. 209 b. Bore of Polepieces. The diameter of the polepieces, or the bore of the field, d v , is given by the diameter of the armature core, the height_o_L the armature winding, and the clearance between the armature winding and the polepieces: 2 x (151) d & = diameter of armature core, in inches; h & = height of winding space, including insulations and binding wires, in inches; h c = radial height of clearance between external surface of finished armature and polepieces, in inches; see Table LXI. TABLE LXI. RADIAL CLEARANCE FOR VARIOUS KINDS AND SIZES OF ARMATURES. RADIAL CLEARANCE, h c . Smooth Armature. DIAMETER OF Disc or Ribbon Core. Wire Core. Toothed ARMATURE. t >r Perforated Wire Wound. Armature. Copper Wire Copper Bars. Wound. Bars. Drum. Ring. inches. cm. inch. mm. inch. mm. inch. mm. inch. mm. inch. mm. inch. mm. 2 4 5 10 t 8 | 1.2 1.6 - ft 0.8 0.8 1.2 A 0.8 .. .. 8 12 18 15 30 45 f 1.6 2.4 3.2 i 1.2 1.6 2.4 i 1.6 2.0 ! 2.4 3.2 4.0 t 1.6 2.4 i 1.2 1.2 1.6 24 30 40 50 60 75 100 125 ? 4.0 4.8 i 3.2 4.0 4.8 5.6 A A A 2.4 3.2 4.0 4.8 I 4.8 5.6 6.4 7.2 I 3.2 4.0 4.8 5.6 i 2.0 2.4 3.2 4.0 75 100 200 250 i 6.4 7.2 uV 5.6 6.4 $ 8.0 9.6 f A 6.4 8.0 4.8 5.6 125 300 ~rV 8.0 .9 7.2 i 6.4 150 400 9.6 TS 8.0 ins" 7.2 200 500 A 11.2 1 9.6 . , 8.0 210 DYNAMO-ELECTRIC MACHINES. [58 The radial clearance, which is to be taken as small as pos- sible, in order to keep the air-gap reluctance at a minimum, ranges between 1/32 and 7/16 inch, according to the kind of the armature and its size. The preceding Table LXI. may serve as a guide in fixing its limits for any particular case. The above table shows that with toothed and perforated armatures the smallest clearance can be used, a fact which is explained by the consideration that the exteriors of these armatures offer a solid body, and may be turned off true to the field-bore. For a similar reason wire-core armatures need a larger clearance than disc-core armatures, since the former cannot be tooled in the lathe, and have to be used in the more or less oval form in which they come from the press. Since copper bars can be put upon the body with greater precision than wires, a somewhat larger clearance is to be allowed in the latter case. Finally, a drum armature, in general, has a higher winding space than a ring armature of same size; the unevenness in winding will, consequently, be more prominent in the former case, and therefore a drum armature should be provided with a somewhat larger clearance than a ring of equal diameter. The figures given in Table LXI. may be considered as aver- age values, and, in specially favorable cases, may be reduced, while under certain unfavorable conditions an increase of the clearance may be desirable. c. Polar Embrace. The dimensions of the magnetic field having thus been determined, half the pole-space angle, a, Fig. 130, can be found from the trigonometrical equation: sina = -; (152) TP p = pole distance, from formula (150); d v = diameter of polepieces, from formula (151). The ratio of polar embrace, or the percentage of polar arc, then, is: 90- -ax^ 59] USEFUL AND TOTAL MAGNETIC FLUX. 211 in which a = half pole-space angle, from (152); p = number of pairs of magnet poles. From (153) follows, by transposition: - 90X(. - from which the pole-space angle, a, can be calculated in the case that the ratio of embrace, ft l , of the polepieces is given. 59. Relative Efficiency of Magnetic Field. The useful flux of the dynamo being found from formula (137), the number of lines of force per watt of output, at unit conductor-velocity, will be a measure for the magnetic quali- ties of the machine, and may be regarded as the relative efficiency of the magnetic field. The field efficiency for any dynamo can accordingly be obtained from the equation: x r x Vc = ^ x where #',, = relative efficiency of magnetic field, in webers per watt of output at a conductor velocity of i foot per second. $ = useful flux of dynamo, from formula (137) or ( 138) ; E' total E. M. F. to be generated in machine, in volts; /' = total current to be generated in machine, in amperes; P' = E' X /' = total capacity of machine, in watts; v c = conductor velocity, in feet per second. The numerical value of this constant, $' 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 LXIL, which is averaged from a great number of modern dynamos of all types of field-magnets: 212 DYNAMO-ELECTRIC MACHINES. [59 TABLE LXIL FIELD EFFICIENCY FOR VARIOUS SIZES OF DYNAMOS. CAPACITY, IN KILOWATTS. VALUE OP $ ' f IN WEBERS PER 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 $' p , obtained by means of formula (155), will be within the limits given in this 220x10' 200 400 600 800 1000 1200 1-100 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 LXIII., 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 WEBERS PEJI 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 curves for 25, 30, 40, 60, 214 DYNAMO-ELECTRIC MACHINES. 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 USEFUL FLUX, IN WEBERS, AT CONDUCTOR VELOCITY, PER SECOND, OP: CAPACITY INT KILOWATTS. 25 feet 30 feet 40 feet 50 feet 60 feet 75 feet 100 feet (= 7.5 m.) (= 9 m.) (=12m.) (=15m.) (=18m.) (= 22.5 m.) (= 30 m.) .1 200,000 167,000 125,000 100,000 83,000 .25 400,000 333,000 250,000 200,000 167,000 . . . .5 700,000 583,000 438,000 350,000 292,000 . 1 1,200,000 1,000,000 750,000 600,000 500,000 400,000 . . 2.5 2,600,000 2,200,000 1,600,000 1,300,000 1,100,000 870,000 . 5 4,600,000 3,800,000 2,900,000 2,300,000 1,900,000 1,500,000 . . 10 8,000,000 6,700,000 5,000,000 4,000,000 3,300,000 2,700.000 25 17,000,000 14,200,000 10,600,000 8,500,000 7,100,000 5,700,000 50 31,000,000 25,800,000 19,400,000 15,500,000 12,900,000 10,300.000 . . 75 44,000,000 36,700,000 27,500,000 22,000,000 18,300,000 14,700,000 11,000,000 100 56,000,000 46,700,000 35,000,000 28,000,000 23,300,000 18,700,000 14,000,000 200 100,000,000 83,300,000 62,500,000 50,000,000 i 41,700,000 33,300,000 25,000,000 300 140,000,000 117,000,000 87,500,000 70,000,000 58,300,000 46,700,000 35.000,000 400 147,000,000 110,000.000 88,000,000 73,300,000 58,700,000 44,000.000 500 173,000,000 130,000,000 104,000,000 86,700,000 68,300,000 52,000,000 600 197,000,000 148,000,000 118,000,000 98,300,000 78,700,000 59,000,000 700 216,000,000 163,000,000 130.000,000 108,000,000 86,700,000 65,000.000 800 235,000,000 176,000,000 141,000,000 117,000,000 94,000.000 70,500.000 900 189,000,000 151,000,000 126,000,000 101,000,000 75,500,000 1,000 200,000,000 160,000,000 133,000,000 107,000,000 80,000,000 1,200 219,000,000 175,000,000 146,000,000 ' 117,000,000 87,500.000 1,500 244,000,000 195,000,000 163,000,000 130,000,000 97.500,000 2,000 275,000,000 220,000,000 183,000,000 147,000,000 110,000,000 60. Total Flux to be Generated in Machine. The total flux to be generated in any dynamo is the product obtained in multiplying its useful flux by the factor of its mag- netic leakage : = Ax , = Ax Ax*_xj* ; (156) $' = total flux to be generated in machine, in lines of force; $ = useful flux necessary to produce the required E. M. F. under the given conditions, from formula (137); A = 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 A 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 LXVI1I., 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 2 1 6 D YNA MO-ELECTRIC MA CHINES. [ 6O 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, \ht 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 2 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. 2 S. P. Thompson, "Dynamo-Electric Machinery," fifth edition, p. 156. 3 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. 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 218 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 : A J* nt permeance of useful and stray paths Permance of useful path or, *= *' + * + *+*, (157) where ^, = relative permeance of the air gaps (useful path) ; ^ a = relative average permeance across magnet cores (stray path); ^ $ = relative permeance across polepieces (stray path); ^ 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 or perforated armature: V = \ x * = \ X *' + *+A-+l. . (15 8 ) The factor, \, 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 6 2] PREDE TERM IN A TION OF MA GNE TIC LEA KAGE. 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 FACTOR OP ARMATURE LEAKAGE, Ai WIDTH OF SLOTS TOOTHED ARMATURES PERFORATED ARMATURES ON OUTER STRAIGHT TEETH PROJECTING TEETH RECTANGULAR HOLES ROUND HOLES CIRCUMFERENCE %^%| fe^^ '<%/2%2 ^&// / %' ^tTTf////???*^ ^^^7^2^n~^^ *>* ^/- w*% 4 %>%#%^.. &mmz, %?%^^ 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" 1.01 1.05 " 1.03 .7 1.03 " 1.01 1.04 " 1.02 B. GENERAL FORMULA 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 ( of medium } Distance in medium Area or, in our case of magnetic conductance: Permeance = Permeability x 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 ^IKQ\ Mean length of path between them ' From this, formulae for the various cases occurring in prac- tice can be derived. 220 DYNAMO-ELECTRIC MACHINES. [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: i to + -S 1 ,) (160) where S lt S ^ = areas of magnetic surfaces; c least distance between them; a i , a z = widths of surfaces S t and S 9 , respectively; a angle between surfaces S 1 and S 9 . b. Two parallel plane surfaces facing each other. If the two surfaces S l and S 9 are parallel to one another, Fig. 133, the angle inclosed is a = o, and the formula for Fig. I33- Two Parallel Plane Surfaces Facing Each Other, the relative permeance, as a special case of (160), becomes: 2 = * to + *?.). .., (161) 6 2] PREDE TERM IN A TION OF MA GNE TIC L EA KA GE. 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 b (162) 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, trr<*r-n Fig. J 35- Two Equal Rectangles at Right Angles to Each Other, the angle a 90, formula (160), consequently, reduces to a X b (163) c + a X - e. Two parallel cylinders. In case the two surfaces are cylinders of diameter, d t and length, /, Fig. 136, the areas of their surfaces are d x TT X I; and if they are placed parallel to each other, at a distance, c, apart, the mean length of the magnetic path is c -\- \d; hence the permeance of the air between them: 9= *^XY. .. (164) 222 DYNAMO-ELECTRIC MACHINES. [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 x 4 x k, x A x n ; (170) (171) The symbols used in these formulae are: $' = relative permeance of clearance spaces; *$" = relative permeance of teeth; $'" = relative permeance of slots; d & = diameter at bottom of slots; d" & = diameter at top of teeth; d v = diameter of bore of polefaces; b^ = breadth of armature slots; b t ~ top width of armature teeth; b\ radial spread of magnetic lines along teeth; / a = length of armature core; / f = length of magnetic field; n' c = number of armature slots; fi l = percentage of polar arc, p'x /?. 180 ' n p = number of pairs of poles, ft = pole angle; fl\ = percentage of effective gap circumference, see Table XXXVIII., 38; k^ ratio of magnetic to total length of armature core, Table XXIIL, 26; k^ factor of field deflection, see Table LXVIL, below; ju permeability of iron in armature teeth, at density employed, see Table LXXV., 81. Formulae (170) and (171) apply directly only to straight- tooth armatures. For projecting teeth the same formulae, how- ever, can be used if the dimensions of the projecting tooth are 64] PREDE TERM IN A TION OF MA GNE TIC LEA KA GE. 229 replaced by those of a straight tooth of equal volume, as indi- cated by Fig. 142, the reduced width of the slot, b Sl , taking the place of the actual width, s . For/^r/^z/^armature? with rectangular holes (Fig. 143) the slot permeance is directly expressed by formula (171), while the permeance of the iron projections is equal to that of straight teeth having equal vol- ume. In formula (170), consequently, the reduced width, b S} , and in (171) the actual width, 6 B , of the holes is to be used. For round and oval perforations, Figs. 144 and 145, respect- ively, the iron projections being transformed into straight Fig. 142. Fig. 143. Fig. 144. Fig. 145. Figs. 142 to 145. Geometrical Substitution of Projecting Teeth and Hole- Projections by Straight Teeth of Equal Volume. teeth of equal volume, the reduced width, b Sl , of the perfora- tion is to be used in both (170) and (171). The permeance of the teeth, 1", on account of the high value of the permeability, /*, at even comparatively high satura- tion of the teeth, is very large compared with the permeance of the slots, 2'", so that for all practical purposes $'" in (168) may be neglected, and we have : X (172) The permeance of the clearance space, 2', furthermore, is so small compared with 2", that their sum 2' -f- 2* is practically equal to ^", and by canceling we obtain the approximate formula: 3 = 2' (173) which can be used with sufficient accuracy in all cases where the magnetization in the teeth is not driven beyond 100,000 lines per square inch (= 15,500 gausses). 2 3 D YNA MO-ELECTRIC MA CHINES. [64 Inserting the values from (109) into (173) we obtain for straight-tooth armatures: x x f or projecting-tooth armatures: - K x 7t x A + (^ ' c x A] x / f *a x o and f or perforated armatures: 7T , 63> 4 P ; (175) i + d\ X ft\) X / f TABLE LXVII. FACTOB OF FIELD DEFLECTION IN DYNAMOS WITH TOOTHED ARMATURES. FACTOR OF FIELD DEFLECTION, fa FOK TOOTHED ARMATURES. RATIO or RADIAL CLEARANCE TO PITCH OF SLOTS ON Product of Conductor Velocity and Field Density, in English Measure. OUTER CIRCUMFERENCE. 500,000 1,000,000 1,500,000 2,000,000 2,500,000 0.1 3 4 4.75 5.25 5.5 .15 2.65 3.45 4.00 4.40 4.6 .2 2.40 3.05 3.45 3.75 3.9 .25 2.20 2.70 3.05 3.25 3.4 .3 2.00 2.40 2.75 2.90 3 .35 1.85 2.20 2.50 2.65 2.75 .4 1.70 2.00 2.25 2.40 2.5 .45 1.65 1.92 2.10 2.25 2.35 .5 1.60 1.85 2.00 2.15 2.2 .55 1.55 1.80 1.95 2.05 2.1 .6 1.53 1.75 1.90 2.00 2.05 .65 1.51 1.72 1.87 1.97 2.02 .7 | 1.50 1.70 1.85 1.95 2 The amount of the field deflection in machines with toothed armatures is primarily governed by the ratio of the clearance space to the pitch of the slots, and only secondarily depends upon the ^product of conductor velocity and field density. 65] PREDE TERM IN A TION OF MA GNETIC LEAK A GE. 23 1 The values for use with formulae (174) and (175) are compiled in the above Table LXVIL, while those for use with formula (176) are contained in the previous Table LXVI. Table LXVIL refers to straight teeth only; in case of armatures with projecting teeth, the average of the values from Table LXVIL and from LXVI. for a corresponding perforated armature must be taken. 65. Relative Average Permeance between the Magnet Cores (2,). Since in dynamo-electric machines the magnet cores, with their ends averted from the armature, are magnetically joined by special " yokes " or by the frame of the machine, forming the magnetic return circuit, the magnetic potential between these joined ends is practically = o, while the full magnetic potential is operating between the free ends toward the arma- ture. The average magnetic potential over the whole length of the magnet cores, therefore, is* one-half of the maximum potential, and the average relative permeance, consequently, one-half of that which would exist between the cores, if they had the same magnetic potential all over their length. For the various forms of magnet cores, by virtue of for- mulse (160) to (165), respectively, we therefore obtain the following relative average permeances : a. Rectangular Cores. The permeance between two rectangular magnet cores, Fig. 146, is the sum of the permeances between the inner surfaces Fig. 146. Rectangular Magnet Cores. which face each other, formula (161), and between the end surfaces which lie in the same plane, formula (162); and there- fore the average permeance : 2 3 2 D YNAMO-ELECTRIC MA CHINES. <* * X / + b X I 2 C c b X~ [65 (177) where a y b, t, and / are the dimensions of the cores in inches, see Fig. 146. b. Round Cores. According to formula 164, we have in this case, see Fig. 147 Fig 147. Round Magnet Cores. - X / d 71 X I - X - 2 C , ...(178) -d 2 c -f- 1.5 d c. Oval Cores. For oval cores, Fig. 148, the permeance path consists of two parts, a straight portion between the inner surfaces, and a Fig. 148. Oval Magnet Cores. curved portion between the round end surfaces. Combining, therefore, formulae (161) and (164), we obtain: (a ) X / 2 C , n X / (179) 65] PREDE TERMINA TION OF MA GNE TIC LEA KAGE. 233 d. Inclined Cores. If the cores, instead of being parallel to each other, are^afit. at an angle, Fig. 149, the distance, <:, in formulae (177), (178), Fig. 149. Inclined Magnet Cores. and (179), respectively, has to be averaged from the least and greatest distance of the cores: c = (180) t. 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. (181) 234 D YNAMO-ELECTRIC MA CHINES. 65 for round cores, according to formula (165): *. = --'><; and for oval cores: >-flx/ + *x..rx,, v (183) In multipolar machines, for c, the smaller of either the mean distance between two magnets, Fig. 151, or twice the Figs. 151 and 152. Mean Length of Leakage Path between Magnet Cores in Multipolar Dynamos. mean distance between magnet core and yoke, Fig. 152, is to be taken. f. Iron-clad Types. In certain types of dynamos, known as " Iron- clad" forms because of their yokes constituting a complete encompassment around the machine, if there are two magnet cores, they are not side by side of each other, but lie in line and are faced by the yokes connecting the same (Figs. 153 and 155). i. Bipolar Iron-clad Type. Considering that in the ordinary bipolar iron-clad type, Fig. 153, the magnetic potential between the pole ends of the ig- I 53- Bipolar Iron-clad Type. cores is unity, between the yoke ends, however, is zero, and at intermediate points, consequently, is given by the ratio of 65] PREDETERMINA TION OF MAGNETIC LEAKAGE. 235 the distance from the yoke to the entire length of the core, and further that only half the magnetic potential exists be- tween the poles and the yokes, and that, therefore, the^aver- age potential between cores and yokes at any point is but one-quarter the maximum potential of the core at that point, we obtain the following expression for the total average per- meance between the cores: X 1.285 (184) In this formula it is assumed that leakage takes place in three directions: (i) from magnet core to magnet core along the entire length of their end surfaces (parallel to the arma- Fig. 154. Leakage Paths in Bipolar Iron-clad Type. ture heads), paths /, /, Fig. 154, having an average potential half that between the poles; (2) from core to core across the surfaces facing the yoke portions of the frame, along a dis- tance, from the pole corners, equal to the distance c between D YNAMO-ELECTRIC MA CHINES. [65 cores and yokes, paths //, //; and (3) from the cores to the yokes along the remainder of the length of the core-surfaces opposite the yokes, paths ///, ///. From Fig. 154 the mean area of these paths, ///, ///, is ob- tained : X / = X TT and the mean length: I / 7T \ I / '"\ The magnetic potential at the leakage division point of the core is /- c the mean potentials of the pole and yoke portions of the core consequently are respectively, and the average potentials of the paths //, 77, between the pole portions of the cores, and of the paths 777, 777, between the yoke portions of the cores and the yokes, are respectively. 2. Fourpolar Iron-clad Type. If the magnets are so wound that consequent poles are pro- duced in the yokes, Fig. 155, then the full magnetic potential Fig. 155. Fourpolar Iron-clad Type. prevails between the cores and the yokes, and the average potential along their length is one-half the potential between 6 5] PREDE TERM IN A TION OF MA GNE TIC LEA KA GE. 237 the poles. For the fourpolar iron-clad type, Fig. 155, having two salient and two consequent poles, the permeance between the cores consequently is: ^ _ a* (1 + m) b X (I + **) '~ Here all the leakage is assumed to take place between the cores and the adjacent yokes, for in this type the distance, e, between the pole-corners is generally not much smaller, if any, than the distance, c 9 between cores and yokes, and conse- quently no additional leakage needs to be considered at this point, unless separate polepieces are used. See formula (196). There being no further stray paths in the types considered, formulae (184) and (185) give the total stray permeances of the bipolar and fourpolar iron-clad types, respectively. 3. Single Magnet Iron-dad Type. There being but one magnet core in this type, Fig. 156, the stray paths from that core to the polepiece of opposite polar- Fig. 156. Single Magnet Iron-clad Type. ity and to the adjoining yokes constitute the entire waste per- meance which can be formulated as follows: ) (186) .g. Horizontal Double Magnet Type. This type, Fig. 157, of which the bipolar iron-clad type can be considered a special case, concerning the magnetic poten- 238 D YNAMO-ELECTR1C MA CHINES. [ 66 tials of the leakage paths, has features similar to the iron-clad form, and the permeance across the magnet cores of the hori- Fig. 157. Horizontal Double Magnet Type. zontal double magnet type, which, at the same time is its total waste permeance, accordingly can be expressed by the formula : e + b X - e + m X - X '-< (, Oi) r- X a Xl / -) ( ^ J_ V *) \ ' * M't 4- A) in which is the magnetic potential at the leakage division points of the magnet cores. 66. Relative Permeance across Polepieces (^,). The amount of leakage across the end and side surfaces of the polepieces, that is, across all their surfaces not facing the armature core, depends upon the shape of the polepieces and upon the design of the machine with reference to an external iron surface (bedplate) near the polepieces. For the most usual shapes the following formulae can be de- rived for the relative permeance across the polepieces: a. Polepieces Having an External Iron Surface Opposite Them. i. Upright Horseshoe Type. In the upright horseshoe type, Fig. 158, the entire direct leakage across the polepieces can be assumed to pass through the iron bedplate, hence: 66] PREDE TERMINA 7 'ION OF MA GNE TIC LEAKAGE. 239 ...(188) - 2 Z S half area of iron surface facing polepieces (centre por- tion of bedplate), in square inches; z distance from polepiece to iron surface (height of zinc base), in inches; y, g, h are dimensions in inches, see Fig. 158. Fig. 158. Polepieces of Upright Horseshoe Type. 2. Horizontal Horseshoe Type. In this type, Fig. 159, the lines from the lower halves of the polepieces leak- to the bedplate, while from the upper halves, and from the end surfaces, they pass across the pole gaps: Fig. 159. Horizontal Horseshoe Type. oj) 2 Z ...(189) 240 DYNAMO-ELECTRIC MACHINES. [66 S l = surface of polepiece opposite bedplate ( half of exter- nal surface) ; *S* 3 = end surface of polepiece; S half area of iron surface facing polepieces (or area of portion opposite one polepiece). 3. Four polar Double Magnet Type. In machines of this type, Fig. 160, there are two leakage paths across the polepieces, the lines from the lower pair of 7 Fig. 160. Fourpolar Double Magnet Type. polepieces passing across the bedplate, those from the upper pair across the pole gap: X 2 Z L (190) Since there are no further essential leakages in this type, formula (190) gives the entire relative permeance of the waste paths for the fourpolar double magnet type. b. Polepieces Having No External Iron Surface Opposite Them. i. Inverted Horseshoe Type with Rectangular Polepieces. For rectangular polepieces, Fig. 161, the mean length of all Fig. 161. Inverted Horseshoe Type with Rectangular Polepieces. leakage paths are equal, and the relative permeance between the polepieces may consequently be expressed by: 66] PREDETERMINATION OF MAGNETIC LEAKAGE. 241 (191) g X (/+ 2h) 71 x 2. Inverted Horseshoe Type with Beveled or Rounded Polepieces. In beveled and rounded polepieces, Figs. 162 and 163, re- spectively, the length of the path across the upper surfaces is Figs. 162 and 163. Inverted Horseshoe Type with Beveled and Rounded Polepieces. somewhat smaller than that of the side surfaces, and the per- meance formula consists of two terms: .= x 2ft x > 7T 7T * x - ' + 5-X ..(192) 3. Single Magnet Type. Here there are four distinct paths for the leakage lines from polepiece to polepiece, viz., across- the end surfaces of the Fig. 164. Single Magnet Type. yoke portions, the end surfaces of the pole portions, the facing surfaces of the pole portions, and the inside projections of the pole portions; hence we obtain, with reference to Fig. 164: 2 4 2 D YNAMO-ELECTRIC MA CHINES. r X h [66 4_ All leakage paths of the single magnet type being considered in this formula, (193) gives the total relative permeance of the waste field of that type. 4. Double Magnet Type. There is no leakage between the magnet cores nor between polepieces and yoke in this type, the total stray permeance of Fig. 165. Double Magnet Type. the double magnet type, Fig. 165, therefore, is given by the formula : 2.= r ?]. (194) / ' e + /. 5. Double Horseshoe Type. In the double horseshoe type, Fig. 166, the only leakage across the polepieces takes place at the end surfaces and at Fig. 166. Double Horseshoe Type. the pole corners, hence we have for this, and for similar sym- metrical bipolar types: 66] PREDETERMINATION OF MAGNETIC LEAKAGE. 243 X/ = 2 X ; /x/ e (195) 6. Iron-clad Type. In iron-clad types, Fig. 167, the leakage from the end sur- faces and the back surface of the polepieces takes place to the Fig. 167. Iron-clad Type. yoke, see formula (204) ; for the permeance across the pole- pieces, only the side surfaces are to be considered, and we obtain: h x x (196) 7. Radial Multipolar Type. In radial multipolar dynamos, Fig. 168, lines pass from the end surfaces of the polepieces across the pole gaps: Fig. 168. Radial Multipolar Type. ..(197) = number of pairs of magnet poles. 244 DYNAMO-ELECTRIC MACHINES. [67 8. Tangential Multipolar Type. The leakage between adjacent polepieces in tangential mul- tipolar machines, Fig. 169, takes place across the length of the magnet cores: Fig. 169. Tangential Multipolar Type. S l = half area of external surface of polepiece; S^ = area of side surface of polepiece; iS", = area of projecting portion of end surface, = end surface area of magnet core. 67. Relative Permeance between Polepieces and Yoke PW- According to the general principle of calculating relative permeances, the magnetic potential between polepieces and yoke is to be taken = ^ with reference to the potential be- tween two polepieces of opposite polarity. For, the yokes serve to join two magnet cores in series, magnetically, and are therefore separated from the polepieces by but one magnet core. If the yokes join the magnets in parallel, then they usually serve as polepieces also, and must be considered as such in leakage calculations. Since the amounts of the leakages in the various paths are proportional to their permeances, in dynamos having an ex- ternal iron surface near the polepieces, most of the leakage takes place between the polepieces through that external sur- face; and in such machines the leakage from the polepieces to the yoke is comparatively small. 6 7] PREDE TERM IN A TION OF MA GNE TIC LEA KA GE. 245 a. Polepieces Having an External Iron Surface Opposite Them. i. Upright Horseshoe Type. From the polepiece area facing the yoke, ,S 3 , Fig. 170, the leakage takes place in a straight line equal in length to that of Fig. 170. Upright Horseshoe Type. the magnet cores, while from the end surfaces the leakage paths are quadrants joined by straight lines: S 3 = projecting area of polepiece, = top area of pole- piece minus area of magnet core. 2. Horizontal Horseshoe Type. The leakage from the polepieces to the yoke partly passes directly across the cores, and partly takes its path through the iron bed; hence, with reference to Fig. 159, page 239, we have approximately: 3 4 = f + s * (200) Sj half area of external surface of polepiece; S 3 = projecting area of polepiece, = area of yoke-end of polepiece minus area of magnet core; / = length of magnet core; z = distance of polepiece from iron bedplate. 246 DYNAMO-ELECTRIC MACHINES. [67 b. Polepieces Having No External Iron Surface Opposite Them. i. Inverted Horseshoe Type with Rectangular Polepieces. In this case the leakage from the side surfaces of the pole- Fig. 171. Inverted Horseshoe Type with Rectangular Polepieces. pieces to the yoke, Fig. 171, is twice that of the upright type 2> 4 = 4'+ - fXk (201) 2. Inverted Horseshoe Type with Beveled or Rounded Polepieces. Similar to the former case we have for these forms of the polepieces, Figs. 172 and 173, respectively: Figs. 172 and 173. Inverted Horseshoe Type with Beveled and Rounded Polepieces. $=^ + /* (202) 3. Horizontal Double Magnet Type. If in this type special polepieces are applied, Fig. 174, lines Fig. 174. Horizontal Double Magnet Type. pass from the lower surfaces of the same to the yoke: 67] PREDETERMINATION OF MAGNETIC LEAKAGE, 247 | ....(203) Here it is supposed that the path from the projecting back surfaces of the polepieces to the yoke below them is shorter than the length of magnet cores; if the latter is not the case, the term in the denominator of the second portion of formula (203) is to be replaced by /, the length of the cores. 4. Iron-clad Types. In the bipolar iron-clad type, with separate poleshoes, Fig. 175, lines leak to the yoke from the back surfaces of the pole- Fig. 175. Bipolar Iron-clad Type with Poleshoes. pieces; hence the relative permeance, half of the total mag- netic potential existing between polepieces and yoke: . (204) 7t 4 As to the denominator of the second term, see remark to formula (203). This amount, formula (204), as well as the relative permeance across the side surfaces of the polepieces, formula (196), is to be added to the relative permeance found by formula (184), iron-clad type without polepieces, in order to obtain the total relative permeance of this type. In the fourpolar iron-clad type, since the total magnetizing force of each circuit is supplied by one magnet only, there is 248 DYNAMO-ELECTRIC MACHINES. [68 full magnetic potential between polepieces and frame, and both terms of formula (204) must consequently be multiplied by 2. 5. Radial Multipolar Type. In this type leakage lines pass from the projecting portions, ,3, Fig. 176, of the back surfaces of the polepieces to those of Fig. 176. Radial Multipolar Type. the yoke, S^, and if the yoke is relatively near to the pole gap, leakage also takes place from the end surfaces of the polepieces to the yoke: X A^ + ^) + f/JLgY ...(205) According to the design of the frame, then, either formula (205) is to be used together with the latter portion of formula (197), or the entire formula (197) is to be combined with the first portion of formula (205), in order to obtain the total joint permeance across the polepieces and from polepieces to yoke of the radial multipolar type. By the proper combination of formulae (167) to (205) the probable leakage factor of any dynamo can be calculated from the dimensions of the machine. D. COMPARISON OF VARIOUS TYPES OF DYNAMOS. 68. Application of Leakage Formulae for Comparison of Tarious Types of Dynamos. In order to illustrate the application of the above for- mulae, and at the same time to afford the means of comparing the relative leakages in various well-known types of dynamos, in the following, frames of various types are designed for the same armature, and the leakage factor for each machine thus obtained is calculated. 68] PREDE TERMINA TION OF MA GNE TIC LEAK A GE. 249 In order to accommodate all the types to be considered here, the armature has been chosen of a square cross-sectioirpm.,- 16 inches core diameter, and 16 inches long. This armature, if wound to a height of about inch, and driven at a speed of 800 revolutions per minute, will yield an output of 50 KW. The polepieces for this armature must have a bore of iy inches, and must be 16 inches long; the pole angle, for all bipolar types, is chosen ft = 136. and the distance between the pole corners, therefore, is 17^ X sin (180 136) 6 inches. Figs. 177 to 186 give the dimensions of various types of frames for this armature, viz., (i) Upright Horseshoe Type; .ins, Fig. 177. Upright Horseshoe Type. (2) Inverted Horseshoe Type; (3) Horizontal Horseshoe Type; (4) Single Magnet Type; (5) Vertical Double Magnet Type; (6) Vertical Double Horseshoe Type; (7) Horizontal Double Horseshoe Type; (8) Horizontal Double Magnet Type; (9) Bipolar Iron-clad Type; and (10) Fourpolar Iron-clad Type, respectively. The probable leakage factors of these machines figure out as follows: i . Upright Horseshoe Type, Fig. 777. By (167): 16 1-3 X (175 - 16) = 3ZS_ '95 2 5 DYNAMO-ELECTRIC MACHINES. By (178): [68 14 X 7T X 20 __ 43.98 X 20 2 X By (188): 1.5 X H 15 _ 24 ' 5 ' X (i2j + 8-|) + 300] _ 2 x 5 (199): 16 x = 4-3 + 3-3 = 7-6. X By (157): A = T 92 +24.5 + 29.1 + 7.6 _ 253.2 = i9 2 192 2. Inverted Horseshoe Type, Fig. 178. Fig. 178. Inverted Horseshoe Type, = 192. = 24.5- By (192): - 6 i X 16 2 X i7i X 7 . * -+ - ^- = 6.2 + 9.4^:15.6. By (202): 85 16 X nj = 4-3 + 4-9 - 9-2. 20 68] PREDE TERMINA TION OF MA GNE TIC LEAK A GE. 25 1 By (157): A = 9- 2 _ 192 192 3. Horizontal Horseshoe Type, Fig. 179. l Fig. 179. Horizontal Horseshoe Type. 2, = 192. , = 24-5- By (189): By (200): I 4 X A = i9 2 + 24.5 + 53-3 + 27.6 192 4. Single Magnet Type, Fig. 180. ^ 192. By (193): 297.4 192 6yt 252 DYNAMO-ELECTRIC MACHINES. [68 192 192 Fig. 180. Single Magnet Type. 5. Vertical Double Magnet Type, Fig. 181. ! - -40& ^ Fig. 181. Vertical Double Magnet Type. a, = 192. By (194): 2 . 2 v j (49J+ 16) X 7 + (228.5 ~ 78.5) , i6X4J ( 16 = 2 (38.2 + 6.8) = 90. ^ _ 192 + 90 __ 282 = ^ ^ 192 192 6. Vertical Double Horseshoe Type, Fig. 182. ^ = 192. By (177): > . . 14 x 16 2 X ^ 29 . 9 .1= 41. 68] PREDETERMINATION OF MAGNETIC LEAKAGE. 253 By (195): = ' 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|) + i4 X 3j , 16 X = 5 -h 10.2 = 15.2. X = T 9 2 + 4i + J 4-6 + I 5- 2 _ 262.8 7. Horizontal Double Horseshoe Type, Fig. 183. X ^' V^l ^S ; M 80-8 l. ins. Fig. 183. Horizontal Double Horseshoe Type. , - 192. By (179): 16 . 6 X 7t X 16 7i + i- X 6 = '9-3 + 2 S-7 = 45- 254 DYNAMO-ELECTRIC MACHINES. [ea 4j X I7j I X 16 j X 16 = 2 x (4-6 -j- 1.6 4- .6) = 13.6. By (201): _ (16 X 6f - 80.8) 4- 25 X 16 16 X - *-+, (.- +- 16 + 11 X 18 45 = 14.2 4- 4.45 4- 6. 15 = 24.8. _ 275.4 8. Horizontal Double Magnet Type, Fig. 184. Fig 184. Horizontal Double Magnet Type. , = 192. By (187): X X H+ 25* X- 16 X 7 , 1 y I0 i x I6 >< H -T- I "2 ^ T " 1 = 8 -5 + 5- 1 -h 5- 1 192 + 31 192 192 5i 6 8] PREDE TERM IN A TION OF MA GNE TIC LEA KA G. 255 9. Bipolar Iron-clad Type, Fig. 185. 2, = I 9 2. By (184): Fig. 185. Bipolar Iron-clad Type. I6x i7i 1.285 X 5^ ' _ I9 2 + 30 222 ^T" = 192 == L15 - 10. Fourpolar Iron-clad Type, Fig. 186. 7 ' 9 Fig. 1 86. Fourpolar Iron-clad Type. By (167): 16 7f -f lyj n X r X 16 9 > 339 By(!8 5 ): DYNAMO-ELECTRIC MACHINES. [68 16 X , r 8} X - = 174+ 107.8 174 = 88.8 281.8 174 19 = 107.8. 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 - 2 55 Horizontal horseshoe type 0.55 Single magnet type 0.32 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 o. 15 Fourpolar iron-clad type 0.62 o. 15 = 2.14 0.15 = 1.70 0.15 = 3-67 0.15 = 2.13 0.15 = 3-i3 o. 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, $, 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 A* - ~ amperes ^m (E potential at terminals, r m = total resistance of shunt circuit) is flowing, in a shunt machine; or of T se series turns traversed by a current of 7 se = / 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 K + at & + at m + at t , (206) 257 258 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; at & = 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 r 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, $'. Transposing (206), we obtain: - (at e + ta & + at r ), ..... (207) in which AT is known from the machine test, at g and at A can be calculated from the useful flux, and at r is given by the data of the armature. The numerical value of at m having been found, we can then calculate the total magnetic flux through the machine. In the following, the two cases occurring in practice are con- sidered separately, viz. : (i) but one material, and (2) two different materials being used in building the magnet frame of the machine. 69] CALCULA T10N OF AC TUAL MA GNE TIC LEAK A GE. 259 a. Calculation of Total Flux when Magnet Frame Consists of but One Material. If but one single material either cast iron, wrought iron, mitis metal, or steel is. used in the magnet frame, the calcu- lation of the total magnetic flux is a very simple operation. For, if /" m denotes the length of the magnetic circuit in the magnet frame, from air gap to air gap, and (B" m is the cor- responding mean specific magnetization, then, according to formula (226), 88, we have: */ = /"* X /((&') (208) But the density in the magnet frame, (B" m , is the quotient of the total flux per magnetic circuit, <" , by the mean sectional area, S m , of one magnetic circuit in the field frame, con- sequently: /m = /'m X / from which follows: (D L (209) Dividing the numerical value of #/ m , as found by formula (207), by the length, l" m , of the circuit, we therefore obtain the numerical value of the specific magnetizing force per inch length for the respective material. By means of Table LXXXVIIL, or Fig. 256, then, the density &" m , corresponding to this particular value of / ((B" m ) for the material employed, can be found; and since we obtain the total magnetic flux per magnetic circuit of the machine from the simple formula 0' = S m X (B* m , ... .......... (210) where S m = mean sectional area of magnet frame, in square inches; (B" m = density of lines of force in magnet frame, corre- sponding to the value of at m -=- l" m in Table LXXXVIIL, or in Fig. 256. 260 DYNAMO-ELECTRIC MACHINES. [69 b. Calculation of Total Flux when Magnet Frame Consists of Two Different Materials. In magnet frames made up of two different materials either of wrought iron cores and cast iron yokes and pole- pieces; or of wrought iron cores and yokes, and cast iron pole- pieces; or of any other combination of two of the various kinds of iron in use for this purpose the calculation of the total magnetic flux is performed by an indirect method. Let us assume that the two materials used are wrought and cast iron, and consequently denote by ^w.i. tne length of one circuit in the wrought iron portion of the frame, in inches; " ^"c.i. the length of one circuit in the cast iron portion of the frame, in inches; " S wAt the mean area of one circuit in the wrought iron por- tion, in square inches; " S c j the mean area of one circuit in the cast iron portion, in square inches; "(B" w . i. the average magnetic density in the wrought iron, in lines of force per square inch; and " &"C.L tne average magnetic density in the cast iron, in lines of force per square inch ; then we have the equation: /m = '"w.I. X / (" in an indirect manner, as follows: The usual flux, <, being known by virtue of formula (137) or (138), respectively, an assumption can be made of the total flux per circuit, $", by adding to the usual flux per circuit, (n z being the number of the magnetic circuits in the ma- chine), from 10 to 100 per cent., according to the size and the type of the dynamo (see Table LXVIII.). In dividing this approximate value of 3>" by the areas vS w L and S cA , respect- ively, the densities (B" w . i. an d >" c .\. are obtained, and by means of Table LXXXVIIL (Fig. 256) the corresponding value of / ("w. an d/ ("C.L)> respectively. Introducing these values in the equation ($" 3^ a value Z is produced which, in general, will differ from the value at m obtained by formula (207). If Z is found smaller than the actual value of at m , then the value of 4>* was assumed too small; if larger, then >" was taken too large. A second assumption of 3>" is now made so that the corresponding value of Z obtained in a similar manner from Table LXXXVIIL and formula (213) will be on the other side of #/ m , /". " = total flux per magnetic circuit, calculated from formula (210), or (212), respectively; $ = useful flux cutting armature conductors,* from (137) or (138), respectively; n z = total number of magnetic circuits in machine. The author, by employing his method of calculating the leak- age from the ordinary machine test, '69, has figured the leakage factors for a great number of practical dynamos 1 of which the test data were at his command, and by combining his results with the researches of Hopkinson, 2 Lahmeyer, 3 Corsepius, 4 Esson, 5 Wedding/' Ives, 7 Edser, 8 and Puffer, 9 has averaged the following Table LXVIII. of leakage factors for dynamos of various types and sizes, which is intended as a guide in making the first assumption of the total flux, for solving equation (212), as well as for dimensioning the field magnet frame (see 60), but which may also be made use of in obtaining an approxi- mate value of the leakage coefficient for rough calculations. From said table the general rule will be noted that the factor of leakage is the greater the smaller the dynamo, which is due to the difficulty, or rather impossibility, of properly dimension- ing the magnetic circuit in small machines. In these the length of the air gaps is comparatively much larger, and the relative 1 For list of machines considered see Preface. 2 J. and E. Hopkinson, Phil. Trans., 1886, part i. 3 Lahmeyer, Elektrotechn. Zeitschr., vol. ix. pp. 89 and 283 (1888). 4 Corsepius, Elektrotechn. Zeitschr., vol. ix. p. 235 (1888). 5 W. B. Esson, The Electrician (London), vol. xxiv. p. 424 (1890); Journal Inst. El. Eng., vol. xix. p. 122 (1890). ' W. Wedding, Elektrotechn. Zeitschr., vol. xiii. p. 67 (1892). 7 Arthur Stanley Ives, Electrical World, vol. xix. p. u (January 2, 1892). s Edwin Edser and Herbert Stansfield, Electrical World, vol. xx. p. 180 (September 17, 1892). 9 Puffer, Electrical Review (London), vol. xxx. p. 487 (1892). 7O] CALCULA TIO^ T OF A CTUAL MA GNE TIC LEA KA GE. 2 63 8JULVM01IX Nl AJLIOVdVO IIP 5 S 11 III SJJLVM OT IX Nl AllOVdVO 8888889 -ifriO >O "S^jFaiS^o.tia; 2 ~ . & $ a . j o ^ O . <-C * V I It &2'S S -S e .as ' :si g o -5 2 8. ^ 2 o> o tx M II t! O ^ s 3 s. |.s g fc/J .- O rt o O _v ^S C fcfl ' g 3 -*- O (^ o ^ tuo C CS 111 O " v a, *> -t: rt r- r- ^3 3 f - g -C3 ^^ S *? 5 S O -5 I ll V 2 |^ O ^ ^3 ^ 1 ^ a, * u "^ ^ 11 .S C cS w . ^ 3 -t-i oj T3 C S 4) > - .1 2 B -^ '" tiO S o -^ 'So I "o - "S 4J o ^ o 2 S t3 o t/1 u rs **- ^ 10 C C w s e 2 rl O o L o ^- -a 8 I o Cu pt, S ^ ^ -c 2 6 B^g c/) c ti? 8 g 1 1 264 DYNAMO-ELECTRIC MACHINES. [ 7O 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 Iron -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 line 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 A 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 \ vol. 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. 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). /3. 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. 2I 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 po'si- 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 " undertype" 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 . G. Bernard Company, Troy, N. Y. ; by the Detroit Electrical Works, 1 Detroit, Mich. ("King" dynamo); the Com-_ FIG. 205 FlQ. 206 FIG. 207 Figs. 187 to 207. Types of Bipolar Fields. mercial Electric Co. 2 (A. D. Adams), Indianapolis, Ind. ; the Novelty Electric Co., 3 Philadelphia, Pa.; the Elektron Manu- 1 Electrical World, vol. xxi. p. 165 (1893). 2 Electrical World, vol. xx. p. 430 (1892). 3 Electrical World, vol. xvi. p. 404 (1890). 272 D YNAMO-ELECTRIC MA CHINES. [ 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. 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., 5 Ampere, N. J.; further, machines of the Keystone Electric Co., 6 Erie, Pa.; the Belknap Motor Co., 7 Portland, Me.; the Holtzer-Cabot Electric Co., 6 Boston, Mass.; the Card Electric Motor and Dynamo Co., 9 Cincinnati, O. ; the La Roche Elec- trical Works, 10 Philadelphia, Pa. ; the Excelsior Electric Co., 11 New York; the Zucker & Levett Chemical Co., 13 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., 16 Detroit, Mich.; the National Electric Manufacturing Co., 16 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). 5 Electrical World, vol. xvii. p. 130 (1891); Electrical Engineer, vol. xiv. p. 199 (1892). 6 Electrical World, vol. xix. p. 220 (1892). ^Electrical World, vol. xxi. p. 470 (1893); Electrical Engineer, vol. xiv. p. 210 (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.) 13 Electrical World, vol. xxi. pp. 286, 306, 471 (1893). 14 Electrical World, vol. xv. p. II (1890). 15 Electrical World, vol. xvi. p. 437 (1890); Electrical Engineer, vol. x. p. <6 9 5 (1890). 16 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., 4 Budapest, Austria ; Allgemeine Elektricitats Gesellschalt, 6 Berlin; Berliner. Maschinenbau Actien-gesellschaft, vorm. L. Schwartzkopff, 6 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. 9 (Bain), Chicago, 111., and by O. L. Kummer & 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 hosseshoe 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. 2 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. Electroteckn., vol. vii, p. 78 (1889); Kittler, " Handbuch," vol. i. p. 930. 5 Grawinkel and Strecker, " Hilfsbuch," fourth edition (1895), p. 287. 6 Grawinkel and Strecker, " Hilfsbuch," fourth edition, p. 288. 7 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 (1894). 12 Electrical Engineer, vol. xiii. p. 397 (1892). 274 D YNA MO- EL EC TRIG MA CHINES. [ 7 2 Jenney Electric Motor Co., 1 Indianapolis, Ind. ; the Porter Standard Motor Co., New York; the Fort Wayne Electric Corp., 2 Fort Wayne, Ind. ; the United States Electric Co., New York; the Holtzer-Cabot Electric Co., 3 Boston; the Card Electric Motor and Dynamo Co., 4 Cincinnati, O. ; the Simp- son Electrical Manufacturing Co., 5 Chicago; the Chicago Electric Motor Co., 6 Chicago; the Bernstein Electric Co., 7 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, 18 Warren, O. ; the Bos- ton Motor Company, 14 Boston; the Elbridge Electric Man- ufacturing Company, Elbridge, N. Y. ; the Woodside Electric Works 1B (Rankin Kennedy), Glasgow, Scotland; by Greenwood & Batley, 1 ' Leeds, England ; by Goolden & Trotter 17 (Atkinson), England; and by Naglo Bros., 18 Berlin. 1 Electrical Engineer ', vol. xiii. p. 182 (1892.) 2 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). 5 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). 11 Grawinkel 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). ^Electrical World, vol. xxi. p. 471 (1893). 15 7 'he 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. 18 Grawinkel and Strecker, " Hilfsbuch," fourth edition, p. 314. g 72] FORMS OF FIELD MAGNETS. 275 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., 2 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 Feldka"mp motor, built by the Electrical Piano Company, 5 Newark, N. J. ; and in the fan motor of the De Mott Motor and Battery Company; 6 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, 9 Manchester, Conn. ; the Duplex Electric Company, 10 Corry, Pa. ; the Gen- 1 Electrical Engineer, vol. xvii. p. 181 (1894). 3 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. ^Electrical World, vol. xxi. p. 240 (1893). 6 Electrical World, vol. xxi. p. 395 (1893). 7 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, 2 England; Oerlikon Works (Brown), 3 Zurich, Switzer- land; Helios Company, 4 Cologne; and by Naglo Bros., e 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, 6 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, 9 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 " (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, " Hilfsbuch," fourth edition, p. 312. 6 Electrical World, vol. xxii. p. 247 (1892). 7 Martin and Wetzler, " The Electric Motor," third edition, p. 126. 9 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." 11 Kittler, " Handbuch," vol. i. p. 879. 12 Electrical Engineer, vol. xiv. p. 50 (1892). 13 Electrical Engineer, vol. xvi. p. 323 (1893). 34 Kapp, " Transmission of Energy," p. 292. 72] FORMS OF FIELD MAGNETS. 277 Wayne Electric Corporation l (Wood), Fort Wayne, Ind. ; La Roche Electric Works, 2 Philadelphia; Granite State Electric Company, 3 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, 6 Schenectady, N.Y. (Thomson-Houston Arc Light type), Detroit Electric Works, 7 Detroit, Mich. ; Eickemeyer Com- pany, 8 Yonkers, N. Y. ; Fein & Company, 9 Stuttgart; and Aachen Electrical Works 10 (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. 1 Electrical World, vol. xxiii. p. 845 (1894); v l- xxviii. p. 390 (1896); Elec- trical Engineer, vol. xvii. p. 598 (1894). 2 Electrical Engineer, vol. xiii. p. 439 (1892). ^ 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. 9 Kittler, " Handbuch," vol. i. p. 944. 10 Kittler, " Handbuch,." vol. i. p. 917. 11 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.) 278 DYNAMO-ELECTRIC MACHINES. [72 In Figs. 205 and 206 the two possible cases of the vertical single magnet iron-clad 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., arid 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 4 (Mor- dey), London, and by Stafford and Eaves, 5 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, 6 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 18 (Garbe, Lahmeyer & Co.), Aachen; Schuckert & Company, 14 Nuremburg, Germany; Oerlikon Works, 15 Zurich; and the Zurich Telephone Company, 16 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 Elektrotechn. Zeitschr., vol. xi. p. 135 (1890). 6 S. P. Thompson, " Dynamo-Electric Machinery," fourth edition, p. 202. 6 Elektrotechn. Zeitschr., vol. xi. p. 122 (1890). I Electrical Engineer, vol. xvii. p. 314 (1894). s Electrical World, vol. xxiii. p. 191 (1894). 9 Electrical World, vol. xxii. p. 15 (1893). 10 Electrical Engineer, vol. xvii. p. 290(1894). II Electrical World, vol. xix. p. 283 (1892). 12 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 Fia.212. FIG. .21 7 FIG. 21 3 FIG. 21 4 FIG. 215 FIG. 21 6 FIG. 21 8 FIG. 21 9 FIG. 220 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 Schenectady, 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, 12 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). 2 Electrical World, vol. xxi. p. 91 (1893); vol. xxiv. p. 421 (1894); Electrical Engineer, vol. xviii. p. 330 (1894). 3 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). 6 Electrical World, vol. xxiii. p. 878 (1894); vol. xxviii. p. 395 (1896). 7 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). 11 Electrical World, vol. xxiii. pp. 475 and 785 (1894); vol. xxviii. p. 423 (1896); Electrical Age, 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, 6 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., 16 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). 2 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. 7 Grawinkel and Strecker, " Hilfsbuch," fourth edition, p. 304. 8 Grawinkel and Strecker, " Hilfsbuch," fourth edition, p. 311. 9 Grawinkel and Strecker, " Hilfsbuch," fourth edition, p. 327. 10 Electrical Engineer, vol. xii. p. 597 (1891). 11 Kittler, " Handbuch," vol. i. p. 934. 12 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 L'Electricien, vol. i. p. 33 (1891). 15 Kittler, " Handbuch," vol. i. p. 916. Zeitschr. f. Elektrotechn., vol. v. p. 545 (1887). 17 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, 1 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, 5 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, 1 * London, England ("Victoria" Dynamo); by M. E. Desro- ziers, 11 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. ^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. 5 500 HP. Generator, Electrical World, vol. xx. p. 224 (1892). 6 Kittler, " Handbuch," vol. i. p. 905. 7 Electrical World, vol. xviii. p. 165 (1891). 8 Elektrotechn. Zeitsckr., 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 Gravvinkel and Strecker, " Hilfsbuch," fourth edition, p. 317. 13 Electrical World, vol. xxviii. p. 372 (1896). u 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 t Fig. 214, is obtained, which is used by the Brush Electrical Engineering Company 1 (Mordey), London, England, and by the Fort Wayne Electric Company a (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, 6 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. * Electrical Engineer vol. xv. p. 46 (1893). 3 Electrical World, vol. xix. p. 13 (1892); vol. xxii. p. 120(1893). 4 Kittler, " Handbuch," vol. i. p. 945. 5 Electrical World, vol. xxv. p. 33 (1895). ' Electrical World, vol. xx. p. 85 (1892). 284 D YNA MO-ELEC TRIG MA CHINES. [ 7 $ 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 2 (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, 6 England; while the single-magnet form (Fig. 222) is employed by the Electron Manufacturing Company 7 (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). * 7^he Electrician (London), vol. xxi. p. 183 (1888), 7 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, 2 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 Bunder-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. 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 if, *'. ,, 4 " 2 - 5.09 1.44 H H 2 Circles 5.01 1.41 3 " 6.14 1.73 4 " 7.09 2.00 @ 8 " 10.03 2.83 B Ring, 1:1 3.85 1.085 Q 1:2 4.09 1,155 1:3 4.43 1.25 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, /. e., that the fl-ux 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 ii times that of least cross-section of armature, if the cores are of good wrought iron, or about. 2j 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 to 4 times the arma- ture section for cast iron field magnets. Professor S. P. Thompson, in his "Manual on Dynamo- 1 Elektrotechn. Zeitschr., vol. xv. p. 50 (February 8, 1894); Electrical World, vol. xxiii. p. 337 (March 10, 1894). 2 Elektrotechn. Zeitschr., vol. xv. p. 206 (April 12, 1894); Electrical World, vol. xxiii. p. 680 (May 19, 1894). 3 Transactions Am. Inst of El. Eng., vol. iv. (May 18, 1887); Electrical Engineer, vol. iii. p. 221 (June, 1887). 76] GENERAL CONSTRUCTION RULES. 293 Electric Machinery," l 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 wrought 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 shouTd be as soft and free from impurities as possible. It is prefer- able, whenever practicable, to have it annealed, and, if not toa 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. [76 cast iron is increased about 5 per cent. ; by 3 per cent, admix- ture it is increased 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 " Mitis metal," or cast wrought 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. 76] 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 LXL, 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-ELECTRIC 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 FIG 226 FiQ.227 FIQ. 228 FlQ 229 FlQ. 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 re^ch 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 maybe 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 1 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 if 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 magnetic insulator, 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. 3 * 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 y 1 ^ 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., LXXI., 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 FOB HIGH-SPEED DYNAMOS WITH SMOOTH-CORE DRUM ARMATURES. CAPACITY IN KILOWATTS. Diameter of Armature Core . (from Table X.) J tov M.53 BS | -I? 11 *o Radial Clearance (from Table LXI.) Radial Length of Gap-Space. Inch. Ratio of Height of Zinc Block to Length of Gap-Space. fJj n = 5*"" "5 ^3 lM 81*5 '- gUCss O..M as ^P-I CAPACITY IN KILOWATTS. Diameter of Armature Coi (from Table XII Height of Winding Spac (from Table XVIJ Radial Clearanc (from Table LXJ Maximum Radi Length of Gap-Sp Inch. Ratio of Height of Zinc Block to Maximum Len of Gap-Space. I N 1 " 1 "o If S 2 12" H" H" 3 34" 15^ 3 15 li 1 5 3 4 15 5 17 If TS JJ| 34 5 12 10 21 14 5 ^T 3f 6 12 15 23 If tt II 4 6f 10 20 25 Hi TS Iff 4i 74 10 25 27 if 3 IST. 8 10 30 50 30 36 it* 4 4 S" 4f 8f 94 8 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. 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 OP ZINC BLOCKS FOR DYNAMOS WITH VARIOUS KINDS OF ARMATURE. HEIGHT OF ZINC BLOCKS. DIAMETER OF Smooth Armature. Toothed ARMATURE CORE. or Perforated Drum. Ring. Armature. Inches. Inches. Inches. Inches. 3 If 4 2 6 2f 2 14 8 4 3 ft 10 5 3i 3 12 5f 4i 31 15 G* 5 4 18 7i 6 5 21 8f- 7 6 24 9f 8 7 27 11 9 8 30 . . 10 84 36 Hi H 79. Pedestals and Bearings. In the design of the base, especially when the portion of the 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 FIQ. 240 SECTION C-D FIQ. 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 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. 307 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 ratia 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 ON JOINT MAGNETIZING FORCE REQUIRED FOR 1 INCH. DIFFER- EQUIVALENT OF JOINT- DENSITY or MAGNET- IZATION. DUE TO MAGNETIC ATTRAC- ENCE DUE TO JOINT, Air Space, Length of Iron, &"m TION. /nff 2 Solid. Jointed. 5C - OC OC T Lines per sq. in. m 3C, Amp. 5 Amp. ,TC .1C 72,134,000 uv 2 "^i Amp. .3133 X &" m 36 Ibs. turns. turns. turns. Inch. Inch. per. sq. in. i 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 50.8 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 308 D YNAMO-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 2\ 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- FlQ.243 FiQ.,244 FI3.245 FlQ. 246 FlQ. 247 FIG 248 FlQ. 249 FlQ 250 .W.I. 'STUD Figs. 243 to 250. Joints in Magnetic Circuits. netic circuit may be solved either by setting the wrought iron into the cast iron, 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. 39 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 \h.t permeability of the material. The number of lines per square centimetre of sectional area set up by a certain magnetizing force in air is conventionally designated by X, that in iron by (B, and the permeability by 81] CALCULATION OF FIELD MAGNET FRAME. the symbol /^ ; between these three quantities, therefore, exists the relation = w , or (E = yu X OC (215) Since for air the permeability j.i = 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 defined 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 OP MAGNETIZATION. PERMEABILITY, /u,. Lines per sq. inch <$>" Lines per cm'. (B Annealed Wrought Iron. Commercial Wrought Iron. Gray Cast Iron. Ordinary Cast . Iron. 20,000 3,100 2,600 1,800 850 650 25,000 3,875 2,900 2,000 800 700 30,000 4,650 3,000 2,100 600 770 35,000 5,425 2,950 2,150 400 800 40,000 6,200 2,900 2,130 250 770 45,000 6,975 2,800 2,100 140 730 50,000 7,750 2,650 2,050 110 700 55,000 8,525 2,500 1,980 90 600 60,000 9,300 2,300 1,850 70 500 65,000 10,100 2,100 1,700 50 450 70,000 10,850 1,800 1,550 35 350 75,000 11,650 1,500 1,400 25 250 80,000 12,400 1,200 1,250 20 200 85,000 13,200 1,000 1,100 15 150 90,000 14,000 800 900 12 100 95,000 14,750 530 680 10 70 100,000 15,500 360 500 9 50 105,000 16,300 260 360 . .... 110,000 17,400 180 260 , .... 115,000 17,800 120 190 120,000 18,600 80 150 125,000 19,400 50 120 f 130,000 20,150 30 100 . . . , . 135,000 20,900 20 85 . 140,000 21,700 15 75 While the permeability of air and of all non-magnetic sub- stances is a constant (for air it is i, and for diamagnetic mate- rials slightly less than i) for all stages of magnetization, that of magnetic materials varies with the degree of saturation. 3 * 2 D YNA MO-ELEC TRIG MA CHINES. [ 8 1 The more lines a certain cross-section of iron carries, the less permeable is it for additional lines, as is evident from the preceding Table LXXV. containing the average permeabilities of different kinds of iron at various degrees of magnetization. At a certain limit, for every kind of iron, a very material in- crease in the magnetizing forces does not appreciably increase the magnetization induced, and the iron is then saturated with lines of force. This limit of magnetization in annealed wrought iron is reached at a density of about (&"= 130,000 lines per square inch, or (B = 20,200 lines per square centimetre; in soft steel at (&"= 127,500 lines per square inch, or (B = 19, Sea- lines per square centimetre; in mitis iron at ($>"= 122,500 lines per square inch, or (B = 19,000 lines per square centimetre; in cast iron with a 6.5 per cent, admixture of aluminum at (B" = 87,500 lines per square inch, or OJ = 13,500 lines per square centimetre, and in ordinary cast iron at (&"= 77,500 lines per square inch, or (B 12,000 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, X, 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 5C = 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 X =100; and an increase of 100 per cent, in the magnetizing force, consequently causes a rise in density of i8j^ 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, t.he limits of the magnetic densities of the different materials are to be fixed with regard to the rela- 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. 313 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 OP MAGNETIZATION. ABSOLUTE SATURATION. Lines p. sq. inch. AREA OF FIELD MAGNET FRAME. Capacity in Kilowatts. iductor Veloc (Table Xtt. 't. per second Average Useful Flux. (Table LXIV.) Lines of force. Av'age Leak'ge Coeffi- cient. Table LXVIII Average Total Flux, Lines of force. Wr'ght Iron, 8m Cast Steel, Sm Mitis Iron, S m/ Cast Iron, 6.5* Al. Sm Cast Iron, ordm'y 3 ' ~ 90,000 85,000 80,000 45,000 ~ 40,000 eq. in. sq. in. sq in. sq. in. sq. in. .1 50 100,000 1.80 180,000 2 2.1 2.2 4 4.5 .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 5 75 1.500,000 i 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 90 160 180 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 1,935 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 3 i6 D YNA MO-ELE C TRIC MA CHINES. [83 TABLE LXXIX. SECTIONAL AREA OF FIELD MAGNET FRAME FOR LOW- SPEED RING DYNAMOS. >, AREA OP FIELD MAGNET FRAME. *b] 3 >M 8 l a lls 3 3i Average Useful Flux. (Table LX1V.) Lines of Av'age Leak'ge Coeffi- cient. Table LXVIH Average Total Flux. *'. Lines of force. Wr'ght Iron, Sm Cast Steel, Sm Mitis Iron, Sm Cast Iron, 6.5* AJ. Sm Cast Iron, ordin'y Sin I force. 90,000 85,000 80,000 45,000 40,000 D sq. in. sq. in. sq. in. sq. in., sq. 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 10,000,000 111 117.5 125 S22 S50 25 30 1 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 75,000,000 833 883 938 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 45 157,000,000 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 2,800 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, ajid x 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. MULTIPOLAR TYPES. SIZE OF CORE. Cylindrical Cores. Rectangular or Oval Cores. Cylindrical Cores. Rectangular or Oval Cores. .. 1 M Diameter of Circular Cross-Section. Area of Rectangular or Oval Section. Height Winding Space. Ratio of Winding Heighl to Diameter of Coi Height of Winding Space. >tio of Winding H to Diam. of Equa Circular Section P. J3 02 fl ~ fe 5 2 Height of Winding Space. atio of Winding 11 to Diam. of Eqiu Circular Section 3 PH Ins. cm. Sq. ins. Sq. cm. Inch. Inch. Inch. Inch. j 2.5 .8 4.9 t/ .50 Q/ .75 2 5.1 3.1 20.4 H .375 "i" .50" 1J4 .625 ji/ .75 3 7.6 7.1 45.4 1 .33 iH .42 19! .58 2 .67 4 10.2 12.6 81.7 1/4 .31 18 .38 2 .50 2V .20 mz .20 4 .22 21 53.3 346 2231 2% .113 3-M .18 3%. .18 .215 24 61. 452 2922 2J4 .104 4 .17 4 .17 5 .21 27 68.6 573 3696 2% .097 4/4 .16 4/4 .16 5V<2 .205 30 762 707 4560 2'M .092 4l/ .15 41^ .15 g .20 33 83.8 855 5515 2% .087 5 .15 4% .145 Q\ .197 36 91.5 1018 6576 3 .083 5J-6 .15 5 .14 7 .195 3*8 DYNAMO-ELECTRIC MACHINES. [ 8S 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 J the equivalent diameter for bipolar types, and from \\ 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| to f the equivalent diameter for multipolar types. In the following Tables LXXXL, 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 /;wzand cast steel only. From Tables LXXXL and LXXXIL 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. 319 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 OF CYLINDRICAL MAGNET COKES FOR BIPOLAR TYPES. DIMENSIONS OP MAGNET CORES, IN INCHES. TOTAL FLUX, Wrought Iron and Cast Steel. Cast Iron. IN WEBEES. Diam. Length. Ratio Diam. Length. Ratio 4n / / m :4n 2 " ' 5.8 33 3 ' H 2% 6 3 30 4 3 6.9 25 T 5 s" 94" 8.0 20% ii* 2 " 2.9 15* 6 8 7.5 22 11 3 8.7 18 13 2Vfs 3.1 14 8 T 9 1T 4J4 8.0 20 % <$4 10.0 16 it 3J4 3.5 13 10 R 5V 8.8 18 13 flZ 11.7 14 JL 4 3.8 12 12 it 7 10.2 16 7 5% 13.1 12 3 4.0 11 15 II 8^ 11.3 14 i; 7 14.9 11 2 5^Z 4.2 10 18 i M 10 12.3 12 t^ 8/4 16.5 10 \/ gi2 4.3 10 21 i $ 12 13.5 10 T 9 5 9^ 16.9 9^ % 7iJ 4.6 9^ 25 i 14 15 9 R 11 17.6 9 &A 8Va 4.9 9 30 i" 16 16 S 11 13 18.9 $4 1^| 10 5.3 8^ 40 !' Ifc 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 BETWEEN RECTANGULAR 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. TO \VlDTH OF CORES. Minimum. (Small Machines.) Average. Maximum. (Large Machines.) 1 1 1.0 1.0 .0 3 4 1.05 1.07 .1 2 3 1.1 1.15 .2 1 2 .15 .22 .3 1 3 .2 .3 .4 4 .25 .37 .5 5 .3 .45 .6 6 .35 .55 .75 7 1.4 .65 .9 8 1.5 .75 2.05 1 9 1.6 .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. 325 84. 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 FlQ.252 FIG. 253 FlQ. 254 Figs. 251 to 255. Various Kinds of Polepieces. pieces makes a right angle to that through the cores (Fig. 252); 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. I 3 Dimensions of Polepiece. Dimensions of Polepiece. o S '3 Thick- 5 1 I p 5 15 ness in S . Area in Centre M !lL IH 1 |? Centre. ^ OB O-aJ <' 1 Square Inches. 2 1 ol J2 2 iJ * Inches. ^ o ^* ^* .*. V N HoW^| O W * Hi ^ &^w^| O u C 5 1 a 31* i a^ 5 JO Jf 53 tD = c o fl || 1 ll^ QJ HH 1 sp Wrought Iron. Cast Iron. a < w 5 O 3 &* 5 e - PQ .1 350.000 If 2| 34 4 9 1 175,000 4 4f | If .25 500,000 2i 8 a 250,000 5 5f a 24 .5 650,000! 2f ^4 6i t a 325,000 6 6f 1 900,000! 3i 4 6 1 a 450,000 7 7f 8* 44 2 l,400,000i 3f 44 7 1 2 675,000 8 9 3| 6f 3 1,800,000 44. 5! 8i a 2i 900,000 94 104 44 9 5 2,500,000 ^i 6i 94 if 1,300,000 11 12 13 10 3,500,000 6 7 104 it 3| 2,100,000 14 15 104 21 15 5,000,000 6| 7f 12 at 2,800,000 15 16 14 28 20 6,000,000 74 8| 13 4* 3,500.000 16 17 174 35 25 7,000,000 8|. 9| 14 24 5 4,200,000 18 19 21 42 30 8,000,000 9 15 2f 5| 4,800,000 20 21 24 48 50 12,500,000 104 HI 18 7 7,000,000 24 25 35 70 75 16,500,000 12-i 131 20 44 8i 9,500,000 28 29J 474 95 100 21,000,000 15 22 4f 94 12,000,000 32 334 60 120 150 30,000,000 184 20i 26 Sf 114 17,000,000 36 374 85 170 200 38.000,000 31 64 21,500,000 40 42 107* 215 300 57iOOO,000 28 38 74 15 30,000,000 46 48 150^ 300 In the second case, Fig. 252, met with in bipolar and multi- ple horseshoe and in tangential multipolar types, the height of the polepieces is determined by the diameter, and the length of the polepiece by the length of the armature, while the area of the cross-section, perpendicular to the flow of the lines, is to be made of the size obtained by formula (216) at the end next to the magnet core, and to be gradually decreased in amount from that end to the opposite end or to the centre of 85] CALCULATION OF FIELD MAGNET FRAME. 327 the polepiece, respectively, according to whether there is but one magnetic circuit, or whether two circuits are parsing through the same polepiece. Since, in bipolar machines, the lines of force are supposed to divide equally between the two halves of the armature, only one-half of the total flux passes the centre of the polepieces, in order to reach the half of the armature opposite the magnets, and the area in the centre of the polepiece consequently needs to be but one-half that at the end next to the core. In case the two circuits passing through each polepiece, Fig. 254, the same applies to the cross-section of the polepiece, at one-quarter the height from either end. For ready use, in the preceding Table LXXXVIL, the dimen- sions of wrought- and cast-iron polepieces for various sizes of bipolar horseshoe type dynamos are calculated for drum and ring armatures, by combining the respective data given in former tables. In the third case, Fig. 253, finally, which is found in single and double magnet types, the length of the magnetic circuit in the polepiece is determined by the diameter of the armature, by the cross-section of the magnet core, and by the height of their winding space; the width, parallel to the armature shaft of the polepiece near the magnet, is given by the width of the magnet core, and that near the armature by the axial length of the latter. The heights, parallel to the axis of the magnet core, in case of a single circuit, are to be so chosen that all of the cross-sections, up to that in line with the pole corner next to the magnet core, have an area at least equal in amount to that obtained by formula (216), and that the section in line with the armature centre has an area of one-half that amount. In case of two circuits meeting at the polepieces (consequent pole types). Fig. 255, the full area has to be provided from either end of the polepiece to the sections in line with the pole corners, half the full area at quarter distance from each pole corner, that is, midway between each pole corner and the pole centre, and sufficient cross-section for mechanical strength only is needed at the centre of the polepiece. PART V. CALCULATION OF MAGNETIZING FORCES. CHAPTER XVII. THEORY OF THE MAGNETIC CIRCUIT 86. Law of the Magnetic Circuit. The magnetic flux through the various parts of the mag- netic circuit being known by means of formulae (137), 56, and (156), 60, respectively, and the dimensions of the magnet frame being determined by the rules and formulae given in Chapters XV. and XVI., the magnetomotive force necessary to drive the required flux through the circuit of given reluctance can now be calculated by virtue of the "Law of the Mag- netic Circuit." For the magnetic circuit a law holds good similar to Ohm's Law of the electric circuit; in the electric circuit: Electromotive Force Current (or Electric Flux) = and analogously, in the magnetic circuit: Magnetomotive Force Magnetic Flu* , R e i uct ance -- ' from which follows: Magnetomotive Force Magnetic Flux x Reluc- tance ................... .................... (222) The Reluctance of a magnetic circuit, similar to the electric case of resistance, can be expressed by the specific reluctance, or reluctivity, of the material, and the dimensions of the mag- netic conductor, thus: Reluctance = Reluctivity X Lengtl L . Area But the reluctivity of a magnetic material is the reciprocal of its permeability (similarly as the resistivity of an electric con- ducting material is the reciprocal of its conductivity), and con- sequently we have: Reluctance = = - K L , ength - ..... (223) Permeability X Area 33 2 DYNAMO-ELECTRIC MACHINES. [87 Combining (222) and (223), we obtain: Magnetomotive Force = Magnetic Flux X Len S th Area Permeability and since the quotient of magnetic flux by area is the mag- netic density, we have : Magnetomotive Force = Magnetic Density x L h Permeability The permeability of magnetic materials depending upon the magnetic density employed in the circuit, see Table LXXV., 81, the quotient of magnetic density and permeability also depends upon the density, and has a fixed value for every degree of saturation and for each material. But this quotient multiplied by the length of the circuit gives the magneto- motive force required for that circuit, and consequently represents the magnetomotive force per unit of length, or the specific magnetomotive force of the circuit. In order to obtain the M.M.F. required for any material, any density and any length, therefore, the specific M. M. F. for the respective material at the density employed is to be multiplied by the length of the circuit: Magnetomotive Force = Specific M. M. F. x Length. (224:) 87. Unit Magnetomotive Force. Relation Between Magnetomotive Force and Exciting Power. An infinitely long solenoid of unit cross-sectional area (i square centimetre), having unit magnetizing force or exciting power (i current-turn) per unit of length (i centimetre) pos- sesses poles of unit strength at its ultimate extremities. If the exciting power per centimetre length, therefore, is i ampere- turn, /. e., y 1 ^ of a current-turn (the ampere being the tenth part of the absolute unit of current-strength), the poles pro- duced at the ends of the solenoid will be of the strength of ^ of a unit pole. Since a unit pole disperses 4 n lines of force, or webers, see 55, the magnetic flux of a unit solenoid of infinite length and of a specific exciting power of i ampere-turn per centimetre is 4 it webers. 88] THEORY OF THE MAGNETIC CIRCUIT. 333 and the density of the flux is 4 TT 4 it webers per square centimetre ', or gausses. The reluctance per unit length of the solenoid, the latter being of i square centimetre sectional area, is that of i cubic centimetre of air, and therefore is unity, or i oersted, hence the M. M. F. of the coil per ampere-turn of exciting power being the product of magnetic flux and reluctance, is 4_7T 10 C. G. S units of magnetomotive force, or gilberts. A magnetomotive force of gilberts being excited by one ampere-turn of magnetizing force, and the magnetomotive force being proportional to the magnet- izing force producing the same, it follows that the entire M. M. F. of a circuit, in gilberts, is 4J7T 10 times the total number of ampere-turns; and inversely, in order to express the exciting power necessary, to produce a certain M. M. F., the number of gilberts to be multiplied by 10 -.796; thus: Number of Ampere-turns = x Number of Gil- 4 n berts 88. Magnetizing Force Required for any Portion of a Magnetic Circuit. The magnetizing force required for any circuit is the sum of the magnetizing forces used for its different parts. 334 DYNAMO-ELECTRIC MACHINES. [88 From (224) and (225), 87, follows that the exciting power required for any part of a magnetic circuit is 10 4 n times the product of the specific M. M. F. and the length of that portion of the circuit: Magnetizing Force = -1^- x Specific M. M. F. x Length. 4 n The product of the specific magnetomotive force, for the particular material and density in question, with the constant factor 10 *$?. represents the exciting power per unit length of the circuit, or the Specific Magnetizing Force; consequently we have: Magnetizing Force Specific Magnetizing Force X Length, or, Number of Ampere-turns = Ampere-turns per unit of Length x Length. Denoting the density of the lines of force in any particular portion of a magnetic circuit by (B, the specific magnetizing force, being a function of the same, by / ((B), and the length by /, the number of ampere-turns required for that portion of the magnetic circuit can be calculated from the general formula: at =/ "I C/2 3 Is- a=/((**a) X /" a , .......... (230) where/ (&" a ) = average specific magnetizing force, in ampere- turns per inch length, formulae (231) to (235); l" & = mean length of magnetic circuit in armature core in inches, formula (236) or (237), respectively. Owing to the circular shape of the armature the area of the surfaces 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. 34* The average specific magnetizing force, therefore, is obtained by taking the arithmetical mean of the extreme values^ __ /('.) = 7 {/('.,)+/(') } in which/ ((&" ai ) = maximum specific magnetizing force, for smallest area of magnetic circuit; see Table LXXXVIII., column for annealed wrought iron; f ('a 2 ) maximum specific magnetizing force, for largest area of magnetic circuit, Table LXXXVIII. ; 3> = useful flux of machine, in webers; S" &1 net cross-section of armature core, in square inches; *S" aa = maximum area of circuit in armature core, in square inches. The area of the magnetic circuit in the armature can be expressed by the product of the net length and the depth of the core, and of the number of poles; hence the minimum area: S" ai = 2 n X 4 X b & X * and the maximum area: S" a2 = 2n p x 4 x b\ x k^ ...... (233) where n v = number of pairs of magnet poles; / a = length of armature core, in inches; b & radial depth of armature core, in inches; b a = maximum depth of armature core, in inches; k^ = ratio of net iron section to total cross-section of armature core, see Table XXIII., 26. In multipolar dynamos the maximum depth b' & of the core is approximately equal to half the tangential width of the pole- pieces; for bipolar machines b' & is half the largest chord that can be drawn between the internal and external armature per- ipheries. For bipolar smooth armatures, Fig. 257, b\ can be 342 DYNAMO-ELECTRIC MACHINES. 91 expressed by the core diameter, i ., (B" s = magnetic densities in wrought iron, cast iron, and in steel, respec- tively, in lines per square inch; /("w.i.), / ("c.i.), / \>" s ) = corresponding specific magnet- izing forces of the respec- tive materials, from Table LXXXVIIL, or Fig. 256; X / Vi ^ / ci. X / // i(B // X /'. = average specific magnetizing force of magnet frame in ampere-turns per inch length; /" w .i., ^"c.i., /*s lengths of magnetic circuit in wrought iron, in cast iron, and in steel, respectively, in inches; /" m = 7" w h 4- /" c>i -f /* g = total length of magnetic circuit in magnet frame, in inches. The densities (B vv-i ., (B C . L , and (B s are the quotients of the total magnetic flux, #',-by the mean total areas, *S* W-1 ., *S"* Cil ., and ^"g, of the magnetic circuits in the respective materials: ",,,. = 1^-; ",,.= %-; '. = J ..... (239) *J w.i. c.i. 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^ 6" 3 , ---- in various portions, / / 2 , / 3 , ---- of its length, the total magnetizing force required for that mate- rial is: 92] MAGNETIZING FORCES. 345 7T ) X /. + (240) where / /& 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' ~ n z X AT = 2' p X n z X AT ' or a = arc tan 35 DYNAMO-ELECTRIC MACHINES. [93 the total number of field ampere-turns being the product of the number, AT, of ampere-turns per magnetic circuit, and of the number, 2 , 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, the 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. ILinesper 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 imtltipolar 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. Fig. 270. Influence of Armature Current upon Magnetic Density in Polepieces. If the average density in the polepieces, $' -+ S p , is denoted by (fc" p , then the distorted densities are in Sections I, I: (B" pl = &" p X i sin a in Sections II, II: &" pn = "P X ^7- (246) The magnetizing force required to produce these densities in the polepieces can be found from af p /(')+/',.), ....(247) 2 where /" p = length of magnetic circuit in the polepieces, in inches; / (V) an d / (" p n) = specific magnetizing forces per inch length for the densities (B" pl and (B" pII , re- spectively, formula (245), for the material used; to be taken from Table LXXXVI., or from Fig. 256. But since the magnetic force necessary to produce the origi- nal average density is *'p=> P X/((B* p ), which is smaller than at'^ we can find the number of ampere- turns by which the field magnetomotive force is diminished on account of this indirect effect of the armature current, by sub- tracting at p from (247). Doing this we obtain: af r = at' p - at v 352 DYNAMO-ELECTRIC MACHINES. [93 The total weakening effect of the armature winding per mag- netic circuit can therefore be found by combining (244) and (248), thus: at- = aS f + of. 271 X l8o .(249) 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: i8o l (250) if the following values of the coefficient / 14 are employed : TABLE XCI. COEFFICIENT OF ARMATURE REACTION FOR VARIOUS DENSITIES AND DIFFERENT MATERIALS. AVEBAGE MAGNETIC DENSITY IN POLEPIECES. Wrought Iron and Cast Steel. Mitis* Iron. Cast Iron. Coefficient of Armature Lines Lines Lines Lines Lines Lines Reaction per sq. in. per sq. cm. 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 F.G .272 Fiq. 275 FIG.. 2?6 FIG. 277 F'G. 278 I FIG. 285 FIG. 286 FIQ. 287 FIG. 288 FIG. 289 FIG. 290 FIG. 291 FIG. 292 FIG. 293 FIG. 294 FIG. 295 FIG. 296 FIG. 297 FIG. 298 FIG. 299 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. [ 94 cuits, 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; d m internal diameter of coil space, in inches; / m = length of coil space, in inches; h m = height of coil space, in inches; V m volume of coil space, in cubic inches; 3 m = diameter of magnet wire, bare, in inches; 6' m = diameter of magnet wire, insulated, in inches; N m = total number of convolutions; Z m = total length of magnet wire, in feet; wtm total weight of magnet wire, in pounds; r m = resistance of magnet wire, in ohms; p m = resistivity of magnet wire, in ohms per foot; A m = - - = specific length of magnet wire, in feet per Pm ohm; A/ m = specific length of magnet wire, in feet per pound. The total number of convolutions filling a coil space of given dimensions with a wire of given size is: #* = ?- x -fc = /m f m (251) m in m 359 ' 3 6 D YNAMO-ELECTRIC MA CHINES. [05 The diameter (insulated) of wire required to fill a bobbin of given size with a given number of convolutions, irrespective of resistance, is: S' m = J L * *- (252) Fig. 304. Dimensions of Coil Bobbin. The total length of wire of given diameter which can be wound on a bobbin of given dimensions, is: D 12 7 m X = . ,6.x From (254) the dimensions of a coil can be calculated on which a certain length of wire of given diameter can be wound. If the internal diameter and the height of the coil space are given, the length can be computed from: / ~ 12 x X X n X 95] COIL WINDING CALCULATIONS. 361 When length and winding depth are known, the internal coil diameter is found from: _ 12 X Z m X " ' which, multiplied by the sectional area of the wire, tf m 2 , gives the cross-section of the wire per unit of current strength, that is, its current density: _ tf m 2 _ Z m m T ' ~ 77 1 ^^ \ in ^^ / m/ * m "^^m The product (# m 2 x An) f 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, i. e., in the case of copper: # m J X p m 12 ohms, at about 60 Cent. ( 140 Fahr.); consequently the current density in the magnet wire: (269) For a given machine, therefore, (^" m being constant) the cur- rent density only depends upon the total length of the wire, and is independent of its size. Formula (269) may be used to determine the practical limits of Z m , by limiting the value of the current density, / m . From (269) follows directly: An= -x^ m ; ............. (270) g96] COIL WINDING CALCULATIONS. 3 6 5 and since the practical value of / m ranges between 240 and 1800 Circular Mils per ampere (= 5300 to 700 amperes- per square inch, or 8. 2 to i.i amperes per square millimetre), we have: .M. per amp. . .(- m ) m in = 20 ^m; ) / for (j m ) ma * = i, 800 C. M. per amp. . . (L m ) max = 150 m . } The total length of magnet wire, in feet, should therefore be from 20 to 150 times the difference of potential between the field terminals, in volts. From (269) we can also derive the following formula, which gives, directly in Circular Mils, the area of a magnet wire effecting a certain magnetizing force at given potential between field terminals, viz. : 12 X An X / m 12 X N m X / m X / t (N m X /...) X (it X / t ) _ATxf t 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, / T , the minimal limit of which is always given* by the circumference of the magnet core, a preliminary value of d m can be quickly determined, and from this the value of / T is easily adjusted if necessary; a re- calculation with the correct value of / T 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 1 "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 6 m , the accurate formula for the area of the wire would be : 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 -^m * m X T'm ~ : ~J?~ X ^ m ) ^m in which P m = energy absorbed in magnet winding, in watts (see 98); consequently: But the resistance of the magnet winding can be ex- pressed by: x (I + - 004 x ^ x " x where wt' m = weight of magnet winding, including insulation, in pounds; k lb = 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 io- 6 X k X AT X / t X m X # m 4 P m X wt' m or, _ 12 X io~ 6 X / 1B X AT X / t X^g m X ^ m a ^ ' m TJ > -* m and since by (272) we have, approximately: &m X <^ m 2 = 12 X 4T X / tl . 96] COIL WINDING CALCULATIONS. we finally obtain: wf m = 144 X io~ 6 X k lt X or, 367 /^rx 4V I 1000 y (374) The constant /& 16 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, Inch. Insula- tion S. C. C. Inch. Space Occupied by Wire. Cir. Mils. of Copper. Square Mils. Ratio of Copper to Weight of Winding. Ibs. per of Constant in Formula Total cu. inch. (274). Volume of t 7T Coil. B. W. G. B. &S. m 6m ~ 6m m 1 &15 &li re) 4 .204 .012 46,656 32,685 .702 .225 32.5 (7) 5 .182 .012 37,637 26,016 .69 .221 31.8 8 .165 .012 31,329 21,383 .683 .218 31.4 'e .162 .010 29,584 20,612 .697 .223 32.2 *9 .148 .010 24,964 17,203 .688 .220 31.7 10 (8) .134 .010 20,736 14,103 .682 .218 31.4 11 (9) .120 .010 16,900 11,310 .669 .214 30.8 12 .109 .010 14,161 9,331 .66 .211 30.4 io .102 .010 ' 12,544 8,171 .65 .208 30.0 is .095 .010 11,025 7,088 .644 .206 29.7 ii .091 .010 10,209 6,504 .637 .204 29.4 (14) 12 .081 .007 7,744 5,153 .665 .213 30.7 15 13 .072 .007 6,241 4,072 .65 .208 30.4 16 (14) .065 .007 5,184 3,318 .64 .205 29.5 17 (15) .058 .007 4,225 2,642 .625 .200 28.8 (18) 16 .051 .007 3,364 2,043 .607 .194 27.9 17 .045 .005 2,500 1,590 .637 .204 29.5 19 .042 .005 2,209 1,385 .627 .201 29.0 18 .040 .005 2.025 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 .032 .005 1369 804 .587 .187 27.0 22 21 .028 .005 1,089 616 .546 .175 25.2 23 22 .025 .005 900 491 .565 .181 26.1 24 23 .022 .005 729 380 .521 .167 24.1 25 24 .020 .005 625 314 .503 .161 23.2 26 25 .018 .005 529 254.5 .48 .1535 22.1 27 26 .016 .005 441 201 .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 DYNAMO-ELECTRIC MACHINES. [97 average value of k lt is = .21, and that of k lt is = 30, and therefore approximately: (AT X /A 2 3 o x ( - -^ ' J y 1000 / (275) m that is to say : x /Ampere-feety I 1000 ) Weight of winding = Watts abs orbed 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 per square inch of radiating sur- face, is found. The actual temperature increase of any mag- net coil can, therefore, be obtained by the formula: P v y HI "m "m * / 5 X -- , where m = rise of temperature in magnets, in Centigrade degrees; P m = energy absorbed in magnet-winding, in watts; ( I m = current in magnet wind- ing, in amperes; JS m - E. M. F. between field terminals, in volts; r m = resistance of magnet winding, in ohms; = radiating surface of magnet coils, in square inches. 97] COIL WINDING 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: SM = An X 71 X /' m = (4n + 2/fc m ) X 7t X /' m J (277) for rectangular magnets: SM = 2 X /' m X (/ + ^-Mm X *); ....(278) and for magnets of oval cross-section (rectangle between two semicircles) : - 2 X /' m X [(' - *) + ( 2 ~ + *- ) X *] --(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, = SM + *m X / T X /* 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: ^M 2 = ^M + 2m X /T X ^ 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: ^ M3 = SM + 2 m x h m x (/T - * y ) (282) In the above formula (277) to (282): SM = radiating surface of prismatic surface of magnet coil; SMI radiating surface of prismatic surface plus one end surface per coil; 37 DYNAMO-ELECTRIC MACHINES. [97 S*M 2 = radiating surface of prismatic surface plus two end flanges per coil; SM S = radiating surface of prismatic surface plus pro- jecting portions of coil flanges; d m = diameter of circular core-section; Z> m = external diameter of cylindrical magnet coil; h m = height of magnet winding, see Table LXXX., 83; l' 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, ^' M , of the magnet cores is given instead of the radiating surface, S M , of the coils, the value of fl' 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 XCIIL, 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 XCIIL, directly be based upon the given surface of the magnet cores. 98. Allowable Energy Dissipation for Giyen 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] COIL WINDING CALCULATIONS. 37 1 Il fc P O 02 a p goj 32 I s II e of per || .o !!? 1 a^ !I iK^ .; o c. S^l i.l O O O O O mo 10 o * 000*00 ^t-OOOifSOOOOQOQ o q T-I i-, o< O 00 ^ ^ ^' r4 TH' rH r^ I-! rH r^ r4 T-H 5< Ot CO O 00 O MS 372 DYNAMO-ELECTRIC MACHINES. [98 perature increase of the coil, the maximum of its energy dissi- pation is also fixed. By transposition of (276) we obtain: J p m = ^ oX 5 M , (283) 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, per watt to the square of core surface; S M = radiating surface of magnet coils, in square inches; see formulae (277) to (282); 6" M = 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 P v S 1 75 and ^m = p X SM = .667^, that is, between .133 and .667 watt per square inch (= .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 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 mi thus being fixed by the temper- 98] COIL WINDING CALCULA TIONS. 373 ature increase specified, the working resistance of the magnet winding can be obtained by means of Ohm's Law, thus^ F F v / P r' m = -f = -/; m = %$ (285) y m J m J m or, 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 = /; while in a shunt dynamo the potential between the field terminals is identical with the known E. M. F. output of the machine, m = E\ 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, /, of the machine, the number of series turns, N ae , can readily be obtained by dividing the former by the latter: A f #.= - r ............... (287) The number of turns multiplied by the mean length of one convolution, in feet, gives the total length of the series field wire: (288) in which the length of the mean turn, in inches, is for cylindrical magnets : 4 = (4n + /V) X 7t', ........... (289) for rectangular magnets : / T = 2 X (/ + V) + h m X 7t ; ....... (290) and for oval magnets (rectangle between two semicircles) : / T = 2 X (/ - b) + (b + /i m ) X 7t ; . . . .(291) where d m = diameter of circular core-section; / = length of rectangular or oval section; b = breadth of rectangular or oval section; h m = height of magnet winding, from Table LXXX., 374 99] SERIES WINDING. 375 An approximate value for the length of the average turn for cylindrical magnets can be obtained from /,= * x d m , (292) where 17 = ratio of length of mean turn to core diameter, see Table XCIV. The ratio 17 depends upon the size of the magnet, and ranges as follows: TABLE XCIV. LENGTH OF MEAN TURN FOR CYLINDRICAL MAGNETS. DIAMETER HEIGHT OF WINDING SPACE, RATIO or MEAN TURN TO CORE DIAMETER, OF MAGNET h m (4n + ^) X 7T CORE, ^m INCHES. 7 ~ 4n INCHES. Bipolar Types. Multipolar Types. Bipolar Types. Multipolar Types. 1 i I 4.71 5.50 2 i u 4.32 5.11 3 1 11 4.19 4.97 4 U 2 4.12 4.71 6 H a* 3.93 4.32 8 If a* 3.83 4.12 10 1* 8* 3.73 4.01 12 2 3 3.66 3.93 15 2i 8i 3.59 3.82 18 2i w 3.54 3.75 21 f to 3.50 3.70 24 2* 4 3.47 3.67 27 at 4 3.45 3.64 30 2 41 3.43 3.62 33 a| 4f 341 3.60 36 3 5 3.40 3.58 The averages given for the height of the winding space /* m , in Tables LXXX. and XCIV., enable an approximate value of the radiating surface, $*, to be found by formulae (277) to (282), respectively, and the latter, together with the specified temperature increase, m , furnishes the allowable energy dis- sipation, P^ , by virtue of equation (283). From formula (285), then, the required series field resistance can be obtained thus: ' = - rr X , y se 75 2 15.5 (293) 37* DYNAMO-ELECTRIC MACHINES. < 99 or: *.5.5C. ..(294) In dividing (288) by (294), finally, the specific length A se , 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 _4_ A - ^-5 - T~ < J7_ 7s X /2 K i-f-.oo 4 X m ^ T v / v / = 6.25 x - 8 V * - x ( l + -4 x ,) , ... .(295) m where A T 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; 9 m = specified temperature increase of magnet wind- ing, in Centigrade degrees; S K = 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 A. n 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 se , by the specific resistance, for, since .- feet ohms = specific resistance X - - = - n- 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 15.5 C.,and the area of the series field conductor, conse- quently, is: tf se 2 = 10.5 X A se = 65 X X v % x/ x(i+.oo 4 xe m ). ...(296) m A O M 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 formulae. Having found the size of the conductor, the number of turns, N Ky from (287), will render the effective height, A' m , of the winding space for given total length, /' m , of coil, by transposition of formula (252), 95, thus: #-*.# x ^^, ........... (297) ^ m (tf'se) 2 being the area, in square inches, of the square, or rectan- gle, that contains one insulated series field conductor (wire, cable, or ribbon). If h' m , from (297), should prove materially different from the average winding depth taken from Table LXXX., the actual values of / T and S M 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, Z se , 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 DYNAMO-ELECTRIC MACHINES. [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 SERIES FIELD WINDING FIG. 305 DIAGRAM OF SERIES WINDING WITH SHUNT COIL REGULATION. FIG. 309 4TH COMBINATION FIG. 310 5TH 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, 33^-, 25, i6f, 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 - X resistance of series field =1.5 / se . 40 Resistance second combination X resistance of series field = 2 33i 1OO] SERIES WINDING. 379 Resistance third combination 7 ^ X resistance of series field = 3 r' 8e . Resistance fourth combination = ~~M x resistance of series field 5 r' K . Resistance fifth combination X resistance of series field = 9 r' 8e . 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 t , 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: ^ -7-- i-s^-n; (298) 'i r n r m Second group: r = *'--*; (299) ~ ^ ^~ Third group: r m = 3 r' se - r i; (300) Fourth group : 'm + *w = s^'se- n; (301) Fifth group: >m + ' + r v = g r' se - r, (302) From this set of equations the resistances of the separate shunt-coils can be derived as follows: DYNAMO-ELECTRIC MACHINES. [ 1OO Inserting (299) into (298) : ri 2 r se /-, whence: rj = (^ ^se - n) X (1.5 r' - r,) = 3 r 'se 8 - 3-5 ^se^l + n 2 _ 6 r , r , 2 fj* S'-'se ' r'se ' The resistance of the leads being very small, r? can be neglected, hence the resistance of coil I: ^=6^- 7 r, (303) (300) into (299) gives: i "^ + 3 '. - ' or: - (3 r ' w - r,) X (2 r^ - rQ (3 ^'se - n) - ( 2 / se - r,) - Neglecting again r? , the resistance of coil II is obtained : ^n = 6r' 8e -5^ (304) From (300) we have, directly: rm = 3^'se- n (305) By subtracting (300) from (301): rj f ; = 2 / se (306) By subtracting (301) from (302): r v = 4 r' se . (307) In the above formulae, r'^ is the resistance of the series field, hot, at maximum E. M. F. output of machine; and r t the resistance of the current-leads at the temperature of the 100] SERIES WINDING. 381 room. The resistance r\ 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 l% r n , and r m , respectively, and carries a total current of .4 / amperes, hence the currents in the branches: r m v . T : - x .4 A m 7 n = - X .4 r u r m + r i r m T r i r ll X 47. m Inserting into these equations the values of the resistances from (303) to (307), respectively, we obtain: y __ (6r'se (6r'se - S n) dr'&e - r\) + (6r'se - 7 r\) (zr'ee - r\) + (dr/se - ^) (6r'se - X.4/ y ,/~I v i 7- r/ > 4 X - 4 iSr'^ - 28r' se r, + 7^ _ I 7 " - 72^ - i 2 i/ 86 r, + 2 X -4 7 - X .4 7 -- .1 7, and / - 36r/M ' ~ 72/8e ri + 35na v , T T v , T > 7 -'m - r~a -- / - f a X -4- X .4- z=: .27. 72r' se 3 -- 121^^ + 47^ 2 In the second combination there are but two parallel 382 DYNAMO-ELECTRIC MACHINES. [ 10O branches, having the resistances r u and r m , and the total cur- rent carried is .333 /amperes ; therefore: / = -^- X .333/= Q 3 ;'' e Vr X ' 333 7 ^11 ~T r III 9 r se ~~ r \ - X .333 7 = - 111 7 > 5 and ^TT 6r' H T r m 9^se -' 0*1 = 7 X .333 /= - 222 7 - 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: /, = 7 V = .1 / = , ......... (308) " II: / = .in /==-, ........ (309) " HI: /m=.*5/=, ....... (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 formulae (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 Giyen Tem- perature Increase. The problem here to be considered is to find the data for a shunt winding which will 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^ , the total energy absorbed in the shunt-circuit, consisting of magnet winding and regulating coil, can be expressed by: where P sh ~ SM = 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, E, of the machine, the current flowing through the shunt-circuit is: P< / 8 h= -J 1 , (313) 383 DYNAMO-ELECTRIC MACHINES. [ 101 and the number of shunt turns, therefore : AT AT* E y sh By means of formulae (289) to (292), which apply equally well to shunt as to series windings, the approximate mean length of one turn is found, and the latter multiplied by the number of turns gives the total length of the shunt wire: .-.(315) By Ohm's Law we next find the total resistance of the shunt- circuit at normal load, viz.: 75 This contains the r x per cent, of extra resistance; in order to obtain the resistance of the shunt winding alone, r" sh must be decreased in the ratio of and we have: r'* = r'* X X M X x * x I , (317) 75 \^ iooy ' ioo 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: ' 8Q " i + .004 x 101] SHUNT WINDING. 385 E* i i ;r x . + ,.... xv (3la) &**?#>*; - + -^ The division of (315) by (318), then, furnishes the specific length of the required shunt wire: i - * 911 = x x ' + x ' + - 4 x 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 sh , 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 X'tto is the specific length of one size of wire and A" sh that of the other, such proportions, Z' sh and Z" 8h , of the total length, Z sh = Z' sh -f Z" sh > are to be taken of each that: ^' 8 h X Z'gh -}- A" 8h x Z" sh Since in this equation every term contains a length as a factor, any length, for instance Z' sh , may be unity, and we have: *'* + **() from which follows the proper ratio of the lengths of the two wires: DYNAMO-ELECTRIC MACHINES. [ 1O1 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: $ 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: (*'*)' + ( L ^\ x (*_) 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 forThe ( ___ i ! d .6 a IS " T Fig. 311. Dimensions of Shunt Coil. two sizes are to be separately determined by formula (257), thus: h - ' l m - h' 4-h" J Z/ *h X dV . d'^ -f- A / - ; - -+- - V /m X 7t 4 where h 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; 6' A and tf" sh = diameters of insulated shunt wires, inch; Z' 8h and Z" 8h total length of the two sizes of wire, in feet; m -2 h" m - = external diameter of coil of first size of wire, identical with internal diam- eter of coil of second size, in inches; / m = length of coil, in inches; if there is more than one coil in each magnetic circuit, / m is the total length of all the coils in one circuit. DYNAMO-ELECTRIC MACHINES. [ 1O2 102. Computation of Resistance and Weight of Magnet Winding. To complete the calculation of the magnet winding, it is necessary to find its actual resistance and its weight. For the resistance in ohms we have : r m = Length x ohms per foot = L m X (10.5 X ~) = 10.5 X ^ = I0 . 5X ^ = . 875X _^, -(325) in which N m = total number of series, or shunt turns on magnets, formula (287) or (314); / t mean length of one turn, in feet; / T = mean length of one turn, in inches, formulae (289) to (292); Z m = total length of magnet wire, in feet, formula (288) or (315); tf m 2 = sectional area of magnet wire, in circular mils, formula (296) or (322). The weight of the magnet winding is the product of the total length of wire by its specific weight, in pounds per foot, the former being the product of number of turns and mean length of turn, and the latter being obtainable from the wire-gauge table. In order to express the weight of the winding by the data known from previous calculations, we proceed as follows: Weight = length in feet X weight per foot = constant X length x specific length, in which : specific weight pounds per foot Constant = - .. s . * - specific length feet per ohm _ ohms X pounds (feet) 2 /ohms per mil -ft. X-T^ ^J X(lbs. p. cu. in. xin. Xsq. ins.) (feet) 2 ' 102] SHUNT WINDING. 3 8 9 and particularly for copper: Constant 7t cir. mils X - / feet \ / "4 / I0>5 X -^V ) X ( .316 X feet X 12 X - \ cir. mils / 1 1,000,000 (feel)^ 10.5 X .316 X 12 X I dr mils y ^ ' ?T ? /N /f .i_\2 vx ~ ~,:i,, -* *v? 1,000,000 (feet) 2 X cir. mils The desired formula for the bare weight, in pounds, of any magnet winding, therefore, is: Wt m = 31.3 x io- 6 x N m x / t x A m , ....(326) where N m = total number of series, or shunt turns on mag- nets; / t = mean length of turn, in feet; A m = specific length of magnet wire, in feet per ohm, formula (295) or (319). Writing (326) in the form 3 wt m = 31.3 X io- X and multiplying both numerator and denominator by the square of the current flowing in the magnet wire, we obtain: amp. 2 X feet 3 = 31-3 X io- 6 X /a 3L3 X (- amp. 2 X ohms' or: / ampere-feet V I IOOO I ^, ra _ , (327) watts which agrees, substantially, with formula (275), 96. The denominator of equation (327), since the specific length of the magnet wire in (326) is given at 15.5 C., represents the energy lost in the magnets at that temperature, that is, the actual energy consumption, at the final temperature (15.5 + m ), of the magnet winding, divided by (i -f .004 x e m ); hence the weight of bare magnet wire necessary to produce a given mag- 39 DYNAMO-ELECTRIC MACHINES. [106 netizing force, AT, at a specified rise, m , of the magnet tem- perature: /^r I IO 1000 w/ m = 31-3 X-V-; -^-x (i + .004 x e m ), (328) v S 1 75 in which AT = number of ampere-turns required; / t = mean length of one turn, in feet; m = specified rise of temperature, in Centigrade degrees; S^ = 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 AT is replaced by AT^and AT ah , 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 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, SK square inches. Solving (328) for m , we obtain: (329) The weight of copper contained in a coil of given dimen- sions is: *m = 4 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. [3'-3x(^)V| wt m .004 x [31-3 x [ -*_j\ x -M 1 L \ 1000 / ^ M J 103] SHUNT WINDING. 391 The total resistance of this shunt regulator must be the sum 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., ' m&x y and a minimum E. M. F., ' min , 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 and the minimum magnetizing force: nt" -2T-2? v I TP" v mm \ v 7" **' e 3 I 33 X I t- X r, 7 I X / g The values of l" K 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: 39 2 DYNAMO-ELECTRIC MACHINES. [103 and for minimum voltage: at" = 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 / ]B in formula (250); in calculating the compensating ampere-turns for the maximum voltage, the value of 15 from Table XCI. is to be taken for a density of EV fail ^ -P* max p ' ' and in case of the minimum voltage, for a density of min E 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, AT m&y , 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: AT^-AT 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 100 X per cent, of the normal resistance, which is mM . A 7 yog A T> IX A f 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 AT AT A T min \ , /ooi\ ~ -*'* (^ AT 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: (332) sh and at minimum voltage we have : JT> (^h)min = , - i , ........... (333) r sh -T r r 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 x coils of the regulator are contained in the same, is found : / T- \ I T \ i \/ vXsh/max V.-'sh/min /OO4\ (Ah)x = (Ahjmax n x X - - , (3d4r) n r where n r is the total number of the coils, or steps, of the reg- ulator. From (334) we obtain by transposition: VXsh/max ^/ = 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., E, of the dynamos, viz. : _ 6 X ' B X E X io 9 *^ ** ~" O AT \/ AT" > 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 and at m = No current flowing in the armature, there is no armature re- action on open circuit, and no compensating ampere-turns are 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: Next a similar set of calculations is made for the normal output: Useful flux at normal output: = 6 X *' p X E X io 9 where E' E + / ' r' & + /r' se , for ordinary compound wind- ing; see (19), 14 and E E -\~ I' X (r' & + r' se ), for long shunt compound winding; see (22), 14. Since, however, 1 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 + ..25 T /. ..(337) In case the machine is to be over compounded f or 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 = 1.05.0+ i.2 5 /V' a (338) The magnetizing forces required at normal load, then, are: <*** = -3133 X TT-X l\\ t - k * r - At 14 _ 180 104] COMPOUND WINDING. 397 Their sum is the total number of ampere-turns needed for excitation at normal output: A T = at this is supplied by shunt and series winding combined, conse- quently the compounding number of series ampere-turns: A T se = A T - A T sh = A T - A T (339) In the above formulae for at^ o and at m , the factors A and A are the leakage coefficients of the machine on open circuit and r I I s?\ I ) 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 ' "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). D YNA MO-ELECTRIC MA CHINES. [104 1C O CO 1O si O 1C 1O I>00>OG6CO1O t- TH 111 ^ ill SB "3 * It SGOO CO TH (N TH C2 TH TH TH 50 O CQ 10 10 TH -THOOS 10 10 CO10- DGO t_i 11.0 JII 105] COMPOUND WINDING. 399 armature, the various positions of the exploring coils being shown in the accompanying Figs. 312 and 313. Appended to this table are the respective leakage factors, obtained in divid- ing for each case the maximum percentage of flux by 100, and also the ratios of the leakage factor at normal output to that on open circuit. 105. Calculation of Compound Winding for Given Temperature Increase. After having determined the number of shunt and series ampere-turns giving the desired regulation, the calculation of the compound winding itself merely consists in a combination of the methods treated in Chapters XX. and XXI. The total energy dissipation, JP mi allowable in the magnet winding for the given rise of m degrees being obtained from for- mula (283), this energy loss is to be suitably apportioned to the two windings, preferably in the ratio of their respective mag- netizing forces, so that the amount to be absorbed by the series winding is: AT 1 AT 1 9 ^ - ^~ X -s X S watts; (340) AT hence, by (294), the resistance of the series winding, at 15.5 C. : _ Ae i r m - js i -|- .004 x 6 m AT 75 ~/ 2 N i+.oo 4 X m ' The number of series turns being readily found from ^se = *yk the total length of the series field conductor is: /', AT^ /' T / 1\/ 'y __ V TPAt* -*-/gg J V gQ /\ /\ ICCLj and this, divided by the series field resistance, furnishes the specific length of the required series field conductor, thus: 400 DYNAMO-ELECTRIC MACHINES. [ 106 I' AT 7 2 - X // T 7 V / V /' = 6.25 X - Vve X (i + .004 X 8 m ), ..... (342) ^M X^m where /' T = mean length of one series turn, in inches. The sectional area of the series field conductor, therefore, analogous to (296), is: #se 2 = 10.5 X A se A T v / v /' = 65 x - x * T x (i + .004 x m ) ...... (343) M A m If one single wire of this cross-section would be impractical, one or more cables stranded of n M wires, each of circular mils, may be used, or a copper ribbon may be em ployed. The actual series field resistance, at 15.5 C., then being: Ac 7Vse x H r se = 10.5 X -rni = 10.5 X - 5-5 IV v /' A/" v /' = .875 x -i- 1 = .875 x * y ($' V A V u se; the actual energy consumption in the series winding is: ^se -* X ^ se and, consequently, the energy loss permissible in the shunt winding: K X (i +.004 X m ) ...... (346) If the extra-resistance at normal load is to be r^ 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: x = .875 x x /', x + ~ x(i+.oo 4 8 m ) (348) In estimating the mean lengths of series and shunt turns, /' T and /" T , respectively, all depends upon the manner of plac- ing the field winding upon the cores. If the winding is per- formed by means of two or more bobbins upon each core, the series winding filling one spool, preferably that nearest to the brush cable terminals, and the shunt winding occupying the remaining ones, then the approximate mean length, /' T , of one series-turn is equal to that of one shunt turn, /" T , and also identical with the average turn, / T , given by Tables LXXX., 83, and XCIV., 99. But, if the field coils are wound directly upon the cores the series winding usually being wound on first the lengths /' T and /" T differ from each other, and can be approximately determined by apportioning from J- to ^ of the average winding height, given in Table LXXX., to the series winding, and the remainder to the shunt winding. TAKT VII . EFFICIENCY OF GENERATORS AND MOTORS. DESIGNING OF A NUMBER OF DYNAMOS OF SAME TYPE. CALCULATION OF ELECTRIC MOTORS, UNIPOLAR DYNAMOS, MOTOR-GENERATORS, ETC. DYNAMO-GRAPHICS. CHAPTER XXIII. EFFICIENCY OF GENERATORS AND MOTORS. l 106. Electrical Efficiency, The electrical efficiency, or the economic coefficient of a dynamo, is the ratio of its useful to the total electrical energy in its armature, the latter being the sum of the former and of the energy losses due to the armature and field resistances; hence the electrical efficiency of a generator : and that of a motor : ^ P F = f - (P * p + P *\ ...... (850) where % = electrical efficiency of machine; P electrical energy, at terminals of machine; P' = electrical activity in armature, or total energy engaged in electromagnetic induction; P & = energy absorbed by armature winding; /> M = energy used for field excitation. In case of a generator, P is the output available at the brushes, while in a motor it is the total energy delivered to the terminals, that is, the intake of the motor. Inserting into (349) and (350) the expressions for P, P M and -P M in terms of E. M. F. current-strength and resistance, the following formulae for the electrical efficiency are obtained: Series-wound generator: ' ............... (351) 1 See "Efficiency of Dynamo-Electric Machinery," by Alfred E. Wiener American Electrician, vol. ix. p. 259 (July, 1897). 406 DYNAMO-ELECTRIC MACHINES. [ 1O7 Shunt-wound generator: E I a * (- \ y < \ I / a ^ J ' ' ' ' (353) &1 -\- 1 (r a -f- r se ) 4- y sh / sh Series-wound motor: *=* / - / ; g P P ' c ~Dff D' I D' Dl I O i D i O A + P e + P ' (357) and that of a motor : p. _ ^_ * in which 77 C = commercial or net efficiency of dynamo; P electrical energy at terminals, /. *., output of generator, or intake of motor; P' electrical activity in armature; P" = mechanical energy at dynamo shaft, i. e., driv- ing power of generator, or mechanical out- put of motor, respectively; P & =: energy absorbed by armature winding; /> M = energy used for field excitation; P = energy consumed by hysteresis; P e = 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 PU, the following set of formulae, resembling (351) to (356), is obtained : Series-wound generator: El ' ('* + Shunt-wound generator: El T 2 ~< sh (359) El f" r / r" '' (360) 498 DYNAMO-ELECTRIC MACHINES. [ 107 Compound-wound generator: Series-wound motor: Shunt-wound motor: El Compound-wound motor: - [/" K + r' K ) + 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 : = 1.3564 X J/B X C^B -/B), .................. (365) where V E = belt velocity, in feet per minute; V'-Q = belt velocity, in feet per second; FK = 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: P FT * = ^ == 1.3564 x*-.x (*-,-/,)' " (366) and the commercial efficiency of a motor, by : . P" _ 1.3564 X P' B X - The commercial efficiency, T/ C , of a dynamo is always smaller than its electrical efficiency, 7/ e , since the former, besides the electrical energy-dissipation, includes all mechanical and mag- 108] EFFICIENCY OF GENERATORS AND MOTORS. 49 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 energy 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 rj c = .6, or 60 per cent., for small dynamos, to rj c = .95,' or 95 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 OP BELTS. Loss IN BELTING 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 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. [109 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' -pn P' P + P & + P' P' (r a ~ 746 /#> ~ and for a motor : P P'-P' X ' X (^ B - /B) ...(368) "* ~ 5' - ^ 7 - [/' 2 (a +) + /sh 2 ^"sh] _ 746 hp _ 1.3564 X PB X (^ B ~/B). ~ ^'7' E' I' ...(369) The energy of conversion, ^ g , is the quotient of the com- mercial and electrical efficiencies, and therefore varies between rj g = = ~ - = .8, or 80 per cent, *7e 75 for small dynamos, and rt e = = = .96, or 96 per cent., Ve -99 for 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 109] 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 KW 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 empl-oyed, 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. 412 DYNAMO-ELECTRIC MACHINES. [109 In the following Table XCVII. the author has compiled the weights, list prices, weight-efficiencies (watts per pound), and specific prices (dollars per KW) for all sizes of dynamos as averaged from the catalogues of numerous representative American manufacturers of high grade electrical machinery: TABLE XCVII. AVERAGE WEIGHT AND COST OF DYNAMOS. CAPACITY IN KILOWATTS. AVERAGE WEIGHT (TOTAL, NET) LBS. WEIGHT PER KILOWATT. LBS. OUTPUT PER POUND WATTS. AVERAGE PRICE, (COMPLETE). PRICE PKR KILOWATT. .5 80 160 6.25 $ 50.00 $100.00 1 150 150 6.67 80.00 8000 2 275 137 7.3 125.00 6250 4 500 125 8.0 170.00 42.50 6 700 117 8.55 210.00 35.00 10 1,100 110 9.1 300.00 30.00 15 1,600 107 9.35 412.50 27.50 25 2,600 104 9.6 625.00 25.00 50 5,000 100 100 1,150.00 23.00 75 7,300 97.3 10.3 1,650.00 22.00 100 9,500 95 10.5 2,200.00 21.50 150 14,000 93.3 10.7 3,150.00 21.00 200 18,500 92.5 10.8 4,150.00 20.75 300 27,000 90 11.1 6,150.00 20.50 400 35,000 87.5 11.4 - 8,100.00 20.25 500 42,500 85 11.8 10,000.00 20.00 600 50,000 83.3 12.0 11,850.00 19.75 700 58,000 82.9 12.1 13,650.00 19.50 800 65,000 81.3 12.3 15,400.00 19.25 1,000 80,000 80 12.5 19,000.00 1900 1,500 120,000 80 12.5 27,750.00 18.50 2,000 160,000 80 12.5 36,000.00 18.00 Since the speeds for the same outputs vary considerably with different manufacturers, the averages given in columns 3 and 6 above refer to medium, or moderate speeds, and must be proportionally reduced for high, and increased for low speeds. 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 of calculating may be materially simplified by subdividing the fundamental formulae in two parts, the one containing those quantities which remain constant for the type in question, while the other embodies all Fig. 314. Cross-Section of Field Magnet and Rectangle Inclosing Armature Core. factors that vary with the output of the machine. By adopt- ing a fixed ratio between the cross-section of the field magnet and the area of the rectangle containing the longitudinal section through the armature core, which is perfectly proper for any particular type of dynamo, and by basing all calcula- tions upon the density of the magnetic lines in the magnet frame, Cecil P. Poole - 1 has obtained a set. of simple formulae which admit of ready separation into a " preliminary " and a "working" part. Representing the area of the magnet frame by the quotient 1 " A Simplified Method of Calculating Dynamo-Output and Proportions,' by Cecil P. Poole, Electrical Engineer, vol. xvi. p. 483 (December 6, 1893). 413 4 1 4 D YNA MO-ELE C 7 'RIC MA CHINES. [ 1 1 of the longitudinal armature section and the number of pairs of poles, Fig. 314, thus: (370) the E. M. F. generated in the armature can be expressed by: E = (B" m X (S m X p) X X ~ c X ~ X io- 8 T 7\7^ 7; V T -7 A m V V // V / V --1 V c V in" ' ' ' X "~ i TV" = 3-82 x T x (B" m x 4 x v c x V x io- 8 , (371) A 72 p where (B" 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; 7V C = total number of armature conductors; n p = number of pairs of magnet poles; n' p = number of bifurcations of current in armature; JV = speed, in revolutions per minute; v 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: 4 ^is X <4 and writing for the number of conductors on the armature : _ d & n L v c P/// X fl\ , a where d & = diameter of armature core, in inches; #"' a = pitch of conductors on armature circumference, in inches; ! = number of layers of armature conductors; formula (371) becomes: E = 3.82 X \ X ..(373) in which the constant has the value: : K = voi'm x * 18 x v If all the dynamos of the type under consideration are to have the same voltage, the same pitch-factor and number of layers of armature conductor, and are to have their armatures connected in the same manner, then E ', 19 , n\ and n' p are constant, and may be transferred from (373) to (374), still more simplifying the working formula, which under these con- ditions becomes: d & = K'x vTlTtf 7 ., (375) 4 1 6 D YNAMO-ELECTRIC MA CHINES. [ 1 1 1 while the corresponding preliminary formula is : K' = 2887 x 4 / E ' x n< * x k . . (376) V &"m X * 18 X V c X ! Having found the armature diameters for the various sizes, their lengths can then be readily obtained by multiplication with/& 18 ; 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 formulae 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: 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: ', (377) 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 : . #=2.5. 1 "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 OP OUTPUT-RATIO IN FORMULA FOR SIZE- RATIO FOR VARIOUS COMBINATIONS OF POTENTIALS AND SIZES. KATIO OF POTENTIALS, E.:3* VALUE OF EXPONENT, X, FOB KATIO OP LINEAR DIMENSIONS, m = 1 to 2 3 to 8 8 and over. Uptoi tto4 10 and over 3.00 2.80 2.60 2.85 2.70 2.55 2.70 2.60 2.50 4 J 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. 1 Considering a given dynamo as a generator, its output, P l , in watts, at the terminals, is the total energy, P' t 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" \ , to be supplied to the generator pulley, must be the total energy, P' t 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, P 9 , 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 P' the energy needed to overcome the internal resistances of "Calculation of Electric Motors," by Alfred E. Wiener, Electrical World, vol. xxviii., pp. 693 and 725 (December 5 and 12, 1896). 419 420 DYNAMO-ELECTRIC MACHINES. [ 112 the motor, or by dividing P' by the electrical efficiency. Des- ignating the electrical efficiency of the machine, /. e., the ratio of its useful to the total electrical energy in its armature, by ?; e , and its gross efficiency, or efficiency of conversion, /. e., the ratio between the electrical activity in the armature and the mechanical power at the pulley, by r/ g , we therefore have: Output of machine as generator: P i = r? e xP'; ............. (378) Output of machine as motor: J>\ = % Xf; ......... .....(379) Power to be supplied to machine when run as generator (driving power): Energy to be supplied to machine when run as motor (intake of motor) : -P. = -f. .............. (881).. Ve Where P lf P 9 = 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" it 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: 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, = :fl = 74* * wa tts 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' = E - I X (r' a + r'J , (383) in which E = E. M. F. active in armature, in volts; E = voltage supplied to motor terminals; / = current intensity at motor terminals; r' a = armature resistance, at working temperature, in ohms; r' se = resistance of series field, warm, in ohms, for series and compound machines; in case of shunt dynamo r' se = 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: f = (384) 422 DYNAMO-ELECTRIC MACHINES. [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 OF ELECTRIC MOTORS OF VARIOUS SIZES. ELECTRICAL OUTPUT ACTIVITY OP MOTOR ELECTRICAL GROSS COMMERCIAL IN ARMATURE, IN EFFICIENCY. EFFICIENCY . EFFICIENCY. IN KILOWATTS. HORSE-POWER. hp *7e ^ % % X Vg p , . 746 x hp % \ .75 .80 .60 .5 1 .82 .82 .67 .9 2 .85 .84 .72 1.8 5 .87 .86 .75 4.0 10 .89 .88 .78 8.5 15 .90 .89 .80 12.6 20 .91 .90 .82 16.6 25 .92 .91 .84 20.5 30 .93 .92 .86 24.5 40 .94 .93 .87 32 50 .945 .935 .88 40 75 .95 .94 .89 60 100 .955 .9425 .90 80 150 .96 .945 .91 118 200 .97 .9475 .92 158 300 .98 .95 .93 236 400 .9825 .9525 .935 318 500 . .985 .955 .94 391 750 .9875 .9575 .945 585 1000 .99 .96 .95 777 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 opposite 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., R = total resistance of circuit, and r = internal resistance of machine, this difference between a generator and a motor can be best expressed 1 by the formulae for the current in the two cases, thus for generator: _ E = R ; for motor: E - E __,, _, _ 7=7 - , 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 D YNAMO-ELECTRIC MA CHINES. [ 1 14 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 N l revolutions per minute produces a total E. M. F. of E\ = E + fy. (r;+ revolts, 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 (/'. + ry volts. The speed necessary to generate this back voltage, speed being proportional to voltage, is: X 114] CALCULATION OF ELECTRIC MOTORS. 4 2 5 which is the speed of the motor at full load, provided- the E. M. F., , 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' & -j- r' se ), of the armature and the series field; and (3) upon its specific generating power, or its capability of producing counter E. M. F. ; /. ., the number of volts, /, it produces at a speed of one revolution per second. The specific generating power of the motor being j\r e" =

^ t'* Oi CO < ffil^2-^ ggssss 'dH * Saipnjoui ' OOOOOtOQOO: COO^H^OCJO5iOiCJ i-Ti4 efi-T! of <* r-T r-' ' * 435 c ^ - C5 Ko.op o. If 1 =S f I s i& * I 3 ^S I Ja S p. III a ^ fc S fj a I c II? E i' Is! IJ* 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. J (i) Counter E. M. F., Current, and Energy Output of Motor. Inserting into the formula for the counter E. M. F., ,,, N, N E ^ X - - X # X io 8 , n\ 60 the value of the useful flux from 86 and 87, 4 n AT ^ se X / _ W Be X I (R (R 10 (R' ' - X (R 4 n where & magnetomotive force, in gilberts; A T =. JV S& X / = magnetizing force, in ampere-turns; (R = reluctance of magnetic circuit, in oersteds; 10 10 i /'' (R' =- x & = - - X - - X -T^- , 4 7T 4^ p S m jj = 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: If the internal resistance of the motor, /. e., armature resist- ance plus series field resistance, is designated by r, and the line potential by , the current flowing in the armature, there- fore is: T N ' 77 jn/ v ' , _ -c _ (R // p 60 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," by E. A. Merrill, Electrical Engineer, vol. xvii. p. 231 (March 14, 1894). 117] CALCULATION OF ELECTRIC MOTORS. 439 and solving for /, we have : 7 = " N c x ^ se ~ ~1 ^~ 7 ' r + ^^ ;XX 6o Xl Hence the work done by the motor: N y N P N ^ = *'x/=-^- 5 x -,-x^ (397) 7V C , ^Ygg, and ' p are constants of the motor, and (R' varies somewhat with the saturation of the field, but may be consid- ered practically constant; if, therefore, we unite all constants by substituting: _ N e X ^e i io 8 ~W~ < W; X to ' the above formulae (395), (396), and (397) become: ' = K X /X N, .......... (398) and p = Kx P x N .......... (400) The value of the constant K can be readily calculated from the windings of the machine and from the dimensions and flux densities of its magnetic circuit. If, however, the values of E, /, and N for any load are given, and it is required to find the counter E. M. Fs., the currents, and the mechanical out- puts for other loads, then K can, far simpler and more accu- rately, be determined by substituting the given values in: E ~ /x r which is obtained from (399) by transformation. (2) Speed of Motor for Given Car Velocity. The speed of the motor required to move the car at a given velocity, with a given reduction gear, is: 440 DYNAMO-ELECTRIC MACHINES. [ 117 N _ feet per min. _ 5280 x 12 x ^ m X s 4r 60 X n X d w 12 ' in which z/ m = speed of car, in miles per hour; 2 = ratio of speed reduction, /. ^., ratio of arma- ture revolutions to those of the car axle; d^ = diameter of car wheel, in inches. (3) Horizontal Effort, and Capacity of Motor Equipment for Given Conditions. The power required to propel a car depends upon five things: friction, grade, condition of track, curvature of track, and speed. No accurate formula can be given for the resist- ance due to friction, condition of track, and curvature, for this resistance will vary largely at different times with the same car, depending upon the care with which the bearings and gears are oiled, and whether the track is wet or dry, clean or dusty, or muddy. A good average practical value of the specific traction resistance, verified by numerous tests, is 30* pounds per ton of weight on the level, and (30 20 X g) pounds per ton on grades, g being the percentage of the grade, that is, the number of feet rise or fall, respectively, in a length of 100 feet. The horizontal force necessary to over- come the traction-resistance caused by a total weight of W t tons, therefore, is: A = Wt X (30 20 X g) pounds, ....(403) and the power, in watts, required to exert this horizontal effort, at a speed of # m miles per hour, will be: pn _ A X ft. per min. X 746 33,000 A x v m x 746 117] CALCULATION OF ELECTRIC MOTORS. 441 In order to facilitate the calculation of the propelling power, or of the motor capacity required for given conditions of trac- tion, the following Table CIII. has been calculated, which gives the power required to propel one ton at different grades and speeds, and which, therefore, furnishes P" by simply mul- tiplying the respective table-value by the total weight, Wt tons, to be propelled, /. ^., the weight of car plus passengers {average weight of passenger = 125 Ibs.): TABLE GUI. SPECIFIC PROPELLING POWER REQUIRED FOR DIFFERENT GRADES AND SPEEDS. HORSE-POWER REQUIRED TO PROPEL 1 TON, PERCENTAGE IF RATED SPEED OP OAR, Z/ m , IN MILES PER HOUR, is : or GRADE, cr & 8 10 12 15 18 20 25 30 .64 .80 .96 1.21 1.45 1.61 2.01 2.41 1 1.07 1.34 1.61 2.01 2.41 2.68 3.35 4.02 2 1.50 1.88. 2.25 2.82 3.38 3.76 4.69 5.63 3 1.93 2.41 2.90 3.62 4.34 4.83 6.03 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 5.22 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 13.67 8 4.07 5.09 6.11 7.63 9.15 10.18 12.73 15.28 9 4.50 5.62 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: Giving to hp values from 15 to 60 horse-power, and to ?; 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 Wt, in tons, can be computed, which the equipment under consideration is able to propel at any given grade : 442 DYNAMO-ELECTRIC MACHINES. TABLE CIV. HORIZONTAL EFFORT OF MOTORS OF VARIOUS CAPACITIES AT DIFFERENT SPEEDS. RATED CAPACITY OF MOTOR EQUIPMENT. PULL AT PERIPHERY OP WHEEL, A, IN POUNDS, AT RATED SPEED OP CAR, V m> IN MILES PER HOUR, OF : 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: =S-X(r + KxW), (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 / can be expressed by transposition of formula (400), and by substituting the expression so found into (406) the required E. M. F. is obtained : ' 2 A X ft E= X K X ..(407) Inserting into (407) the value of N found from (402), we have : 304 x K X X z A X 4, K X z ' (408) Knowing E, 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. 418. Formulae for Dimensions Relative to Armature 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, 3C" = 40,000 lines per square inch (or JC = 6200 lines per square centimetre) can be admitted. The practical working densi- ties, as given in Table LXXVI., 81, are: (&" 90,000 lines per square inch ((& = 14,000 lines per square centimetre), for wrought iron, " 85,000 lines per square inch ((B = 13,200 lines per square centimetre), for cast steel, and &" = 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 DYNAMO-ELECTRIC MACHINES. 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 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: / m = .i25d a , .............. (410) and height: The gap area, then, will be: S 8 = d & 7i X .3*4 = .94*4% 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 : *i = .2^, .... ......... (412) which, by adding 5*/4T for clearance, makes the total distance between the two pole faces : * 9 = .2sV^ ............. (413) Allowing .05 |/^ a 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: 4n = d* - -25 |/^~- 2 X .i<4 = .8c " 490 x~, ..(433) u f* 45 DYNAMO-ELECTRIC MACHINES. [121 from which, for forged steel ...(434) armature: d & - X E = 1.22 . 400 for wrought-iron or cast-steel 400 armature: d & = X E = 1.63 E. . . . 300 and for cast-iron armature: d & = - - x = 2.45 E. 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 3C" = 40,000, is: at e = .3133 X 40,000 x .05 Vd & X 1.2 = 750 Vd & , . .(435) where 1.2 is taken to be the probable factor of field deflec- tion, see Table LXVL, 64. Magnetizing force required for armature: x .2 d* 9 for wrought iron: #4 = 1.5 Vd & for cast steel: #/ a = 1.8 Vd & for cast iron: at & = 17.6 Vd & Magnetizing force required for magnet frame, cast steel of density " m = 85,000: 'm =/ (85,000) x i.2 for ring armatures, at s = 30 x n & X r, for drum armatures. For sparkless collection then we must make: afg = at v + at s , or, for ring armatures : .3133 x oe N~r k. x a i' = k n x V- x -^-5 (- 12 a x - 2 p ISO 2 ' p whence: and similarly for B > ~^7~ 180 ' ; I** In order to reduce all the terms of (445) to a common basis, we express the densities of the lines in the armature core and in the field frame by the field density, thus: " m = magnetic densities in gaps, armature core, and magnet frame, respectively; S, -^a, ^m = areas of magnetic circuit in air gaps, armature core, and field frame; /I factor of magnetic leakage. And furthermore, since the trigonometrical tangent of the angle of lead is the quotient of armature ampere-turns by total field ampere-turns, see 93, we can express the compen- sating ampere-turns as a function of 3C", as follows: y A W) n' p 1 80 The total number of ampere-turns per magnetic circuit, con- sequently, is: AT = -3133 x oe" x i" s + / fatf x -^ j x /" a + / ^ x oe" x ^ x /" m + %^ x Ai?P (446) Every term being a function of the field density 3C", a curve for AT can be obtained by plotting the curves for the com- ponents at g , at & , at m , and #/ r , for different ordinate values of JC", and subsequent adding of the abscissae. In then trans- forming the ordinates from field density into the correspond- ing proportional values of E. M. F., by simply adding a new scale, the magnetic characteristic of the dynamo is obtained, which gives the E. M. F. generated as a function of the mag- ntizing power. In Fig. 325 the curves OA, OB, OC, and OD give the ampere-turns required for the air gaps, for the armature core, for the field frame, and for compensating the armature reac. tion, respectively, as the field density, and, with it, the arma- ture- and frame-density increases. OA is a straight line owing to the fact that in air the ampere-turns required are proper- 47 8 DYNAMO-ELECTRIC MACHINES. [127 tional to the density desired. OB is the saturation curve for laminated wrought iron, and OCthat for the material employed in the field frame, for values of the density ranging from zero to the maximum employed at the largest overload the machine AMPERE TURNS Fig- 325. Construction of Magnetic Characteristic of Dynamo, from its Components. is intended for. Any point, e, on the characteristic curve OE is then obtained by adding all the abscissae of OA, OB, OC, and OD that have the same ordinate Ox, thus: xe xa -j- xb -\- xc -f- xd . If the magnet frame consists of two or three different mate- rials, either two or three distinct curves, as the case may be, have to be plotted instead of the curve OC, or one single curve may be laid out in which the addition of the component abscis- sae has been made by the formula: //Ax 3C' ./&; x ^ m X /" X ^ x X X /" c . s . . (447) 127] D YNA MO- GRA PHICS. 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 OA by means of the approx- imate formula: *gar at* = .3133 + x x x X/' -f .00001 X ^V a X - T X 2 n ( = 3e" x .3133 x r e + ^ x A x x /" a .00001 X (448) 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 k^ for different mean maximum load densities are taken from the following Table CV. : TABLE CV. FACTOR OP ARMATURE AMPERE-TURNS FOR VARIOUS MEAN FULL-LOAD DENSITIES. ENGLISH UNITS. METRIC UNITS. Mean Density in Armature Core at Maximum Ampere- Turns per inch of Magnetic Circuit in Constant in Approximate Formula for Armature Ampere - Mean Density in Armature Core at Maximum Ampere- Turns per cm. of Magnetic Circuit in Constant in Approximate Formula for Armature Ampere- Output. Armature Turns. Output. Armature \ lurn ?:_ . Lines p. sq. in. Core. k ~ ~W~ Lines per cm a Core. /(a) jj J v^aj 20 ~~ (B a 25,000 4.5 .00018 4,000 1.8 .00045 30,000 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 i s to De taken for the factor of compensating am- pere-turns, instead of .0000 1, 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 and .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, tf/ gar , 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 3C" 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 full frame is plotted by computing A X K" X ^ -^m > for a series of values of 3C", and by multiplying taken from Table LXXXVIII. or LXXXIX., or from Fig. 259, for the respective material, with the length /" m , of the magnetic circuit in the field frame. In case of a composition frame this process is to be performed according to formula (447). In now adding, by means of a compass, the abscissae of the line OA to those of the curve OC, such as CE = XA, the curve OE results, which is the required characteristic. 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\ = i^ inch. Mean area in cast iron, S m = 79 square inches; in armature, S & = 50 square inches; in gaps, S g = 158 square inches. Number of armature conductors, jiV c = 216. Coefficient of magnetic leakage, /I = 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 in the present case the magnetizing force per inch 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 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 4/m 8000 12000 16000 TOTAL NUMBER OF AMPERE TURNS Fig. 327. Practical Example of Construction of Characteristic. Density," respectively, are obtained, and now the line at 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 / 20 must first be determined. From formula (138) we have, for the useful flux, at normal load : 6 X (125 + 5) X io 9 - ! - hence, 216 X 1200 3,000,000 = z T,-=- *\ 5 = 3,000,000 webers, 60,000 lines per square inch, for which Table CV. gives: .00022. 128] DYNAMO-GRAPHICS. 483 Calculating now the value of at s&T for 5C" = 20,000, we find by formula (448) : at s&T = 20, ooo 1. 3133 X i sV + .o 22 X 1.25 X X 15 ; i6o\ -|- .00001 X 216 X I = 20,000 (.324 -f .013 -f .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 (9, 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 frame, furnishes the re/juired 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,OOO,000 3C = -o- = d> = 19,000, this third scale is obtained by placing " 125 volts " opposite that density, arid 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 y consisting of the straight-line portion, AB t and of the curved 1 Brunswick, L? Eclair age Elec., August 31, 1895; Electrical World, vol. xxvi. p. 349 (September 28, 1895). 4 8 4 DYNAMO-ELECTRIC MACHINES. [128 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 A K H K' H' 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] DYNAMO-GRAPHICS. 45 129. Determination of the E. M. F. of a Shunt Dy- namo for a Given Load. ' If E, Fig. 329, is the E. M. F. developed by the machine at no load, viz. : E = ^ 8 h X r sh , 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, <9, with the point A on the AMP.TURiNS AT, AT 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 = e & = /X r a + * r , where / X r & is the drop caused by the armature resistance r a , and = tan ot l , and E N m X E ...(449) The values of r m and (r m -\- 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 t and E^ , respectively, for which hold the following relations: N ****'"V S and: The required regulating resistance, therefore, is directly: Example: A shunt dynamo for 100 volt? and 40 amperes having an armature resistance of r & = .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] D YNA MO- GRA PHICS. 489 The drop at 40 amperes is : e & = 1.5 x / X 1\ = 1.5 x 40 X .12 = 7.2 volts, and the characteristic gives, for E ioo and E' ioo -|- 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) : N m X E 4200 x ioo 'm + r t = T7=r-= - -5 =51.8 ohms, and AT X 4200 X ioo AT' 10,500 r r = 51.8 40.0 = 1 1. 8 ohms. 40.0 ohms, Z 60 ui -to 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. 490 D YXAMO-ELECTRIC MA CHINES. b. Regulators for Shunt Machines of Varying Speed. If N is the normal, and N^ the maximal, or minimal abnor- mal speed, as the case may be, then the speed ratio, 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< ATJl N m C AT, AT AT' AT M 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, /, must be multiplied by the speed-ratio, //. 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 /, corresponding to the E. M. F. at normal speed, N 9 is connected with O, then the intersec- tion, E n9 of the line OE with curve 7, is the E. M. F. which the machine would yield at the speed JV l . For, in the first moment, the E. M. F. E, 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 AT to A T', causing an increase of the E. M. F. to E" , on account of which the magnetizing power is further increased to AT", and so on, until at E n the equilibrium is reached. But the potential of the machine is to be kept con- 131] D YNA MO- GRA PHICS. 49 1 stant; for this purpose, that magnetizing force, AT^ is to be found which produces the E. M. F. E at the speed N l . 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 E x N _ E_ n JV, volts at normal speed, IV, it follows that it is only necessary to draw EA J_ OA, to make AH = E. = * and to draw BE^ \ OA. The abscissa of the intersection, E l , 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 l being known, the regulating resistance can be computed as follows : For N l > N: E E X W m E^N m AT, AT 49 2 > YNAMO-ELECTRIC MA CHINES. [131 whence : For N^ < N: r r or: -F--T\ (451) If at distance OC = JV m a parallel, CD, to the axis of or di nates 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. N -\- o. 10 N E 120 = -~- = - ! - = 1. 1 ; E. = = - = 109 volts; JV N n i.i and for decreasing speed: . N' N 0.09 N , E 120 ' = - = " -' = ' 9 ' ; > = = =- 132 volts - 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^ 15,400; Ampere-turns at minimum speed, AT \ =27,600. Hence: 20,000 . . N m 5000 convolutions; and consequently: 131] D YNAMO-GRAPHICS. 493 5000 X 120 r - + r ' = .5,400 =39-0 ohms. 5000 X 120 r m = - =21.8 ohms. 27,600 r T = 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 ,= 109 V i > ^1 1 AMPERE TURNS Fig. 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 l , 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. [131 had to the open circuit curves I and II, Fig. 336, for normal speed, JV, and for minimum speed, 7V 2 , respectively. If AT ampere-turns are requisite to produce, at normal speed and on open circuit, the potential, E, to be regulated, AT AT 2 Fig. 336. Shunt Regulating Resi'stance for Constant Potential at Variable Load and Variable Speed. the magnetizing force for minimum speed is found by deter- mining the abscissa AT Z for on curve II, which at the same time also is the abscissa for the potential on curve I, a being the ratio of minimum to normal speed. The value of ^7" 2 can therefore be derived without plotting curve II, by adding to E the drop e & , 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 T l , the desired regulating resistance for variable load and variable speed is: ....(452) where N 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 30 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 AMPERE TURNS 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 ^N = N + . E 6 = ~ = ~ = 54.5 volts, ^ 2500 ampere-turns (from Fig. 337); and for full load and minimum speed: & = E + e a = 60 + 3 = 63 volts, -AT N - . N N ^ = = ~~ = 7 volts, 496 DYNAMO-ELECTRIC MACHINES. [131 AT^ = 5500 ampere-turns (from Fig. 337), N m = ^ = ^^ = 1833 convolutions. Connecting the points A and B, 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 F 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: E 6 K r m = - - = rr - = 20 ohms, 7 sh .06 X 50 r r = 44 20 = 24 ohms; or, directly, by formula (452): r r = ,833 X 60 X - - = M ohms. for which formula (455) would show that N" is an inverse function of >, that is, of the current-intensity, /, of which the flux is a direct function. But by making K" 3> greater than K " in the same propor- tion as E exceeds E I x ^, constant speed at varying load can be attained. K and K" are constants for the respective machines, and therefore cannot be varied proportional to / ; the flux >, however, is a direct function of the exciting power, and is inversely proportional to the reluctance of the magnetic circuit; approximate constancy of N\ consequently, can be produced (i) by making the motor of a higher reluctance than 5 D YNA MO-ELE C '1 *RIC MA CHINES. [133 the generator, either by increasing the length of the air gap or by reducing the section of the iron in the former, or (2) by making the magnetizing force of the generator greater than that of the motor by winding a greater number of field turns on its magnets. The proper way, however, is to select for the motor a somewhat smaller type, corresponding to the smaller capacity required for it, and to so design its magnet frame, air gap, and windings as to create a characteristic whose ordinates for any current intensity are proportional to the corresponding ordinates of curve II, Fig. 339. 133. Determination of Speed and Current Consumption of Railway Motors at Varying Load. 1 The speed of the car and the current required for the motor equipment are to be found for different grades of track, i. e., for varying propelling power. To solve this problem, the speed characteristic of the .motor I' I CURRENT INTENSITY Fig. 340. Speed Characteristic of Railway Motor. giving the motor speed, or still better, the car velocity, as a function of the current-intensity is plotted. Let W t = total weight to be propelled, in tons; v m = velocity of car, in miles per hour; g = grade of track, in per cent., /. e., number of feet of rise in a horizontal distance of 100 feet; 1 J. Fischer-Hinnen, Elektrotechn. Zeitschr., vol. xv. p. 401 (July 19, 1894). 133] DYNAMO-GRAPHICS. 5 O1 / = current required to propel W^ tons, at g% grade, with a velocity of v m miles per hour; E' = potential of line; 7/ e = mean electrical efficiency of railway motor; then we have, by formula (384), 117: P" _ 2 X W, X v m X (39 + 20 X g) = ~~ ...(456) In this v m is not known, but since the car velocity increases in direct proportion with the current strength, /, it is only 8 10 12 14 16 18 20 22 24 CURRENT-INTENSITY, IN AMP. Fig. 341. Practical Example of Graphical Determination of Car- Velocity and Current-Consumption at Different Grades. necessary to calculate, from (456), one value, /', for any value, v' m , of the velocity. By plotting the result, the point x\ Fig. 340, is obtained; and if we now connect x' with <9, and prolong the line Ox 1 until it intersects the speed-characteristic at x, the co-ordinates of this point, x, are the required values I and v m for current consumption and car velocity, respec- tively, for the particular grade in question. Example: An electric railway car of a seating capacity of 34 passengers weighs 2\ tons, its electrical equipment ij tons; the average efficiency of the motors from one-fifth to 502 DYNAMO-ELECTRIC MACHINES. [133 full load is 82 percent, and the line potential is 500 volts. Its speed characteristic is given in Fig. 341. The car velocity attained at, and the current required for, different grades up to 5 per cent, is to be determined for maximum load. Including the conductor and motorman, the full carrying capacity of the car is 36 persons, which, at an average of 125 pounds per head, make a total load of 2j tons; the maxi- mum weight to be propelled, therefore, is: W t = 2*/ 2 + i% + 2 # = 6 tons. Inserting the given data into (356), we obtain: 2 x 6 X For v m = 6.83 miles per hour, the equation for the current takes the following convenient form: /' = .02927 x 6.83 x (30 + 2og) = 2 x (3 + 2), from which, for : g = o %, i 0, 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\, ....#',, corresponding to the above values of /' are found and connected with O. Then the co-ordinates of the intersections # , x l9 ....^ 5 of the lines Ox' , Ox\, ---- Ox\ 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 Cir- cuit, Smooth King, High-Speed Series Dynamo: 10 Kilowatts. Single Magnet Type. Cast Steel Frame. 250 Volts. 40 Amps. 1200 Beys. p. Min. a. CALCULATION OF ARMATURE. i. Length of Armature Conductor. According to 15, Chap- ter III., the percentage of polar arc, in this case, is between .75 and .85; the machine being a small one, we take /3 l = .78, for which, in Table IV., 15, we find a unit armature induc- tion of e = 64 x iQ- 9 volt per foot per bifurcation; and since the number of pairs of armature circuits in bipolar machines is ' p = i, the total unit induction, is also = 64 X io~ 8 volt. Next we consult Table V., 17, and Table VI., 18, and obtain, as best adapted for the machine under consideration, a mean conductor velocity of z/ c = 80 feet per second, and an average field density of 3C" = 19,000 lines per square inch, respectively. 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., 19, to be about ' 250 -f- .12 x 250 = 280 volts. Hence by means of formula (26), 19, we can now directly calculate the length of the active armature conductor required: 280 X io 8 _ 2ftft f Z *-6 4 X 80 X 19,000 ~ 2Si 2. Sectional Area of Armature Conductor, and Selection of Wire. Taking a current density of 500 circular rails per ss DYNAMO-ELECTRIC MACHINES. [134 ampere, we find the cross-section of the armature conductor, according to formula (27), 20: d a 2 = 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 5184 = 10,368 circular mils. The diameter of No. 15 B. W. G. wire is d & = .072* bare, and (T 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: <4 = -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 : * = ,4x^=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: Allowing 16 per cent, of the circumference for spaces be- tween the coils, we have: n w = .84 x 535 = 448, 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: = -3 2 5 - o80 _ .088 6 ' 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 / a = = 54 inches. 448 X 3 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. : o = 4*213 and 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 + 9 + 10, and 32 = 10 -j- n -{- n, it follows 508 DYNAMO-ELECTRIC MACHINES. 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, n c = 56 into (46) the number of convolutions per coil is obtained: 448 X 3 _ 56 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 (7, one-half, 7, 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. 59 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 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-J = 9j inches, and the arithmetical mean of the external and internal diame- ters is the mean diameter of the core : <*'"= ^ (15 + 9i) = i inches. Inserting the value of b & into formula (234), 91, the maxi- mum depth of the armature core is obtained: *'a = 2 1 X y ^| - i = 5.92 inches; hence, by (232) and (233), the minimum and maximum cross- sections: ^ai = 2 X 5-J- X 2-J X .90 = 26.5 square inches, and Si* 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: mn 2,083,000 . (B ai = ^ == 78,700 lines per square inch, and (B" a2 = ~ = 38,100 lines per square inch, 54-7 5 10 DYNAMO-ELECTRIC MACHINES. [134 for which Table LXXXVIIL, p. 336, gives the specific mag- netizing forces /((B" ai ) = 29.5, and /((B* aa ) 7- 1 ampere-turns per inch. According to formula (231), therefore, the mean specific magnetizing force is: /((B" a ) = (29.5 -j- 7.1) = 18.3 ampere-turns per inch, and to this, according to Table LXXXVIIL, corresponds an average density of: (&" 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 (si + ' + .3*5 x * x 2gg = 95J feet J 8 Hence, by (58), p. iqi, the bare weight of the armature winding: wt & = .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: wt & = 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: X 955 X (-^T I = .24 ohm. 4X2 134] EXAMPLES OF GENERATOR CALCULATION. 511 By Fig. 343 the surface of the armature core is : 2 x (5^ -f- 2-J) X I2-J X 7t 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 -^- 25 = 26 megohms per square inch-mil at 100 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 4o 3 X .24 = 460 watts. The frequency is: 1 200 2v, = = 20 cycles per second; the mass of iron in the armature core, from (71), 32: 12! X n X 2-J x 5| X .90 M=- i* ^ z_ .292 cubic feet; for (B" a = 68,500, Table XXIX. gives the hysteresis factor: rf = 27.3, 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 h = 27.3 X 20 x .292 = 160 watts, P e = .034 X 2o 2 x .292 = 4 watts. By (65), p. 107, then, the total energy dissipation in the armature is: P A 460 -f 160 -f 4 = 624 watts. 5 r 2 DYNAMO-ELECTRIC MACHINES. [ 134 The heat generated by this energy, according to (79), 34,' is liberated from a radiating surface of S A = 2 x I2-J- X n X (5j- + 2-J -f i-|) = 715 square inches, whence follows the rise in armature temperature, by (81), p. 127 : the specific temperature increase, 0' 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 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 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, 15 X TT 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. : p ' = I 5 2 X 5i X .89 x 1.200 X 19,000 X io- 6 = 23,500 watts, and for the running value of the armature, by formula (90), 39: P' & = - - = .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 roo 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 bes_t modern dynamos. The relative efficiency of the magnetic field, by formula (155), 59, is: X 80 = 14,880 webers per watt - at unit velocity, and, according to Table LXII., 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 = -fr X 40 X 672 X 2,083,000 = 65.7 foot-pounds. and by (95), 41, the force acting at each armature con- ductor: A = -7375 X 5r44 * 1 o- =.178 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" 2 , about 5 per cent, below the average den- sity OC", or iJC", = 19,000 X 1.05 = 20,000, and JC" 2 = 19,000 x -95 = 18,000; hence the side thrust: / t = ii X io- 9 X 15 X 5i X (20,ooo 2 - 18,000') = 64J pounds. D YNA MO-ELECTRIC MA CHINES. [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 -f 5 x .088) = 8J inches, the brush-surface diameter of the commutator is chosen 4 = 8J 2X$ = 7 inches, by allowing -f" radially for the height of the connecting lugs, as shown in Fig. 343. If we make the thickness of the side Fig. 343. Dimensions of Armature and Commutator, IO-KW. Single-Magnet Type Generator. mica hi = .030", Table XLVL, 48, and if we fix the number of bars to be covered by the brush as k = i-J, the circum- ferential breadth of the brush contact, by (115), becomes: = - 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 +^030 = 71", 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. 515 which we subdivide into two brushes of i inch width, each. Allowing y between them for their separation in the holder, and adding T y for wear, we obtain the length of the brush- surface from (114), page 169, thus: / c = 2| X i-J- + 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 TT X 1200 f v^ = -- - = 2200 feet per minute, hence the speed-correction factor for the specific friction pull, by (119), p. 179: 22OO Inserting the values into (120) and (121), the formulae for the energies absorbed by contact resistance and by friction re- duce to /U. 00.68 x|^=;MJXA, and P t 6 X io- 5 X .85 / k X 2 x .68 X 2200 = .i526/ k . Taking from Table XLVII. the values of p k and / k for brush tensions of i, 2, 2-J-, 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 '+ ^S 26 X .95 = .618 HP.; "2 " " /> k + P t = 3.15 X .12 +.1526 X 1.25 -.569 HP.; " 2* " " A + Pt = 3-15 X .10 + .1526 X 1.6 -559 HP.; " 3 " " P* + Pt = 3.i5 X .09 + .1526 X 1.9 -574 HP., 5 l6 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 XL VIII., 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, 147 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: 4 = t . 2 x = 8 , inches; by (122), p. 185, and Table XLVIL, the journal diameter: <4 = -003 X y 2 8o x 40 X 1/1200 = 1$ inch; and, by (128), p. 190, and Table LIV., the length of the journal: / b = .1 x i-J X V I2 o 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 / s 3^", 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: 134] EXAMPLES OF GENERATOR CALCULATION. 5 1 ? 14. Pulley and Belt. Taking a belt-speed of z> B = 3500 feet per minute, Table LVIIL, 54, the pulley diameter becomes^ by (129), p. 191: inches. the size of the belt, by Table LIX. : /* B = -^ inch, B = 4 inches, and the width of the pulley: p = 4 -f 1 = 4J inches. b. DIMENSIONING OF MAGNET FRAME. 1. Total Magnetic Mux.From Table LXVIIL, 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 -|- u 33 per cent, less (see note to Table LXVIIL, 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 webers. 2. Sectional Area of Magnet Frame. According to formula (216) and Table LXXVIIL, 82, we obtain the cross-section of the magnet frame : = 3.650.000 = 29 4 e 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: 29.4 _ . - Y = o inches. J 8 3. Polepteces and Magnet Core. The bore of the field is found by summing up as follows: DYNAMO-ELECTRIC MACHINES. [134 Diameter of armature core = 15.000 inches Winding 6 x .088 = .528 " Insulation and binding 2 x .080 = .160 " Clearance (Table LXI.) 2 x A = - l8 7 " dr> = 15.875 inches k- I 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, and rounding off the total height of the machine, we obtain 21 inches, leaving the length of the magnet core; / m =21 2X5 = 11 inches. The distance between the pole-tips is obtained by formula (150) and Table LX., 58, as: /r p = 5-5 X (15! - 15) = 4-8 inches, while the assumed percentage of polar arc corresponds to a pole angle of fi = 140, or a pole space angle of a = 40, and therefore furnishes: /' p = 15! x sin 20 = 5J inches, the larger value being preferable on account of smaller leak- age. 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 y clearance we ob- 134] EXAMPLES OF GENERATOR CALCULATION. 5 J 9 tain the desired distance, and making the width of the pole- shoes 16 inches, the total width of the frame becomes: 5 + 2J- + 16 = 23J 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 yy _ _ _ 2,083,000 ^(i5 + 15*) X - 2 X .89 X ^(5i + 5l) I 7)5 lines per square inch, the product of field density and conductor velocity is 3C" X z> c = I 7,5 X 80 = 1,400,000; hence the permeance of the gaps, by Table LXVI. and formula (167), page 226: X ~ X .89 x 5i 1-325 X (i5l - 15) 1.16 2. Permeance of Stray Paths. The area of the pole-shoe end surface, 5, Fig. 164, is, according to Fig. 344: = 54.5 square inches. This into (193) gives the total relative permeance of the waste field: <$ 2a i x 5 , 3 _* I X 54-5 +51 X M- + 7 X M ^ , 2 t X 51 , 51 X 2 " ^^ '= 5-5 + T 7-3 + i-3 + 2.0 = 26.1. 520 DYNAMO-ELECTRIC MACHINES. [134 3. Probable Leakage Factor. From (157), p. 218: A = ,02.5 + 26.! = "8.6 = j 266 102.5 102.5 This being smaller than, and only 1.2 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\ = 1.325 x 05-3- J 5) = r - 16 inch - Area, by (141), p. 204: S g = 15-5^ X X -89 x 5| = 119 square inches. Density, by (142), p. 204: 2, 08^,000 3C = - = 17,500 lines per square inch. Magnetizing force required, by (228), p. 339, <**g = 3 I 33 X 17,500 X 1.16 = 6360 ampere-turns. 2. Armature Core. Length of path, by (236), p. 343: 00 -|- 20 l\ = i X TT X '- 6 ' Q<> - + 2-| = i4| inches. Minimum area of circuit, by (232), p. 341: S &J = 2 x 5-J X 2-J X .90 = 26.5 square inches. Maximum area of circuit, by (233), p. 341, and (234), p. 342: S a3 = 2 X 5i X 2i X i - i X .9? = 54-7 sq. in. Average specific magnetizing force, by (231), p. 341: = - (29.5 X 7.1) = 18.3 ampere-turns per inch. 134] EXAMPLES OF GENERATOR CALCULATION. 521 Magnetizing force required, by (230), p. 340: #/ a = 18.3 X i4i = 265 ampere-turns. 3. Magnet Frame (all cast steel). Length of portion with uniform cross-section (core and yokes) : ^m = 1 1 + 2 X (5 -f H) 26 in ches. Area of magnet core and yokes: S m = 5 X 5-J = 29.4 square inches. Density: (&" m = - - = 90,000 lines per square inch. Specific magnetizing force (Table LXXXVIIL, or Fig. 256): / ("m) 57 ampere-turns per inch. Mean length of portion with varying cross-section (pole- pieces), from formula (243) : l "v = 2 f + ( 8 + 7f X ~ ) - 5?V = l8 inches. Minimum area: ^ Pl = 5 X 5f = 29.4 square inches. Maximum area: ^ Pa = M5l X ^ X .78 + 2 x ~ j X 51 = I2 sq. in. Average specific magnetizing force, by formula (241) : - = 30.8 ampere-turns per inch. Corresponding flux density, by Table LXXXVIII. : (B" 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. [134 4. Armature Reaction. According to Table XCI., 93, the coefficient of armature-reaction for (B" p = 80,000, in cast steel, is k^ = 1.25, hence, by formula (250), the magnetizing force required to compensate the magnetizing effect of the armature winding: at, = 1.25 x *l?J gives the number of series turns: = 275. 40 The length of the mean turn, by (290), being 'T 2 (Si + 5) + 2 X TT = 28 inches, the total length of the series field wire is obtained, by for- mula (288) p. 374: Formulae (278) and (282) give the radiating surface of the magnet: S M3 = 2 X ii X (51 + 5 + 2 X n) + 2 X 2 x (28 - si) = 466 square inches, hence by (294) the resistance required for the specified tem- perature increase: ij - - -- = .104 ohm, 75 40" i + .004 x 3 134] EXAMPLES OF GENERATOR CALCULATION. 5 2 3 and therefore by (294) the specific length of the magnet-wire: \ _^li = 6170 feet per ohm. . 104 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"), which have a joint specific length of 2 x 3138.6 6237 feet per ohm. Allowing f inch for the core- flanges, formula (296) gives, for this wire, an effective wind- ing depth of 2 X . IQ2 2 = 3275 X = 1. II Actual resistance of magnet-winding (from wire gauge table) : r m = 642 X 2 319 = .1025 ohm at 15.5- C., or r' se = .1025 x 1.12 = .115 ohm at 45.5 C. Weight of magnet winding, bare : wt 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, 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 | x r' m = 9 x r' 8e , " second " = $/- x r' K =11.5 X r'^, " third " = *- x r' ae = 15.67 X r' M , " fourth " = .y. x ^' 8e = 24 x r' M , fifth " =VxV M = 49 X r*, 524 D YNAMO-ELECTRIC MA CHINES. [ 1 34 By the proceeding shown in 100 we then obtain the follow- ing formulae for the resistances of the five coils: _ (11.5 r '** - r\] X (9^'se ^i) ~ 5" 8e - 8.2 r i; '. (457) _ (15.67 r^ n) X (11.5 r' 8e r t ) " (15.67 r^ - n) - (11.5 r'se - r,) 160.2 r' se a 27.2 r' 8e r\ -\- rf 4- I^y r^ = 38.2 r'se - 6.5 r t ; (458) r ln = resistance of third combination minus res. of leads = 15.67 r> m -/-,; (459) r iv = res. of fourth comb, minus res. third comb. = (24 - 15.67) r'se =-- 8.33 ^ e ; . (460) r v = res. of fifth comb, minus res. fourth comb. = (49 - 24) r' 8e = 25 r' se (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' ge .115 ohm, and the resistance of the leads rj = .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: r \ 45-5 X .115 8.2 X .01 5.15 ohms, r n = 38.2 x .115 - 6.2 x .01 = 4.32 " >m= T 5-67 X .115 - -oi 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: 134] EXAMPLES OF GENERATOR CALCULATION, 525 First combination: /, = -JT^-T X.I/ r u r m "T r i r m + r \ r u 4 ' 32XI ' 79 X.IX40 4.3 2 X 1-79 + S..S5 X i.79 + S^S X 4-3 2 = ^^ X 4 = ^^ X 4 = .8 ampere. 7.73 + 9.22 + 22.35 39.3 T* rm 0.22 11 ^ r l r m + r l r n -\-r ll r m X 3^3 x 4 - -95 amp. /m " *i r n + ^m + r n r m X ' * 7 = ~^~f X 4 = 2 -3 amp. Second combination: 7 m -7377 X .08 7 ^Y X 3.2 = 2.3 amperes. Third combination: 7 m = .06 7 = 2.4 amperes. Fourth combination: 7 m = 7 IV = .04 7 = 1.6 amperes. Fifth combination: 7 m = 7 IV = 7 V = .02 7 = .8 ampere. The maximum current intensities passing through the five coils, consequently, are: 7j = .8 amp.; or, in general: 7, =.2 X .i7= .027, (462) 7 n = .95 amp.; or, in general: 7 n = .3 X .o87= .0247, (463) 7 m = 2.4 amp. ; or, in general: 7 m = .06 7, (464) 7 IV = 1.6 amp. ; or, in general: 7 IV = .04 7, (465) 7 V = .8 amp. ; or, in general: 7 V = .02 7 (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 D YNAMO-ELECTRIC MA CHINES. [134 P. w>>; mi 1 -^ 8-0 *&. +$0 COIL NUMBER. 3J* $ .2SS 8< 32 O 11* P JP IP I .8 No. 21 B. & S. 810 1012 5.15 400 1.05 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. & S. 1624 1015 .96 150 .76 V .8 No. 21 B. & S. 810 1012 2.88 224 .58 /. 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- 4o 2 X (.275 4- .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 h = 160, P Q = 4, P k = .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 4- 160 4- 4 4- 235 4- 182 4- 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 dynamos 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 3j" length, . 20 Ibs. Armature, complete, . 300 Ibs. Frame : Magnet core and polepieces (see Fig. 344 and 134, c, 2), (5 X 26 + 54.5) X 5-J 1084 cu. ins. of cast steel, . 310 Ibs. Field winding ( 134, c, i), core insu- lation, flanges, etc., .... 140 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, e, 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 _ _ i= 9.5 watts per pound. 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 Revs, 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 DYNAMO-ELECTRIC MACHINES. [135 drum armatures, namely, ft l =-.75. Hence, by Table IV., p. 50: e = 62.5 X io~ 8 volt per bifurcation; the number of bifur- cations is n' v = i. The best conductor velocity, from Table V., p. 52 : v 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) : ^. Xio* 62.5 X 5 X 30,000 2. Sectional Area of Armature Conductor, and Selection of Wire.Ky (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 9 02 5 = 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 : <*'a = 3 X (.095" + .007*) + .016' = .322 inch. 3. Diameter of Armature Core. From (30): d' & = 230 x = 28| inches. 400 By Table IX. : <4 = -97 X 28 J = 28 inches. 135] EXAMPLES OF GENERATOR CALCULATION. 529 4. Length of Armature Core. By (37) and Table XVII , p. 73: 28 x n X (i - .08) n w - - = 252. .322 By (39), p. 74, and Tables XVIII. and XIX. : .8 (.090 -j- .O7o)_ ,322 By (40), p. 76: 12 X 3 X 7 /547\ V *<*/ . = 37J inches. 252 X 2 In this the active length of the armature conductor has been divided by 1.04, taking into consideration the lateral spread of Fig. 345. Armature Cable, 300- KW Bipolar Horseshoe-Type Generator. the field in the axial direction, and assuming the same to amount to 4 per cent, of the length of the armature core. 5. Arrangement of Armature Winding. By (45) p. 89, and Table XXI: and -500 x 2 (c)m = - = I0 - Two values of n c between these limits can be obtained, viz. : = _ 252x2 2 = 8 4 , and 252 X 2 = *- 3 = 56. j 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: = 84. By (47), P- 89, then: 2 52 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. Ms 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)i P- 96: A = 547 X 1 1 + i-3 X -T = 1070 feet. 1 + i-3 X J-JJT J = 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 (58), p. 101, then: // a = .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: r & = - X 1070 X .001144 = .0146 ohm, at 15.5 C. 135] EXAMPLES OF GENERATOR CALCULATION. 53* 7. Radial Depth, Minimum and Maximum Cross- Section, and Average Magnetic Density of Armature Core. By (123), and Table XLVIIL, p. 183: d. = i.55 x>-= 8 inches; see also Table XLIX., p. 185; therefore: j 28 _ 8 &* = - (<4 4) = - = 10 inches, and from (234), p. 342, or Fig. 347 : *'. = 10 x y i = 13.4 inches. 10 Fig- 347- Dimensions of Armature Core, 3OO-KW Bipolar Horseshoe- Type Generator. Hence by (232), p. 341: ^"a, = 2 X 37J- X 10 X .95 = 712 square inches, and by (233), p. 341: ^"a 2 = 2 x 37i X 13.4 X .95 = 956 square inches. From (138), p. 202 : - 6 x 512.5 X io 9 1 X 84 X 4 ^ 45 > 76 > 000 W6berS; consequently: " a , = = 64,200 lines per square inch, S3 2 DYNAMO-ELECTRIC MACHINES. [135 and 415,760,000 ($> ^ = ^ -- 47,800 lines per square inch. , P- 34i, and from Table LXXXVIIL, p. 336: * \ - , (47,8oo) _ 15.2 -f 9.1 a) = 12.15 ampere-turns per inch, to which correspond : (B" a = 58,000 lines per square inch. 8. Energy Losses in Armature^ and Temperature Increase. By (68), p. 109: ^ 1.2 x 6oo 2 X .0146 = 6307 watts. ^ = - = 6.67 cycles per second; (70) P- 18 X n x 371 X 10 X .9 , . M - Q = II -5 cu bic feet; From Table XXIX., (&" a = 58,000): 77 = 20.92 watts per cubic feet; From XXXIII., (tf, = .010*): 8 = .0242 watt per cubic feet. By (73), P- 112: P h = 20.92 x 6.67 x 11.05 = 1540 watts. By (76), p. 120: P^ = .0242 X 6.67 2 x 11.05 12 watts. By (65), p. 107: A = 6307 + 1540 + 12 = 7859 watts. From Table XXXV., p. 124: 4 = 35 X 28 -f 2 x .8 = n inches. By (78), P. 124: S A = (28 + 2 x .8) X nr(37i+ I - 8 x Ir i) = 5412 s< ^' ins ' 135] EXAMPLES OF GENERATOR CALCULATION. 533 Ratio of pole area to radiating surface: 30 X 7t X 37t X .75 _ For this ratio and a peripheral velocity of * x 4 6 o - 51} feet per second. Table XXXVI., p. 127, gives: e' a = 44.7C. ; consequently by(8i): a = 44.7 X 0| = 65 Centigrade, and the resistance of the armature, when hot, is: r' a = .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 /c = 8 -- ~ amperes per inch. 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 2 X 37i X .88 x 400 X 30,000 X io~ 6 = 310,000 watts. B y (90), p. 135: P>& = 6i$'x 30,000 = - 0167 Watt per P Und f c PP er > at unit field density; this also verifies the calculation, see Table XXXIX., p. 136. By (i55), P- 211 : ^' p ~ gi2*g x6oo X 5 ~ 74: ^ webers per watt, at unit velocity; by Table LXIL, p. 212, this is not too high. 534 DYNAMO-ELECTRIC MACHINES. [135 10. Torque, Peripheral Force, and Upward Thrust of Arma- ture. B 7 (93), P. 138: r = ~2 x 600 X 168 X 45,760,000 = 5420 foot-pounds. By (95), p- 138: 512.5 X 600 ' = ' 7375 X 50 X 168 X .88 = 30 - By (103), p. 141: / t = ii X io- 9 X 28 X 37i X (3Q,6oo 2 - 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 webers. By (217), p. 314, wrought-iron cores and yoke being used: i; 5,000,000 S wl = ^ ? = 611 square inches. 90,000 By (216), p. 313, and Table LXXVI., the minimum section of the cast-iron polepieces: = 55,000,000 = 11W) e . nches 5O,OOO 2. Magnet Cores. Selecting the circular form for the cross- section of the magnets, their diameter is: d m = \/ 61 1 x - = 28 inches. 7t Length of cores, from Table LXXXI., p. 319, by interpola- tion: / = 35 inches. 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: h = = 22 inches. SCALED I NCH=1 FT. Fig. 348. Dimensions of Field Magnet Frame, soo-KW Bipola* 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 (.090" 4- -070") = .320 Clearance (Table LXI. p. 209) 2 x T y, = .375 29.983 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 = 37J inches. Height of polepieces, same as bore: h v = 30 inches. Thickness in centre, requiring half of the full area: 1 100 2 X 37i Height of pole-tips: = 14.7, say 15 inches. 1/30 A/30 8 - i2 2 ] = I] inch. 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 z> c = 3> 000 X 5 = i,5 00 > 000 therefore, by (167), p. 226, and Table LXVI. : _ 1-35 X (30 - 28) 2.7 2. Permeance by Stray Paths. By (178), p. 232: _ 28 X 7t X 35 _ 4 1 *> ~ 2 x 16 + 1.5 X 28 - ** l 135] EXAMPLES OF GENERATOR CALCULATION. 537 By (188), p. 239: 7 X [37i X (28 + 15) + 850] 3, = = 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 K -- 16 *, Fig- 349- Top View of Polepiece, 300 KW Bipolar Horseshoe-Type Generator. S 3 = 16 x 37|- -f i6 2 X - - 28* - = 386 square inches, hence by (199), p. 245: _. 386 37j X 30 35 = ii + 7-4 = 18.4, 2 X 35 + (30 + 22) X - 3. Probable Leakage Factor. By (157), p. 218: .4 _ 652 _ " , . 536 + 41.6 + 56 ~^~ Total flux: <' = 1.215 x 45,760,000 = 55,700,000 webers. d. CALCULATION OF MAGNETIZING FORCES. i. Air Gaps. Length, by (166), p. 224: l\ = 1.35 x (30 28) = 2.7 inches. 53 8 DYNAMO-ELECTRIC MACHINES. [135 Area, by (141), p. 204: S g = 29 x - X .88 X 37 J = 1500 square inches. Density, by (142), p. 204: 3C" = = 30,500 lines per square inch. Magnetizing force required, by (228), p. 339: af e = -3 I 33 X 30,500 x 2.7 = 25,800 ampere-turns. 2. Armature Core. Length, by (236), p. 343, see Fig. 350: T I 7-1 l\ = 18 x n X P- -f 10 = 27.85 inches. Fig. 350. Flux Path in Armature, aoo-KW Bipolar, Horseshoe-Type Generator. Minimum area, by (232), p. 341 : Sk, = 2 X 37| X 10 x .95 = 712 square inches. Maximum area, by (233), p. 341 and (234), p. 342: Sa a = 2 X 37i X 13.4 X 95 = 956 square inches. Average specific magnetizing force, by (231), p. 341 : /(64,*oo)+/(47,8oo) Magnetizing force required, by (230), p. 340: at & 12.15 X 27.85 = 340 ampere-turns. 135] EXAMPLES OF GENERATOR CALCULATION. 539 3. Wr -ought-iron Portion of Frame (Cores and Yoke). Length: ''wj. = 2 X 35 + 22 + 44 = 136 inches. Area: S vi = 28" = 6i5f square inches. 4 Density: (B* wi = ">7 > _ 2 0)000 ii nes p er square inch. Specific magnetizing force: /("w.i.) = 5-7 ampere-turns per inch. Magnetizing force required: af wL = 50.7 x 136 = 6900 ampere-turns. 4. Cast-iron Portion of Frame (Polepieces). Length, by (243), page 348: l \.\. 35 + 2 = 37 inches. Minimum area (at center): S"c.i.i = 15 X 37i = 5 62 i square inches. Corresponding maximum density: (B" ci >x 5g>7 00 > oc 3 _ 49)500 ii nes per S q U are inch. Maximum area (at poleface): SaL, = ( 30 X w X y|^- + 2 X ij j X 37i = MOO sq. ins. Corresponding minimum density : 45,760,000 &" ci2 = 3L^_^__ = 32,700 lines per square inch. Average specific magnetizing force: /*".) = \ [/(49,5oo) +/( 3 2 )7 oo)] - I55 + 57 ' 6 = 106.3 ampere-turns per inch. Corresponding average density: &" ci = 43,500 lines per square inch. 540 DYNAMO-ELECTRIC MACHINES. [135 Magnetizing force required: at ci 106.3 X 37 = 3930 ampere-turns. 5. Armature Reaction. By (250), p. 352, and Table XCL: at v = 1.73 X - X = 5700 ampere-turns. 2 IOO 6. Total Magnetizing Force Required. B 7 (227), p. 339: ^T 7 = 25,800 -f 340 -f 6900 -f 3930 + 5700 = 41,670 ampere-turns. e. CALCULATION OF MAGNET WINDING. Shunt winding to be figured for a temperature increase of 15 C. Regulating resistance to be adjusted fora 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 = .3133 x (30,500 X 1.078) x 2.7 = 27,800 ampere-feurns. Armature core: at '* = /(5 8 >oo X 1.078) X 27.85 = 14.2 X 27.85 = 400 ampere turns. Wrought iron: 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 e^qual weights of each, the resultant specific length is: = - 419 X4 - = 834 feet per 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. 54 2 DYNAMO-ELECTRIC MACHINES. [ 135 The height of the winding space derived from the above value of / T is: A m = - - -- 28 2 J inches, and this into formula (277), page 369, gives the radiating sur- face of the magnets: S x = (28 + 2 x z\ ) n X 2 (35 2-|) = 6730 square inches, an allowance in length of 2^ inches per core being made for flanges, spools, and insulation. Hence by (312), p. 383: p> * ^f X 6730 x 1.18 = 1590 watts, by (314), p. 384: ^ sh = 41,670 Xjoo = shunt _ turns . J 59 and by (315), p. 384: Ah = I3>I i 2 X96 ^ 104,800 feet. consequently, ^sh = I0 1* = 125.5 ohms, resistance of winding, cold 834 (15-5 C.); and by (318), p. 385: T-'sn = 125.5 X (i + .004 x 15) = 133 ohms, resistance of winding, warm (30.5 C). By (317), P. 384: r "sb = J 33 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: 1^_5 - _ 2720 pounds, bare wire, ~ (.0419 135] EXAMPLES OF GENERATOR CALCULATION. 543 or, see Table XXVI., p. 103: wt' sh = 1.03 x 2720 = 2800 pounds, covered wire. B y (3 2 5)> P- 388, we receive: 06 otfsh = 3i-3 X io- 6 X 13,100 x X 834 = 2730 Ibs., which checks the above figure. Formula (257), p. 361, gives: X .04.800 X ' 95 (' 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 h 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: 14:00 Ibs. (covered) of No. 13 B.W.G. wire (.095" + .010") and 1400 Ibs. (covered) of No. 11 B. & S. wire (.091" -f .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 9f 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 : at" g = .3133 X (30,500 x .9025) x 2.65* = 22,800 ampere-turns. Armature core: at\ =7(58,000 x .9 02 5) X 27.85 = 10.3 x 27.85 270 ampere-turns. Wrought iron: at"w.i. =7(90,000 X .9025) X 136 = 33-2 X 136 = 4520 ampere-turns. Cast iron : P- 393, is: r T = (.18 + .15) X r' 8h = .33 + 133 = 44 ohms. By (332), P. 393: - > . (/*h)max = ~ = 4.o6 amperes. * For the minimum density the product 3C' X V c being 1,500,000 X .9025 = 1,353,750, Table LXVI. gives a coefficient of field-deflection k^ = 1.325, which makes the length of the magnetic circuit in the gaps /" g = 1.325 X (30 28) = 2.65 inches. 135] EXAMPLES OF GENERATOR CALCULATION. 545 % (333), P- 393 : (7 sh ) min = - - = 2.54 amperes. Supposing that the regulator is to have 60 contact-steps, so as to give an average regulation of ij 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: GAUGE DIAMETER SECTIONAL AREA CARRYING CAPACITY, AMPS. NUMBER. (inch). (Cir. Mils), v (6500 Cir. Mils p. A.) No. 6. B. &S 162 26,251 4.04 No. 9B. W. G 148 21,904 3.38 N0..7B.&S 144...... 20,817 3.21 No. 10 B. W. G 134 17,956 2.76 No.8B.&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 4.06 - 2.54 4.o6 -- 3-38 4.06 -- 2.54 X 60 = i , X 60 = 27 _4.o6 - _32_i 6 " - 4.06 -- 2.54 ' 4.06 2.76 " = irf-i:"TM X *>==5i, and ^ = fJ*J-_!J4 X 6o = 6o; 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- 406: 500 .X 600 _ 300,000 V * = 500 X 600 + 603. i8 2 X .0184 + 3 .i8 2 X 157 " 308,280 = -975, or 97.5 fa 2. Commercial Efficiency and Gross Efficiency. The energy lost by hysteresis and eddy currents was found P h -j- P & = 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 ~ rt _ * = 308,280 + I55 * + . 2 ,ooo 3-783* := ^' ^ M ' 8 *'' and the gross efficiency: 3. Weight Efficiency. The net weight of the machine is esti- mated as follows: Armature: Core, 11.05 cu. ft. of wrought iron, 5,300 Ibs. Winding, insulation, binding, etc., . 700 " Shaft, commutator, pulley, etc., . 3,000 <. i Armature, complete, .... 9,000 Ibs. Frame : Magnet cores, 28" X 70 = 4 43,100 cu. ins. of wrought iron, 12,075 Ibs. Keeper, 28 X 22 x 7 2 = 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, ooo " Bedplate, bearings, zinc blocks, etc., . . . . . 10,000 ll 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, . . ' "-.. ' . / '. - J 700 Ibs. Total net weight of dynamo, . . 57,700 Ibs. Hence, the weight efficiency: 3 0>00 = 5.2 watts per Ib. 57>7o 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 Yolts. 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. T. Determination of Number of Shunt Ampere- Turns. Use- ful flux required on open circuit: hence by 104: 44,700,000 - -3I33 X - -- X 1.325 (30 - 28) -3 X 33 X 29,800 x 2.65 = 24,700 ampere-turns. = 10.3 x 27.85 = 290 ampere-turns. 54^ DYNAMO-ELECTRIC MACHINES. [ 136 X I3 6=/ (88, 2 oo) x I3 6 46.4 X 136 = 6310 ampere-turns. 2I X /44, 7o,ooo V "~HOT- X37 = 99.6 x 37 3680 ampere-turns. AT sh = AT Q = 24,700 + 290 -f 6310 + 3680 = 34,980 ampere-turns. 2. Determination of Number of Series Amp ere- Turns. Total E. M. F. at normal output, by (333), p. 393: E' 1.05 x 500 -f- 1.25 X 603 x .0184 = 539 volts; and therefore: 48,200,000 <*' g -= -3133 x 2 -~j5; x 1.35 (30 - 28) = '3*33 X 32,100 x 2.7 = 27,100 ampere-turns. = 13.7 x 27.85 = 380 ampere-turns. ./1. 2 15 X 48, 200, 'W.L=// - ^5775" ,000\ ) X I36 =/ (95,2oo) X 136 = 67.8 x 136 = 9220 ampere-turns. 2x56^.5 = 123.9 x 37 = 4580 ampere-turns. a/ r = 1.76 x 4 X 3 X ^|*- = 5820 ampere-turns. 2 I oO AT = 27,100 + 380 -j- 9220 -f 4580 -\- 5820 = 47,100 ampere-turns. Consequently, by (339), p. 397: ioo - 34,980 = 12,120 ampere-turns. 136] EXAMPLES OF GENERATOR CALCULATION. 549 b. CALCULATION OF MAGNET WINDING. i. Series Winding. By (338), P. 396: = 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: N^ = * 2 '* = 20, or 10 turns per core; hence the series field resistance, at 15.5 C., by (344), p. 400: and the weight: wt se = 20 x -' X (5 X 19 X 13,094) = 6031bs., bare wire; or, w/'ae = 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 (319), p. 385: X ^ X 1.18 X (i + .004 X 22') , = 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 X 667 = ^ 0503 + 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 55 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: b y (346), p. 400 : 22-1 ^sh = - X 6730 6oo 2 x .00135 X (i + .004 X 22j) = 2020 530 = 1490 watts; by (3"), P- 3 8 3 : ^sh = i49 X 1.20 = 1788 watts; by (3H), P- 3 8 4: 25 = 10,270 turns; , .' Z sh = 10,270 x = 82,160 feet; by (315), P- sh = 10, Weight: *** = 82,160 x 2X ' - = 1825 Ibs., bare wire, o wt'fr = 1.035 X 1825 = 1890 Ibs., covered wire; Resistance: r ah = ! -- = 117 ohms, resistance of shunt winding, 15.5 C.; by (318), p. 385: r' ah = 117 X (i + -4 X 22^) = 127.5 ohms, resistance of shunt winding, 38 C. ; by (317), P- 384^ r '& I2 7-5 X 1.20 = 153 ohms, resistance of entire shunt circuit, normal load. ' Sab= 3.43 amperes, shunt current, normal load. 3. Arrangement of Winding on Cores. Total weight of series winding: . wt' 9G = 620 Ibs. Total weight of shunt winding: . o//' sh = 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. u 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" -f- .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 lls: Scinches, 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, /. 63 ' 000 -=6* inches. 2 X 80,000 X 10 X .9 Internal diameter of armature core, Fig. 352: 35| - 2 x 6{ = 211 inches. 137] EXAMPLES OF GENERATOR CALCULATION. Mean diameter of core: d'\ = 21$ + 6|-f i^- = 30ft- inches. Maximum depth of core, from (234), p. 342: 555 '= 63 A X /I - i = 14.8 inches. Fig- 352. Dimensions of Armature Core, so-KW Double-Magnet Type, Low-Speed Generator. By (232), p. 341: S &1 = 2 x 10 X 6| x .90 = 121 square inches. By (233), p. 341: S^ = 2 x 10 x 14-8 X .90 = 266 square inches. 0,630,000 ai = i2i~ : ~ 79, 6o lmes P er s q uar e inch. 0,630,000 aa ~ 266 ~ 3 6 ' 200 lmes P er square inch. By (231), p. 341: /(<&'.) =j[/ (79 5 6oo) + 7(36,200)] = 3 ' 7 + 6 - 7 = 18.7 ampere-turns per inch. Corresponding average density: &" a = 69,000 lines per square inch. 556 DYNAMO-ELECTRIC MACHINES. [137 7. Weight and Resistance of Armature Winding. B y (53) P- 99 : B Y (58), P- 101: 0/4 = .00000303 x 137,980 x 1360 = 568 Ibs., bare wire. B y (59), P- I02 : o//' 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 4Q0 2 X .0256 = 4950 watts. From Fig. 352 : X * X && - 138 X iA X- X 10 X .90 1728 = 3.61 cubic feet; ~ ~~ = 3>33 c y cles P er second ; from Table XXIX. (&" a = 69,000): r/ = 27.61 watts per cubic foot; from Table XXXI. (tf, = .020"): s = .138 watts per cubic foot. By (73). P- II2: jP h = 27.61 X 3-33 X 3-61 = 320 watts; By (76), P. 120: P e = .138 X 3.33* X 3-61 = 6 watts. By (65), p. 107: A = 4950 + 320 + 6 = 5276 watts. 137] EXAMPLES OF GENERATOR CALCULATION. 557 By (79), P- I2 5' 5 A = 2 X 30fV X n X (10 + 6| + 4 X i^-) = 4360 square inches. Ratio of pole-area to radiating surface: 38j X TT X 10 X .70 _ 4360 From Table XXXVI., p. 127, by interpolation: fi a - 44 C. By (81), p. 127: Armature resistance, hot: r' & = .0256 X (i + -004 X 53i) = -0314 ohm, at 69 C. 9. Circumferential Current Density, Safe Capacity and Running Value of Armature; Relative Efficiency of Magnetic Field. By (84), p. 131: i c = j - = 685 amperes per inch circumference. Table XXXVII., p. 132: 6 a = 40 to 60 C. By (88), p. 134: P' = 1.33 X 38|- 2 X 10 X .85 X 200 X 20,000 X io~* = 67,000 watts. By (90), P- 135 : p l& = 133 X 400 = <0047 watt per pound of coppert 568 X 20,ooc at u ^ fidd dengity By (i55)> P- 2II: = 9, 630, ooo x 5800 W ebers per watt, at unit X 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 webers. 558 DYNAMO-ELECTRIC MACHINES. [137 By (217), P. 314: = 12,000,000 = ^ 3 are 90,000 By (220), p. 314: 12,000,000 = re i 45,000 2. Magnet Cores. The two cores being magnetically in parallel, each must have one-half the area -5"' w .i. found above for wrought iron, and making their breadth equal to that of the armature core, their thickness is found: _33i3_ _ ^ ^ or sav flj inches. 3. Polepieces. Thickness at ends joining cores: 2 x 6f = 13J inches. Bore, by Table LXL, p. 116: 4, = 3 8 + 2 X \ = 38| inches. Length of centre portion (equal to diameter of armature core) : 38} inches. Depth of magnet winding (Table XXX., p. 115): 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 : /' p = 383- X sin 27 .= 15 inches, which is 4.45 times the total length of the gap space (compare Table LX., p. 208). Thickness in centre, required for mechanical strength only: 3^ inches. Thickness of pole-tips: - 15') = 1| inch. 137] EXAMPLES OF GENERATOR CALCULATION. 559 All other dimensions of the frame can be directly derived from Fig. 353. i 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. - -4375 = -439 inch ; Ratio of radial clearance to pitch: .125 .1765 = I43; Product of field density and conductor velocity: 20,000 x 32 = 640,000, hence by Table LXVIL, p. 230, the factor of field deflection * = 35 and by (174), p. 230: 3. = * [3^1 X 7t X .70 + (-439 + -219) X 138 X .85] Xio _ 4 3 X = . = 544. 75 560 DYNAMO-ELECTRIC MACHINES. [ 137 2. Permeance of Stray Paths. By (194), p. 242: j (5H + 10) X 13* + 3i X 10 io X ij ) ^ = 2 j - 18 h 15 + i* j -2(53.1 + .9) = 108. 3. Probable Leakage Factor. By (157), p. 218: 544 -4- 108 X D ^* ~ - = 1.20. 544 Ratio of width of slot to pitch: 4375 _ ~ 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_io: = 9 Q6Q ooo W ebers. 414 X 200 Air gaps: <*.. = -3133 X 9 -^- X .75 = .3^33 X 22)2 oo X .75 = 5216 ampere-turns. Armature core: il x 39 = 605 ampere-turns. /" a = 2 8| X n X ~ "^ o 27 + 6-| + 3i = 39 inches. Wrought iron: 38 = 36.5X38 = 1387 ampere turns. 137] EXAMPLES OF GENERATOR CALCULATION. 561 Cast iron: i.2 4 X 9> X22 2Xl3iXlo .24X9r6o,ooo\ ,./ _ 9.060,000 " if /i.24X9ro,ooo\ ,./ _ 9.00,000 _ v - 2 /( 2 V T ,i y 10 J + ' / ?" ~ \ ^(38|7rX.7)Xio + 2Xif)- J " = 79 X 6-i + 79+ 2 25 ' 4 X 22 = 514 + H48 = 1662 ampere-turns, the length of the uniform cross-section being 2 x 3^ = 6J inches, and the mean length of the varying cross-section, by (243), p. 348: - -4- i4 4- i4 = 22 inches. 2 AT&. = 5216 -|- 605 -f- 1387 -f- 1662 = 8870 ampere-turns. 2. Series Magnetizing Force. E' = 125 -f 1.25 x 4 X .0256 = 137 volts. * = 6 X I37 X I0 ' = 9,930,000 webers. 414 X 200 Air gaps: 0,030,000 <*** = -3!33 X - -a X 75 = -3133 X 24,300 X .75 = 5710 ampere-turns. Armature core: = 3J>_ L_Z x ^Q 820 ampere-turns. 1 r / ^12,300,000^ _ f /9,93Q, h 2 L 7 V 270 J^ J \ 428. 562 DYNAMO-ELECTRIC MACHINES. [137 Wrought iron: ^...=/( i - 24X I 9 3 f' ooo )x 3 8 = 54.2x38 : = 2060 ampere-turns. Cast iron: ,000 . _ X 22 = 9 8.6 X 6 + 98.6 + 28.2 X 22 = 640 + 1400 = 2040 ampere-turns. The average specific magnetizing force of the variable section, -i( 9 8.6 + 28.2) = 63.4, corresponds to an average density of (B" p = 41,000 lines per square inch, from which Table XCL, p. 352, gives J4 = 1.71. The maximum density in the armature teeth, at normal load, is: _ 9,93> 000 __ 7 X -7 X (35f X n - 138 X A) X 10 X .90 0,030,000 = - - = 62,000 lines per square men, and for this, Table XC., p. 350, gives 13 = .36. Hence by (250), P- 352: at r = r. 7 i X 4I4 X 2 X ' 36 R X 27 = 3830 amp. -turns. 2 IOO . . AT = 5710 -|- 820 -f- 2060 -f- 2040 + 3830 = 14,460 ampere-turns. AT se = 14,460 8870 = 5590 ampere-turns. e. CALCULATION OF MAGNET WINDING. Temperature-increase permitted, m = 19 C. Percentage of extra-resistance in circuit at normal load, r x = 35 %. 137] EXAMPLES OF GENERATOR CALCULATION. 563 i. Series Winding. Apportioning one-third of the total winding depth, h m = 2f", to the series winding (AT se being about one-third of AT), about i inch will be taken up by the latter, hence, if the series coil is wound next to the core, the mean length of a series turn : /' T 2 (10 -|- 6J) -j- i x n = 36.64 inches, and the mean length of a shunt turn: l\ 2 (12 -f 8j) -f- if X 7t = 47 inches. The radiating surface of each magnet is: SM = 2 (10 -j- 6f -|- 2} it) x (18" i") = 860 square inches. By (343), P. 4oo, thus: = 910,000 circular mils. For 22 No. 4 B. & S. wires (.204" -f- .012") the actual area is: 22 x 4 J ,743 = 918,346 circular mils. Number of turns required per magnetic circuit, if both coils are in series: By (344), p. 400, for the two series coils: 64 = - 00098 r' 8e = 1.078 X .00098 = .00106 ohm, at 34.5 C. and the total weight: 7#/ se = 2 x 14 X ~~ X 22 x .1264 = 238 Ibs., bare wire; w/'ge = 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: *sh = - 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" -j- .007") with a specific length of 398 feet per ohm. By (346), p. 400: P 8h = . x 86o _ 400 * x i = 2l8 _ 85 = I33 watts . By (312), p. 383: ^' S h = 133 X 1-35 = l8 watts. By (314), p. 384: ^ 8 h = 887 * I25 - 6170 turns per magnet. IoO By (315), p- 384: Z 8h = 6170 x ~== 24,200 feet per core. Total weight : wt sh = 2 x 24,200 x .01243 '= 604 Ibs., bare wire. wt'sh 1.0325 X 604 = 624 Ibs., covered, or 312 Ibs. per magnet. Shunt resistance per core: = 60.8 ohms, at 15.5 C. r' 8h 60.8 X 1.076 = 65.5 ohms, at 34.5 C. ^"sh = 65.5 x 1.35 = 88.4 ohms, each shunt circuit. Exciting current: / Bh = = 1.4:2 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: J X 22 78 Height of series winding: 4 X .216 = .864 inch. 137] EXAMPLES OF GENERATOR CALCULATION. 565 Number of shunt wires per layer: 17 =210. .071 Number of layers of shunt wire: 6l70 _ og Height of shunt winding: 26 x .071 = 1.84:6 inch. Allowing .1 inch for core covering and insulation between layers, the actual total depth of magnet winding is: h m .864 + 1.846 -j- .1 = 2{$ inches. Actual-magnetizing force at full load: AMPERE- TURNS. Series magnetizing force, AT ae = 14 x 4 = 5600 Shunt magnetizing force, AT sh = 26 X 240 X 1.42 = 8850 Total magnetizing force, . . . . A T =14,4:50 /. CALCULATION OF EFFICIENCIES. i. Electrical Efficiency. By (353), p. 406: -, __ _ 125 X 400 Ye ~ - jjg- 125 X 400 + (400 + 2 X i.42> 2 X .0314 + 400* X .00106 -f (2 X i-42) a X 2. Commercial Efficiency. Allowing 2500 watts for commuta- tor- and friction-losses, we have by (361), p. 408: = 55,630 + 332 + 2500 58,462 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 6f- = 6075 cubic inches of wrought iron, . - ; 1700 Ibs. Polepieces, [45 X 45 ~ (38f X | + 2 X 18 X 3i + 2 x 15 X if)] X 10 = 6970 cubic inches of cast iron, . . . . . 1800 " Field winding and insulation (250 -{- 650) Ibs = . . . . .- . . 900 " Dynamo portion of bed, bearings, etc., . 750 " Frame, complete, . . . . . 5150 Ibs. Fittings: Brushes, holders, and brush-rocker, . ".. ., loo.lbs. Switches, series field regulator, cables, etc., 100 " Fittings, complete, . . ,.. . . ; 200 Ibs. Total net weight of dynamo, -. . . 8200 Ibs. The specific output, therefore, is: - r- 6.1 watts per pound. 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. Taking Table IV., p. 50, gives: e 60 x io~ 8 volt per foot; Table V., p. 52: v c = 96 feet per second; 138] EXAMPLES OF GENERATOR CALCULATION. 5 6 7 and Table VIII., p. 56: 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: 3C" = f X 60,000 = 40,000 lines per square inch. Consequently, by (26), p. 55: = 5 X 153 X io- = 332 feet 60 X 96 X 40,000 2. Area and Shape of Armature Conductor. By 20: tf a 2 = 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: 7t 960,000 x 6- = 1.2 inch. .625 X io 6 This making too massive a single conductor, we divide it into 4 bars of .3 inch average width. 3. Diameter of Armature Core, Number of Conductors. B y (30), p- 58: 06 <4 = 230 x = 96 inches, 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: ^ a = 96 2 x . 125 .625 = 95-J- inches, 568 DYNAMO-ELECTRIC MACHINES. and the number of armature conductors: [138 95J X 4X (-3+ ' 4. Length of Armature Core. By (40), p. 76: 12x332 = <>Q inch es. 200 5. Radial Depth, Minimum and Maximum Cross- Section, and Average Magnetic Density of Armature Core. By (137), P. 201: = 6_X5X. 5 3Xio' g 99 ooo,000 webers. 200 X 232 By (48), p. 92, and Table XXII.: 99,000,000 = 8 inches. 10 X 70,000 X 20 X-9O External diameter of armature core, Fig. 354, Fig- 354- Dimensions of Armature Core, I2OO-KW ID-Pole Radial Innerpole-Type Generator. d\ 96 -f 2 x 8 = 112 inches. Mean diameter of armature core, d'" & 96 -f- 8 = 104 inches. The width of one-half field space is x. 7 8 = inches, 138] EXAMPLES OF GENERATOR CALCULATION. 569 hence, by Fig. 354: b' & = Vi2 a -|- 8 2 = 14! inches. By (232), p. 341 : S &1 = 10 x 20 x 8 X .9 = 14,400 square inches. B 7 (233), P- 34i: S a2 = 10 x 20 x 144 X .9 = 28,100 square inches. By (231), P- 34i: l8 -5 +6.5 - " 14,400 28,100 = 12.5 ampere-turns per inch. Average density: (B" a 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: Fig. 355. Dimensions of Armature Conductor, I2OO-KW lO-Pole Radial Innerpole-Type Generator. Minimum thickness of bar on inner circumference: 94j X TT 4 X 200 - .050" = .3211 inch. 57 DYNAMO-ELECTRIC MACHINES, [138 Maximum thickness of bar on inner circumference: _5 _ .050' = .3260 inch.' Minimum thickness of bar on outer circumference: Maximum thickness of bar on outer circumference: ii3iX n __ = t3 95 7 i nch . 4 X 200 Area of conductor on inner circumference: (tf a ) a = 4 x 625 x 32I ' r + 326.0 = 808 ^ 875 square mils Area of conductor on outer circumference: (d' a y = 4 x 625 X 390.8 + 395.7 = 983 ^25 squar e mils. Mean length of armature turn: 2 x (20 -f- 8 -f 2 x |) = 59J- inches. Total length of armature winding: T 200 x Z t = -- 2. 1 992 feet. Weight: (808,875 + 983,125)! wt & .00000303 x X 992 = 3440 Ibs. Armature resistance: r & = l -* x 992 X - ^ - = .000091 ohm, at 15.5 C. 896,000 x ^ 7T 8. Energy Losses in Armature, and Temperature Increase. By (68), p. 109: P* = 1.2 X 8ooo 2 X .000091 = 7000 watts. 138] EXAMPLES OF GENERATOR CALCULATION. 571 ... 104 XTT X 20 X 8 X .9 u - r M = - y = 27.2 cubic feet. 1728 ^V", = - 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 ^ = .015"): c = .0258 X i-5 a = .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 2 X 27.2 = 580 watts. By (65), p. 107: p^ = 7 ooo -f 11,220 + 580 = 18,800 watts. By (79), P- 125: 5 A = 2 x 104 x n x (20 -f- 8 + 4 X f) = 20,250 sq. ins. Ratio of pole area to radiating surface : 94 X it X 20 X .78 _ 20,250 From Table XXXVI., p. 127: By (81), p. 127: 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 7t 57 2 DYNAMO-ELECTRIC MACHINES. [138 % (88), p. 134: P' = 96* x 20 x .85 x 232 x 40,000 x io- 8 = 1,510,000 watts. By (90), p. 135: p , = 153 X 8000 _ watt copper, at unit 3440 X 40,000 density. = 777() webers 99,000,000 153 X oooo velocity. b. DIMENSIONING OF MAGNET FRAME. 1. Total Magnetic Flux, and Sectional Area of Frame. By (156), p. 214, and Table LXVIII. : $' = 1. 12 X 99,000,000 = 111,000,000 webers. By (218), p. 314: I IT, OOO,OOO tn*t\ - u S CB = - - - = 1310 square inches. 85,000 2. Magnet Cores. There being io magnetic circuits through the io cores, each circuit containing two of the magnets in series, the sectional area of one 'core must be one-fifth of the total frame area obtained; making the breadth of the cores 19J inches, that is, inch narrower than armature and polepieces, their thickness is found : - = 13J inches. The length of the cores is obtained from Table LXXXIIL, p. 321, the nearest cross-section being 12 x 24 inches, for which / m = 16 inches. 3. Polepieces. External diameter of field frame, by Table LXI., p. 209: 500 llnes per square mch > which, however, is within the practical limits of magnetization for cast steel (see Table LXXVI., p. 313), making a re-dimen- sioning of the frame unnecessary. d. CALCULATION OF MAGNETIZING FORCES. 1. Air Gaps. Actual density: ^ 99,000,000 ^" = 2C4o = 39,000 lines per square inch. By (228), p. 339: af g '3*33 X 39,000 X 2.8 = 34,200 ampere-turns. 2. Armature Core. By (236), p. 343: 25T+4 l\ = 104 X 7f x -$-2 h 8 = 28 inches; 360 /(&" a ) =/(58,75o) = 12.5 ampere-turns per inch. By (230), p. 340: at & = 12.5 X 38 = 350 ampere-turns. 3. Magnet Frame. Length of path (see Fig. 356): 2 X (3i + 1 6 + 3 + 4 J) = 54 inches. For cast steel, / (97, 500) = 86 ampere-turns per inch. By (238), p. 344: a/ m 86 x 54 = 4650 ampere-turns. 576 DYNAMO-ELECTRIC MACHINES. [138 4. Armature Reaction. Mean density in polepieces: 5 X^Tx^o = 57.* Hnes per square inch.-" " hence by (250), p. 352, and Table XCI. : at, = ,. as x 2 X 8oo X -- = MfiO ampere-turns. IO loO 5. Tk/fc/ Magnetizing Force Required. By (227), p. 339: A T 34, 200 + 350 + 4650 -f 4450 43,650 ampere-turns. e. 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 1} 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 j- inch for the bobbin flanges, and for insulation and clearance, it is thus found that 8J 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 i J inch. This gives a mean winding depth of 4 X 8f + L( 4 + i|)X7 = 3 inches. m Mean length of one turn: / T = 2(19^ -|- 13!) -f 3^ x 7t 77 inches. Radiating surface of each magnet: S* = 2 (19^ -f 13^+ 3i X ?r) 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: o^m = 77 X i5f X 3^ X .21 = 890 pounds. EXAMPLES OF GENERATOR CALCULATION. 577 hence by (329), p. 390: \ 75 j x x x " X 12 ' I38s " = 44 C 890 -- .004 x [31-3 X 140 2 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 8h = 4^50 x 77 x r 2Q x (l H _ OQ4 x 440) = 2635 150 12 feet per ohm. No. 8 B. VV. G. wire (165" + .010") has a specific length of 2637 feet per ohm. By 312, p. 383: ^' 8 h = ~ - X 2 x 1480 x 1.20 = 2080 watts per magnetic circuit. By (314), p. 384: ^ sh = 43,650 x 150 = 3150 turns per d 2OOO 3150 X 2080 ~ = 20,200 feet, per pair of magnets. = 7.67 ohms, 2 coils in series, at 15.5 C. By (318), P. 385: 7- 6 7 X (i + .004 X 44) = 9.0 ohms, one group, at 59-5 C. 57 8 DYNAMO-ELECTRIC MACHINES. [138 B 7 (317) P- 3 8 4: r "sb = 9-0 X 1.20 10.8 ohms, one shunt branch, at normal load. .. / 8h = '5 = 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: J 3-9 X 5 = 69.5 amperes, while the joint shunt resistance of the 10 coils is: 9.0 = 1.8 ohm, at 59.5 C. Total weight: w/ sh = 5X7-7 _ g3Q pounc i s bare wire. .0046 wt'sh = 8330 x i. 022 1 = 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. ^y (35 2 )> p. 406: _ 150 X 8000 " 150 X 8000 + 8069.5" X .000105 +5 X 13.9* 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 + 40,000 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, .... 25,000 Ibs. Frame : Magnet cores, 10 x 19^ X 13^ X 16 = 42,100 cu. ins. of cast steel, - . . 1 1, 500 Ibs. Polepieces, 10 X 22| X 20 X 2J- 10,050 cu. ins. of cast steel, 2,800 " Yoke, L 735 x 59 2 - 43* j ) X 20*- = 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, '". . 42 , OO o Ibs. Fittings: Brush shifting and raising de- vices, brushes, studs, etc., 1 3,000 Ibs. Switches, cables, etc., . . 1,000 " Fittings, complete, . . . . . 4 , 000 lbs . Total net weight of dynamo, . 71,000 Ibs. Weight efficiency: 1,200,000 71,000 16.9 watts per Ib. 5^0 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 Yolts. 50 Amps. 400 Revs, per Min. a. CALCULATION OF ARMATURE. 1. Length of Armature Conductor. A - .75; = ' 8 ( V ' 75) = 7iV = 57-5 X ID-' v. p. ft. # c = 60 feet per second; JC" = 15,000 lines per square inch; E' = 1.10 X 600 = 660 volts. By (26), p. 55: Za = 3x660x10- = 57.5 X 60 X 15,000 2. Sectional Area of Armature Conductor. B Y (27). P- 57: 25 >000 ^ I f (%> 2 5>\1 _ 20 -5 + 2-9 - l|/V~6 ~/ +/ V 5 4 yJ" ~ = 11,7 ampere-turns per inch. Average density: &" a = 57,000 lines per square inch. 7. Weight and Resistance of Armature Winding. By (53), p. 99: z t = . . x 38?o = 95oo feet By (58), p. 101: wt & .00000303 x 5184 X 9500 = 149 Ibs. By (59), P- I02 : wt\ 1.078 x 149 ~ 161 Ibs. By (61), p. 105: r a = * a X 9500 = .002 = ,528 ohm, at 15.5 C. 4X3 8. Energy Losses in Armature, and Temperature Increase. M = 37i X n X .3 Xjj. X :,8j = f g 1728 ^ x _ 2Q C y C i es p er second. 60 By (68), p. 109: A = 1.2 X so 2 X .528 = 1585 watts. By (73), p. 112: A = 20.35 X 20 X 1.89 = 780 watts. By (76), p. 120: P* = .094 X 2o 2 X 1.89 70 watts. By (65), p. 107: /> A = 1585 + 780 + 70 = 2435 watts. By (79), P- I2 5- SA = 2 X 37i TT X (13 + 24- + 4 X |) = 4000 sq. ins. $139] EXAMPLES OF GENERATOR CALCULATION. 583 Ratio of pole area to radiating surface : 34 x n X 13 X -75 = 26 4000 By (81), p. 127: e a = 42 x - 25i C. 4000 r' & = (i + .004 X 25^) X .528 = .583 ohm, at 41 C. b. DIMENSIONING OF MAGNET FRAME. 1. Total Magnetic Flux, and Sectional Areas of Frame. By ( J 5 6 ), P- 2I 4- #' = 1.30 x 8,250,000 = 10,700,000 webers. By (217), P. 3M: = 10,700,000 = 119 re inches 90,000 By (218), p. 314: 10,700,000 ,S C8 = - - = 126 square inches. 85,000 2. Magnet Core. The magnet being hollow, its internal diameter must be determined first. Diameter of shaft, by (123), p. 185: = i-3 X /i/ 3 - = 4 inches. 400 Making the hole in the core 4^ inches in diameter, the ex- ternal core diameter becomes: dm = \/ ("9 + J 5-9) X ~ = 13 inches. 3. Polepieces. ^ P = 35 - 2 X (.324 + |) = 34 inches, /'p = 34 x sin 7j = 4| inches. Providing the same distance between all projecting portions of opposite polarity, the shape shown in Fig. 357 is obtained, having a mean width of about 12 inches per magnetic circuit. The axial thickness of the polepieces, therefore, must be: 584 DYNAMO-ELECTRIC MACHINES. 126 rt . . , 31 inches, 3X12 leaving the length of the magnet core: 4, = '3 - 2 X 3i = 6 inches. [139 Fig. 357. Dimensions of Armature Core and Field Magnet Frame, 3O-KW 6-Pole, Single-Magnet Innerpole Type, Moderate-Speed Generator. C. CALCULATION OF MAGNETIC LEAKAGE. i. Permeance of Gap Spaces. OC" X # c = 15,000 X 60 = 900,000. By (167), p. 226: + 35) X n x .835 X 13 _4 1-25 X (35 ~ 34) 2. Permeance of Stray Paths. From Fig. 357: = ^ = 520. 6X (2 X I3+I2X3J) = 53-3 + 90-7 = 144. 139] EXAMPLES OF GENERATOR CALCULATION. 585 3. Probable Leakage Factor. S3 o+.44 = 1J88 520 d. CALCULATION OF MAGNETIZING FORCES. 1. Air Gaps. Actual density: OC" > 2 5> 000 _ I4)000 lines per square inch. 59 By (228), p. 339: af g -3 X 33 X Mooo X 1.25 = 5480 ampere-turns. 2. Armature Core. By (236), p. 343: ?+7** l\ = 37^ X 4 h H = *4t inches; From Table LXXXVIII., p. 336, for wrought iron: / (57,000) =11.7 ampere-turns per inch; By (230), p. 340: at & = 11.7 X i4f = 170 ampere-turns. 3. Magnet Frame. Wrought iron portion: Length, /" w .i. = 6 + 3i + i 10 inches. Area, S wi . (13* 4^ a ) - = 116.8 square inches. 4 Specific magnetizing force, / ((B w .i.) =/ (92,000) = 56.5 ampere-turns per inch. Magnetizing force required, #/ wi = 56.5 x 10 = 565 ampere-turns. Cast steel portion: Length, ^c. s . = 2 X (9i + 6) = 304 inches. Minimum cross-section, Sc.8., =3Xio-J-X3-J-=no square inches. 5 86 DYNAMO-ELECTRIC MACHINES. [139 Maximum cross-section, ^c.s. a = 3 X 18 X 34 = 189 square inches. Average specific magnetizing force, 10,700,000 = - =. 50.5 ampere-turns per inch. Magnetizing force required: 0/ C8 = 50.5 x 3i = 1540 ampere-turns. 4. Armature Reaction. Density in polepieces: _,, 10,700,000 .. , (B p = - - = 20,500 lines per square inch. jX 34 X * X .75 X 13 By (250), p. 352: at t = 1.25 X 3<3 x * x 1|! = 3130 ampere-turns. 5 . Total Magnetizing Force Required. By (227), p. 339: AT= 5480+170 + 565 + 15^0+3130 = 10,885 ampere-turns. e. CALCULATION OF MAGNET WINDING. Limit of temperature increase, e m = 22 C. By (287), p. 374: N~ = - 218 turns. Allowing a winding depth of 7 inches, the mean length of one turn is ^ = (13 + 7) X n 62.8 inches; hence, by (288), p. 374: 218 X 62.8 Ae = = 1140 feet. 8^ = 27 X 7t X 6 + 6 X 14 X 3 = 760 square inches. r^ := ~x ^ X : = .082 ohm, at 15.5 C. 75 5o i +.004 X 22 Ase - IT ^- = 13,900 feet per ohm. .002 140] EXAMPLES OF GENERATOR CALCULATION. 587 The coil being round and of comparatively large diameter, a single wire, No. 00 B. W. G. (.380" + .020") can be em~ ployed without difficulty. Number of turns per layer: 5i n .38 + .02 Number of layers: Net depth of winding space : h' m 17 X (.38 -f .02) = 6.8 inches. Adding to this the thickness of the bobbin and insulation, we have ^ m 7 inches, as above. Weight of winding: wt se = 1140 X .437 500 Ibs., bare wire: wt'se = 1.022 x 500 = 510 Ibs., covered wire. Resistance: r K = 500 X .00016 = .08 ohm, at 15.5 C. Actual magnetizing force: AT ae = 13 X 17 X 50 = 11,050 ampere-turns. 14:0. Calculation of a Multipolar, Multiple Magnet , Toothed-Ring, Low-Speed Compound Dynamo : 2000 KW. Radial Outerpole Type. 16 Poles. Cast- Steel Frame. Drum-Wound Ring Armature. 540 Yolts. 3700 Amps. 70 Revs, per Min. a. CALCULATION OF ARMATURE. i. Length of Armature Conductor. For /3 l = . 70, we have 180(1 .70) 16 and ft = 3 ^r - 2 x 31 = '51. 588 DYNAMO-ELECTRIC MACHINES. [ 14O From Table IV., p. 50: e = 55 X io~ 8 volt per foot; ~ = ^j- X io~ 8 = 6.875 X io~ 8 volt per foot. n v 8 From Table V., p. 52: v c 42.8 feet per second. From Table VI., p. 54: OC" = 35,000 lines per square inch. From Table VIII. , p. 56: E' 1.02 X 540 551 volts. B y (26), p. 55: 8 feet a 6.875 X 42-8 X 35' 2. Mean Winding Diameter of Armature. By (30), P- 58: d\ = 230 X - - = 140} inches. 3. Area and Shape of Armature Conductor ; Size and Number of Slots. By 20: oY = 600 X ^- = 278,000 circular mils, o or 278,000 X - = 219,000 square mils. 4 A bar, -} inch high by inch wide, has a cross-section of 218,750 square mils. Arranging 6 such bars in each slot, as shown in Fig. 358, the width of the slot is found -}-J- inch, its total depth, 3^ inches, and the distance between mean wind- ing diameter and external circumference is obtained i-| inch, hence by (34), p. 70: X .) X x . 2 X TT this being the nearest number divisible by 16. 140] EXAMPLES OF GENERA TOR CALCULA TION. 4. Length of Armature Core. By (48), p. 92: 5 8 9 5. Arrangement of Armature Winding. By (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. B Y (138)* P- 201 : By (48), p. 92 : 188,000,000 .90 = 61 inches, 59 DYNAMO-ELECTRIC MACHINES. [ 14O allowance being made for 6 air-ducts of \ inch width, and for 2 phosphor-bronze end-frames of inch thickness, thus: 6 x -J -f 2 x -J- = 2j inches. Total radial depth of armature core : 6J + 3-J = 10 inches. Maximum depth of armature core: H -|- io 2 = Vio* + io 2 = 14 ii b\ \ I 144 X sin^ I + io 2 = Vio' + io 2 = 14 inches. 4 By (232), p. 341: S &1 = 16 x 29^ X 6| X .9 = 2920 square inches. By (233), p. 341: 6" a2 = 16 X 29 J- X 14 X .9 = 5950 square inches. P- 34i: / (31,600)= ^= I 5- = 10.4 ampere-turns per inch. Average density: (B" a = 58,000 lines per square inch. 7. Weight and Resistance of Armature Winding. (57), P- ioo : A = / i + .293 x X 535 = 12.400 feet. / By (58), p. 101: wt & = .0000303 x 278,000 x 12,400 10 5 425 Ibs. By (61), p. 105: r & = ^-gi X 12,400 X 2 ^'000= -00183 ohm, at 15.5 C. 8. Energy Losses in Armature, and Temperature Increase. By (72), p. 112: 134 X 7t X io - 336 X 3 X \\ X 294 X .9 1728 = 55 cubic feet. 140] EXAMPLES OF GENERATOR CALCULATION. 59 l 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: jV t = ~ x 8 9.33 cycles per second. By (68), p. 109: P & = 1.2 X 37oo 2 X 00183 = 30,000 watts. By (73)1 P- II2: P h = 18.1 X 9.33 X 55 = 9300 watts. By (76), p. 120: P e = .081 X 9 .33 2 X 55 = 400 watts. By (65), p. 107: / A 30,000 -f- 9300 -f- 400 39,700 watts. By (79). P- I2 5: SL 134 X n x 2 X (36 + 10) = 38,700 sq. inches. Ratio of pole area to radiating surface : 144! X TT X 32 X .70 _ 10,200 _ 38,700 ~ 38,700 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\ , rep- resenting the loss in the solid portion of the core, and the latter, P\ , 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\ , 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 1 1, 1897); Electrical World, vol. xxix. p. 325 (March 6, 1897). 592 DYNAMO-ELECTRIC MACHINES. [140 the smallest density (in the largest section, at the periphery of the armature) multiplied by a factor, W' which depends upon the ratio, of minimum to maximum width of tooth, and upon the shape of the slot, ranging as follows: RATIO r(b\\ FACTOR J I -7 1 b\ V * / h 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, f h , of the armature, and the total hysteresis loss in well-designed machines is so small compared with the C'^Moss 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 calcu- 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 GENERA TOR CALCULA TION. 593 mass of the teeth about n cubic feet is near its maximum amount, we have: P\ = 18.1 X 9-33 X (55 - n) = 745 watts; Minimum density in teeth: 188,000,000 188,000,000 3425 (*-?) 2 X .70 X I 144 X ) X 2 9 X .9 = 55,000 lines per square inch; Hysteresis factor for this density: rj 19.21 watts per cubic foot. Ratio of minimum to maximum width of tooth: X * 1JL 336 't * T-T- /\ "- j 336 Tooth-factor, by interpolation from the above table: . '. P\ = 19.21 X 9-33 X ii X i-53 = 3 watts. The total hysteresis loss, therefore, theoretically accurate, is J* h 7450 -|- 3000 = 10,450 watts. This is about 12^- per cent, greater than the value found on p. 591 (P 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 (i5 6 ) P- 2I 4' 0' = 1.15 x 188,000,000 = 216,000,000 webers. By (218), p. 339 : 216,000,000 - 85,000 = 2540 square inches. 594 D YNA MO-ELECTRIC MA CHINES, [140 2. Cores. The length of the polepieces being 32 inches (equal to length of armature core), and their circumferential width being jeA 144-f 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 c . s . = 8 X 25 x 13 = 2600 square inches. Length of cores, by Table LXXXIIL, p. 321: / m = 16 inches. 3. Polepieces. Bore: P- 400: *- X 38,780 X 231.25 X 87 *-' ---- 65 x : I4 6o x 37 r x (I + - 4 x 37i) = 532,000 circular mils. Using a iQ-wire cable, the area of the wire required is : 532,000 - = 28,000 circular mils. 19 The nearest gauge wire is No. 8 B. W. G. (.165" + .010"), making a cable-diameter of 5 X (.165 -j- .010) = .875 inch. The winding depth available accommodates = 4 layers 600 DYNAMO-ELECTRIC MACHINES. [ 14O of this cable; hence there are required: 16 - = 4 turns per layer, 4 and the axial length of the series coil is 4 X .875 = 3 inches, leaving for the shunt coil a length of 16 3j = 12 inches. B y (344), P- 400: T 19 Joint resistance of all series coils: = .000147 ohm at 15.5' C. Total weight, bare: o// se = 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 (31,700) A^ = - - X X 1.20 X (i 4- .004 X 37i) ~ X540 = 4690 feet per ohm. No. 5 B. W. G. wire (.220" -f .012") has 4688 feet per ohm, and therefore gives the required resistance. By (346), p. 400: Ah = 3 ~- X 1460 - 231.25" X .00235 X (i + .004 X 37i) / D = 730 - 143 = 587 watts. By (312), P- 383: P'sb = 5 8 7 X 1.20 = 705 watts per magnet. 140] EXAMPLES OF GENERATOR CALCULATION. 60 1 By (314), P- 383: - (31,700) x i x 540 ^ Number of turns in one layer: 12 = 760 turns per core. = 51; .232 Number of layers required: 760 - 1 * -: 15. Winding space taken up: 15 x .232 = 3^ inches. By (315), P- 384: Ah = 51 X 15 X = 5540 feet per core. Total weight, bare : wt^ = 16 x 5540 X .1465 = 13,000 Ibs., or 812 Ibs. per core. Total resistance: r h = 16 X 5540 X .0002128 = 18.9 ohms, at 15.5 C. By (318), p. 385: r' 8h = 18.9 X (1.004 X 37i) = 21.7 ohms, at 53 C. By (317), P- 384: r" sh = 21.7 X 1.20 26 ohms, entire shunt circuit. ' Ah = ^r 20.8 amperes, shunt current, at normal load. 20 Actual magnetizing force : AT se = 2 X 16 X 231.25 = 7,500 ampere-turns. AT 8h = 2 X 51 X 15 X 20.8 = 31,800 " Total exciting power : A V 39,300 ampere-turns. 602 DYNAMO-ELECTRIC MACHINES. [140 6. CALCULATION OF EFFICIENCIES. 1 . Electrical Efficiency. B 7 (353),_ P- 406: n ~ 540 X 3700 540 X 3700 + (3720. 8) 2 x .00216 -+- 3700 2 x .000147 + 20.8 2 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 % = V- - = l = -947> or 94.7 #. 2,043,300 + 9700 -\- 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, 194 X 7t x 32 X 5 = 97,500 cubic inches of cast steel, .... 27,000 " Polepieces, 16 X 20 X 32 X ij = 19,000 cubic inches of cast steel, .- ... 5,ooo " Field-winding, spools, and insulation, . 20,000 " Supporting lugs, flanges and bosses on frame, outboard bearing, etc., . . 15,000 " Frame, complete, . \ . -<,- . 90,000 Ibs. [ 141 EXAMPLES OF GENERA TOR CALCULA TION. 603 Fittings: Brush-shifting and raising devices, brushes and holders, etc., . . . . 4,000 Ibs. Switches, connections, cables, etc., . 1,000 " Fittings, complete, . . . , . 5,000 Ibs. Total net weight of dynamo, . ' . 165,000 Ibs. Weight efficiency: 2,000,000 ' - = 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 Volts. 500 Amps. 600 Revs, per Min. (Calculation in Metric Units.) a. CALCULATION OF ARMATURE. i. Length of Armature Conductor. From 15: = .70, From Table IV., p. 50: e l = 3.8 x lo^ 5 volt per metre per bifurcation. From Table V., p. 52: # c = 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 I0~ 5 3.8 X .4 X 385 604 DYNAMO-ELECTRIC MACHINES. [141 2. Sectional Area of Armature Conductor. B y ( 2 8), P. 57: (a) 2 min = .2 X ^ = 50 mm. ', or by (29) p. 57: ( 5 "t~ 38.5) X (22 n + 23 + 2 X 9) _ 30+ .3 X 22 By (196), p. 243: 19 + 42.5 X ~ 610 DYNAMO-ELECTRIC MACHINES. [ 141 B ) T (204), p. 247 : 2 X l =4 X (8 X2 3 ) "4 _ _ _, 19.75 16.5 3. Probable Leakage Coefficient, and Total Flux. By (157), p. 218: 1900+166+17 + 110 2193 t 1F , A = - =: 1.1D. 1900 1900 By (158), p. 218, and Table LXV. : A' = I.04X 1.15 =1.20, . . 0' = 1.20 x 8,120,000 = 9,750,000 webers. d. CALCULATION OF MAGNETIZING FORCES. 1. Air Gaps. Actual density : 8,120,000 5C = - - 3690 gausses; 2200 hence by (229), p. 340: at g = .8 X 3690 x 1.16 = 3430 ampere-turns. 2. Armature Core. By (237), p. 343: l" & = 61 X TT X 6o + 10 4- 2 X 5 = 5 1 cm - By (230), p. 340, and Table LXXXIX: at & = 4. i X 51 = 210 ampere-turns. 3. Magnet Cores. (B wi = 75 ' = 1 2, 800 gausses. 2 X22 2 - 4 ' . 0*w.i. = 13.8 X 21 = 290 ampere-turns. 141] EXAMPLES OF GENERATOR CALCULATION 611 4. Polepieces. Density at joint with cores: ^ = 9,750,000 =12>8oogausseg; 2 X 22~ 4 Density at poleface: 8,120,000 (B P2 = - - - = 3940 gausses, -X 81.6 X 7t X 23 X .70 By (241), p. 346, and Table LXXXIX. : /(& \ = /( I2 f 8o ) +/(394Q) = 15-2 +2-34 J PJ 2 2 = 8.77 ampere-turns per cm. Corresponding average density: 75 gausses. Length of circuit in polepieces, see Fig. 361 : /" p = 10 cm. .. / p = 8.77 x 10 = 90 ampere-turns. 5. Yoke. /(n,8oo) = ii. i ampere-turns per cm. ; ^o*= 9 cm - ( Fi g- 36i); ., tf/ ag> = 1 1. 1 x 90 = 1000 ampere-turns. 6. Armature Reaction. For(& p = 10,750 gausses, Table XCI., p. 352, gives >& 14 =.1.25 Maximum density in iron projections: 8,120,000 - = 15, 700 gausses, - X .70 X (72.2 X TT 128 X 1.2) X 23 X.88 for which Table XC., p. 350, gives an average coefficient of brush lead of 1S = .4. 6 12 DYNAMO-ELECTRIC MACHINES. [14=1 Hence by (250), p. 352: at, = ,.,5 X . x 2400 ampere-turns. 7. 70/tf/ Magnetizing Force Required. Summing up we have: AT = 3430 -f- 210 -j- 290 -j- 90 -f- 1000 -f- 2400 = 7420 ampere-turns. e. CALCULATION OF MAGNET WINDING. Temperature increase desired, m = 35 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: ^ m = -3 6 X 22 = 8 cm., and therefore the mean length of one turn: / T = (22 -f 8) X n = 94.25 cm. Hence by (318), p. 385, if the two coils are connected in series, each taking 100 volts, x r x '- 5 x (I + - 4 x 35) = 119.5 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 3 m = 1.6 mm., bare, ortf' m = 1.6 -\- .25 = 1.85 mm., covered. This wire will give the required temperature increase with 50 X 122 ~ ~~ 53 per cent extra-resistance in circuit. Radiating surface: = (22 + 2 X 8) X n x (16.5 - .5) = 1910 cm 8 . $141] EXAMPLES OF GENERATOR CALCULATION. 613 By (314), p. 384: 2IO Number of turns possible per layer: |J " 'V= 8 Number of layers required: - 86 Net winding depth needed : #m = 4i X 1.85 = 76 mm. By (315), p. 384: Z sh = 86 x 41 X 9 = 3320 m. . '. >' ah = = 27.2 ohms, per coil, at 15.5 C. By (318), p. 385: r' 8h = 27.2 X (i +.004 X 35) = 31.0ohms,atso.5 C. By (3 1 ?), P- 384: ''"sh = 2 X 31.0 x 1.53 = 94.8 ohms, total resistance of shunt circuit. * ^sh = ^ = 2.11 amperes. Actual magnetizing force : ^7"=86X4i X 2. ii = 7440 ampere-turns. Weight per coil, bare: wt sh = ^x 17.8 =59 kg., IOOO 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 55 Dynamo. 1 105 Yolts. 90 Amps. H20 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 / TO.& V TT II2\ S g = -l- -f-iif x 7t X fa 1 X 9 = I2 5 square ins. The useful flux (see below, 142, <., i, p. 616): $ = 2,600,000 webers, therefore the field density: X" = -- > oc g 20,800 lines per square inch. The conductor velocity being ii x 7t 1420 /- = - X - =68 feet per second, 12 60 the product of density and speed is 3C" X f'c = 20,800 X 68 = 1,415,000, for which Table LXVL, p. 225, gives a factor of field deflec- tion: 12 = 1.30. 1 Silvan us P. Thompson, " Dynamo-Electric Machinery," fourth edition, p. 416 and Plate V. 614 142] EXAMPLES OF LEAKAGE CALCULATION. Hence, by (167), p. 226: 2 _ L5 __ J^5_ " 1.30 X (n| - lof) .975 " 2. Stray Permeances. By (177)1 p- 232: "Tk Fig. 362. 9.5 KW Phoenix Dynamo. By (192), p. 241: 10 X 9 6J + 10 X I The projecting area of the yoke, at each core is / 6 i \ S = [ -h 2 ) x 9 = 47.25 square inches, hence, by (202), p. 246, $ = I 7 - 2 ! _|_ _ _9_X 4| 8 * 8} + (6 4- 4* = 5-4 + 2.5 = 7.9. 6i6 DYNAMO-ELECTRIC MACHINES. [142 3. Probable Leakage Factor. B Y (i57), P- 218: \ I28 + 9.6 + io.6 + 7. 9 _ 156.1 _ A 1,44, 128 128 b. 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: /' = 90 -|- -^r- = 92.65 amperes, and the total E. M. F. : E' = 105 -j- 9 2 - 6 5 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 9 = = 2,600,000 webers. 1 80 X 1420 The magnet winding consists of 108 series and 3454 shunt turns, and the two series coils are connected in parallel, the two shunt coils in series to each other, consequently: AT^ 1 08 X = 4860 ampere-turns, 2 and AT sh = 3454 X 2.65 = 9140 ampere-turns; making the total actual exciting power: AT 4860 + 9140 = 14,000 ampere- turns. 2. Magnetizing Force Required for Magnet Frame. By (228), p. 340: at g = .3133 X 20,800 X .975 = 6350 ampere-turns. B 7 (230), P- 34o: at & = 91 x ii-J = 1050 ampere-turns, 142] EXAMPLES OF LEAKAGE CALCULATION. 617 the average specific magnetizing force being: f ((&" a ) f (100,000) = 91 ampere-turns per inch, and the length of the path in the armature core: l\ = 9 A X n X ^-^ + i A - "4 inches - B 7 (250), P- 352: af r = 1.56 X - X 2 92 ' 53 X ~ ~ 2460 ampere-turns, the factor 1.56 corresponding to a poleface density of /(($>" p) = - = 26,000 lines per square inch. n-f x 7f x~y^ x .9 360 Hence, magnetizing force left for field frame: at m 14,000 (6350 -\- 1050 -j- 2460) 4140 ampere-turns. 3. Total Magnetic Flux ; Actual Leakage Factor. The mag- net frame is entirely of cast iron; the path length in the same is (Fig. 362): '' m = 2 x (8f + 5) + 6+ 3 X ^ =37-7 inches, and the mean area of it is: 5m = 33 X 7 X 9 + 4-7 X 9 X 9 = 66 squafe inches Inserting these values into (209), p. 259, we obtain: , /$'\ 4140 f \~ I =no ampere-turns per inch. According to Table LXXXVIII., p. 336, this specific mag- netizing force corresponds to a magnetic density in highly permeable cast iron, of 0' " m = ^ = 50,000 lines per square inch. 6i8 D YN A MO-ELECTRIC MA CHINES. [143 from which, by formula (210), p. 259, follows the total mag- netic flux: 0' 66 X 50,000 = 3,300,000 webers. 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 A = 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 : 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: i-3 X (25^ - 24) 1.95 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: 4 + l6 ) X TO + 4 X 16 16 X 7t . 2X161 24 f 9i+7-T 9f J~ __ 267 -f- 85 352 __ A, - - A > 4 207 207 <. 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 -J- 59 (.36 -f- .25) = 690 -f- 36 = 726 volts. By (138), p- 202: 6 X 726 X io 9 # = - - = 12,000,000 webers. 760 X 480 By (139)' P- 202: = 23,100 lines per square inch. By (228), p. 339: at K = .3133 X 23,100 X 1.95 = 14, 100 ampere-turns. By (232), p. 341: 5 a , = 2 X (16 2) X 4j X .865 = 109 square inches (54 square inches per side being given). By (233), p. 341: S & , - 2 X (16 - 2) X 4i X |- - i X .865 = 230 square inches. By (231), p. 341: , , __ /(IIO,000) +/(52,200) _ 2 9 -f 10.2 = 150 ampere-turns per inch. 620 DYNAMO-ELECTRIC MACHINES. [ B y (236), P. 343: l\ = 19-1 x TT X 9 \^ + 4i = 22f inches. B y (230), p. 340: #/ a = 150 x 22f = 3400 ampere-turns. The angle of lead was measured to be about 20, therefore b Y (25), P- 352: at r = 1.40 X 760 X X -^ = 3500 ampere-turns. The total magnetizing force of the machine is: AT = 984 x - = 29,000 ampere-turns. The frame is all wrought iron, having a uniform cross-sec- tion of S m 10 x 1 6 = 1 60 square inches, and the length of each circuit in the frame is: I'm 75 inches. Hence we have: 75 X - ~ = 29 ' ~~ l 1 ^ 100 + 34oo -f 3500) = 8000 ampere-turns, from which: . / $>' \ 8000 / * I = = 106. 7 ampere-turns per inch. Consulting Table LXXXVIIL, p. 336, we find: 0' = 102,000 lines per square inch; 1 60 or, the total flux : $' = 160 x 102,000 16,400,000 webers. .-. A = 16 ' 400 ' 000 ^ 1.36. 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. <7. Probable Leakage Factor. (From Fig. 364). <- 35"- y ^BEDPLATE OPPOSITE FIELI3S = 625 8Q. INS. Fig. 364. 200-KW " Edison " Bipolar Railway Generator. By (167), p. 226: - ( 23} X n + 25^ X 7t X ^i ) X 34| 4\ ">/ 1.30 x By (178), p. 232: 2 X I2J + 1.5 X 25 - 2 3 f) = 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: I f34lX (2o| + - -X 26) +625! $ 3 =^- _J = 6o. 9 . 2 X 71 B y (i99) P- 245: 2 4 =345 + - 341 X 26_ _ =I6<5< 2 X3' + (26 + 2i)x - By (157), p. 218: i _ 45 1 + 3 8 -7 + 60.9 + 16.5 _ 567.1 _ 4~^~ isr : & 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 9 228 X 450 = 3o,5oo,ooo webers. -?o, 500,000 . . 3C = - = 27,000 lines per square inch. H35 By (228), p. 339: af g = .3133 X 27,000 X 2.52 = 21,300 ampere-turns. By (232), p. 341: S Al 2 x 34j X 8f x .85 = 502 square inches. By (233), P- 34i : S. a = 2 X 34l X 8f x y *-jjk - i X .85 = 665 square ins. By (231), p. 341: /(<'.) = I -[/ (60,500) +/(45 ? 70o)]^ I3>2 + 8 - 6 = 10.9 ampere-turns per inch. By (236), p. 343: ^ = i5i X 7f X 9 + 2 ^ + 8| - 23.9 inches. 144] EXAMPLES OF LEAKAGE CALCULATION. 623 B Y (230), P- 34o: at & = 10.9 X 23.9 = 260 ampere-turns. By (250), p. 352: AOO -4- 3.6 2^4; at, =,.I S X.I4X 7 "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 8h = 3 = 3.6 amperes; 5y hence, the total magnetizing force actually exciting th ; machine at full load: AT 8000 X 3.6 -|- 46 x 400 = 47,200 ampere-turns; and by (207), p. 258: at m = 47,200 (21,300 -j- 260 + 7000) = 18,640 ampere-turns. The section of the cores is: Sin = 2 5 2 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 *S" w .i. 5 square inches. The cross-section at centre of polepieces is: 34i X "-J = 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: , 885 - 405 Sc.i. = 405 + - " ~ =565 square inches, O 624 DYNAMO-ELECTRIC MACHINES. 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, /" c>i =36 inches. By (213), p. 261, we consequently have the equation: I2 X / + X which is satisfied by $' = 37>5 oo oo > for, by inserting this value of #', we obtain: = 120 X / (75>) -f 3 6 X / (66,300), and with reference to Table LXXXVIII., p. 336, this becomes: 120 x 24.7 -f- 36 x 436 = 2960 -f 15,700 = 18,600, which is practically identical with the actual number of ampere- turns. Hence, the actual leakage factor: A = 37,500,000 = t 33 30,500,000 In this instance, the probable value obtained is about 2^2 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. 400 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 '-^If- = 683 feet. 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. 625 Conductor velocity: v = (44i^ : ij-i)X 12 The total E. M. F. is x = 74- *5 feet per second. Figs. 365 and 366. 36o-KW Thomson-Houston Fourpolar Railway Generator, hence, by (144), p.. 205: 3C" = = 34,000 lines per square inch. 72 x 683 X 74-25 . . 7> c X 3C" = 74.25 X 34> 000 = 2,520,000. Ratio of radial clearance between armature and field to pitch of slots: therefore, by Table LXVL, p. 225: 12 = 2.0, and by Table LXVII., p. 230: 13 = 4.6; average: k^ 3.3. Hence, by (175), p. 230: T [45 X 7t + (1.24 + .094) X 90] X 82' _ 4 1 80 X 25 3-3 X (45 ~44i) 626 DYNAMO-ELECTRIC MACHINES. [145 By (181), p. 233: ii X - h J 4 X 2 9 = 6 9-5 + 43 = 112.5. B y (197), p. 243: = 132-5- _ 858 + 112.5 + 132-5 _ "3 _ , - 8 < A - '"858" - 858 - Ratio of width of slot to pitch : It : i-553 = -523- for which Table LXV., p. 219, gives a factor of armature leakage of A, = 1.04; hence the total probable leakage coefficient: A' = 1.04 x 1.285 = 1.34, b. Actual Leakage Factor. The machine is compound-wound, having 19,200 shunt am- pere-turns and 66.00 series ampere-turns on each magnet; the total exciting power per circuit, two coils being magnetically in series, therefore, is: AT = 2 X (19,200 -j- 6600) = 51,600 ampere-turns. By (228), p. 339: a * g = -3 X 33 X 34, o X 1.65 = 1 7, 600 ampere-turns. By (232), p. 341: 5 ai = 4 X 9f X 25 X .85 = 828 square inches. 145] EXAMPLES OF LEAKAGE CALCULATION. 627 B y (233), p. 341: S** 4 X 2 - X 25 x .85 = 1252 square inches. By (231), p. 341: f it** \ - f (62,500) + / (41, 200) _ 14.2 -f 7-8 / ^ *> ~~ ~~ 2 = 11 ampere-turns per inch. By (236), p. 343^ T+'" /"a = 3'i X n X --- h 9l + 2 x i J = 26J inches. , P- #4 = ii X 26 J = 300 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 at v = 2 x 360 x - - X -^5- = 3100 ampere-turns. 4 loo The magnetizing force left for the magnet frame, con- sequently, is: at m = 51,600 (17,600 -f- 300 -}- 3100) = 30,600 ampere-turns. The magnet frame is of cast iron; each circuit has a length of l" m 90 inches; the total cross-section of the cores is: 2 X 22 X 25 = 1 100 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, we have: 628 DYNAMO-ELECTRIC MACHINES. [ 146 - / #' \ 30,600 /I 1= * = 340 ampere-turns per inch; $' 62,500 lines per square inch; $' = 1125 X 62,500 = 70,500,000 webers. The useful flux is : , 2 x 6 X 620 X io 9 = = 51,600,000 webers; 360 X 400 consequently: A'= 7 'f' 000 =1.37. 51,000,000 The formulae for the probable leakage factor, for this ma- chine, gave a value 2\ 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. 220 Yolts. 850 Revs, per Min. a. Conversion into Generator of Equal Electrical Activity. Assuming a gross efficiency of 90 per cent., and an electrical efficiency of 91 per cent, (see Table XCIX., p. 422), the elec- trical energy active in the armature of the motor is, by (382), p. 420: pl= 746 x 25 = 20 ^ 800watts> and the E. M. F. active, by (383), p. 421 : E' = 220 x .91 - 200 volts; hence, by (384), p. 421, the current capacity: 20,800 7 : ~^o~~ = 104 amperes, which, in the present case of a series motor, is also the current intensity to be suppled to the motor terminals. 146] EXAMPLES OF MOTOR CALCULATION. 629 Intake of motor, by (381), p. 420: 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 104 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: ft i = .75; e = 62.5 x io~ 8 volt; v c = 40 feet per second; 3C" = 20,000 lines per square inch. B Y (26), p. 55: ^-421 -=400 feet. 62.5 X 40 X 20,000 B y (27), p. 57: tf a 2 300 x 104 = 31,200 circular mils. 2 No. 8 B. & S. (.128" -|- .016") have 2 X 16,510 = 33,020 cir- cular mils area. By (30), P. 58: d\ = 230 X ~j^ = xo-j-f inches. Approximate size of slot, by Table XV., p. 70: r x w . 12 No. 8 B. & S. wires, arranged in 6 layers (see Fig. 368) with .020" slot-lining give a slot, Making the pitch ^ inch, the number of slots is obtained, Fig. 367: , n| X TT = *-r~ = 74- 6 3 DYNAMO-ELECTRIC MACHINES. Hence, by (40), p. 76: 146 _ 400 X 12 74 X 6 = 10J inches; and by (138), p. 202: Figs. 367 and 368. Dimensions of Armature Core, 25-HP Inverted Horseshoe Type Series Motor. making the maximum density in the teeth at full load: a* _ 3,180,000 t ~~/ - \~ ( 9J Tr^ ~ ti ) X 74 X io| X .90 X -75 V 74 / 2 = 130,000 lines per square inch. The shape-ratio of the armature core is: therefore by Table XXIV., p. 96: L t = 2.90 X 400 = 1160 feet; whence: and = .00000303 X 33,020 X 1160 = 116 Ibs. X 1 1 60 X .000626 = .092 ohm, at 15.5 C. 4X 2 146] EXAMPLES OF MOTOR CALCULATION. 631 c. Energy Losses in Armature, and Temperature Increase. Shaft diameter, by (123), p. 185: internal diameter of discs: 3 inches. S ai (9! 3^) X i of X .90 = 61.7 square inches. ,S a2 = uj- x ioj- X .90 = 113.5 square inches. io -1 7.5 ampere- turns per inch Average density: A = 1194 + 70 4- 4 = 1268 watts. By (78), p. 125: ^ = i if X n X [ioj + 1.8 X (.5 X n| + 2 X = 913 square inches. 632 DYNAMO-ELECTRIC MACHINES. Ratio of pole area to radiating surface : ii j X 7t x io| X .75 ~~ [146 for this ratio, and for v c = 40 feet per second, Table XXXVI., p. 127, gives: 6' a = 44 C., hence e a = 44 X ~ = 61 C. .-. 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: " w .i. 75> lines per square inch; ' T"1 Fig. 369. Dimensions of Magnet Frame, 25 HP Inverted Horseshoe Type Series Motor. and that in the cast iron: (fc" ci 30,000 lines per square inch. 0' = 1.20 x 3,180,000 = 3,820,000 webers. 3,820,000 . , wi _ 51 square inches. 75,000 146] EXAMPLES OF MOTOR CALCULATION. = 137 square inches . 633 Cross-section of cores, rectangle, 5^" X 5^", between two semi-circles of 5^" diameter; (Figs. 369 and 370) : 5i X 5i + 5i 2 X = 50.5 square inches. Fig- 37- J oint of Magnet Core and Yoke, 25 HP Inverted Horseshoe Type Series Motor. Length of cores, by Table LXXXIII., p. 321 : 4i = 7J inches. Cross-section of yoke: 15" X 8J" (= 127.5 square inches). Core projection, rectangular: loj x 2-J X 8J. Area of contact of same with yoke, Fig. 370: (lof 4- 2 x 2|) x 81 -j- 5^5 = 160 square inches. Polepieces: = '~~ X (i + .004 X 20) = .0125 ohm, at 35.5 C. Total weight of wire, bare: wt^ 2 X 23 X 3 X 3 -- X .244 = 87 Ibs. h. Speed Calculations. E. M. F. lost in armature and series winding: 104 X (.115 + -0125) = 13 volts. Actual E. M. F. active in armature: E' = 220 13 = 207 volts. (Spare magnetizing force being provided, this increase does not affect the above calculations.) Torque, by (93), p. 138: T - --; - X 104 X 444 X 3,180,000 = 172.5 foot-lbs. Specific generating power: e" = -L - = 14.6 volts at i revolution per second; 550 hence, by (389), p. 426, the speed at any supply voltage, E: . = 60 X - 8.52 X - i4- 14. = 4.11 E - 54. For E = 220 volts: JV 9 904 54 = 850 revs, per min. " E = 200 volts: N z = 822 - 54 = 768 revs, per min., etc. /". Calculation of Efficiencies. Electrical efficiency, at normal load: = aoo X .Q4-(..I 5 = 200 X 104 Commercial efficiency at normal load: _ 200 X 104 - (iQ4 a X .1275 + 74 + i5) 200 X 104 - 20,800 (1380 4- 1574) _ 17,846 _ 20,800 ~ 20,800 80 147] EXAMPLES OF MOTOR CALCULATION. 637 Commercial efficiency, at J 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): X -.800 - [(|y X .380 + I5 74] _ y - 15,600 = .85. - X 20,800 4 Commercial efficiency, at ^ load: ^x 20,800 - [YM x 1380 + 1574] i . 10,400 - X 20,800 2 - =.88. Commercial efficiency, at J load : - X 20,800 - f( - ) X 1380 + 1574! n ,^- !i '=1540 i 5200 >X 20,800 4 Commercial efficiency, at 50 per cent, overload: _ ij x 20,800 - (i. 5 2 x 1380 + 1574) _ 26,526 4 X 20,800 '31,200 " 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 Yolts. 1400 Revs, per Min. a. Conversion into Generator of Equal Electrical Activity. Table XCIX. gives: P' = 12,600 watts. By Table VIII. : E' = 125 .06 X 125 = 117.5 volts. 638 DYNAMO-ELECTRIC MACHINES. [147 Current in armature, at full load, by (384), p. 421 : T , 12,600 -g^~ / ' = - - = 107 amperes. ii?-5 Intake, by (381), p. 420: ^ = 12,600 = 1 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 i o~ 8 volt p. ft.; V G =9 2. 5 'feet p. second; 3C" = 26,000 lines per square inch. Xi = . "7-5 X "?' = 7 6feet. 65 X 92.5 X 26,000 tf a 2 = 250 x 107 = 26,800 circular mils. 2 No. 11 B. W. G. (.120" -f- .016") have a sectional area of 6\ = 2 x 14,400 = 28,800 circular mils. 02. C d a = 230 x L = 15.3 inches. By Table IX., p. 59: <4 J 5-3 X .98 = 15 inches. Allowing i\ inches for 50 division strips of. 15" width, we have: conductors . I2O -j- .Ol6 . 136 per layer. - = ftj inches. 147] EXAMPLES OF MOTOR CALCULATION. 639 // a = 3 x /i + /I/- 1 - -- i \ = 9 inches. ) = / (io7,5 00 ) +/(36,ooo) _ 190 + 6.7 = 98.4 ampere-turns per inch. Average density: &" a = 101,000 lines per square inch. 2 x (6f + 3 )+i X * A; 6 3 - X 7 2 33 8 * ^4 = 2 33 X 2 x .0436 = 20| Ibs. r a = ^ X 233 x .00072 = .021 ohm, at 15.5 C. c. Energy Losses in Armature, and Temperature Increase. _. 12 X 7t X 6-f X 3 X .85 M -. ~"~" = >355 C -Wj = r = 23.33 cycles per second. P A 1.2 X io7 2 X .021 = 290 watts. A = 5- 8 X 23.33 X -355 = 363 watts. A = - 2 95 X 23.33 2 x .355 = 57 watts. /> A = 290 -f 363 -f 57 = 710 watts. ,9 A = 2 x 12 x TT X (6| -f 3 + 4 x i) = 780 sq. inches. e - = 42 x 7^ = 38 c - 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 webers. ^ m = 4 ' 2 25> ^ 95 square inches. Breadth of cores: |f = 15 inches. t 640 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. 371. Fig. 371. Dimensions of Armature Core and Field-Magnet Frame, I5-HP Bipolar Iron-Clad Type Shunt Motor. e. Calculation of Magnetizing Forces. af e .3133 X 26,000 x 1.4 X | = 7120 ampere-turns, at & 98.4 x 14 = 1380 ampere-turns. af m = 101 x 85 = 8500 ampere-turns. at r = i. 80 x - [ X ^g- = 1400 ampere- turns. AT 7120 + 1380 + 8500 + 1400 18,400 ampere-turns. f. Calculation of Magnet Winding. Since the motor is not intended for continuous work, a high increase, m = 40 C., is permitted. Regulating resistance, at full load, r x = 23 per cent. Height of winding space, estimated: 2-J- inches. / T = 2 (6f + 15) + 2\ x 7t 50 inches. 147] EXAMPLES OF MOTOR CALCULAl^JON. 641 18,400 150 A sh = -f~- X ~ X 1.23 X (i + -004 X 40) = 874 feet per ohm, corresponding to No. 13 B. W. G. (.095" -j- .010"). 5 M = 2 x (6| -f 15 + 2|- TT) X 2 x 8i = 1000 sq. inches. /" 8h = X 1000 x 1.23 = 655 watts. Number of turns per layer: 8* .095 -|- .OIO Number of layers required : = 80; - 22. 80 Depth of magnet winding: h' m = 22 x (.095 -+- .010) = 2.S2 inches. Z 8h = 2 x 80 x 22 x -5^ = 14,650 feet. ^sh = g = 16 75 ohms, shunt resistance, at 15.5 C. r'*. = 16.75 X (i + -004 X 40) = 19.4:5 ohms, shunt resistance, at 55.5 C. ^8h = 19-45 X 1.23 = 23.9 ohms, res. of entire shunt-circuit, at full load. / S h = - - = 5.23 amperes, shunt current, at normal load. *3* V Total actual magnetizing force: AT = 2 x 80 x 22 x 5.23 18,400 ampere-turns. Total weight, bare: wt^ = l6 ' 75 = 400 Ibs., or 200 Ibs. per core. .0419 642 DYNAMO-ELECTRIC MACHINES. [147 g. Speed Calculations. E. M. F. consumed by armature winding: 107 x .024 = 2.6 volts. E. M. F. active in armature: E' - 125 - 2.6 = 122.4 volts. Torque : r ^ -i^- x 107 x H4 X 3.500,000 == 63.3 foot-pounds. Specific generating power: I4OO Speed, at any voltage, E : 0>4 , = 60 x - 8. 5 a x * 5 . 63 - 3 ) = H. For E - 125: N^ 1428 - 28 = 1400 revs, per minute. 11 E = 110: N z 1256 - 28 = 1228 revs, per minute. " E = 100: N^ = 1142 28 = 1114 revs, per minute. h. Calculation of Current for Various Loads. Current for full load, by (392), p. 428: T , _ 125 - 1/125* - 4 X .024 X (746 X 15 + 200 ) 2 x .024 = 107 amperes. Current for load : 125 A/ 125* - 4 X .024 X (746 X 15 X - + 2000) /' = K * 2 X .024 = 40 amperes. Current for load : 125 - A / i25 2 4 X .024 x (746 X 15 X - + 2000) /' = - L: 2 X .024 = 63 amperes. 147] EXAMPLES OF MOTOR CALCULATION. 643 Current for load : I2 5 ~ /t/ T2 5 2 - 4 X .024 x (746 X T 5 X ~ + 2000) j< _ _ r __ 4 _ 2 X .024 = 86 amperes. Current for 25 per cent, overload: I , _ 125 - i2 4 X .024 X (746 X 15 X TJ + 20Q o) 2 X .024 = 126 amperes. Current for 50 per cent, overload : /' I2 5 ~ 25 a 4 X .024 X (746K 15 X ij + 2OO ) 2 X .024 159 amperes. Current for maximum commercial efficiency, by (393), p. 429: = .1/537+2000 + /535V _ .024 \ I2 5/ 535 ^ I2 5 from which follows that the maximum commercial efficiency is obtained at about five times the normal load. Current for maximum electrical efficiency, by (394), p. 429: _ MS = U6am pe reS) .024 y 125 125 which corresponds to about i times the normal load. /. Calculation of Efficiencies. Electrical efficiency, at normal load: - I22 -4 X 107 -- 107' X .024 5.23* x 19.45 122.4 x 107 = 13. ,00 -,75 -535 = ij^oo 13.100 ^3,100 Commercial efficiency, at normal load : = I22 -4 X 107 - (107 X .024 + 535 + 35 2 + 13,100 33 ? DYNAMO-ELECTRIC MACHINES. [148 Commercial efficiency at } load: = 122.4 X 86 - (86 a X .024 + 2887) 7455 71 122.4 X 86 " 10,520 Commercial efficiency at load: _ 122.4 X 63 - (6 3 2 x .024 + 2887) _ 4738 ^2.4 X 63 ~ ffc Commercial efficiency a<- J load: _ 122.4 X 40 (4Q 2 X .024 + 2887) _ 1975 _ 122.4 x 40 ~ 4900 Commercial efficiency at 25 per cent, overload: __ 122.4 X 126 - (126* X .024 -f 2887) _ 12,153 _ 7 Q 122.4 X 126 15,420 Commercial efficiency at 50 per cent, overload: = I22 ' 4 X 159 - (i59 9 X .024 + 2887) __ 16,006 122.4 x 159 19,500 In this case the efficiencies at overload are higher than the normal load efficiency. 148. Calculation of a Compound Motor for Constant Speed at Varying Load : Radial Outerpole Type. 4 Poles. Toothed Ring Armature. Cast-Steel Frame, 75 HP. 440 Tolts. 500 Revs, per Min. a. Conversion into Generator of Equal Electrical Activity. P' = 60,000 watts (by Table XCIX., p. 422). E 1 = 440 .045 x 440 = 420 volts. , 60,000 / = - = 143 amperes. 420 b. Calculation of Armature. /?, = .70; e 55 x To~ 8 volt p. ft. ; v c = 65 feet p. sec. ; 3C" = 30,000 lines per square inch. = , X 420 X io- = 55 X 65 x 30,000 tf a a = 400 x 143 = 57,200 circular mils. 148] EXAMPLES OF MOTOR CALCULATION. 645 4 No. ii B. W. G. wires (.120" -|- .016"), have an actual area of: 4 x 14,400 = 57,600 circular mils. d\ = 230 x ~ = 2$$ inches. For this diameter, Table XV., p. 70, gives a slot of 1 1 X T V inch; actual slot for 36 No. n B. W. G. wires, see Fig. 372, is 1-J--J- inch deep and -J| inch wide. Fig. 372. Dimensions of Armature-Slot, 75 HP Fourpolar Compound Motor. Number of slots: n' = X ~ S5 X " = 9i inches. s vy 112 X ' 4 6 X 2 X 420 X io 9 _ 112 X 9 X 500 10,000,000 = 10,000,000 webers. = 137 + 7-6 = 72.3 ampere-turns per inch. 646 DYNAMO-ELECTRIC MACHINES. [148 Average density : (&" a = 96,000 lines per square inch. Z, = 1*J* + Jl_'.tt.><_? x II2 X 9 = ^540 feet. o// a = 2540 X 4 X .0436 = 442 Ibs. bare wire. r & = - - X 2540 X .000717 = .114 ohm at 15.5 C. 4X4 *-. Energy Losses in Armature, and Temperature Increase. M = (27 X TT X 4 T V " T H X H X 112) X 9i X .875 1728 = 1.44 cubic foot. N l = ^ X 2 == 16.67 cycles per second. P & 1.2 X H3 2 X .114 = 2800 watts. /> h = 46.85 X 16.67 x 1.44 = 1120 watts. P e = .0665 X i6.67 2 X 1-44 = 30 watts. P^ 2800 -f 1 1 20 4- 30 = 3950 watts. 5 A = 27 x 7t x 2 X (9j : + 2|-f- i|^ x TT = 3000 square inches. 6. = 41 X 39S = 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 webers. Width of frame (equal to length of armature core) : 9J inches. Breadth of cores: 12,000,000 - = 8 inches. 2 X 80,000 X 9i Thickness of yoke: 12,000,000 4 80,000 X 9t Length of cores: ^ m = 7| inches. Breadth of polepieces: ^ P = 3 T f X sin. 314 = 16| inches. 148J EXAMPLES OF MOTOR CALCULATION. 647 Distance between pole-corners: /' p 31} 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 : rt 6 X 2 x 440 X ie> 9 vP = 10, =?oo,oco webers. 112 x 9 X 500 TP// 2 x 440 X To 8 3C =- -= 29,500 lines p. sq. m 72 x 3C"o X f'c = 29,500 X 65 = 1,920,000. 648 DYNAMO-ELECTRIC MACHINES. [148 Ratio of clearance to pitch: 112 From Table LXVIL, p. 230: ia = 5.25. at go = .3133 X 29,500 x T 3 g-X 5.25 9100 ampere-turns. i r / 10,500,000 \ / 10,500,000 \ ~j at &0 = - X |^/ L 4 x 9* X 2| X .875J + \ 4 X 9i X 7i X .875^ J - /("Qooo) +/ (42,5o) v _ _ 2 9Q +8 p\ ^u p\ z\j 2 2 = 2980 ampere-turns. 'm. =/( I '^^/ g T 5 ;7 ! r : ) x 60 =/ (83,000) x = 36.1 x 60 2170 ampere-turns. .*. AT 9100 -f 2980 -|- 2170 = 14,250 ampere-turns. Magnetizing Force required at Full Load. 9 = i_X , X 4-5 XJ. = 9,900,000 webers. 112 X 9 X 500 JC" = 29,500 x - - = 27,800 lines per square inch. 44 af g = .3133 X 27,800 x A- X 5.0 = 8150 ampere-turns. / (103, 700) 4- / (40,000) 122. 5 + 7-S at & = y ^ ' } J v ' ^ X 20 = ' y J X 20 2 2 = 1300 ampere-turns. a *m =/ (7^,300) X 60 = 29.2 x 60 = 1750 ampere-turns. at r = 1.25 x 112 X 9 X X >4 ^ I3 ^ - 1350 amp. -turns. 4 loo .'. AT 8150 -f- 1300 -f- 1750 + 1350 = 12,550 ampere-turns. Magnetizing Force for Series Differential Winding. AT se AT - AT se = 12,550 - 14,250 = - 1700amp.-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) taking its place. [In the present machine, this can be achieved by increasing the radial depth of the armature core from 2%" to 3^", whereby the average specific magnetizing force is reduced to/((B" ao ) = 29.5 ampere- turns per inch at no load and to /((B" a ) = 23.5 ampere-turns per inch at full load, making the corresponding magnetizing forces tf/ ao 59 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 AT = 1 1, 860 ampere-turns, and at full load AT 11,720 ampere-turns; the remaining small difference of 140 ampere- turns can easily be taken care of by slightly enforcing the armature-reaction, either by widening the polepieces, or in giving the brushes a somewhat greater backward lead; and we have then a self-regulating shunt-motor of practically constant speed for all variations of load.] f. Calculation of Magnet Winding. Series Winding. 1700 N m = = 12 turns per magnetic circuit, H3 or 6 turns per core. Allowing 1000 circ. mils per ampere, and taking 2 cables of 7 wires each, the size of each wire is: c = 23,400 X 674 = 1,580,000. Ratio of radial clearance to pitch: .. 2 X H Factor of field-deflection, by Table LXVIL, p. 230: 13 = 4.5. -. at g = .3133 X 23,400 X 4-5 X (n nf) = 4120 ampere-turns. B y (237), P- 343^ l\ = 7f x n x 9 ~^ Q 27 4- 2j + 2 x H = i if inches. /*.) == ^r [/ feooo) 4-7(42,500)] = ^_j = 23.9 ampere -turns per inch. . . at & = 23.9 x i if = 280 ampere-turns. l" m 44 inches, length of circuit in frame. / ((B" a ) ~ 7(85,000) = 44 ampere-turns per inch (cast steel). . . ( jf m 44 x 44 = 1940 ampere-turns. AT 4120 -j- 280 -j- 1940 = 6340 ampere-turns. e. Calculation of Magnet Winding. fl m = 25 C. r x = 45#- Depth of winding space: h m = 1 inch. ^T = (4| + i) X TT = 18 inches. ^ = 6| x TT x 2 x (6J J) = 255 square inches. Connecting all four cores in series across the primary terminals, each circuit of two cores will take one-half the voltage, or 250 volts, hence: 6740 18 A " h = 250 X 7i X I>45 X (l + - 4 X 25<>) = 60,5 feet per ohm, which corresponds to No. 23 B. W. G. (.025" -f .005"). 660 DYNAMO-ELECTRIC MACHINES. [ 150 P' sh = ~ X 255 x 1-45 = I2 3 watts. 7 N^ 634 ( 25 = 12,800 turns, per magnetic circuit, or 6400 turns per core. Each layer can hold = 200 wires. .030 Number of layers required : 6400 ^o 200 Actual winding depth: ^'m = 3 2 . X .030 = .96 inch. Z sh = 4 x 200 X 32 X -- = 38,400 feet, total, 4 cores. r sh = -~- = 634 ohms, at 15.5 C. r' sh = 634 X (i + .004 x 25) = 697 ohms, at 40.5 C. r" S h = 6 97 X 1.45 = 1010 ohms, entire shunt-circuit. / S h ~ = .495 ampere. 1010 Actual excitation, full load: AT 2 x 200 x 32 X .495 = 6340 ampere-turns. Weight of magnet winding: // sh 38,400 x .00189 = 72J pounds, total, bare wire: o//' Bh = 1.07 x 72^ = 78 pounds, total, covered wire, or 19J pounds, covered, of No. 23 B. W. G. wire per core. 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, 604 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 lag, 30, 421 of lead, 30, 349, 350, 421 of pole-space, 210, 211 Application of connecting for- mula, 152-155 of generator formulae to motor calculation, 419 of permeance formula, 220- 223 Arc of belt-contact, 193 of polar embrace, 49 Arc-lighting dynamos, designing of, 455-459 magnetic density in armature of, 91 regulation of, 458, 459 series-excitation of, 37 Area, see Sectional Area, and Surface. 661 662 INDEX. 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-, see Disc-Armature. energy-losses in, 107-122 load limit and maximum safe capacity of, 132-135 perforated, or pierced, see Perforated Armature. pole-, or star-, see Star- Armature. principles of current-genera- tion in, 3 ring-, see Ring-Armature. running-value of, 135, 136 smooth core-, see Smooth Core Armature. toothed core-, 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, formula 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, 77 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 magnetizing force for com- pensating, 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, 58i, 589, 604, 657 circumferential current-den- sity in, 130-132 connecting-formula 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 rise- of temperature in, 126- 130 - types of, 143-147 weight of, 101, 102 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 turn, length of, on magnets, 374 useful flux of dynamos, 212- 214 INDEX. 663 Average values of hysteretic re- sistance, no volts between commutator sections, 88, 151 weight and cost of dynamos, 412 Axial multipolar type, 270, 282 B Back E. M. F., see Counter E. M. F. 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, 5i6 Belt-velocity, 193 Belt-driven dynamos, see High- Speed Dynamos. Belts, calculation of, 193-195, 517 losses in, 409 Bifurcation of current in arma- ture, 48, 49, 51, 104 Binding-posts, see Conveying Parts. Binding wires, for armatures, 75 Bipolar dynamos, act of commuta- tion 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, see Motor-Generator. Bore of polepieces, 209, 210 Bottom-insulation of commutator, 171 Brass, current-densities for, 183 for brushes. 173, 176 for commutators, 169 for dynamo-base, 300 safe working load of, 189 Breadth of armature cross-section , 92 of armature-spokes, 189, 190, 5i6 of belt and 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 change of air-gaps, 483 Brushes, arrangement of, on commutator, 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 Burke, James, on insulating ma- terials, 86 Bushing, pole-, Dobrowolsky's, 49 Butt-jointing of magnet-frame, 306, 307 Cables, see Stranded Wire Con- ductors. Calculation of armature, 45-195, 413-416, 505, 527, 552, 566, 580, 587, 603, 629, 638, 644, 652, 656 of efficiencies, 405-410, 526, 546, 565, 578, 602, 636, 643 of electric motors, 419-442, 628-652 of field magnet frame, 313- 327, 5i7 534. 557. 572, 583, 593, 607, 632, 639, 646, 657 of generators for special pur- poses, 455-463 of leakage-factor, 217-263, 519, 536, 559, 573, 584, 595, 609, 614-628, 633 of magnetic flux, 200-216, 517, 53i, 554, 568, 581, 589, 605, 638, 645, 657 of magnetizing forces, 339-3 56, 520, 537, 547, 560, 575, 585, 596, 610, 634, 640, 647, 654, 658 66 4 INDEX. Calculation of magnet- win ding, 359-401, 486-497, 522, 540, 549, 562, 576, 599, 612, 635, 640, 649, 654, 659 of motor generators, 452-454, 655 of railway motors, 431-442, 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 Cast iron, in, 178, 189, 288, 312, 313, 448 steel, in, 189, 288, 289, 293, 448 Cast- wrought iron, see Mitis Metal. Causes of sparking, see Sparking. C.-G.-S. units, 7, 47, 199, 332, 333 Characteristic curves, 476-483 Charging accumulators, dynamos for, see Accumulator-Charg- ing Dynamos. Checks on armature calculation, 130, 132, 135 Cheese-cloth, varnished, for arma- ture-insulation, 85 Chord-winding, see Ring Arma- ture, Drum- Wound. 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 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 r 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 efficiency, see Effi- ciency, Commercial. copper, specific resistance of, 104, 105 wrought iron, permeability of, 311 Commutation, act of, 29 effect of, in generator and motor, 30 sparkless, promotion of, 30, 62, 172, 173, 297, 298, 299, 459,. 463-470, 471, 472 sparkless, in toothed and per- forated armatures, 62 Commutator, construction and di- mensioning of, 168-170, 514 distribution of potential on, 3I ~ 33 1 f principle of, 13,14 thickness of insulation for, 171 Commutator-divisions, difference of potential between, 88, 151 number of, 87, 88 Compactness of railway motors r 432 Comparison of efficiency-curves of motors, 431 of various types of dynamos, 248-256 Compensating ampere-turns, see Armature-Reaction. Compound-dynamo, constant po- tential of, 43 efficiency of, 42, 43, 406, 408 E. M. F. allowed for internal resistance of , 56 INDEX. 665 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, 563, 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, insulate 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, 5i5 Crocker, Professor F. B., on high- potential dynamos, 462 on unipolar dynamos, 25, 26 Cross-connection of commutator- 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, see Alterna- ting Current. collection of, from armature coil, 12 commutated, fluctuations of, 14-21 constant, see Constant Cur- rent. continuous, direct, or uni- directed, see Continuous Cur- rent. direction of, in closed coil, 12 in single inductor, TO in electric motors, 427-429, 642 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 of contact-resistance and fric- tion of commutator-brushes, 177, 178 of eddy current factors, 121 of hysteresis factors, 1 14 of potentials around arma- ture, 32, 33 of relative hysteresis-heat in armature-teeth, 68 666 INDEX, Curves of specific temperature- increase 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, 201 Cycle of magnetization, 109, no, in, 113, 115, 119, 121 Cylinder armature, see Drum Ar- mature. Cylindrical magnets, 232, 234, 289, 2*91, 318, 319, 320,323, 369, 374, 375 Data for winding armatures, 155- 167 general, of railway motors, 435 Dead wire on armature, 94 Deflection of lines of force in gap- space, see Distortion of Mag- netic Field. Definition of armature, 4 of closed and open coil wind- ing, 143 of dynamo-electric machine, 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, 45 5-463 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 Diagram 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, 166 - 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 D.ielectrics, properties of, 83-86 Difference of potential, see Elec- tro-Motive Force. Differentially wound motor, 406, 408, 426, 428, 644 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 of toothed and perforated ar- matures, 65-72 of unipolar dynamos, 443- 446, 652 see also Length, Breadth, Diameter, Sectional Area, etc. Direct-driven machines, see Low- Speed Dynamos. INDEX. 667 Direction of current, 10, 30 of E. 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, Dobrowolsky's pole-bushing, 49, 296 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 Force, Elec- tro-Dynamic. Draw-bar pull of railway motors, 440-442 Driving-horns for drum armatures, . 73. HO Driving-power for generator, 408, 420 Driving-spokes for ring armatures, 186, 188-190, 516 Drop of voltage due to internal resistances, 37, 39, 43 Drum armatures, allowance for division-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 space in, insulation of, 78, 79 radiating surface of, 123-125 size of heads in, 123, 124 speeds and diameters of, 60 total length of conductor on, 95 Duplex, or double, armature wind- ing, 149, 150, 151, 156, 160, 161, 165, 166, 167 Dynamo-electric machines, defini- tion of, 3 physical principles of, 3 Dynamo-graphics, 476-502 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, see Accumulator Charging Dynamos. list of, considered in prepara- tion of Tables, see Preface. 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 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 & Trpt- ter. Aurora Electric Co., 272 668 INDEX. Dynamos of various Manufactu- rers Con tin ued. 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 11 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 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, 277 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 Edison General Electric Co., 168, 270, 284, 305, 398, 435, 458, 621 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 Dynamos of various Manufactu- rers Continued. 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 El well-Parker Electric Construc- 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., 170, 270, 277, 278, 280, 282, 284, 435 General Electric Traction Co., 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. Immisch & Co., 276, 618 India Rubber, Guttapercha and Telegraph Works Co. , 272 Interior Conduit and Insulation Co., 277, 283 Jenney Electric Co., 273 Jenney Electric Motor Co., 274 Johnson & Phillips, 273 Johnson Electric Service Co., 278 Kapp, Gisbert, see Johnson & Phillips. INDEX. 669 Dynamos of various Manufactu- rers Con tin ued. 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 Elektricitats- werke. Lahmeyer, W., see Aachen Elec- trical Works. Lahmeyer, W. & Co., see Elek- tricitats-Actien-Gesellschaft. Lafayette Engineering and Elec- tric 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 Premier Electric Co., 274 Riker Electric Motor Co., 274, 280, 281 Royal Electric Co., 170 Schorch, 276 Schuckert & Co., 49, 276, 278, 281, 282 Schuyler Electric Co., 459 Schwartzkopff, L., see Berliner Maschinenbau Actien-Gesell- schaft. Shawhan-Th resher 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 Manufacturing Co., 274 Dynamos of various Manufactu- rers Con tinued. Snell, Albion, see General Electric 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-EntzCo., 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 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 Dynamotor, see Motor-Generator. Ebonite, see Hard Rubber. Eccentricity of polefaces, 298 Economic coefficient, see Effi- ciency, Commercial. Eddy current loss in armature, calculation of, 119-122 Eddy currrents in armature con- ductors, 107, 119 in armature core, 107, 119- 122 in polepieces, 295 Edge-insulation of armature, 79, 82 Edser, Edwin on magnetic leak- age, 262 Effective height of armature wind- ing, 74 of magnet winding, 377 670 INDEX. 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 electrical, 37, 38, 39, 40, 42, 43, 405, 406 gross, 409, 410 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 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 Arma- ture. Emission of heat from armature, 126, 127 Empirical formula for heating of drum armatures, 129 Enamel, for armature-insulation, 7.8, 94 End-insulation of commutator, 171 End- rings for armature-core, 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 Equations, fundamental, for dif- ferent excitations, 36-43 for relative permeance, 219- 223 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 of core-leakage in toothed and perforated armatures, 219 of eddy-current-loss, 120, 121, 122 of field-deflection, 225, 230, 231 of hysteresis-loss, 112, 113, 115 of magnetic leakage, 215, 217- 265 of safety, 189, 190 Fay, Thomas, J., on constant speed motors, 427 Feather-keys, 309 Feldkamp motor, 275 INDEX. 6 7 I 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 magnetic, 199, 331 total, of dynamo, 214, 257-261 useful, of dynamo, 92, 133, 200-202, 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 Force, Electro-Motive, see Elec- tro-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 Formulas 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, 120, 121 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 6 7 2 INDEX. 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- 435 Gearless railway motors, 434 Generation of E. M. F., 4, 5, 22, 47. 48 Generator, electric, definition of, 3 " 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 Grotrian, Professor, on hollow magnet-cores, 291 Grouping of armature-coils, 147- 155 of magnetic circuits, 353-356 Gun-metal, 169 H Hard rubber, 85 Hardness, magnetic, no Heads in drum-armatures, size of; 123, 124 Heat, effect of , on hysteresis, 117, 118 on insulation-resistance, 85 Heat, radiation of, from armature, 126, 127 Heating of armatures, 127, 129, 130, 132 of magnet-coils, 368-371 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 Hysteretic exponent, 116 resistance, no, in I 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 Conductor. Ineconomy of small dynamos, 472 INDEX. 673 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, 5io 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, no, 113, 115, 118, 119, 120, 121, 122 for magnet-frame, 30, 288, 289, 293, 294, 300, 305-309 hysteretic resistance for vari- ous kinds of, in permeability 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 Ives, Arthur Stanley, on magnetic leakage, 262 Jackson, Professor Dugald C., on ratio of tnagnet- to armature 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, 516 friction in, 406-409, 526, 546, 565, 578, 602, 636, 643, 651 K Kapp, Gisbert, on diametral cur- 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 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 6 74 INDEX. 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 Leather, safe working strength of, 193 Leatheroid, for armature-insula- tion, 79, 85 Lecher, Professor, on unipolar dynamos, 25 Length of armature-conductor, 55, 95-100 of armature-bearings, 190-192, 5i6 of armature-core, 76 of armature-shaft, 184 of commutator brush -surf ace, 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- 135 of magnetization, 313 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, 201 definition and unit of, 199 Linseed oil; for armature-insula- tion, 83, 85 Load-limit of armature, 132-135 Long connection type of series armature winding, 157, 158 shunt compound winding, 41, 42 Loop winding, see Lap Winding. 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, Magnetic. intensity, see Density, Mag- netic. leakage, see Leakage, Mag- netic. permeability, see Permeabil- ity. pull on armature, see Arma- ture-Thrust. reluctance, see Reluctance. 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, 116 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 INDEX. 675 Magnetomotive force, 331 Magnet-winding, calculation of, 359-401, 450, 451, 486-497, 522, 540, 549. 562, 576, 599. 6l2 . 635, 640, 649, 654, 659 methods of excitation of, 35- 43 " Manchester " dynamo, 276 Manganese, in cast steel, 288, 289 Manufacturers, see Dynamos of various Manufacturers. 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, of shunt-dynamo, 39. 40 safe capacity of armature, .132-135 MeanE. 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 (cloth, paper, plate), 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, 4- 12 Motor, electric, calculation of, 419-442, 628-652 definition of, 3 Motor-generators, calculation of-,- 452-454, 655 Multiple circuit winding, see Par- allel Winding. Multiplex, or multiple, winding, 149, 150, 151, 160, 165 Multipolar dynamos, classification of, 269, 270, 279 -285, 287 connecting formula for, 154, 155 f 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 Munroe 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, see Efficiency, Net. Neutral points on commutator, 148, 459 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. 159-163 of armature divisions, 90 of brushes in multipolar ma- chines. 34, 102 of coils in armature, 15-2.1, 87, 90, 153-155. 158-163 of commutator divisions, 87, 88 of convolutions per commu- tator division, 89 of cycles of magnetization, no, in, 112, 119, 121 of layers of wire on armature, 74. 508 of lines of force per square inch, 54, 91 of pairs of magnet poles, 48, 5i, 53 676 INDEX. Number 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, 7i of useful lines of force, 7, 9, 92, 133, 200-202, 2II-2I4 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 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 wind ings, 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, 8 1 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, 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 Permissible energy-dissipation, in armature, 127 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-Met- allurgical Dynamos. Plugs, for switch connections, 182, 183 Points, neutral, on commutator, 148 INDEX. 677 Polar arc, percentage of, 49, 203, 207, 210 Pole-armature, see Star- Armature. Pole-bridges, 296 Pole-bushing, 49, 296 Pole-corners, 207, 208, 298 Pole-faces, eccentricity of, 298 Pole-shoes, bore of, 209, 210 construction-rules for, 293- 299 dimensioning of, 325-327 magnetic circuit in, 346, 348 Pole-strength, unit of, 199 Pole-surface, 127, 128, 204 Pole-tips, 296, 298 Poole, Cecil P., on simplified method of armature calcula- tion, 413 Position of brushes, ideal, 29 Potential, distribution of, around armature, 31-33 magnetic, 224 Power for driving generator, 420 for propelling car, 440-442 Power-transmission, dynamos for, Qi, 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 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 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, 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 density in armature of, 91 toothed armatures 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, 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 ar- matures, 592 6y8 INDEX. Ratio 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-en trancy of armature-winding, 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 increase and peripheral velocity of armature, 127, 128 Relation between temperature increase 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 magnet-winding, 375, 376, 384, 388, 399, 400 Resistance-method of speed-con- trol for railway motors, 436 Reversing field, strength of, 471, 4.72 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 Ribbon armature-cores, 93 copper-, for series field wind- ing, 36, 376 Ring-armatures, bearings for, 192 core-densities for, 91 definition of, 4 diameters of shafts for, 187 drum-wound, 35, 89, 99, 100, 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, see Spiral Wind- ing. Robinson, F. Gge., on disruptive strength of insulating mate- rials, 86 Rockers, 527 Rotary transformer, see Motor- Generator. Rotation, direction of, in genera- tor, 10 in motor, 422, 423 Round magnet cores, see Cylin- drical Magnets. Rubber, for armature-insulation, 78, 83, 85 INDEX. 679 Rule, for connecting armature coils, 152 for direction of current, 10 for direction of motion, 10 Running value of armature, 135, 136 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 drum arma- tures, 129 on hollqw magnet cores, 292 on lamination of armature core, 93 Screwed contact, 182, 183 Screw-stud, 308 Sectional area of armature-con- ductor, 57 of armature-core, 92 of magnet-frame, 313-316 of magnetic circuit, 204, 230, 341, 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. 649 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, 37 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, 3747382, 522, 586, 635 principle of, 36, 37 Sever, George F., 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, IIO, 113, 115, 120, I2If 122 Shellaced materials, for armature 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 Shunt-coil regulator for series winding, 377-382, 523-526 Shunt-dynamo, efficiency of, 38, 39, 40, 406, 407, 408 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. 541, 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-wind- ing, 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 68o INDEX. 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. Span, polar, see Polar Arc. Sparking, 29, 30, 62, 172, 173, 297, 298, 299,459 Specific armature induction, 51 energy-loss in armature, 126 energy-loss in magnets, 372 Specific 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 Sprague motor, 398 Spread, lateral, of magnetic field, 529 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, Electric. Steel, for armature-shafts, 184-186 for magnet-frame, 288, 289, 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 Stratton, Alex., on distribution of magnetic flux, 397 Stray paths of magnetic flux, 218, 300, 398 INDEX. 681 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, 514 of magnet-coils, 369 Switches, design of, 181-183 Symbols for armature windings, 150 used in formulae, see List of Symbols. Symmetry of magnetic field, 140, 304 Tables, list of, see Contents. Tangential multipolar type, 244, 270, 281, 282 pull, see Force. Tape, for armature-insulation, 78 Taper-plugs, 182, 183 Teeth in armature, see Toothed Core Armatures. Temperature-increase in arma- ture, 126-130 in magnet-coils, 368-371 Temperature, influence of, on hys- teresis, 117, 118 on insulation-resistance, 85 Tension, best, for brush-contact, 176-179, 515 safe, in materials, 189, 193 Theory, modern, of magnetism, 199 Thickness of armature-insulations, 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, I 272, 273, 274, 276, 277, 278, 282, I 283 Thompson, Professor Silvanus P^ on homopolar and heteropolai 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 dimensioning 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, 59i 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 motor- generators, 454, 656 Transformer, rotary, see Motor- Generator. 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, 167 682 INDEX. Triply re-entrant armature-wind- ing, 150, 156, 162, 163, 164, 167 Troughs, micanite, for insulating armature-slots, 81, 82 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, 153- 157 of field-magnets, 269-285 of polepieces, 296 of series- windings, 157, 158 of slots for iron -clad arma- tures, 66 U Under-type, 270, 278, 287 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, 513, 534 Unwound poles,. 470 Upright horseshoe type, 239, 245, 249, 263, 269, 270, 527, 547, 621 Useful magnetic flux, 92, 133, 200- 202, 2II-2I4 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 Webster, A. G., on unipolar dy- namos, 25 Wedding, W., on magnetic leak- age, 262 Wedge-shaped armature-conduct- ors, 78, 101, 567 Weight-efficiency of dynamos, 33, 410-412 Weight of armature winding, 101, 102 of insulation on round copper wire, 103 of magnet winding, 366-368, 388-390 of parts of dynamos, 527, 546, 565, 579, 602 Width, see Breadth. Wiener, Alfred E., on calculation of electric motors, 419 on commutator-brushes, 171 on dynamo-calculation, see Preface. 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. INDEX, 683 Winding of magnets, see Magnet- Winding. Winding-space, height of, in ar- matures, 70, 71, 74, 75 height of, in magnets, 317, 36i, 371, 375,377. 386, 387 Wire, copper, 101, 104, 119 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 Working-stress, safe, 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, see Wave- Wind- ing, Zinc blocks, 300-303 PUBLICATIONS OF THE W. J. JOHNSTON COflPANY. The Electrical World. An Illustrated Weekly Review of Current Progress in Electricity and its Practical Applications. Annual subscription $3.00 General Index to The Electrical World, 1883-1896 8.00 Atkinson, Philip, Ph.D. The Elements of Static Electricity 1.50 Bedell, Frederick, Ph.D., and Crehore, Albert C., Ph.D. Alternating Currents. 2.50 Bell, Dr. Louis. Electrical Transmission of Power 2.50 Cox, Frank P., B.S. Continuous- Current Dynamos and Motors 2.00 Crosby, O. T., and Bell, Dr. Louis. The Electric Rail way in Theory and Practice. 2.50 Davis, Charles M. Standard Tables for Electric Wiremen 1.00 Foster, H. A. Central-Station Bookkeeping 2.50 Gerard's Electricity. Translated under the direction of Dr. Louis Duncan. With chapters by Messrs. Duncan, Steinmetz, Kennelly and Hutchinson 2.50 tiering, Carl. 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