HANDBOOK OF SMALL TOOLS A REFERENCE BOOK FOR THE TOOLMAKER COMPRISING THREADING TOOLS, TAPS, DIES, CUTTERS, DRILLS AND REAMERS TOGETHER WITH A COMPLETE TREATISE ON SCREW-THREAD SYSTEM BY ERIK OBERG Associate Editor of" Machinery," Author of “ Shop Arithmetic for the Machinist,” "Advanced Shop Arithmetic," “Solution of Triangles,” " The Use of Logarithmsetc. FIRST EDITION NEW YORK JOHN WILEY & SONS, Inc. London: CHAPMAN & HALL, Limited - Copyright, 1908, BY ERIK OBERG Stanbope jpress F. H. GILSON COMPANY BOSTON, U.S.A. THE GETTY CEMtn LIBRARY PREFACE. In the following pages the author has endeavored to present an original and, as far as possible, complete treatise on the design and construction of small cutting tools, such as threading tools, taps, dies, milling cut¬ ters of all classes, reamers, drills, counterbores, hollow mills, etc. The material has been prepared with special regard to the requirements of the tool-maker, tool drafts¬ man, foreman, inspector, and superintendent, for specific information relating to tools of the class mentioned. The immediate reason for the placing of this book on the mar¬ ket is the lack of definite data on this class of work in existing treatises on shop practice, and the book has been written to supply a distinct demand in this direction. The author also wishes to emphasize the fact that the information given is authentic, and that the book places on record the most modern practice in tool manufacture, the experience gained by him during several years con¬ nection with one of the foremost tool-making firms in the country, the Pratt & Whitney Company, being the basis of the treatise. In arranging the material, a great deal of space has been devoted to tables, formulas, and general data, giving the tool-maker and the designer of tools specific working figures; and while methods and processes have not been neglected, the author’s personal experience has been that the demand of the tool-making trade is for directions what to do rather than how to do it. An effort has been made to prepare the material for this book so as to give specifi¬ cally, in plain figures, in tables, and in formulas, the iii iv PREFACE desired information. While the book is of a practical character, and intended for the use of practical men, theoretical considerations have not been overlooked, and formulas and deductions of formulas are included where- ever considered advisable. Those who have no interest m the deduction or use of formulas will find the results sought foi directly in the tables, without calculations. The portion of Chapter II devoted to change gearing for the lathe has been prepared with the intention of present¬ ing this matter in as simple a manner as possible, in order to meet the requirements of those whose knowledge of mathematics is limited; hence the rather extended and elementary treatment of this subject. The majority of the tables are original, and have never been published before, except those which have appeared under the author’s name in Machinery, in which, in the form of separate articles, a great deal of the material has already been published. In the preparation of the mate¬ rial the author has also made use of some portions of articles contributed from time to time to Machinery by Mr. A. L. Valentine, Mr. E. R. Markham, and Mr. A. E. Johnson, and credit is here given to these writers. The author is also under obligation to the publishers of Machinery for the use of a considerable number of engrav¬ ings and for permission to use several articles previously contributed by him to this journal, and copyrighted by The Industrial Press, publishers of Machinery. Brooklyn, N. Y., November, 1908. ERIK OBERG. CONTENTS CHAPTER I. SCREW-THREAD SYSTEMS. PAGE Introductory . 1 The United States Standard Thread. 2 Formulas for Determining the Number of Threads per Inch 7 Principal Requirements for a Desirable Screw Thread. 8 The Sharp V-Thread. 9 Comparison between the United States Standard and the Sharp V-Thread. 13 The Advantage of Fine Pitches. 14 Points of Advantage of the Sharp V-Thread. 15 Threads for Machine Screws. 16 The Whitworth Standard Thread. 16 Advantages and Disadvantages of the Whitworth Thread .... 20 The British Standard Fine Screw Thread. 20 British Association Standard Thread. 22 Briggs Standard Pipe Thread. 25 Whitworth Standard Thread for Gas and Water Piping. 27 Square Threads. 28 The Acme Thread. 29 French and International Standard Threads. 31 Miscellaneous Systems of Threads in Common Use. 34 Standard Proportions for Machine Screws. 38 CHAPTER II. METHODS AND PRINCIPLES OF THREAD-CUTTING.— MEASURING THREADS. Thread-Cutting. 43 Determining the Change Gears for Thread-Cutting. 50 Simple Gearing. 52 Lathes with Reduction Gearing in Head-Stock. 54 Compound Gearing . 55 v VI CONTENTS PAGE Fractional Threads. 57 Cutting Metric Threads with an English Lead Screw. 58 Cutting an English Thread with a Metric Lead Screw ..... 61 General Principles of Thread-Cutting. 66 Measuring Threads. 69 Testing the Lead of Taps and Screws. 92 Testing the Lead by Gauges. 93 Comparators for the Lead of Taps and Screws. 95 CHAPTER III. THREADING TOOLS. — DEFINITIONS OF TAPS. Simple Forms of Thread Tools. 99 Thread-Tool Holders. 102 Single-Point Cutters. 104 Chasers. 105 The Making of Threading Tools. 106 Thread Tools with Side Clearance. 121 Threading Tools for Taper Taps. 124 The Influence of the Thread Miller on Threading Tools .... 129 Square-Thread Tools. 132 Special Thread Tool Holder. 136 Definitions of Different Kinds of Taps. 138 CHAPTER IV. HAND TAPS. Hand Taps Made in Sets . 142 Cutting Taps with Dies . 157 Requirements for Correctly Threaded Taps . 158 Fluting . 159 Grinding Fluting Cutters . 166 Relief of Taps . 176 Change of Pitch in Hardening . 178 Hardening Taps . 187 Dimensions of Ordinary Hand Taps . 190 Dimensions of Acme and Square Thread Taps . 192 Machine Screw Taps. 194 Pulley Taps . 207 CONTENTS vii CHAPTER V. TAPPER TAPS AND MACHINE TAPS. —SCREW MACHINE TAPS.—HOBS AND DIE TAPS. PAGE Tapper Taps. 210 Machine Taps.215 Screw Machine Taps. 225 Hobs and Die Taps. 228 CHAPTER VI. TAPER TAPS.—MISCELLANEOUS TAPS. Taper Taps in General. 236 Pipe Taps . . . .'. 242 English Taper Pipe Taps. 247 Pipe Hobs. 250 Taper Boiler Taps. 253 Patch-Bolt Taps. 255 Mud and Wash-out Taps. 256 Blacksmiths’ Taper Taps. 257 Pipe Taps and Drills Combined. 258 Stay-Bolt Taps. 259 Straight Boiler Taps. 263 Straight Pipe Taps. 265 Adjustable Taps. 268 Kind of Steel Used for Taps. 276 CHAPTER VII. THREADING DIES. Spring Screw Threading Dies. 278 Roughing and Finishing Spring Screw Dies. 293 Classes of Threading Dies. 297 Solid Dies. 298 Split Adjustable Dies. 303 Die Holders. 308 Holder for Spring Screw Dies. 310 Inserted Chaser Dies. 312 Grinding Threading Dies. 315 Self-opening Dies. 317 Vlll CONTENTS CHAPTER VIII. PLAIN AND SIDE MILLING CUTTERS. PAGE Introductory. 319 Plain Milling Cutters. 320 Number of Teeth in Plain Milling Cutters.325 Hardening.337 Grinding.339 Side or Straddle Milling Cutters. 343 Number of Teeth in Side Milling Cutters. 348 Interlocked Cutters. 351 High-speed Steel for Milling Cutters. 355 CHAPTER IX. MISCELLANEOUS MILLING CUTTERS. End Mills.360 Angular Milling Cutters.367 Cutters for Fluting Spiral-teeth Milling Cutters.368 Fixture for Grinding Angular Milling Cutters. 369 Formed Cutters.'. 371 Importance of Grinding Eccentrically Relieved Cutter Teeth Radially.379 Forming Tools. 381 T-Slot Cutters. 389 Metal Slitting Cutters.392 Inserted-Blade Milling Cutters. 393 Inserted-Tooth Formed Milling Cutter. 397 Special Form of Milling Cutters. 399 CHAPTER X. REAMERS. Introductory.403 Hand Reamers.403 Relief.407 Reamers with Helical Flutes.409 Threaded-End Hand Reamers.410 Precautions in Hardening Reamers.421 Principles of Grinding Reamers.421 Fluted Chucking Reamers. 423 Rose Chucking Reamers.426 CONTENTS IX Jobbers’ Reamers. Shell Reamers. Taper Reamers. Grooved Chucking Reamers Center Reamers. Flat-sided Reamers. Adjustable Reamers. PAGE 430 432 438 456 459 461 462 CHAPTER XI. DRILLS. — COUNTERBORES. — HOLLOW MILLS. — LATHE ARBORS. Twist Drills. Thickness of Web. Relieving the Land of Twist Drills. Hardening Twist Drills. Grinding Twist Drills.. Factors Determining the Keenness and Durability of the Cutting Edge. Dimensions of Twist Drills. The Drilling of Deep Holes. Counterbores . Counterbores with Inserted Pilots. Counterbores with Interchangeable Bodies and Guides. Hollow Mills. Solid Lathe Arbors.* 469 474 476 478 480 481 482 486 490 496 497 500 502 SMALL TOOLS. CHAPTER I. SCREW-THREAD SYSTEMS. Introductory. Notwithstanding all that has been written about standard screw-thread systems, data which completely cover all the recognized standards are very scattered, and it is often necessary to search for information in many various handbooks and works of reference. For this reason we will of necessity, before entering upon the subject of taps and tap-making, devote our attention to the different kinds and systems of thread in common use. While a great many more systems than we will review in the following have been proposed from time to time, only those which are mentioned below have been officially recognized by mechanical men, or gained prestige by means of universal use and adoption. It will be found that the list given embraces all standards, whether in use principally in the United States, in Great Britain, or on the European continent. Any one having to do with tool-making, and, of course, tap-making in particular, must be equally familiar with the systems abroad as with those of this country, because the trade relations between the United States and Great Britain and the continent make it necessary to produce a great number of tools in this country, made in accordance with the systems in vogue in the country where the tools are to be used. The recognized British standards are also used to a great l 2 SMALL TOOLS extent by machine builders in this country, and even the number of American manufacturers who introduce what is termed the French and International standards in their establishments is steadily growing. To question the advisability of such a course is not within the limi¬ tations of this treatise, but the fact is referred to merely in order to point out the universal use of all the standard systems of screw threads, and to call attention to the necessity of a complete record of the peculiarities of each system. Standard Systems. The most common systems which will be treated in detail in the following pages are: The United States standard thread, The sharp V-thread, The Whitworth standard thread, The British standard fine screw thread, The British Association standard thread, The Briggs standard pipe thread, The Whitworth standard thread for gas and water piping, The square thread, The Acme thread, and finally The French and International standard threads. The United States Standard Thread. The United States standard thread, usually denoted U. S. S., has a cross section as shown in Fig. 1. The sides of the thread form an angle of 60 degrees with one another. The top and bottom of the thread are flattened, the width of the flat in both cases being equal to one- eighth of the pitch of the thread. In this connection it SCREW-THREAD SYSTEMS 3 may be appropriate to define the expression “ pitch ” as well as "lead,” as these two are often confused and the word “ pitch,” in particu- f i lar, often, though improperly, p 1 used in place of “number of threads per inch.” The pitch of a thread is the dis¬ tance from center to center of two adjacent threads. It is equal to the reciprocal value Fig. 1. United States Standard Thread of the number of threads per inch, or, if expressed in a formula, If, for instance, the number of threads per inch in a cer¬ tain case is 16, then pitch = — = 0.0625 inch. 16 The lead of a screw thread is the distance the screw will travel forward if turned around one complete revolution. It is evident that for a single-threaded screw the pitch and the lead are equal. If the screw is provided with a double thread, then the lead is equal to two times the pitch. These definitions should be strictly adhered to, as great confusion is often caused by the different meanings being given to the expressions “ pitch ” and lead.” If we now return to the United States standard thread, we will notice that if the thread is flattened one-eighth of the pitch at top and bottom, the depth of the thread is equal to three-quarters of the depth of a corresponding thread sharp both at top and bottom. If p equals the pitch of the thread, d the depth, and / the width of the 4 SMALL TOOLS flat, we can express the relation between these quantities in the following formulas: 1 p - -, number of threads per inch d = | X p X cos 30° = 0.64952 p, Assuming again a case with 16 threads per inch, we find by using our formulas, depth of thread = 0.64952 X = 0.0406 inch, 16 and the width of the flat = — = 0.0078 inch. 8 In Table I the depth of the thread and the width of the flat for the most common number of threads per inch are given. A column is also given for the double depth of the thread. This quantity is of value when wanting to find the root diameter of the thread, this diameter evi¬ dently being equal to the outside or standard diameter less the double depth of the thread. As this figure there¬ fore is of particular importance it is given in all the fol¬ lowing tables for various forms of thread. There will be noticed in some cases in Table I apparent errors in the last decimal figure in the column for the double depth of the thread, this figure not being in all cases exactly two times the figure for the depth of the thread as stated in the second column. This depends, of course, upon that the figures given are not even decimal values, and in all cases wherever the fifth decimal, which is not given, is above 5, the fourth figure is raised to the nearest higher digit. SCREW-THREAD SYSTEMS 5 TABLE I. ELEMENTS OF THE UNITED STATES STANDARD THREAD. No. of Threads per Inch. Depth of Thread. Width of Flat. Double Depth of Thread. No. of Threads per Inch. Depth of Thread. Width of Flat. Double Depth of Thread. 21 0.2887 0.0556 0.5774 18 0.0361 0.0069 0.0722 2f 0.2735 0.0526 0.5470 20 0.0325 0.0062 0.0650 21 0.2598 0.0500 0.5196 22 0.0295 0.0057 0.0590 2f 0.2474 0.0476 0.4949 24 0.0271 0.0052 0.0541 2f 0.2362 0.0455 0.4724 26 0.0250 0.0048 0.0500 21 0.2259 0.0435 0.4518 28 0.0232 0.0045 0.0464 3 0.2165 0.0417 0.4330 30 0.0217 0.0042 0.0433 31 0.1999 0.0385 0.3997 32 0.0203 0.0039 0.0406 31 0.1856 0.0357 0.3712 34 0.0191 0.0037 0.0382 4 0.1624 0.0312 0.3248 36 0.0180 0.0035 0.0361 41 0.1443 0.0278 0.2887 38 0.0171 0.0033 0.0342 5 0.1299 0.0250 0.2598 40 0.0162 0.0031 0.0325 51 0.1181 0.0227 0.2362 42 0.0155 0.0030 0.0309 6 0.1083 0.0208 0.2165 44 0.0148 0.0028 0.0295 7 0.0928 0.0179 0.1856 46 0.0141 0.0027 0.0282 8 0.0812 0.0156 0.1624 48 0.0135 0.0026 0.0271 9 0.0722 0.0139 0.1443 50 0.0130 0.0025 0.0260 10 0.0650 0.0125 0.1299 52 0.0125 0.0024 0.0250 11 0.0590 0.0114 0.1181 56 0.0116 0.0022 0 0232 12 0.0541 0.0104 0.1083 60 0.0108 0.0021 0.0217 13 0.0500 0.0096 0.0999 64 0.0101 0.0020 0.0203 14 U.0464 0.0089 0.0928 68 0.0096 0.0018 0.0191 15 0.0433 0.0083 0.0866 72 0.0090 0.0017 0 0180 16 0.0406 0.0078 0.0812 80 0.0081 0.0016 0.0162 In Table II are given the number of threads per inch corresponding to a given diameter, as well as the root diameter for all standard screws. When denoting that a certain thread is to be of the same shape as the United States standard, but the number of threads per inch is not in accordance with the standard number of threads for the diameter in question, it is usual to state the num¬ ber of threads and add “United States Form,” U. S. F. Thus, while 1| — U. S. S. means a tap or a screw 1J inches in diameter with 6 threads per inch, this being the stand¬ ard number for this diameter, if 12 threads per inch are 6 SMALL TOOLS wanted, the tap or screw would be denoted 1| — 12 U. S. F. The United States standard thread is some¬ times, though at the present time rarely, called the Sellers thread, naming it from its originator, Mr. William Sellers. TABLE II. NUMBER OF THREADS PER INCH CORRESPONDING TO A GIVEN DIAMETER. United States Standard Thread. Diameter. No. of Threads. Diameter at Root of Thread. Diameter. No. of Threads. Diameter at Root of Thread. A 64 0.0422 U 5 1.4902 A 50 0.0678 iA 5 1.5527 £ 40 0.0925 h 5 1.6152 A 36 0.1202 1A 5 1.6777 A 32 0.1469 2 41 1.7113 A 28 0.1724 21 41 1.8363 1 20 0.1850 21 41 1.9613 A 18 0.2403 2f 4 2.0502 | 16 0.2938 21 4 2.1752 A 14 0.3447 2f 4 2.3002 I 13 0.4001 21 4 2.4252 A 12 0.4542 21 31 2.5038 11 0.5069 3 31 2.6288 11 0.5694 31 31 2.7538 f 10 0.6201 31 31 2.8788 ft 10 0.6826 3f 31 2.9753 1 9 0.7307 31 31 3.1003 it 9 0.7932 3f 31 3.2253 1 8 0.8376 31 3 3.3170 1A 7 0.8769 31 3 3.4420 H 7 0.9394 4 3 3.5670 1A 7 1.0019 41- 21 3.7982 li 7 1.0644 41 21 4.0276 1A 6 1.0960 41 2f 4.2551 if 6 1.1585 5 21 4.4804 1A 6 1.2210 51 21 4.7304 il 6 1.2835 51 21 4.9530 iA 51 1.3263 51 21 5.2030 it 51 1.3888 6 21 5.4226 Hi 51 1.4513 . . SCREW-THREAD SYSTEMS 7 Formulas for Determining the Number of Threads per Inch. In order to fix definitely the proper number of threads per inch for any given diameter of screw in the United States standard system, the following formula is used: p = 0.24 V D + 0.625 - 0.175, in which formula p equals the pitch of the thread for any bolt or screw of the diameter D. To illustrate the use of this formula, we take, for example, a two-inch bolt, and by proper substitution we find p = 0.24\/2 + 0.625 - 0.175 = 0.2138 inch. The reciprocal value of this, or is the proper number of threads per inch for a two-inch bolt. It is evident that the fraction is not used in such a form, but is approximated by the value 4\ threads per inch, as otherwise the screw-cutting operation and selec¬ tion of change gears would be altogether too complicated. The formula given above is the one originally pro¬ posed by William Sellers, the originator of the United States standard thread. It is applicable to all screws one-quarter inch and larger in diameter. For diameters below one-quarter inch the formula should be changed to p = 0.23 V D + 0.625 - 0.175. The modification above, which has met with general acceptance, changing the coefficient 0.24 to 0.23, was pro¬ posed by Mr. George M. Bond in 1882. The purpose of the change was to make the formula applicable to screw 8 SMALL TOOLS threads for bolts which are smaller in diameter than one-quarter inch, inasmuch as Mr. Bond’s formula tends to increase the number of threads per inch more rapidly as the diameter decreases than is found to result from the use of the original formula. It will be proper to remark in this connection that screws |§, and {§ inch in diameter according to the formula ought to have 10, 9, and 8 threads per inch respec¬ tively, but in Table II the number of threads is given as 11, 10, and 9, because this conforms with the usual manu¬ facturing practice. Principal Requirements for a Desirable Screw Thread. The principal requirements for a screw thread, and in fact the required conditions which led to the adoption of the United States standard thread, are as follows: 1. That it shall possess a strength that, in the length or depth of a nut, shall be equal to the strength of the weakest part of the bolt, which, of course, is at the bottom of the thread of the screw. 2. That the tools required to produce the thread shall be easily made, and shall not appreciably change their form by reason of wear. 3. That these tools shall be capable of being easily sharpened, and set to the correct position in a lathe. 4. That a minimum of measuring and gauging shall be required to test the diameter and form of the thread. 5. That the angles of the sides shall be as acute as consistent with required strength. 6. That the thread shall not be unduly liable to become loose in cases where the nut may require to be fastened and loosened occasionally. SCREW-THREAD SYSTEMS 9 From the comparisons which we shall make in the following between the United States and other kinds of threads it will be apparent that the former thread form fills the requirements better than any other kind of thread hitherto proposed. The Sharp V-Thread. The sharp V-Thread, a diagram of which is shown in Fig. 2, is very similar to the United States standard thread, except that theoreti¬ cally it is not provided with any flat either at the top or bottom of the thread. In common practice, however, it has proven necessary to pro¬ vide this thread with a slight flat on the top of the thread. Fig. 2. Sharp V-Thread Several reasons may be mentioned necessitating this. In the first place, it is very difficult to produce a per¬ fectly sharp edge on the top of the thread, and, in the case of a tap, the sharp edge would be very likely to be impaired in hardening, leaving the top of the thread less perfect than if provided with a slight, uniform flat. In the second place, the sharp edge would wear away very rapidly, both in the case of a tap and a screw, and as the wear could not be expected to be uniform, the ultimate result would be far less desirable than the one obtained by slightly flattening the top of the thread from the beginning. The necessity of providing the sharp V-thread with a flat at the top of the thread has, however, caused some difficulty. A standard outside diameter must necessarily be adhered to, and if then a flat is provided, there must 10 SMALL TOOLS be an increase in the angle diameter of the thread, or the diameter measured halfway between the theoretical top and bottom of the thread as shown in Fig. 3. This diameter is evidently of the greatest importance, since it is obvious that if there are any variations in this dimen¬ sion it will directly influence the fit between the screw and the nut. Inasmuch as there is no recognized standard as to how much of a flat the top of the thread ought to be >4 Depth of Thread Fig. 3. Definitions of Screw-Thread Terms provided with, various manufacturers each have their own practice in this particular, which necessarily causes much confusion. The gauges made by one firm do not always correspond to the taps manufactured by another. The question is still more confusing on account of the fact that many manufacturers do not even have a definite standard for all gauges and taps manufactured by them, but working to their old established plug gauges often produce large taps with smaller flats on the top of the thread, proportionally, than the flats on smaller taps. The conditions mentioned are evidently a serious draw¬ back in regard to the sharp V-thread, and it is to be expected that the manufacturers as well as the users of SCREW-THREAD SYSTEMS 11 taps with sharp V-thread will before long settle upon a definite standard. Some manufacturers have used the same flat for the sharp V-thread as is used for the Briggs standard pipe tap thread, which, although theoretically rounded at top and bottom, is, in this country at least, made with a small flat on the top of the thread. The width of this flat is selected so as to give exactly the same angle diameter as is obtained when rounding the top of the thread in accordance with Briggs’ original proposition. This flat is equal to about one-twenty-fifth of the pitch. TABLE III. ELEMENTS OF THE SHARP V-THREAD. No. of Threads per Inch. Depth of Thread. Width of Flat. Double Depth of Thread. No. of Threads per Inch. Depth of Thread. Width of Flat. Double Depth of Thread. 21 0.3849 0.0178 0.7698 18 0.0481 0.0022 0.0962 2f 0.3646 0.0168 0.7293 20 0.0433 0.0020 0.0866 21 0.3464 0.0160 0.6928 22 0.0394 0.0018 0.0787 2f 0.3299 0.0152 0.6598 24 0.0361 0.0017 0.0722 2f 0.3149 0.0145 0.6298 26 0.0333 0.0015 0.0666 21 0.3012 0.0139 0.6025 28 0.0309 0.0014 0.0619 3 0.2887 0.0133 0.5774 30 0.0289 0.0013 0.0577 31 0.2665 0.0123 0.5329 32 0.0271 0.0012 0.0541 31 0.2474 0.0114 0.4949 34 0.0255 0.0012 0.0509 4 0.2165 0.0100 0.4330 36 0.0241 0.0011 0.0481 41 0.1925 0.0089 0.3849 38 0.0228 0.0011 0.0456 5 0.1732 0.0080 0.3464 40 0.0217 0.0010 0.0433 . 51 0.1575 0.0073 0.3149 42 0.0206 0.0010 0.0412 6 0.1443 0.0067 0.2887 44 0.0197 0.0009 0.0394 7 0.1237 0.0057 0.2474 46 0.0188 0.0009 0.0377 8 0.1083 0.0050 0.2165 48 0.0180 0.0008 0.0361 9 0.0962 0.0044 0.1925 50 0.0173 0.0008 0.0346 10 0.0866 0.0040 0.1732 52 0.0167 0.0008 0.0333 11 0.0787 0.0036 0.1575 56 0.0155 0.0007 0.0309 12 0.0722 0.0033 0.1443 60 0.0144 0.0007 0.0289 13 0.0666 0.0031 0.1332 64 0.0135 0.0006 0.0271 14 0.0619 0.0029 0.1237- 68 0.0127 0.0006 0.0255 15 0.0577 0.0027 0.1155 72 0.0120 0.0006 0.0241 16 0.0541 0.0025 0.1083 80 0.0108 0.0005 0.0217 In Table III the depth of the thread and the flat for various pitches, as figured from the formulas below, are 12 SMALL TOOLS given. The standard pitches corresponding to certain diameters are stated in Table IV in the same manner as for the United States standard thread. In the formulas p equals the pitch, d the depth, and / the flat on the top of the thread. 1 qri == ____ number of threads per inch’ d = p X cos 30° = 0.86603 p, TABLE IV. NUMBER OF THREADS PER INCH CORRESPONDING TO A GIVEN DIAMETER. Sharp V-Thread. Diameter. No. of Threads. Diameter at Root of Thread. Diameter. No. of Threads. Diameter at Root of Thread. TS 72 0 0384 U 5 1 4036 A 56 0 0628 1ft 5 1 4661 f 40 0 0817 If 41 1 4901 fa 32 0 1021 1ft 41 1 5526 fa 24 0 1153 2 41 1 6151 24 0 1465 2f 41 1 7401 1 20 0 1634 21 41 1 8651 fa 18 0 2163 2f 41 1 9901 t 16 0 2667 21 4 2 0670 A 14 0 3138 2f 4 2 1920 1 12 0 3557 2f 4 2 3170 fa 12 0 4182 2f 4 2 4420 f 11 0 4675 3 31 2 5051 tt 11 0 5300 31 31 2 6301 f 10 0 5768 31 31 2 7551 • « 10 0 6393 3f 31 2 8421 i 9 0 6825 31 31 2 9671 ft 9 0 7450 3f 31 3 0921 l 8 0 7835 3f 3 3 1726 i* 8 0 8460 31 3 3 2976 7 0 8776 4 3 3 4226 i fa 7 0 9401 41 21 3 6475 n 7 1 0026 41 2f 3 8702 ift 7 1 0651 4f 2f 4 0902 if 6 1 0863 5 21 4 3072 i fa 6 1 1488 51 21 4 5572 H 6 1 2113 51 2f 4 7707 ifa 6 1 2738 5f 2f 5 0207 if 5 1 2786 6 21 5 2302 m 5 1 3411 SCREW-THREAD SYSTEMS 13 In applying these formulas let us assume a case of a screw with 12 threads per inch. We then find: depth of thread = 0.86603 X yr = 0.0722 inch, and flat on top of thread JL_ 12 25 1 300 = 0.0033 inch. Attention must be called to the fact that the formula for the width of the flat is selected simply to give an arbitrary value, which is not recognized as any standard element of the sharp Y-thread. In figuring the depth of the thread this flat is disregarded, and the depth is arrived at as if the thread were exactly sharp. Comparison between the United States Standard and the Sharp V-Thread. The two standards referred to hitherto are the two forms of thread most commonly used in the United States. The objection to the sharp V-thread as compared with the United States standard thread is that the compara¬ tively sharp points of the teeth are very frail and liable to injury from contact with other objects. The groove at the bottom of the thread also being sharp, facilitates fracture under strain, and is a source of weakness in the screw. The depth of the thread being considerably greater than that of the United States standard thread, subtracts from the effective area of the screw, or the sectional area at the bottom of the thread, thus impairing the tensile strength of the threaded bolt. It is true that the V-thread in itself is a trifle stronger than the United States standard thread, but the increased danger of a screw with the latter form of thread failing, due to the threads stripping, as compared with that of a screw with 14 SMALL TOOLS sharp V-threacls ; is more apparent than real, as experience has shown that a screw with a full United States standard thread will fail almost invariably by breaking across the diameter at the bottom of the threads before the threads themselves will shear or strip. Experiments carried out with the object of determining the exact relation between the strength of the two forms of thread in question have proven that smaller screws provided with the United States standard thread have approximately one-quarter more strength, medium-sized ones one-sixth more, and larger ones one-eighth more strength to resist tension than screws having an ordinary sharp V-thread. The resistance to torsion of screws with the former thread is about one-third, one-quarter, and one-fifth greater, respectively, than those provided with a sharp V-thread. The Advantage of Fine Pitches. Another valuable feature of the United States standard thread as compared with the sharp V-thread is the greater endurance or life of a tap provided with the former thread and the greater duty of which it is capable, owing to the liberal flats at the top and bottom of the thread. Still another feature of superiority of the former system is the tendency in some sizes to employ finer pitches than those of the V-thread. This can be easily seen in regard to a number of sizes by referring to Tables II and IV. It may be well to point out that even the pitches of the United States standard thread are rather coarse for many pur¬ poses, and manufacturers of special machinery are inclined to modify the system. If this could be done in such a way that a recognized system with finer threads could be universally adopted, to be used in cases where the United States standard proved too coarse, then all would be well. SCREW-THREAD SYSTEMS 15 But if various branches of manufacturers adopt standards of their own, great confusion will result. In Great Britain, as we will see later, great pains have been taken to establish a system of fine screw threads, to be used in special cases as a substitute for the regular Whitworth thread. This system of fine screw threads promises to be generally adopted. Such an organized effort should be effected in this country in regard to the United States standard thread, so that, while both the form and the number of threads per inch corresponding to certain diameters are retained for such purposes, where they prove effective, in accordance with the original system, a series of finer pitches with the same thread form should also be adopted to be used where the coarser thread does not answer the purpose as well. One such system has been proposed and adopted by the Association of Licensed Automobile Manufacturers. As this system has been favored only by a limited group of manufacturers it can hardly be classed with the standard systems of thread. We will, however, return to this sub¬ ject later and give more detailed information regarding this system. Points of Advantage of the Sharp V-Thread. In spite of all that we have said in favor of the United States standard thread, the sharp V-threacl will long con¬ tinue to be in general use, due primarily to the fact that it has so thoroughly established itself in the mechanical industries. This form of thread has also another strong claim because of being admirably adapted to the mak¬ ing of steam-tight joints. It answers this purpose best, perhaps, of all common forms of thread, and all patch- bolt taps, boiler taps, stay-bolt taps, and arch-pipe taps are as a rule provided with a sharp V-thread. There is 16 SMALL TOOLS no variation of any consequence at the top and bottom of the thread, as there may be in the United States standard form of thread, with the resulting liability of leakage through the clearance thus formed. Threads for Machine Screws. The sharp V-thread is also used for machine screws. In these screws, however, while the bottom of the thread is sharp, the top is flattened considerably. No data can be given for this latter flat, as it does not conform to any system or standard, the flat being large or small only to conform to the manufacturer’s once established gauges. There has been, however, a strong movement for adopting the United States standard thread form for machine screws, which, of course, would be of great advantage. The only objection to using this thread form for small screws is that flattening only one-eighth of the depth of a full V-thread provides practically a sharp thread on very fine pitches, and a larger proportion than one to eight between the width of the flat and the pitch of the thread would be desirable in such cases. The standard pro¬ portions for machine screw threads adopted by the American Society of Mechanical Engineers fills this requirement, and we will return to this system later. The Whitworth Standard Thread. The Whitworth standard thread is used chiefly in Great Britain, but to a certain extent also in the United States. Its use here, however, has greatly diminished since the United States standard thread commenced to gain general approval. The Whitworth standard is the older one of the two, and is the first recognized screw thread system. For this reason as well as for its decided merits, which will be referred to later, it commands close attention. SCREW-THREAD SYSTEMS 17 In the Whitworth standard the sides of the thread form an angle of 55 degrees with one another. The top and the bottom of the thread are rounded as shown in Fig. 4. The radii for these rounded portions are determined by the depth of the thread, which is two-thirds of the depth of a thread of the same angle, sharp at top and bottom. The radii at the top and at the bottom are the same. If V and d mean the pitch and the depth of the thread, respectively, and r the radius of the top or bottom, d = | X ^ X cot 27° 30' = 0.64033 p, r = 0.1373 p* * In any thread system where the thread is rounded at top and bottom, the radius can be determined by the formula given below, if the pitch, the depth of the thread, and the angle between the sides of the thread are given. Let p = pitch of thread, d = depth of thread, w = inclusive angle of thread, and r = radius at top and bottom. (See Fig. 5.) Then 1 . w 1 -sm- As an example of the application of this formula let us figure the radius required for a Whitworth thread having say 10 threads to the 18 SMALL TOOLS TABLE V. ELEMENTS OF WHITWORTH STANDARD THREAD. No. of Threads per Inch. Depth of Thread. Radius. Double Depth of Thread. No. of Threads per Inch. Depth of Thread. Radius. Double Depth of Thread. 2J 0.2846 0.0610 0.5692 18 0.0356 0.0076 0.0711 2§ 0.2696 0.0578 0.5392 20 0.0320 0.0069 0.0640 2£ 0.2561 0.0549 0.5123 22 0.0291 0.0062 0.0582 2f 0.2439 0.0523 0.4879 24 0.0267 0.0057 0.0534 2f 0.2328 0.0499 0.4657 26 0.0246 0.0053 0.0493 21 0.2227 0.0478 0.4454 28 0.0229 0.0049 0.0457 3 0.2134 0.0458 0.4269 30 0.0213 0.0046 0.0427 31 0.1970 0.0422 0.3940 32 0.0200 0.0043 0.0400 31 0.1830 0.0392 0.3659 34 0.0188 0.0040 0.0377 4 0.1601 0.0343 0.3202 36 0.0178 0.0038 0.0356 41 0.1423 0.0305 0.2846 38 0.0169 0.0036 0.0337 5 0.1281 0.0275 0.2561 40 0.0160 0.0034 0.0320 51 0.1164 0.0250 0.2328 42 0.0152 0.0033 0.0305 6 0.1067 0.0229 0.2134 44 0.0146 0.0031 0.0291 7 0.0915 0.0196 0.1830 46 0.0139 0.0030 0.0278 8 0.0800 0.0172 0.1601 48 0.0133 0.0029 0.0267 9 0.0711 0.0153 0.1423 50 0.0128 0.0027 0.0256 10 0.0640 0.0137 0.1281 52 0.0123 0.0026 0.0246 11 0.0582 0.0125 0.1164 56 0.0114 0.0025 0.0229 12 0.0534 0.0114 0.1067 60 0.0107 0.0023 0.0213 13 0.0493 0.0106 0.0985 64 0.0100 0.0021 0.0200 14 0.0457 0.0098 0.0915 68 0.0094 0.0020 0.0188 15 0.0427 0.0092 0.0854 72 0.0089 0.0019 0.0178 16 0.0400 0.0086 0.0800 80 0.0080 0.0017 0.0160 inch. The pitch, p, is 0.1; the depth of the thread, d, according to the formula given for the depth of Whitworth threads is 0.064; the angle, w, is 55 degrees. The radius 5\° 0.064 “1 . /51 l) 2 J Sm ( 2 i • / 55 \° -sm lyl Carrying out this calculation we find radius = 0.0137, which corresponds to the result which would have been obtained from the simplified formula r = 0.1373 p already given for the radius of the Whitworth thread. SCREW-THREAD SYSTEMS 19 If we apply these formulas to the case of a screw with 8 threads per inch, we find: depth of thread = 0.64033 X ^ = 0.0800 inch, and 8 radius at top and bottom = 0.1373 X ^ = 0.0172 inch. The values of d and r are given in Table V for different numbers of threads per inch. Table VI gives the number of threads per inch corresponding to different diameters. TABLE VI. NUMBER OF THREADS PER INCH CORRESPONDING TO A GIVEN DIAMETER. Whitworth Standard Thread. Diameter. No. of Threads. Diameter at Root of Thread. Diameter. No. of Threads. Diameter at Root of Thread. Ill 60 0.0412 If 5 1.4939 A 48 0.0670 in 5 1.5564 i 40 0.0930 n 41 1.5904 A 32 0.1162 in 41 1.6529 1*6 24 0.1341 2 41 1.7154 A 24 0.1653 2J . 41 1.8404 1 20 0.1860 21 4 1.9298 A 18 0.2414 2f 4 2.0548 I 16 0.2950 2f 4 2.1798 A 14 0.3460 2f 4 2.3048 1 12 0.3933 2f 31 2.3841 A 12 0.4558 2f 31 2.5091 1 11 0.5086 3 31 2.6341 A 11 0.5711 H 31 2.7591 1 10 0.6219 3f 31 2.8560 A 10 0.6844 3f 31 2.9810 1 9 0.7327 3f 31 3.1060 A 9 0.7952 3f 31 3.2310 1 8 0.8399- 3f 3 3.3231 i A 8 0.9024 3J 3 3.4481 n 7 0.9420 4 3 3.5731 i A 7 1.0045 41 2f 3.8046 il 7 1.0670 41 2f 4.0546 i A 7 1.1295 4f 2f 4.2843 if 6 1.1616 5 2f 4.5343 i A 6 1.2241 51 2f 4.7621 H 6 1.2866 51 2f 5.0121 i A 6 1.3491 5f 21 5.2377 if 5 1.3689 6 21 5.4877 in 5 1.4314 . 20 SMALL TOOLS Advantages and Disadvantages of the Whitworth Thread. The Whitworth form of thread has two points of merit that commend it highly where heavy service is required. First, screws with this form of thread have all of the strength possessed by screws with United States standard threads, with the advantage over the latter of having no sharp edges or corners from which fractures may start. Secondly, screws and nuts with this form of thread will work well together after continued heavy service where the other forms of thread would fail. Whitworth threads are used in the United States chiefly on special screws, such, for instance, as screws for gasoline needle valves where a liquid-tight and yet working fit is desired. It is also often used for locomotive boiler stay bolts. The objections to the Whitworth form of thread are that the angle of 55 degrees cannot be measured or simply laid out with ordinary tools, and that the rounded corners at the top and the bottom of the threads are extremely difficult to produce with the degree of precision required in tools for thread cutting. Here the United States standard thread has a decided advantage, as the angle is easily obtained, and the flat at the top and bottom of the thread can be easily and accurately made. The Whit¬ worth standard thread system is denoted B. S. W. (British Standard Whitworth screw thread) in Great Britain, where it is the recognized standard. The British Standard Fine Screw Thread. The British Standard fine screw thread is a system of threads recently adopted in Great Britain. The form of the thread is the same as that for the Whitworth stand¬ ard, but there is a greater number of threads per inch SCREW-THREAD SYSTEMS 21 corresponding to a certain diameter than in the Whit¬ worth system. The fine screw-thread system is denoted B. S. F., and applies to screws one-quarter inch in diameter and larger. The reason for adopting this standard was founded on the complaints of many manufacturers that the regular Whitworth standard gave altogether too coarse pitches for a number of purposes, and while the old system was well adapted for a variety of construc¬ tions, it was not the best obtainable for those designs where shocks and vibrations had to be taken into con¬ sideration. The pitches for the system of fine screw threads are based approximately on the formula P = for sizes up to and including one inch; and on the formula P = for sizes larger than one inch in diameter. In the above formulas P = pitch, or lead of single-threaded screw, d = diameter of screw. As an example of the application of these formulas let us find the required number of threads per inch for a half-inch and a 3-inch screw. In the former case the first formula would be used: Pitch = ^0.25 _ 0.630 10 10 0.063 inch. The number of threads per inch = (approx.). 1 pitch 1 0.063 16 22 SMALL TOOLS In order to find the number of threads per inch for a 3-inch screw we employ the second formula given: = 0.199 inch. The number of threads per inch pitch 0.199 (approx.). It is evident that where the number of threads would be a fractional value it is approximated to the nearest whole number, except in the case of and 4J threads per inch, where fractional values are used. In Table VII the number of threads per inch cor¬ responding to certain diameters is given. It must be plainly understood that this standard is not supposed to make the regular Whitworth standard thread superfluous, but is simply intended to offer a possibility of a standard fine screw thread for purposes where the regular Whitworth thread would be too coarse. This standard applies only to screws larger than one-quarter inch in diameter. For smaller screws the British Association standard is used. British Association Standard Thread. The British Association standard thread, is the stand¬ ard system for screws of small diameter in Great Britain. It is hardly used at all in the United States, excepting in the manufacture of tools for the English market. The features of the thread form k-— p —d Fig. 6. British Association Stan- arg s j m q ar to those of the dard Thiead Whitworth thread, but the angle between the two sides of the thread is only 47 de¬ grees 30 minutes, and the radius at the top and the bottom SCREW-THREAD SYSTEMS 23 of the thread (see Fig. 6) is proportionally larger, the reason being that the depth of the thread is smaller in relation to the pitch than in the Whitworth standard thread. If p, d, and r signify the pitch, the depth, and the radius at the top and bottom of the thread, respectively, then d = 0.6 p, TABLE VII. NUMBER OF THREADS PER INCH CORRESPONDING TO A CERTAIN DIAMETER. British Standard Fine Screw Thread. Diameter. No. of Threads. Diameter at Root of Thread. Diameter. No. of Threads. Diameter at Root of Thread. I 25 0.1988 Iff 7 1.7545 A 22 0.2543 2 7 1.8170 t 20 0.3110 2f 7 1.9420 A 18 0.3664 2i 6 2.0366 1 16 0.4200 2f 6 2.1616 A 16 0.4825 21 6 2.2866 1 14 0.5335 2f 6 2.4116 H 14 0.5960 2f 6 2.5366 I 12 0.6433 2| 6 2.6616 H 12 0.7058 3 5 2.7439 1 11 0.7586 3f 5 2.8689 U 11 0.8211 3f 5 2.9939 l 10 0.8719 3f 5 3.1189 1A 10 0.9344 31 41 3.2154 n 9 0.9827 3f 41 3.3404 1A 9 1.0452 3} 41 3.4654 1? 9 1.1077 3f 41 3.5904 i A 9 1.1702 4 41 3.7154 if 8 1.2149 4f 4 3.9298 i A 8 1.2774 41 4 4.1798 n 8 1.3399 4f 4 4.4298 i A 8 1.4024 5 4 4.6798 if 8 1.4649 51 31 4.8841 itt 8 1.5274 51 31 5.1341 if 7 1.5670 5f 31 5.3841 7 1.6295 6 31 5.6341 if 7 1.6920 24 SMALL TOOLS The various sizes of screws in this system are numbered, and a certain number of threads per inch always corre¬ sponds to a given diameter. Table VIII gives all the detailed information in regard to diameter of screws, pitches, and depth and radius of thread, which is neces¬ sary for originating tools with this form of thread. The system is founded on metric measurements, hence diame¬ ter and pitch are given also in millimeters. TABLE VIII. ELEMENTS OF BRITISH ASSOCIATION STANDARD THREAD. British Associ¬ ation Diameter. Pitch. Depth of Thread. Radius. Double Depth of Thread. Num¬ ber. Milli¬ meters. Inches. Milli¬ meters. Inches. Inches. Inches. Inches. 0 6.0 0.2362 1.0 0.0394 0.0236 0.0072 0.0472 1 5.3 0.2087 0.90 0.0354 0.0212 0.0064 0.0425 2 4.7 0.1850 0.81 0.0319 0.0191 0.0058 0.0383 3 4.1 0.1614 0.73 0.0287 0.0172 0.0052 0.0345 4 3.6 0.1417 0.66 0.0260 0.0156 0.0047 0.0312 5 3.2 0.1260 0.59 0.0232 0.0139 0.0042 0.0279 6 2.8 0.1102 0.53 0.0209 0.0125 0.0038 0.0250 7 2.5 0.0984 0.48 0.0189 0.0113 0.0034 0.0227 8 2.2 0.0866 0.43 0.0169 0.0101 0.0031 0.0203 9 1.9 0.0748 0.39 0.0154 0.0092 0.0028 0.0184 10 1.7 0.0669 0.35 0.0138 0.0083 0.0025 0.0165 11 1.5 0.0591 0.31 0.0122 0.0073 0.0022 0.0146 12 1.3 0.0511 0.28 0.0110 0.0066 0.0020 0.0132 13 1.2 0.0472 0.25 0.0098 0.0059 0.0018 0.0118 14 1.0 0.0394 0.23 0.0091 0.0055 0.0016 0.0109 15 0.90 0.0354 0.21 0.0083 0.0050 0.0015 0.0099 16 0.79 0.0311 0.19 0.0075 0.0045 0.0014 0.0090 17 0.70 0.0276 0.17 0.0067 0.0040 0.0012 0.0080 18 0.62 0.0244 0.15 0.0059 0.0035 0.0011 0.0071 19 0.54 0.0213 0.14 0.0055 0.0033 0.0010 0.0066 20 0.48 0.0189 0.12 0.0047 0.0028 0.0009 0.0057 21 0.42 0.0165 0.11 0.0043 0.0026 0.0008 0.0052 22 0.37 0.0146 0.098 0.0039 0.0023 0.0007 0.0046 23 0.33 0.0130 0.089 0.0035 0.0021 0.0006 0.0042 24 0.29 0.0114 0.080 0.0031 0.0019 0.0006 0.0038 25 0.25 0.0098 0.072 0.0028 0.0017 0.0005 0.0034 SCREW-THREAD SYSTEMS 25 This system was originated in Switzerland as a stand¬ ard for screws used in watch and clock making; it is therefore also, at times, referred to as the Swiss small screw-thread system. Briggs Standard Pipe Thread. The Briggs standard pipe thread is made with an angle of 60 degrees; it is slightly rounded off both at the top and at the bottom, so that the depth of the thread, instead of being equal to the depth of a sharp V-thread (0.866 0 8 X pitch), is only four-fifths of the pitch, or equal to —, n if n be the number of threads per inch. The difficulty of producing a thread with rounded top and bottom has, however, caused the manufacturers in this country to modify the original standard. In¬ stead of rounding the bottom of the thread it is made sharp as shown in Fig. 7. The top is slightly flattened instead of rounded, the flat being carried down just far enough to tangent the top circle Fig. 7. Brigg’s Standard of the correct thread form. Pipe Thread Form This thread is used for pipe joints, as indicated by the name, and for many purposes in locomotive boiler work. The taps for producing Briggs standard pipe thread are provided with a taper of three-quarters inch per foot on the diameter. The pipe size is expressed by its nominal size, which, however, is considerably smaller than the actual size. In Table IX the nominal and actual sizes of the tube are given, as well as the corresponding number of threads per inch, the depth and the double depth of the thread. These latter values are figured as being 0.833 X p and 2 X 0.833 X p, respectively, p being the pitch of the 26 SMALL TOOLS thread. This gives the correct depth of a V-thread with a flat on the top as called for by the formula depth = 0.8 X--- - 1 -—, number ol threads per inch but gives a thread sharp at the bottom of the thread, this being at variance with the original standard as expressed by the formula, but conforming to practical usage. The flat on the top of the thread = - 0.0381^ - number of threads per inch’ or approximately one-twenty-fifth of the pitch. TABLE IX. ELEMENTS OF BRIGGS STANDARD PIPE THREAD. Nominal Size of Tube. Actual Outside Size of Tube. No. of Threads per Inch. Depth of Thread. Width of Flat on Top of Thread. Double Depth of Thread. 1 0.405 27 •0.0309 0.0014 0.0617 i 0.540 18 0.0463 0.0021 0.0926 i 0.675 18 0.0463 0.0021 0.0926 h 0.840 14 0.0595 0.0027 0.1190 1 4 1.050 14 0.0595 0.0027 0.1190 1 1.315 14 0.0724 0.0033 0.1449 n 1.660 14 0.0724 0.0033 0.1449 i* 1.900 14 0.0724 0.0033 0.1449 2 2.375 14 0.0724 0.0033 0.1449 2* 2.875 8 0.1041 0.0048 0.2082 3 3.500 8 0.1041 0.0048 0.2082 3* 4.000 8 0.1041 0.0048 0.2082 4 4.500 8 0.1041 0.0048 0.2082 4} 5.000 8 0.1041 0.0048 0.2082 5 5.563 8 0.1041 0.0048 0.2082 6 6.625 8 0.1041 0.0048 0.2082 7 7.625 8 0.1041 0.0048 0.2082 8 8.625 8 0.1041 0.0048 0.2082 9 * 9.688 8 0.1041 0.0048 0.2082 10 10.750 8 0.1041 0.0048 0.2082 * By the action of the Manufacturers of Wrought-iron Pipe and Boiler Tubes at a meeting held in New York, May 9, 1889, a change in size of actual outside diameter of 9-inch pipe was adopted, making the latter 9.625 instead of 9.688 inches, as given in the table of Briggs Standard Pipe Diameters. SCREW-THREAD SYSTEMS 27 Whitworth Standard Thread for Gas and Water Piping. The Whitworth standard thread for gas and water piping is used to some extent in this country. The form of this thread is the Whitworth form, and the only differ¬ ence from the regular Whitworth standard is the number of threads per inch. The sizes and number of threads per inch, with corresponding depth of thread, are given in Table X. TABLE X. ELEMENTS OF WHITWORTH STANDARD THREAD FOR GAS AND WATER PIPING. Nominal Size of Tube. Actual Size of Tube. No. of Threads per Inch. Depth of Thread. Radius. Double Depth of Thread. £ 0.385 28 0.0229 0.0049 0.0457 i 0.520 19 0.0337 0.0072 0.0674 I 0.665 19 0.0337 0.0072 0.0674 f 0.822 14 0.0457 0.0098 0.0915 f 0.902 14 0.0457 0.0098 0.0915 f 1.034 14 0.0457 0.0098 0.0915 £ 1.189 14 0.0457 0.0098 0.0915 1 1.302 11 0.0582 0.0125 0.1164 i£ 1.492 11 0.0582 0.0125 0.1164 l£ 1.650 11 0.0582 0.0125 0.1164 if 1.745 11 0.0582 0.0125 0.1164 if 1.882 11 0.0582 0.0125 0.1164 if 2.021 11 0.0582 0.0125 0.1164 if 2.160 11 0.0582 0.0125 0.1164 G 2.245 11 0.0582 0.0125 0.1164 2 2.347 11 0.0582 0.0125 0.1164 2£ 2.467 11 0.0582 0.0125 0.1164 2£ 2.587 11 0.0582 0.0125 0.1164 2f 2.794 11 0.0582 0.0125 0.1164 2 f 3.001 11 0.0582 0.0125 0.1164 2f 3.124 11 0.0582 0.0125 0.1164 2f 3.247 11 0.0582 0.0125 0.1164 2f 3.367 11 0.0582 0.0125 0.1164 3 3.485 11 0.0582 0.0125 0.1164 3£ 3.698 11 0.0582 0.0125 0.1164 3* 3.912 11 0.0582 0.0125 0.1164 3f 4.125 11 0.0582 0.0125 0.1164 4 4.339 11 0.0582 0.0125 0.1164 28 SMALL TOOLS Square Threads. The square thread is shown in Fig. 8. The sides of the thread are parallel, and as the name indicates, the depth of the thread is equal to the width of space between the teeth, this space being equal to one-half of the pitch. In Table XI the depth of the thread is given for certain numbers of threads per inch. The square form of thread is usually made about twice as coarse in pitch as the V or United States standard threads, and partly for this reason and partly because of the perpendicular walls of the thread it is a troublesome thread to cut with taps and dies. There is also difficulty where more than one cut is made to produce the finished screw, due to the succeeding taps or dies not having a lead exactly like the one of the partly cut thread, and consequently the thread already formed is cut away. This form of thread is largely used on adjusting and power-conveying screws. While, theoretically, the space between the teeth is equal to the thickness of the tooth, each being one-half of the pitch, it is evident that the thickness of the tooth must be enough smaller than the space to admit at least an easy sliding fit. In threads with angular sides this slight variation may be taken care of by a small increase of the angle diameter in the nut, but in the case of a square thread with perpendicular sides it is obvious that the only provision possible is a slight increase of the width of the space above the thickness of the tooth. SCREW-THREAD SYSTEMS 29 TABLE XI. ELEMENTS OF THE SQUARE THREAD. No. of Threads per Inch. Depth of Thread. Double Depth of Thread. No. of Threads per Inch. Depth of Thread. Double Depth of Thread. 1 0.5000 1.0000 8 0.0625 0.1250 H 0.3750 0.7500 9 0.0556 0.1111 H 0.3333 0.6667 10 0.0500 0.1000 if 0.2857 0.5714 11 0.0455 0.0909 2 0.2500 0.5000 12 0.0417 0.0833 2* 0.2000 0.4000 13 0.0385 0.0769 3 0.1667 0.3333 14 0.0357 0.0714 3* 0.1429 0.2857 15 0.0333 0.0667 4 0.1250 0.2500 16 0.0312 0.0625 4$ 0.1111 0.2222 18 0.0278 0.0556 5 0.1000 0.2000 20 0.0250 0.0500 5* 0.0909 0.1818 22 0.0227 0.0455 6 0.0833 0.1667 24 0.0208 0.0417 7 0.0714 0.1429 The Acme Thread. The Acme thread, shown in Fig. 9, has of late become widely used, having in most instances taken the place of the square thread on account of its better wearing quali¬ ties and the comparative ease with which this thread can be produced. Of all the thread systems which we have treated, this is the only one where a standard provision has been made for clearance at the top and in the bottom of the thread. The screw provided with an Acme thread is made of standard diameter, but the nut into which it is to fit is made over size in its total diameter. The rela¬ tionship between screw and nut is plainly illustrated in Fig. 10. If the diameter of the screw is A over the top of 30 SMALL TOOLS the thread, and B at the bottom or root of the thread, the corresponding diameters in the nut are A -f 0.020 and B + 0.020 inch. Referring again to Fig. 9, it will be noticed that the sides of the thread form an angle of 29 degrees with one another. Considering the screw only, if p is the pitch, d the depth of the thread, / the width of the flat at the top of the thread, and c the width of the flat at the root of the thread, then Fig. 10. Dimensions of Thread in Screw and Nut, Acme Standard d = ^ + 0.010 inch, Aj f = 0.3707 p, c = 0.3707 p - 0.0052 inch. Table XII contains the values of d, /, and c for certain common numbers of threads per inch. Having given the formula for the depth of the thread it is clear that Diameter at root of thread = total diameter— (p + 0.020). This formula regards screws as well as taps for Acme thread nuts. The formulas for d and / given above refer to screws only. On taps the flats at the top and the bottom are alike and equal c, or 0.3707 p — 0.0052 inch. The diameter of the tap equals diameter of screw + 0.020, which is evident from what has previously been said about the size of the thread in Acme thread nuts. The Acme thread has many good points, not the least of which is its strength and the ease with which it may be cut, compared with the square thread. This is due to the greater strength of the teeth in both taps and dies, as well as to the facility with which the cuttings free themselves. SCREW-THREAD SYSTEMS 31 This thread is recommended as a substitute for, and in preference to, the square form of thread. TABLE XII. ELEMENTS OF THE ACME STANDARD THREAD. No. of Threads per Inch. Depth of Thread. Width of Flat at Top of Thread. Width of Flat at Root of Thread. Double Depth of Thread. 1 0.5100 0.3707 0.3655 1.0200 H 0.3433 0.2471 0.2419 0.6867 2 0.2600 0.1853 0.1801 0.5200 21 0.2100 0.1483 0.1431 0.4200 3 0.1767 0.1236 0.1184 0.3533 31 0.1529 0.1059 0.1007 0.3057 4 0.1350 0.0927 0.0875 0.2700 41 0.1211 0.0824 0.0772 0.2422 5 0.1100 0.0741 0.0689 0.2200 51 0.1009 0.0674 0.0622 0.2018 6 0.0933 0.0618 0.0566 0.1867 7 0.0814 0.0530 0.0478 0.1629 8 0.0725 0.0463 0.0411 0.1450 9 0.0656 0.0412 0.0360 0.1311 10 0.0600 0.0371 0.0319 0.1200 12 0.0517 0.0309 0.0257 0.1033 French and International Standard Threads. The French and International standard threads are of the same form as the United States standard, and the formulas given for the latter form of thread apply to the former. The pitches, however, are stated in the metric measure, and are somewhat finer for corresponding diame¬ ters than the United States standaid thread. This is a distinct advantage, especially on the smaller sizes. The standard thread of the International system, denoted S. I., was adopted by the International Congress for the uni¬ fying of screw threads, held at Zurich, 1898. This system conforms in general with the system earlier adopted in France, the French standard thread, denoted S. F., but some slight variations occur, as can be easily seen from 32 SMALL TOOLS Table XIV, where the diameters and corresponding pitches are given. In order to provide for clearance at the bottom of the thread, the Congress referred to above specified that “the clearance at the bottom of the thread shall not exceed one-sixteenth part of the height of the original triangle. The shape of the bottom of the thread resulting from said clearance is left to the manufacturers. How¬ ever, the Congress recommends rounded profile for said bottom.” By this provision, choice is given manu¬ facturers in the several countries interested of making the bottoms of their threads flat or rounded, as desired, and yet have them conform to a common standard so as to interchange if necessary. TABLE XIII. ELEMENTS OF THE FRENCH AND INTERNATIONAL SYSTEM STANDARD THREAD. Pitch, Mm. Depth of Thread, Inches. Width of Flat, Inches. Double Depth of Thread, Inches. 8 0.2046 0.0394 0.4092 7.75 0.1982 0.0382 0.3964 7.5 0.1918 0.0369 0.3836 7.25 0.1854 0.0357 0.3708 7 0.1790 0.0344 0.3580 6.75 0.1726 0.0332 0.3452 6.5 0.1662 0.0320 0.3324 6.25 0.1598 0.0308 0.3196 6 0.1534 0.0295 0.3068 5.75 0.1470 0.0283 0.2940 5.5 0.1406 0.0271 0.2812 5.25 0.1343 0.0259 0.2685 5 0.1279 0.0246 0.2557 4.75 0.1215 0.0234 0.2429 4.5 0.1151 0.0221 0.2301 4.25 0.1087 0.0209 0.2174 4 0.1023 0.0197 0.2046 3.75 0.0959 0.0185 0.1918 3.5 0.0895 0.0172 0.1790 Pitch, Mm. Depth of Thread, Inches. Width of Flat, Inches. Double Depth of Thread, Inches. 3.25 0.0831 0.0160 0.1662 3 0.0767 0.0148 0.1534 2.75 0.0703 0.0135 0.1406 2.5 0.0639 0.0123 0.1279 2.25 0.0575 0.0111 0.1151 2 0.0511 0.0098 0.1023 1.75 0.0448 0.0086 0.0895 1.5 0.0384 0.0074 0.0767 1.25 0.0320 0.0062 0.0639 1 0.0256 0.0049 0.0511 0.9 0.0230 0.0044 0.0460 0.8 0.0205 0.0039 0.0409 0.75 0.0192 0.0037 0.0384 0.7 0.0179 0.0034 0.0358 0.6 0.0153 0.0030 0.0307 0.5 0.0128 0.0025 0.0256 0.4 0.0102 0.0020 0.0205 0.3 0.0077 0.0015 0.0153 0.25 0.0064 0.0012 0.0128 SCREW-THREAD SYSTEMS 33 In Table XIII the necessary data as to depth of thread and flat at top and bottom of thread are given. We may remark that in this country the rounded profile at the bottom is not in vogue, the form of the thread being made an exact duplicate of the United States standard form. TABLE XIV. DIAMETERS AND CORRESPONDING- PITCHES. French and International Systems Standard Thread. French System. Diameter, Mm. 3 4 5 6 7 8 9 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 Pitch, Mm. 0.5 0.75 0.75 1.0 1.0 1.0 1.0 1.5 1.5 2.0 2.0 2.5 2.5 2.5 3.0 3.0 3.0 3.5 3.5 3.5 4.0 4.0 4.0 4.5 4.5 4.5 5.0 5.0 Diameter at Root of Thread, Mm. 2.35 3.03 4.03 4.70 5.70 6.70 7.70 8.05 10.05 11.40 13.40 14.75 16.75 18.75 20.10 22.10 24.10 25.45 27.45 29.45 30.80 32.80 34.80 36.15 38.15 40.15 41.51 43.51 International System. Diameter, Mm. 6 7 8 9 10 11 12 14 16 18 20 22 24 27 30 33 36 39 42 45 48 52 56 60 64 68 72 76 80 Pitch, Mm. 1.0 1.0 1.25 1.25 1.5 1.5 1.75 2.0 2.0 2.5 2.5 2.5 3.0 3.0 3.5 3.5 4.0 4.0 4.5 4.5 5.0 5.0 5.5 5.5 6.0 6.0 6.5 6.5 7.0 Diameter at Root of Thread, Mm. 4.70 5.70 6.38 7.38 8.05 9.05 9.73 11.40 13.40 14.75 16.75 18.75 20.10 23.10 25.45 28.45 30.80 33.80 36.15 39.15 41.51 45.51 48.86 52.86 56.21 60.21 63.56 67.56 70.91 34 SMALL TOOLS In order to facilitate any necessary conversion of milli¬ meters into inches a metric conversion table is appended. (See Table XV.) TABLE XV. MILLIMETERS CONVERTED INTO INCHES. Mm. Inches. Mm. Inches. Mm. Inches. Mm. Inches. Mm. Inches. 0.01 0.0004 0.35 0.0138 0.69 0.0272 4 0.1575 38 1.4961 0.02 0.0008 0.36 0.0142 0.70 0.0276 5 0.1969 39 1.5354 0.03 0.0012 0.37 0.0146 0.71 0.0280 6 0.2362 40 1.5748 0.04 0.0016 0.38 0.0150 0.72 0.0283 7 0.2756 41 1.6142 0.05 0.0020 0.39 0.0154 0.73 0.0287 8 0.3150 42 1.6535 0.06 0.0024 0.40 0.0157 0.74 0.0291 9 0.3543 43 1.6929 0.07 0.0028 0.41 0.0161 0.75 0.0295 10 0.3937 44 1.7323 0.08 0.0031 0.42 0.0165 0.76 0.0299 11 0.4331 45 1.7716 0.09 0.0035 0.43 0.0169 0.77 0.0303 12 0.4724 46 1.8110 0.10 0.0039 0.44 0.0173 0.78 0.0307 13 0.5118 47 1.8504 0.11 0.0043 0.45 0.0177 0.79 0.0311 14 0.5512 48 1.8898 0.12 0.0047 0.46 0.0181 0.80 0.0315 15 0.5905 49 1.9291 0.13 0.0051 0.47 0.0185 0.81 0.0319 16 0.6299 50 1.9685 0.14 0.0055 0.48 0.0189 0.82 0.0323 17 0.6693 51 2.0079 0.15 0.0059 0.49 0.0193 0.83 0.0327 18 0.7087 52 2.0472 0.16 0.0063 0.50 0.0197 0.84 0.0331 19 0.7480 53 2.0866 0.17 0.0067 0.51 0.0201 0.85 0.0335 20 0.7874 54 2.1260 0.18 0.0071 0.52 0.0205 0.86 0.0339 21 0.8268 55 2.1653 0.19 0.0075 0.53 0.0209 0.87 0.0343 22 0.8661 56 2.2047 0.20 0.0079 0.54 0.0213 0.88 0.0346 23 0.9055 57 2.2441 0.21 0.0083 0.55 0.0217 0.89 0.0350 24 0.9449 58 2.2835 0.22 0.0087 0.56 0.0220 0.90 0.0354 25 0.9842 59 2.3228 0.23 0.0091 0.57 0.0224 0.91 0.0358 26 1.0236 60 2.3622 0.24 0.0094 0.58 0.0228 0.92 0.0362 27 1.0630 61 2.4016 0.25 0.0098 0.59 0.0232 0.93 0.0366 28 1.1024 62 2.4409 0.26 0.0102 0.60 0.0236 0.94 0.0370 29 1.1417 63 2.4803 0.27 0.0106 0.61 0.0240 0.95 0.0374 30 1.1811 64 2.5197 0.28 0.0110 0.62 0.0244 0.96 0.0378 31 1.2205 65 2.5590 0.29 0.0114 0.63 0.0248 0.97 0.0382 32 1.2598 66 2.5984 0.30 0.0118 0.64 0.0252 0.98 0.0386 33 1.2992 67 2.6378 0.31 0.0122 0.65 0.0256 0.99 0.0390 34 1.3386 68 2.6772 0.32 0.0126 0.66 0.0260 1 0.0394 35 1.3779 69 2.7165 0.33 0.0130 0.67 0.0264 2 0.0787 36 1.4173 70 2.7559 0.34 0.0134 0.68 0.0268 3 0.1181 37 1.4567 Miscellaneous Systems of Thread in Common Use. Besides the systems previously treated, which we have classified as standard systems of thread, there are a SCREW-THREAD SYSTEMS 35 number of systems which have never become recognized standards, but which nevertheless are used to a greater or smaller extent in special trades. Instrument and Watch Makers’ Systems .—The standard screw thread of the Royal Microscopical Society of Lon¬ don, England, is employed for microscope objectives, and the nose pieces of the microscope into which these objec¬ tives screw. The form of the thread is the Whitworth form; the diameter of the male gauge is 0.7626 inch. The number of threads per inch is 36. TABLE XVI. WHITWORTH STANDARD THREAD SYSTEM FOR WATCH AND MATHEMATICAL INSTRUMENT MAKERS. Diameter of Screw, Inches. No. of Thrds. per Inch. Diameter of Screw, Inches. No. of Thrds. per ' Inch. Diameter of Screw, Inches. No. of Thrds. per Inch. 0.010 400 0.022 210 0.050 100 0.011 400 0.024 210 0.055 100 0.012 350 0.026 180 0.060 100 0.013 350 0.028 180 0.065 80 0.014 300 0.030 180 0.070 80 0.015 300 0.032 150 0.075 80 0.016 300 0.034 150 0.080 60 0.017 250 0.036 150 0.085 60 0.018 250 0.038 120 0.090 60 0.019 250 0.040 120 0.095 60 0.020 210 0.045 120 0.100 50 In Table XVI are given the sizes and corresponding number of threads for Whitworth standard screw pitch system for watch and mathematical instrument makers. This system is adopted by many instrument makers both in the United States and Europe. Lag Screw Threads .— There is no recognized standard for the sizes and corresponding number of threads for 36 SMALL TOOLS lag screws. Table XVII gives the number of threads according to common practice. While lag screws are largely made according to this system, there is, however, a number of varying systems in use. TABLE XVII. LAG SCREW THREADS. Diameter of Screw. Number of Threads per Inch. Diameter of Screw. Number of Threads per Inch. i 10 f 5 A 9 TS 5 1 8 1 5 A 7 I 4 i 6 1 4 A 6 Gas-Fixture Threads. — Thin brass tubing is threaded with 27 threads per inch, irrespective of diameter. The so-called “Ornament brass sizes’’ have 32 threads per inch. The standard sizes of the thread are 0.196 inch (large ornament brass size) and 0.148 inch (small orna¬ ment brass size). Fine Screw-Thread Systems. — We have previously referred to the desirability of the adoption of a standard system with the United States standard form of thread but with a finer pitch than called for by this standard. We also mentioned the system which has been proposed by the Association of Licensed Automobile Manufacturers. In this system the diameters and corresponding number of threads are as follows: 28 i . . 18 24 tt. . 16 24 f. . 16 20 i . . 14 20 i. . 14 SCREW-THREAD SYSTEMS 37 The objection to the adoption of this standard by a single body of manufacturers is obvious. Even if the standard is one which would recommend itself for general use, it would have been better if the opinions and the needs of machine builders in general had been taken into consideration. Besides, there is reasonable doubt whether the standard referred to is not too fine for ordi¬ nary construction even where the need of a fine-pitch standard has presented itself. Automobile construction is, of course, so specialized a manufacture that here doubtless may arise requirements which do not present themselves elsewhere. It seems as if the pitches of the British standard fine screw thread were well selected for a fine-pitch screw thread, at least with a few slight modifications. It would be well if a system of such a kind could be adopted. The number of threads corresponding to a certain diam¬ eter given in Table XVIII will be found very suitable for a fine pitch screw standard, and may serve as a guide in selecting fine pitches until a recognized standard is pro¬ posed and adopted. TABLE XVIII. PROPOSED FINE SCREW-THREAD SYSTEM. Diam¬ eter of Screw. Number of Threads. Diam¬ eter of Screw. Number of Threads. Diam¬ eter of Screw. Number of Threads. Diam¬ eter of Screw. Number of Threads. i 26 i 14 10 21 7 A 24 13 if 9 2f 7 t 22 i 13 if 9 3 7 1V 20 12 11 9 31 6 i 18 1 12 2 8 31 6 A 16 ii 11 21 8 4 6 16 i| 11 2 \ 8 tt 14 if 10 2f 7 38 SMALL TOOLS Standard Proportions for Machine Screws. Finally, we will give our attention to a new standard system for machine screws which promises to gain uni¬ versal recognition. A committee appointed by the Ameri¬ can Society of Mechanical Engineers to investigate the subject of machine screw proportions and to recommend standard specifications for machine screws, made its first report at the December meeting, 1905. Some criticism, however, of this report mado it necessary to call for a second, and what was intended to be a final, report at the May meeting, 1906. In the discussion that fol¬ lowed this report there were, however, several diverging opinions expressed on this subject, and the committee was therefore continued and was supposed to report at the December meeting in the same year. For some reason the report, however, was not accepted by the Association until the Indianapolis meeting in May, 1907. Below are pre¬ sented some of the most important points of consideration in the new standard for machine screws which has been accepted by the American Society of Mechanical Engineers. The standard diameters of machine screws are to be 21 in number. The included angle of the thread is 60 degrees, and the flat at the top and bottom of the thread for the basic standard is one-eighth of the pitch. The uniform increment between all sizes from 0.060 inch to 0.190 inch is 0.013 inch, and for larger sizes 0.026 inch, making the largest size 0.450 inch in diameter. The number of threads is made a function of the diameter as expressed by the formula 6 5 Number of threads per inch = ——- • 1 D + 0.02 This formula, however, gives the results approximately only, as even numbers of threads are chosen in order to avoid fractional or odd numbers. SCREW-THREAD SYSTEMS 39 TABLE XIX. FORMULAS FOR PROPOSED STANDARD FOR MACHINE SCREWS AND TAPS. BASIC STANDARD THREAD, U. S. FORM. T.P.I. = Number of Threads per inch. Screws. Max. external diam. = basic external diam. Max. pitch diam. = basic pitch diam. Max. root diam. = basic root diam. 0 336 Min. external diam. = basic external diam. — m Min. pitch diam. = basic pitch diam. Min. root diam. = basic root diam. T.P.I. +40 0.168 T.P.I. + 40 T0.10825 0.168 "I |_TTj: + T.P.I. + 40_]' Taps. Max. external diam. = basic external diam. Max. pitch diam. = basic pitch diam. 0.10825 0.224 + T.P.I. + T.P.I.+40 ‘ 0.224 + T.P.I.+40' Max. root diam. Min. external diam. basic root diam. + basic external diam. + 0.336 T.P.I. +40* 0.112 T.P.I.+ 40 ’ Min. pitch diam. Min. root diam. = basic pitch diam. = basic root diam. 0.112 + T.P.I.+ 40^ 0.112 + T.P.I.+ 40' In regard to the limits for variation from the basic standard, the maximum screw shall conform practically in all respects to the basic standard. The minimum screw shall have a flat at the bottom of the thread of one-six¬ teenth of the pitch, and the difference between the maxi¬ mum and the minimum root diameter will allow at the bottom of the thread any width of flat between one- sixteenth and one-eighth of the pitch. (See Figs. 11 and 12.) The maximum tap shall have a flat at the top of the thread equal to one-sixteenth of the pitch, and the difference between the maximum and the minimum 40 SMALL TOOLS TOP OF THREAD ■ j *-.000868 Figs. 11 and 12. Machine Screw Thread Standard Adopted by the American Society of Mechanical Engineers; 16 and 72 Threads per Inch SCREW-THREAD SYSTEMS 41 external diameter will allow at the top of the thread any width of flat between one-sixteenth and one-eighth of the pitch. The minimum tap shall conform to the basic standard in all respects except in diameter, as plainly shown in the cuts. The difference between the minimum tap and the maximum screw is settled upon in order to allow for errors in pitch and for the wear of the tap in service. The formulas in Table XIX give the relations between the various dimensions determining the sizes of taps and screws in this standard. TABLE XX. DOUBLE END TEMPLET THREAD GAUGES FOR INSPECTION OF SCREWS. Thickness = vh?itch X 1.443. Threads per Inch. Thickness. Threads per Inch. Thickness. 80 0.161 30 0.263 72 0.170 28 0.273 64 0.180 24 0.295 56 0.193 22 0.308 48 0.208 20 0.323 44 0.217 18 0.345 40 0.228 16 0.361 36 32 0.240 0.255 14 0.385 The reference thread gauges should be made from unhardened steel, 0.35 per cent carbon, and a set should include both reference thread gauges for screws and refer¬ ence thread gauges for taps, each of these to represent the maximum and minimum diameters. Table XX gives the thickness of double end templet thread gauges, for each pitch of the standard screws recommended, for the prac¬ tical inspection of machine screws. The formula Thickness = \/pitch X 1.443 42 SMALL TOOLS provides a limit for the error in lead on screws and taps. These templet thread gauges are to be made of steel, hardened, and being double ended and having maximum and minimum limits, respectively, are to represent at the largest end the pitch and root diameters of the basic stand¬ ard, while at the small end they should represent the minimum limits for the pitch and root diameters of screws. The threads of these templet gauges should be made by taps having the thread enough larger than the standard in the outside diameter to insure clearance at the top of the thread of the screw. In addition to the threaded holes, these gauges should have plain cylindrical holes represent¬ ing, respectively, the external diameter of the maximum and minimum screw. In Chapter IV, tables are given stating all dimensions for taps and screws made according to this system of standard machine screw threads. CHAPTER II. METHODS AND PRINCIPLES OF THREAD-CUTTING. — MEASURING THREADS. Thread-Cutting. Comparison between Usual Methods .— There are two common ways of producing screw threads, cutting the threads in a lathe or cutting them by means of dies. The first method, and the one with which we will deal here, is the one used whenever any greater degree of accuracy of pitch and diameter is desired. By special methods, and by extreme care in making the dies as well as cutting the thread, screws within close limits of accuracy may be produced by means of dies; but for cutting the threads of taps, where any original error or imperfection would be duplicated in all the pieces of work afterward threaded by the tap, the only desirable method is the cutting of the thread in a lathe. All screws of any considerable length must also be cut in this manner, as accuracy in lead can¬ not be insured unless the accuracy of a tested lead screw is duplicated in the piece threaded. Examples have been pointed out where, in using dies for thread cutting, the inaccuracy of ordinary commer¬ cial dies in the pitch has been so great as to cut a thread which, if continued for a foot in length, would have had an error of one-eighth inch in the lead. If the thread is cut with dies by hand there is also a chance for error in the starting of the die. The thread may not be true with the axis of the work, for although most dies intended for use by hand are either themselves provided with a guide 43 44 SMALL TOOLS or mounted so that the piece to be threaded enters a guide before reaching the die, this guide does not always fit the piece closely enough to start the die perfectly true. In all these respects lathe threading is superior, and can¬ not be too strongly recommended in all cases where a thread of good qualities is required. Cutting Screws without the Aid of a Lead Screw. — Because the lead of a screw being cut always depends upon the lead of a thread that has been previously cut, any incorrectness in the master thread (as in a lathe, in the thread of the lead screw) will be reproduced in the screw. For ordinary purposes, the errors in the lead of lead screws of lathes of good manufacture are insignifi¬ cant, but occasions arise when these errors must be taken into consideration. In order to avoid the duplication of errors of this character, Messrs, de Fries & Co., Diissel- dorf, Germany, have designed a new screw-cutting lathe, working on the principle of producing a thread independ¬ ently of a previously cut lead screw. The lathe employed for this purpose is of common design, the feature of extraordinary interest being the arrangement for feeding the carriage; a flexible steel band is used for this purpose instead of the lead screw. This band is located centrally between the two ways of the bed, and one end of the band is fastened to the front end of the carriage, while the other end extends under the head-stock and is fastened to a drum, turned accurately to a definite diameter. When this drum is revolving, the steel band is wound up on it, and thus feeds the carriage. The drum, of course, must be large enough so that the steel band when winding up does not reach fully one complete turn around the drum, because if it reached more than one turn around, the band in winding up on itself would be wound up on a larger diameter than that of the drum, thus causing THREAD-CUTTING — MEASURING THREADS 45 incorrect results. The drum is driven from the cone pulley by means of a worm and worm wheel. For the return, another steel band is fastened to the rear end of the carriage, this band extending to the rear end of the lathe and running over an idle pulley. A counterweight is suspended from this band heavy enough to pull the carriage back when released from the pull at its front end. This lathe is not used for cutting the whole screw from start to finish, but simply for finishing the thread. The arrangement is by its construction too weak to stand up for the heavy cuts necessary for rough thread¬ ing. The thread is therefore cut in an ordinary screw¬ cutting lathe, somewhat over size, and then placed in this special lathe mentioned and there finished. It is claimed that by this machine it is possible to cut the most cor¬ rect thread as yet produced for commercial purposes. Cutting Threads in the Thread Milling Machine. — A method of producing threads which has been but lately brought into more general use is the milling of the thread in special thread milling machines, which, while embodying the principles of a lathe, are provided with a cutter head in place of the lathe tool-post, and a cutter, driven from the countershaft in place of the ordinary tool. As this method contains all the principles which insure accuracy in thread-cutting in a lathe, equally per¬ fect threads will result from milling. The cutting of threads in a thread milling machine is also more economi¬ cal, at least when fairly long threads are to be cut. The thread is milled to its full depth at once, and as the center of the cutter is always at the same height as the center of the work, there is no risk of improper setting of the tool. The only objection that could be advanced is that the cutter head is tilted to the angle of helix of the thread, and consequently, if the same cutter is used for all diam- 46 SMALL TOOLS cters with the same number of threads per inch, the thread form will be slightly inaccurate, owing to the different angles to which the cutter head is tilted. For all ordinary angles of helix, that is, for all diameters provided with a pro¬ portionate pitch, this inaccuracy, however, is so small as to command no consideration. Method of Rolling Threads. — Some manufacturers of taps finish the thread by a process named rolling. The tap is first rough threaded, and afterward passed through These rollers are provided with circular grooves of the same shape as the thread, and in order to insure the cor¬ rect lead, each roller must be cut with its grooves one- third of the pitch in advance of the next preceding roller. All the rollers are mounted in the same horizontal plane if the tap passes through them vertically, or in the same vertical plane if the tap passes through them in a hori¬ zontal direction. What has been said in regard to rolling threads may be better understood by referring to Fig. 13, where the outline of a chuck with three rollers is shown. The pieces A provided with circular grooves are THREAD-CUTTING —MEASURING THREADS 47 the rollers. These are mounted in adjustable blocks B, the back ends of which are tapered to correspond to the taper of the ring C, which encloses the whole arrange¬ ment and serves the purpose of providing for the adjust¬ ment. By screwing the ring C down, the rollers are evidently pushed toward the center of the chuck, and screwing the ring up permits the rollers and the blocks to recede. The blocks, when adjusted, are held in posi¬ tion in relation to the center line of the body D by means of binding screws entering from the front face at an angle of 45 degrees and binding in grooves in the blocks. This arrangement is used for rolling smaller taps. For larger ones the ring C is eliminated, and the rollers are mounted in blocks, adjustable by screws in a similar manner to the jaws in universal chucks. This manner of finishing tap threads is very economical, and the tap thread fills all reasonable requirements. It is particu¬ larly of advantage for finishing taps with thread forms having radii at top and bottom, as it saves the necessity of complicated thread tools, the roughing operation taking no account of the round at top and bottom, this being impressed in the tap by the rollers when finishing. One special way of producing threads by rolling, which, however, can hardly be considered as directly concerning the tool-maker, is the process of rolling threads on rough wire or forged blanks without previous rough threading. The blank is then rolled between two dies or blocks having grooves of the right pitch, form, and angle of lead, and the thread is formed by displacement of the metal, which causes the finished screw to be larger in diameter than the blank. One die is usually stationary, while the other has a reciprocating motion. A device of this description, intended to be used for thread-rolling on a punch press, was shown by Mr. S. 48 SMALL TOOLS Oliver in the July, 1907, issue of Machinery. In Fig. 14, A is a punch holder to fit the punch press. B is the bolster, or a piece of cast iron about 1 inch thick, upon which are located two cast-iron blocks, one made station¬ ary and the other adjustable by slotting B, so that the block can be forced ahead by the set screw C. There is a groove in the stationary block and a tongue in the punch holder A to prevent the dies from getting out of Fig. 14. Device for Thread-Boiling in a Punch Press line. The screw D is for holding a thin piece of steel as a stop so that the thread can be cut to the desired length. The screw E holds a wire supporting the piece to be threaded until the upper die, F, comes down and carries it past the lower die, G. In cutting the die, it may be made in one piece, H being the circumference of the thread to be rolled and G x the desired length for the lower die. F x is the desired length for the upper die, which must be longer than the lower die so that it will roll the wire past the die THREAD-CUTTING —MEASURING THREADS 49 G and permit it to drop out of the way. The part K must be cut out when cutting in two parts. The proper angle to which to cut the die depends on the pitch of the thread. The pitch divided by the circumference of the screw to be rolled will give the tangent of the angle. In cutting the die, which must be of good tool steel and hardened after making, the shaper is used. The cut is taken with a tool that can be taken off and put back again without changing its location, such a tool, for instance, as a circular threading tool. In case the point should happen to get dull, the tool can then be removed for grinding. If the feed screw should not have the desired graduations on it, a brass index plate can be made very quickly and used on the machine. The brass plate should be of a good size and cut accurately in a milling machine, and a pointer clamped on the shaper. Cutting Threads by Rapidly Revolving Hardened Disk. — An interesting method for producing threads was shown in the January, 1908, issue of Machinery, by Mr. Oskar Kylin. In Fig. 15 this method is illustrated. It is used for threading studs, pins, etc., of manganese steel, this material being so hard that it cannot be cut by any kind of tool steel. A plain, hardened tool-steel disk, hav¬ ing the edge made according to the angle of thread, is employed. This disk is revolved at a high speed, and at the same time forced into the work, which is revolved slowly. Due to the friction between the edge of the disk and the work, and the softening of the material, owing to the heat generated by the friction, the disk wears away the stock and by means of this creates the thread. The stock is coming off in very small, thin scales like chips, which to some extent remind one of the scales of a fish. An ordinary lathe has been rigged up for the purpose by removing the tool-post and top rest and 50 SMALL TOOLS substituting for them the fixture shown in the cut. The disk must be driven independently by an overhead drum or some similar arrangement. The peripheral speed of the disk is usually between 3000 and 4000 feet per minute. The operation is unavoidably slow and expensive, and the method is used only when no other way is possible. Cutting Threads in the Lathe. — Having mentioned the most common methods for producing threads we will now review the fundamental principles of cutting threads in the Fig. 15. Cutting Threads by a Rapidly Revolving Disk lathe. While well known to all mechanics, it is necessary to dwell upon this question to some extent in order to complete the subject in hand. Determining the Change Gears for Thread-Cutting. The determining of the change gears for gearing the lathe to cut the desired thread seems to be a never decreasing source of difficulty. Of course, all lathes are now provided with a gear-cutting index for gearing the lathe to cut standard threads. When it is required, how- THREAD-CUTTING — MEASURING THREADS 51 ever, to determine the change gears for an odd or a frac¬ tional pitch, many a man otherwise efficient is at a loss. While the principles and rules governing the calculation of change gears are very simple, they of course pre¬ suppose some fundamental knowledge of the use of com¬ mon fractions. If such knowledge is at hand, the subject of figuring change gears, if once thoroughly understood, can hardly ever be forgotten. It should be impressed upon the minds of all who have found difficulties with this subject that the matter is not approached in a logi¬ cal manner, and is usually grasped by the memory rather than by the intellect. Before answering the question in regard to any rules for figuring change gears, let us there¬ fore analyze the subject. The lead screw B of the lathe (see Fig. 16) must be recognized as our first factor, and the spindle as the second. If the lead screw has six threads per inch, then, if the lead screw makes six revolutions, the carriage travels one inch, and the thread-cutting tool travels one inch along the piece to be threaded. If the spindle makes the same num¬ ber of revolutions in a given time as the lead screw, it is clear the tool will cut six threads per inch. In such the spindle stud J, and gear E on the lead screw, are alike. If the spindle makes twice the number of revolutions of the lead screw, the spindle revolves twelve times while the tool moves one inch, and conse¬ quently twelve threads per inch will be cut. But in order to make the spindle revolve twice as fast as the Fig. 16. Simple Gearing a case the gear D on 52 SMALL TOOLS lead screw, it is necessary that a gear be put on the spindle stud of only half the number of teeth of the gear on the lead screw, so that when the lead screw revolves once the spindle-stud gear makes two revolutions. Simple Gearing. Suppose we wish to cut nine threads per inch with a lead screw of six threads per inch, as referred to above. Then the six threads of the lead screw correspond to nine threads on the piece to be threaded, which is the same as saying that six revolutions of the lead screw correspond to nine revolutions of the spindle; or in other words, one revolution of the lead screw corresponds to 1| of the spindle. From this it is evident that the gear on the lead screw must make only one revolution while the spindle-stud gear makes 1J. Thus, if the lead-screw gear has, for instance, 36 teeth, the gear on the spindle stud should have only 24, the smaller gear, of course, revolving faster than the larger. If we express what has been pre¬ viously said in a formula we have threads per inch of lead screw _ teeth in gear on spindle stud threads per inch to be cut teeth in gear of lead screw Applying this to the case above, we have 6 = 24 9 36’ The values 24 and 36 are obtained by multiplying 6 and 9, respectively, by 4. By multiplying both the numerator and the denominator by the same number we do not change the proportion. As a general rule we may then say that the change gea~s necessary to cut a certain num¬ ber of threads per inch are found by placing the number of threads in the lead screw in the numerator, the num- THREAD-CUTTING — MEASURING THREADS 53 ber of threads to be cut in the denominator, and then multiplying numerator as well as denominator by the same number, by trial, until two gears are obtained the numbers of teeth of which are both to be found in the set of gears accompanying the lathe. The gear with the number of teeth designated by the new numerator is to be placed on the spindle stud (at J, Fig. 16), and the gear with the number of teeth corresponding to the denominator on the lead screw B. A few examples of this will more clearly explain the rule. Suppose the number of teeth of the change gears of a lathe are 24, 28, 32, 36, and so forth, increasing by 4 teeth up to 100. Assume that the lead screw is pro¬ vided with 6 threads per inch, and that 10 threads per inch are to be cut. Then _6 = 6X4 = 24 10 10X4 40 By multiplying both numerator and denominator by 4 we obtain two available gears with 24 and 40 teeth, respectively. The 24-tooth gear goes on the spindle stud, and the 40-tooth gear on the lead screw. . Assuming the same lathe and gears, let us find the gears for cutting 11J threads per inch, this being the standard number of threads for certain sizes of pipe thread. Then _6_ = 6X8 = 48 Hi lli X 8 92* It will be found that multiplying by any other number than 8 would not, in this case, have given us gears with such numbers of teeth as we have in our set with this lathe. Until we get accustomed to figuring of this kind, we can, of course, only by trial find out the correct number by which to multiply numerator and denominator. 54 SMALL TOOLS The number of teeth in the intermediate gear F, Fig. 16, which meshes with both the spindle-stucl gear and the lead-screw gear, is of no consequence. Lathes with Reduction Gearing in Head-Stock. In some lathes, however, there is a reduction gearing in the head-stock of the lathe, so that if equal gears are placed on the lead screw and the spindle stud, the spindle does not make the same number of revolutions as the lead screw, but a greater number. Usually in such lathes the ratio of the gearing in the head-stock is 2 to 1, so that with equal gears the spindle makes two revolutions to one of the lead screw. This is particularly common in lathes intended for cutting fine pitches or, in general, in small lathes. In figuring the gears this must, of course, be taken into consideration. As the spindle makes twice as many revolutions as the lead screw with equal gears, if the ratio of the gears be 2 to 1, that means that if the head-stock gearing were eliminated, and the lead screw instead had twice the number of threads per inch as it has, with equal gears the spindle would still revolve the same as before for each inch of travel along the piece to be threaded. In other words, the gearing in the head- stock may be disregarded if the number of threads of the lead screw is multiplied by the ratio of this gearing. Sup¬ pose, for instance, that in a lathe the lead screw has eight threads per inch, that the lathe is geared in the head- stock with a ratio of 2 to 1, and that 20 threads are to be cut. Then 2X8 = 16 = 16_ X± = 64 20 20 20 X-4 80 ’ which two last values signify the numbers of teeth in the gears to use. THREAD-CUTTING — MEASURING THREADS 55 Sometimes the ratio of the gearing in the head-stock cannot be determined by counting the teeth in the gears, because the gears are so placed that they cannot be plainly seen. In such a case, equal gears are placed on the lead screw and the spindle stud, and a thread cut on a piece in the lathe. The number of threads per inch of this piece should be used for the numerator in our calculation instead of the actual number of threads of the lead screw. The ratio of the gearing in the head-stock is equal to the ratio between the number of threads cut on the piece in the lathe and the actual number of threads per inch of the lead screw. Compound Gearing. The cases with only two gears in a train referred to are termed simple gearing. Sometimes it is not possible to obtain the correct ratio excepting by introducing two more gears in the train, which, as hardly need be mentioned, is termed com¬ pound gearing. This class of gearing is shown in Fig. 17. The rules for figuring com¬ pound gearing are exactly the same as for simple gearing excepting that we must divide both our numerator and de¬ nominator into two factors, each of which is multiplied by the same number in order to obtain the change gears. Suppose a lathe has a lead screw with six threads per inch, that the numbers of the teeth in the gears available are 30, 35, 40, and so forth, increasing by 5 up to 100. 56 SMALL TOOLS Assume that it is desired to cut 24 threads per inch. We have then By dividing up the numerator and denominator into factors, and multiplying each pair of factors by the same number, we find the gears: 6 _ 2 x 3 _ (2 X 20) X (3 X 10) _ 40 X 30 24 4 X 6 (4 X 20) X (6 X 10) 80 X 60 ' The last four numbers indicate the gears which should be used. The upper two, 40 and 30, are driving gears, the lower two, with 80 and 60 teeth, are driven gears. Driv¬ ing gears are, of course, the gear D, Fig. 17, on the spindle stud, and the gear P on the intermediate stud K, meshing with the lead-screw gear. Driven gears are the lead- screw gear, E, and the gear N on the intermediate stud, meshing with the spindle-stud gear. It makes no differ¬ ence which of the driving gears is placed on the spindle stud, or which of the driven is placed on the lead screw. Suppose, for a final example, that we wish to cut If threads per inch on a lathe with a lead screw having six threads per inch, and that the gears run from 24 and up to 100 teeth, increasing by 4. Proceeding as before we have _6 = 2 X 3 = (2 X 36) X (3 X 16) = 72 X 48 If 1 X If (1 X 36) X (If X 16) 36 X 28 ’ This is the case directly illustrated in Fig. 17. The gear with 72 teeth is placed on the spindle stud J, the one with 48 on the intermediate stud K, meshing with the lead-screw gear. These two gears (72 and 48 teeth) are the driving gears. The gears with 36 and 28 teeth are placed on the lead screw and on the intermediate stud, as shown, and are the driven gears. THREAD-CUTTING — MEASURING THREADS 57 Fractional Threads. Sometimes the lead of the thread is expressed by a fraction of an inch instead of stating the number of threads per inch. For instance, a thread may be required to be cut having a three-eighths-inch lead. In such a case the expression “three-eighths lead” should first be transformed to “number of threads per inch,” after which we can proceed in the same way as has already been explained. To find how many threads per inch there is when the lead is stated, we simply find how many times the lead is contained in one inch, or, in other words, we divide one by the given lead. Thus one divided by three- eighths gives us 2§, which is the number of threads per inch of a thread having three-eighths-inch lead. To find change gears to cut such a thread we would proceed as follows: Assume that the lead screw has 6 threads per inch and that the change gears run from 24 up to 100 teeth, increasing by 4. Proceeding to find the gears as before we have _6_ = 2 X 3 = (2 X 36) X (3 X 24) = 72 X 72 2§ 1 X 2§ (IX 36) X (2§ X 24) 36 X 64 * The rule for finding the number of threads per inch, when the lead is given, may be expressed by the formula number of threads per inch 1 lead of thread What has been said in the foregoing in regard to the figuring of change gears for the lathe may be summed up in the following rules: 1. To find the number of threads per inch if the lead of a thread is given, divide one by the lead. 58 SMALL TOOLS 2. To find the change gears used in simple gearing, when the number of threads per inch on the lead screw and the number of threads per inch to be cut are given, 'place the number of threads on the lead screw as numerator and the number of threads to be cut as denominator in a fraction, and multiply numerator and denominator by the same number until a new fraction results representing suitable numbers of teeth for the change gears. In the new fraction, the numera¬ tor represents the number of teeth on the spindle stud, and the denominator the number of teeth in the gear on the lead screw. 3. To find the change gears used in compound gearing, place the number of threads per inch on the lead screw as numerator and the number of threads per inch to be cut as denominator in a fraction, divide up both numerator and denominator into two factors each, and multiply each pair of factors (one factor in the numerator and one in the denomi¬ nator making “a pair”) by the same number until new fractions result representing suitable numbers of teeth for the change gears. The gears represented by the numbers in the new numerators are driving gears, and those in the denominators are driven gears. Cutting Metric Threads with an English Lead Screw. It often happens that screws or taps having threads cut according to the metric system are required. The lead of these screws is expressed in millimeters. Thus, instead of saying that a screw has so many threads per inch, it is said that the screw has so many millimeters lead. Sup¬ pose, for example, that we have a lathe having a lead screw with 6 threads per inch, and that a screw with 3 millimeters lead is required to be cut. We can find the change gears to be used in the same manner as has been previously explained THREAD-CUTTING — MEASURING THREADS 59 for screws cut according to the English system, if we only first find out how many threads per inch we will have if we cut a screw with a certain lead given in millimeters . Thus, in this case, we must find out how many threads there will be in one inch if we cut a screw with 3 millimeters lead. There are 25.4 millimeters to one inch, so that, if we find out how many times 3 is contained in 25.4, we evidently get the number of threads in one inch. To find out how many times 3 is contained in 25.4, we divide 25.4 by 3. It is not necessary to carry out the division. We can 25 4 simply write it as a fraction in the form this then being O the number of threads per inch. We now proceed as if we had to do only with English threads. We place the number of the threads on the lead screw in the lathe as the numerator in a fraction, and the number of threads to be cut, which number is expressed by the fraction denominator. Then we have 25.4 3 •, as the 6 25.4 * 3 This seems very complicated, but as we remember that the line between the numerator and the denominator in a fraction really means that we are to divide the numerator by the denominator, then if we carry out this division we get 25.4 = 6X3 = _18_ 3 25.4 25.4' If we now proceed as in the case of figuring change gears for any number of threads per inch we multiply numerator and denominator by the same number until we find suitable numbers of teeth for our gears. In the 60 SMALL TOOLS case above we can find by trial that the first number by which we can multiply 25.4 so that we get a whole num¬ ber as result is 5. Multiplying 25.4 by 5 gives us 127. This means that we must have one gear with 127 teeth whenever we cut metric threads by means of an English lead screw. The gear to mesh with the 127-teeth gear in this case has 90 teeth, because 5 times 18 equals 90. If we summarize what we have just said in rules, we would express them as follows: 1. To find the number of threads per inch, when the lead is given in millimeters, divide 25.4 by the number of millimeters in the given lead. 2. To find the change gears for cutting metric threads with an English lead screw, place the number of threads per inch in the lead screw multiplied by the number of milli¬ meters in the lead of the thread to be cut as the numerator of a fraction and 25.4 as the denominator, and multiply numerator and denominator by 5. The numerator and denominator of the new fraction are the gears to be used. These same rules expressed in formulas would be 25.4 number of threads per inch = .— -r-. - —— — r lead in millimeters and number of threads per lead in millimeters g inch in lead screw x of screw to be cut gear on spindle stud. 25.4 x 5 “ gear on lead screw Of course it is sometimes necessary to compound the gears, because the gear on the spindle stud would other¬ wise get too many teeth, that is, would be too large. Sup¬ pose, for an example, that we wish to cut a screw having 6 millimeters lead on a lathe having a lead screw with 8 threads per inch. According to our rule and formula the gear on the spindle stud would then have 8x6x5, or 240 teeth. As no lathe is provided with a change gear THREAD-CUTTING —MEASURING THREADS 61 with so many teeth, we must use compound gearing. In this case we would proceed as follows: 8 X 6 X 5 = 48 X 5 = 48 X 120 25.4 X 5 127 x 1 127 x 24’ which is exactly the same method as has already been explained under the head of compound gearing in con¬ nection with the figuring of change gears for English v screws. The method of mounting these gears is shown in the diagram, Fig. 18. What should in particular be impressed upon the mind of the student is that there is no difference in method of figuring the gears whether the thread to be cut is given in the English or in the metric system. If given in the latter system, simply transform the “lead in mil¬ limeters” to “number of threads per inch” and pro¬ ceed in exactly the same way as if the thread had been given according to the English system. The 127-tooth gear is alw when cutting metric threads placed on the lead screw i an English lead screw. Cutting an English Thread with a Metric Lead Screw. The method of figuring the change gears for a case where an English screw is to be cut by a metric lead screw is simply the reverse of the one already explained. We 62 SMALL TOOLS simply transform the millimeter lead of the metric lead screw into “ number of threads per inch.” This we do in the same way as explained before, by dividing 25.4 (which is the number of millimeters in one inch) by the number of millimeters in the lead of the metric lead screw. After having obtained this number of threads per inch, we proceed as usual, putting the number of threads per inch of the lead screw in the numerator and the number of threads per inch to be cut in the denominator of a fraction, simplifying the fraction, and multiplying numer¬ ator and denominator by 5 to get the number of teeth in the change gears. Suppose, for example, that we wish to cut 5 threads per inch with a lead screw having ,4 millimeters lead. The number of threads per inch of the lead screw is then 25 4 , and we find our gears by writing our fraction 25.4 4 5 This fraction can be simplified by actually dividing as a result. 25.4. K . , . , , 25.4 ——- by 5, m which case we get 5X4 Multiplying both numerator and denominator by 5 gives us then 25.4 X 5 _ 127 5X4X5“ 100’ which gives us the numbers of teeth in our change gears. The formula expressing this calculation would take this form: 25.4 x 5 gear on spindle stud number of threads iead in millimeters g gear on lead screw per inch to be cut ' of lead screw ° THREAD-CUTTING—MEASURING THREADS 63 Expressed as a rule this formula would read: To find the change gears for cutting English threads on a metric lead screw, place 25.4 as the numerator and the threads per inch to he cut multiplied by the number of milli¬ meters in the lead of the lead screw in the denominator of a fraction, and multiply numerator and denominator by 5. The numerator and denominator of the new fraction are the change gears to be used. In this case too, of course, it sometimes becomes neces¬ sary to compound the gears, in order to get gears which are to be found in the set of gears provided with the lathe. Sometimes the gears may be available, but they are so large that the capacity of the lathe does not permit them to be placed in a direct train; then, also, it becomes necessary to compound the gears. Take the case which we have already referred to, where we were to cut a screw with 5 threads per inch, using a lead screw having 4 milli¬ meters lead. We then obtained the gears with 127 and 100 teeth respectively. Now suppose that the lathe does not possess a change gear with 100 teeth to be placed in a direct train. The gears to be used in a compound train would then have to be found as has already been described and as shown in the following calculation: 25.4 X 5 127 127 X 1 _ 127 X 25 5 X 4 X 5 100 50 X 2 50 X 50 ’ The 127-tooth gear is always put on the spindle stud when cutting English screws with a metric lead screw. A diagram of the arrangement of the gears in the last example is shown in Fig. 19. If there is any special reduction gearing in the head of the lathe, this must of course be taken into consideration, in the manner already described under the heading “ Lathes with Reduction Gearing in Head-Stock.” 64 SMALL TOOLS For those who prefer formulas to rules expressed in words the whole previous discussion may be simply stated screw in millimeters and C is inch of same lead screw, then as follows: Let us first take the case of an English thread to be cut on a lathe pro¬ vided with a metric lead screw. As there are 25.4 millimeters in one inch, the number of threads per inch on the metric lead screw equals 25.4 divided by the pitch of the lead screw expressed in milli¬ meters; in other words, if a is the pitch of the lead the number of threads per C = 25A . a Let c be the number of threads per inch to be cut on the piece to be threaded; then the ratio of the change gears is C = 25.4 -f- a _ 25.4 c c a X c Change gears conforming to this ratio will cut an exactly correct pitch. Multiply both denominator and numera¬ tor by 5, thus making the formula read 127 5aX c Thus it will be seen that if a gear with 127 teeth is introduced in the train of gears and other gears are selected, as indicated by the values a and c, the correct change gears can be found without any trouble whatever. THREAD-CUTTING —MEASURING THREADS 65 Let us assume for an example that the pitch of the lead screw (a) equals 4 millimeters, and that 5 threads per inch (c) are to be cut. Then the ratio of gears = 127 20 X 5 127 driver. 100 driven. If the lathe has a capacity of taking a 127- and 100- tooth gear in a direct train, these gears are used; other¬ wise, gears have to be compounded, and it is readily seen that trains of gears composed as follows: drivers 127 - 24. 40 - 60’ driven drivers 127 - 30 . 50 - 60’ driven drivers 127 - 32. 64 - 50’ driven and many other combinations will serve the purpose, the gears above being such as generally go with any lathe. The 127-tooth gear in this case ought to be mounted on the spindle stud. If we now take the case of a metric thread to be cut on a lathe provided with an English lead screw, we will find a formula for the ratio in the same manner. Suppose d — the number of threads per inch on the lead screw, e — the pitch in millimeters on the screw to be cut, and / = the number of threads per inch of same screw. Then referring to what has previously been said, / = and the ratio of the change gears ~ = e J d 25.4 -h e d X e _ 5d X e 25.4 _ 127 Then, as before, it will be readily seen that even in this case a gear with 127 teeth is necessary, and no other gear can replace it, either in the first case or in this, 66 SMALL TOOLS as 127 is a 'prime factor. In order to illustrate this for¬ mula with an example, let us assume that the lead screw has 8 threads per inch (d), and that a screw with 6 milli¬ meters pitch (e) is to be cut. The ratio of gears is then 40 X 6 127 * and trains of gears composed as follows: drivers 96 - 90 . 127 - 36’ driven drivers 100 - 60 . 127 - 25’ driven drivers 80 - 75 . 127 - 25’ driven and others can be used in this case. Of course the 127- tooth gear ought to be mounted on the screw in this case. General Principles of Thread-Cutting. The operations for cutting a thread are shortly as fol¬ lows. The first step is to turn to the exact outside diameter. This of course is more or less modified in the case of taps, which are often wanted to be a trifle over-size. When turning a blank to be threaded with Whitworth thread, or with any thread form with a round top, the piece should be turned from 0.002 inch over-size for quarter-inch size to 0.004 inch for 1-inch size to insure that the rounded form shall be perfect on the top of the threads. In cutting the thread, the threading tool, which will be treated in detail later, is of course the first consideration. If the tool is correct in itself, it must also, in order to produce a correct thread, be set square with the axis of the work, which is done by a thread gauge. The height of the top face of the tool should be exactly at the same height as the center line of the piece to be threaded. If it is not, the form of the thread will not be correct even if the thread THREAD-CUTTING—MEASURING THREADS 67 tool be perfect, inasmuch as the latter must be duplicated in a plane through the center of the piece to be threaded. The thread is cut by successive small cuts; the last or finishing cuts should be made with a very fine feed to insure a smooth surface of the thread. A thin lubricant of lard oil and turpentine is excellent for thread-cutting. Mr. F. E. Shailor, in Machinery, March, 1907, says that when meeting with difficulty in obtaining a smooth thread, such as is required for screw gauges and taps, one good way to obtain a smooth thread is to turn the tap nearly to size and harden it, then draw the temper to a “ light blue.” When turning to size, if the tool does not stand up well, draw still lower, the object being to leave just enough temper in the tap to make the steel firm. By making light chips with a hard thread tool a glossy, smooth thread will result. Another advantage gained by hardening the tap before finishing is that it will greatly eliminate the chances of the lead changing after the final hardening. It is, however, not advisable to follow this practice except in certain cases when a smooth thread is the very highest object desired, because it is well known that steel will, as a rule, lose its qualities of endurance and strength by successive hardening and annealing. Multiple Threads. — Multiple threads, double, triple, etc., are used in cases where a quick lead is required but a deep thread is not desirable. It may be that the diameter of the screw is so small, comparatively, that a deep thread would seriously impair its strength or be entirely impos¬ sible. Two, three, or more threads of less depth but with the same lead as the coarse thread may then be substituted. This condition is plainly illustrated in the upper part, A, of Fig. 20. The lead of a multiplertbreaded screw is the distance it will travel in the nut for one turn of the screw, or in other words, the distance from 68 SMALL TOOLS center to center of the same thread. The pitch is the distance from center to center of adjacent threads (see Fig. 20). A great deal of confusion has always existed in regard to the correct way to designate a multiple-threaded Fig. 20. Single and Multiple Threads screw. The safest way is to state the lead and the class of thread, whether double or triple, etc. Thus, one-quarter- inch lead, double, means a screw with double thread, which, when cut, has the lathe geared for 4 threads per inch, but THREAD-CUTTING —MEASURING THREADS 69 each thread is cut only to a depth corresponding to 8 threads per inch. This same condition is also expressed by 4 threads per inch, double. These two ways of expressing the number of multiple threads are both correct, but the former is always the safer to use in order to avoid misunder¬ standings, provided of course that the word “lead” is used and understood in its correct sense. A way of expression which under no circumstances could be misunderstood, and if misunderstood, would be inexcusable, would be to say: one-quarter lead, one-eighth pitch, double thread. When cutting a multiple thread it is obvious that the lathe must be geared the same as if cutting a single thread of the same lead as the multiple one. One thread is then cut at a time, and the tool advanced after each thread an exact amount corresponding to the pitch of the screw, by disconnecting the spindle and the lead screw; the other thread is then cut independently of the first, and so forth. Multiple threads are cut even more advantageously by means of chasers having several teeth. In such a case there is no need of advancing the thread tool, as all the threads will be cut at once. The lathe must be geared, of course, to correspond to the lead of the screw to be cut, not to the pitch of the chaser. If the latter were done, a single- threaded screw would evidently result. Measuring Threads. When the thread of a screw or a tap is cut, the necessary measuring or gauging of the outside diameter as well as of the angle diameter, and the testing of the lead, is commonly the next thing required if accuracy is of importance. The outside diameter can be measured by ordinary micrometers. The angle diameter, which is the most important, must be measured by special means. 70 SMALL TOOLS Brown and Sharpe Thread Micrometers. — The Brown and Sharpe Manufacturing Company are the originators of a system of measuring the angle diameters of taps by means of a special micrometer shown in Fig. 21. The fixed anvil is V-shaped so as to fit over the thread, while the movable point is cone-shaped so as to enable it to enter the space between two threads and at the same time be at liberty to revolve. The contact points are on the sides of the thread, as they necessarily must be if it is the angle diameter which is to be determined. The cone- rig. 21. Brown and Sharpe Thread Micrometer shaped point of the measuring screw is slightly rounded so as to insure that the point will not bear in the bottom of the thread; there is also provision for sufficient clearance at-the' bottom of the V-shaped anvil to prevent the top of the thread bearing at this point. Considering this, it is evident that the actual outside diameter of a screw or a tap has no influence upon the reading of the micrometer, and as screws, at least those made according to the United States standard system, are not intended to bear upon the top of the thread when screwed into a nut, but upon the angular sides, it is obvious THREAD-CUTTING —MEASURING THREADS 71 that measuring in this manner constitutes the only real test of the size of a screw or tap. As we measure one-half of the depth of the thread from the top, on each side, the diameter of the thread as indicated by the micrometer, or the pitch diameter, is the full size of the thread less the depth of one thread. Referring to Fig. 22, when the point and anvil are in contact, zero on the micrometer barrel represents a line drawn through the plane AB, and if the caliper is opened, say to 0.500, it represents the distance of the two planes 0.500 inch apart. While the movable point measures all pitches, the fixed anvil is limited in its capacity, for if made large enough to measure eight threads per inch it would be too wide at the B i'ig. 22. Principle of Brown and Sharpe Thread Micrometer top to measure twenty threads per inch, and if made to measure twenty threads per inch it would be so small that the coarser thread would not obtain a proper bearing in the anvil. The Y anvil swivels, however, and therefore adapts itself automatically to different angles of helix of the thread. The only criticism that might be advanced in regard to this tool is that the Y anvil has flat sides, which, when pressed against the helical surface of the screw thread, will theoretically cause an over-size reading. This point was not lost sight of in designing this tool, but the difference between the micrometer reading and the theoretically correct figure is so slight as to permit of being wholly disregarded in practical work. 72 SMALL TOOLS To find the theoretical angle diameter, which is measured by the micrometer, one subtracts the depth of the thread from the standard outside diameter. The depths of the threads for all United States, V, and Whit¬ worth standard threads were given in the first chapter. In Tables XXI and XXII in this chapter are given the angle diameters for all standard United States and V thread screws, that is, the reading of the Brown and Sharpe thread micrometer if the screw or tap is correct. TABLE XXI. ANGLE DIAMETERS (BROWN AND SHARPE THREAD MICROMETER READING) FOR UNITED STATES STANDARD SCREWS. Diam¬ eter of Screw. Thrds. per Inch. Angle Diameter. Diam¬ eter of Screw. Thrds. per Inch. Angle Diameter. Diam¬ eter of Screw. Thrds. per Inch. Angle Diameter. A 64 0.0524 A 9 0.8653 2 41 1.8557 A 50 0.0807 l 8 0.9188 21 41 1.9807 I 40 0.1088 i A 7 0.9697 2} 41 2.1057 A 36 0.1382 4 7 1.0322 2§ 4 2.2126 A 32 0.1672 i A 7 1.0947 21 4 2.3376 A 28 0.1955 U 7 1.1572 2f 4 2.4626 1 20 0.2175 i A 6 1.2042 2f 4 2.5876 A 18 0.2764 if 6 1.2667 2f 31 2.6894 i 16 0.3344 i A 6 1.3292 3 31 2.8144 A 14 0.3911 H 6 1.3917 31 31 2.9394 1 13 0.4500 i A 51 1.4444 31 31 3.0644 A 12 0.5084 4 51 1.5069 3f 31 3.1751 * 11 0.5660 itt 51 1.5694 31 31 3.3001 A 11 0.6285 4 5 1.6201 3f 31 3.4251 i 10 0.6850 m 5 1.6826 3| 3 3.5335 A 10 0.7475 4 5 1.7451 3f 3 3.6585 9 0.8028 5 1.8076 4 3 3.7835 Ball-Point Micrometers. — If one has standard plug gauges on hand, and it is thus not necessary to actually measure the angle diameter but merely compare it with the standard gauge, a ball-point micrometer, such THREAD-CUTTING —MEASURING THREADS 73 TABLE XXII. ANGLE DIAMETERS (BROWN AND SHARPE THREAD MICROMETER READING) FOR STANDARD SHARP V-THREAD SCREWS.* Diam¬ eter of Screw. Thrds. per Inch. Angle Diameter. Diam¬ eter of Screw. Thrds. per Inch. Angle Diameter. Diam¬ eter of Screw. Thrds. per Inch. Angle Diameter. 72 0.0505 it 9 0.8413 2 44 1.8075 56 0.0783 l 8 0.8917 2ft 44 1.9325 i 40 0.1033 1 Vo 8 0.9542 24 44 2.0575 32 0.1292 7 1.0013 2* 44 2.1825 24 0.1514 iA 7 1.0638 24 4 2.2835 24 0.1826 H 7 1.1263 2ft 4 2.4085 4 20 0.2067 l* 7 1.1888 24 4 2.5335 A 18 0.2644 if 6 1.2307 2f 4 2.6585 4 16 0.3209 iA 6 1.2932 3 34 2.7526 A 14 0.3756 14 6 1.3557 3ft 34 2.8776 4 12 0.4278 iA 6 1.4182 34 34 3.0026 A 12 0.4903 if 5 1.4518 34 34 3.1085 ft 11 0.5463 itt 5 1.5143 34 34 3.2335 ft* 11 0.6088 if 5 1.5768 34 34 3.3585 4 10 0.6634 lit 5 1.6393 34 3 3.4613 44 10 0.7259 if 44 1.6825 3ft 3 3.5863 ft 9 0.7788 iff 44 1.7450 4 3 3.7113 as shown in Fig. 23, is all that is necessary. The balls, which are made in one piece with stems which are Fig. 23. Bail-point Micrometer for Comparing Angle Diameters * The figures given are for the theoretical angle diameter. If the sharp V-thread for practical purposes is provided with a flat on the top of the thread, the figures for the angle diameter, as given, should be increased by an amount equal to width of flat x 1.732. 74 SMALL TOOLS inserted in the anvil and the face of the measuring screw respectively, are made in certain sizes corresponding each to a certain series of pitches. It is evident that as the object is not measuring but only comparing the angle diameters, there is no need of the balls being in any exact relation to the pitch, nor does one need a certain size of ball for each pitch of thread. A certain relation between the size of the ball points and the pitch of the thread, however, must be maintained, inasmuch as the Fig 24. Determining the Size of Ball Points ball point used for a certain pitch must not be so large as to bear only at the top or edge of the thread and not on the sides, nor be so small as to tangent the flat in the bottom of the thread. The most desirable size of ball point would of course be one that would tangent the sides of the thread at the angle diameter as shown in Fig. 24. The diameter of such a ball for the United States or V standard threads is easily figured. If the point of tangent, A, is located at the angle diameter of the thread, the line AB equals one-half the pitch. The radius AC of the ball point THREAD-CUTTING — MEASURING THREADS 75 equals two times CD, if we consider only 60-degree threads, the angle DAC then being 30 degrees. Conse¬ quently, if d is the diameter of the ball point and p the pitch of the thread, consequently CD = AD X tan 30°, CD = 7 ; AD = 4 - = ^X tan 30°, or d = p X tan 30°. 4 4 From this we see that the best size of ball point for a certain pitch is a diameter equal to 0.577 times the pitch. But ball points may be used that are only about one- third of the pitch or that are as large as to be 0.8 times the pitch in diameter. In Table XXIII are given the sizes of balls suitable for the most common numbers of threads per inch. This table applies to threads of United States standard and sharp V form. TABLE XXIII. BALL POINTS FOR MICROMETERS FOR COMPARING ANGLE DIAMETERS. "Threads per Inch. Diameter of Ball. Threads per Inch. Diameter of Ball. 24 0.022 9 0.060 22 0.025 8 0.070 20 0.028 7 0.080 18 0.030 6 0.090 16 0.035 51 0.100 14 0.035 5 0.110 13 0.040 4£ 0.120 12 0.045 4 0.130 11 0.050 31 0150 10 0.055 3 0.170 76 SMALL TOOLS Three-Wire System for Measuring Threads. —A method for measuring very correctly the angle diameter by means of ordinary micrometers and three wires of equal dia¬ meter has long been known. In this system three wires are used as shown in Fig. 25, one wire being placed in the angle of the thread on one side of the piece and the other two on the opposite side, one on each side of the corre¬ sponding thread, measuring over the whole with a microm- Fig. 25. Measuring Threads by the Three-Wire System eter. The formula for the micrometer reading is obtained as follows: In Fig. 26 assume that m is the bottom of a V thread, the circle showing one wire in place. Then angle a = 30°; sin 30° = 0.5; = mn or 2 no = mn. As no U.5 and np are radii of the same circle, it follows that i mp = 3 no = 1^ x diameter of wire. Multiplying by 2 to add a length mp for the opposite THREAD-CUTTING — MEASURING THREADS 77 side gives 2 mp = 3 X diameter of wire. Hence for V thread, Diameter of screw — - T - ,, - t— r number or threads per inch + (3 X diameter of wire used) = micrometer reading. For United States form we have to take into account the flat at the bottom of the thread, so instead of using the United States constant 1.299 we' add to it one-eighth Fig. 26. Deducing the Formula for the Micrometer Reading of 1.732, or 0.2165, giving as a constant 1.5155, making the formula Diameter of screw 1.5155 number of threads per inch + (3 X diameter of wire used) = micrometer reading. These formulas may be expressed in a shorter form by denoting the measurements as follows (see Fig. 25): 78 SMALL TOOLS D = diameter of screw, M = measurements over wires, W = diameter of wires, P = pitch of thread = -- 1 _ number of threads per inch The following formulas will then apply to V threads- M = D - 1.732 P + 3F. D = M + 1.732 P - 3 W. The same formulas for the United States standard thread are M = D - 1.5155 P + 3 W, D = M + 1.5155 P - 3 W. Suppose that we apply these formulas to a screw with United States standard thread form; the screw is 1J inches in diameter, with 12 threads per inch. The wires used for measuring are 0.070 inch in diameter. The micrometer reading for a correct screw should then be 1* ~ 1-5155 X py + 3 X 0.070 = 1.5837. If the micrometer reading happens to be 1.591 in the above case, that would indicate that the angle diameter of the screw is not correct. The amount of the error would be found by using the second formula, which gives the diameter of the screw when the dimension over the wires is known. 1.591 + 1.5155 X —■ - 3 X 0.070 = 1.5073 = the actual diameter of the screw. From this we see that our screw is 0.0073 too large in angle diameter. The outside diameter of course may be correct, H inches, but the flat on the top of the thread may be incorrect so as to account for the difference. THREAD-CUTTING —MEASURING THREADS 79 The above formulas together with a table giving the values of 1.732 P and 1.5155 P for various numbers of threads were given by Mr. J. Dangerfield in the American Machinist, issue of May 31, 1906. The table has been extended somewhat, so as to give all standard pitches in common use. (See Table XXIV.) TABLE XXIV. VALUES OF CONSTANTS USED IN FORMULAS FOR MEASURING ANGLE DIAMETERS OF SCREWS BY THE THREE-WIRE SYSTEM. No. of Threads per Inch. V Thread, 1.732 P. U. S. Thread, 1.5155 P. 2i 0.7698 0.6736 2f 0.7293 0.6381 21 0.6928 0.6062 2f 0.6598 0.5773 2f 0.6298 0.5511 21 0.6025 0.5271 3 0.5774 0.5052 31 0.5329 0.4663 31 0.4949 0.4330 4 0.4330 0.3789 41 0.3849 0.3368 5 0.3464 0.3031 51 0.3149 0.2755 6 0.2887 0.2526 7 0.2474 0.2165 8 0.2165 0.1894 9 0.1925 0.1684 10 0.1732 0.1515 11 0.1575 0.1378 12 0.1443 0.1263 13 0.1332 0.1166 14 0.1237 0.1082 15 0.1155 0.1010 16 0.1083 0.0947 No. of Threads per Inch. V Thread, 1.732 P. U. S. Thread, 1.5155 P. 18 0.0962 0.0842 20 0.0866 0.0758 22 0.0787 0.0689 24 0.0722 0.0631 26 0.0666 0.0583 28 0.0619 0.0541 30 0.0577 0.0505 32 0.0541 0.0474 34 0.0509 0.0446 36 0.0481 0.0421 38 0.0456 0.0399 40 0.0433 0.0379 42 0.0412 0.0361 44 0.0394 0.0344 46 0.0377 0.0329 48 0.0361 0.0316 50 0.0346 0.0303 52 0.0333 0.0291 56 0.0309 0.0271 60 0.0289 0.0253 64 0.0271 0.0237 68 0.0255 0.0223 72 0.0241 0.0210 80 0.0217 0.0189 This system for measuring the angle diameter of thread has also been treated at some length by Mr. Joseph M. Stabel in the January, 1904, issue of Machinery. He shows a special micrometer gauge adapted for the purpose of meas- 80 SMALL TOOLS uring with the aid of three wires. This instrument is illus¬ trated in Fig. 27. It is composed of a regular micrometer with its anvil cut off and its frame fixed into a base plate, which in turn rests upon three hardened feet. Great care should be taken when milling the slot for the micrometer frame in'the base plate, as the frame must stand perfectly perpendicular with the base if accurate results in measuring are to be obtained. Upon the base plate rests the plate b, Fig. 27. Special Micrometer for Measuring Threads by Three-Wire System which serves as the anvil of the micrometer. This anvil should be hardened, ground, and lapped perfectly parallel. It is held in position by the screws c. The screw holes should not pass entirely through the plate b, but leave the top surface of this plate perfectly solid and free from any obstructions. The wires are shown in positions at e. It is of course not necessary to have this special measuring instrument, as an ordinary micrometer answers the purpose THREAD-CUTTING —MEASURING THREADS 81 for at least all fine pitches, but it is apparent that the tool shown makes this measuring very much easier to handle than it would be with regular micrometers. In Machinery, March, 1907, Mr. F. E. Shailor shows a method for securing and holding the wires while measuring with ordinary micrometers. As shown in Fig. 28, the three wires are fastened in a small wooden handle. It is evident that each handle with its wires can be used only for a Fig. 28. Method of Holding Wires comparatively small number of pitches, and for diameters which are within close range. Where a great deal of measuring is to be done the arrangement shown in Fig. 27 is therefore to be recommended. 82 SMALL TOOLS TABLE XXV. MEASURING V AND UNITED STATES STANDARD THREADS BY MEANS OF THE THREE-WIRE SYSTEM. Diameter of Screw. Number of Threads per Inch. Diameter of Wire Used. Dimension over Wires, V Thread. Dimension over Wires, U. S. Thread. \ 18 0.035 0.2588 0.2708 i 20 0.035 0.2684 0.2792 i 22 0.035 0.2763 0.2861 i 24 0.035 0.2828 0.2919 A 18 0.035 0.3213 0.3333 1T> 20 0.035 0.3309 0.3417 A 22 0.035 0.3388 0.3486 A 24 0.035 0.3453 0.3544 i- 16 0.040 0.3867 0.4003 i 18 0.040 0.3988 0.4108 i 20 0.040 0.4084 0.4192 A 14 0.050 0.4638 0.4793 T5 16 0.050 0.4792 0.4928 i 12 0.050 0.5057 0.5237 h 13 0.050 0.5168 0.5334 i 14 0.050 0.5263 0.5418 A 12 0.050 0.5682 0.5862 A 14 0.050 0.5888 0.6043 t 10 0.070 0.6618 0.6835 f 11 0.070 0.6775 0.6972 f 12 0.070 0.6907 0.7087 A 10 0.070 0.7243 0.7460 A 11 0.070 0.7400 0.7597 10 0.070 0.7868 0.8085 11 0.070 0.8025 0.8222 1 12 0.070 0.8157 0.8337 A 9 0.070 0.8300 0.8541 A 10 0.070 0.8493 0.8710 1 8 0.090 0.9285 0.9556 i 9 0.090 0.9525 0.9766 1 10 0.090 0.9718 0.9935 A 8 0.090 0.9910 1.0181 A 9 0.090 1.0150 1.0391 l 8 0.090 1.0535 1.0806 l 9 0.090 1.0775 1.1016 lj 7 0.090 1.1476 1.1785 H 7 0.090 1.2726 1.3035 if 6 0.150 1.5363 1.5724 li 6 0.150 1.6613 1.6974 if 5i 0.150 1.7601 1.7995 if 5 0.150 1.8536 1.8969 it 5 0.150 1.9786 2.0219 THREAD-CUTTING —MEASURING THREADS 83 TABLE XXV.— Continued. Diameter of Screw. Number of Threads per Inch. Diameter of Wire Used. Dimension over Wires, V Thread. Dimension over Wires, U. S. Thread. 2 4 h 0.150 2.0651 2.1132 2* 4 * 0.150 2.3151 2.3632 21 4 0.150 2.5170 2.5711 2* 4 0.150 2.7670 2.8211 3 3J 0.200 3.1051 3.1670 31 31 0.200 3.3551 3.4170 31 31 0.250 3.7171 3.7837 H 3 0.250 3.9226 3.9948 4 3 0.250 4.1726 4.2448 41 2* 0.250 4.3975 4.4729 4* 2| 0.250 4.6202 4.6989 4f 2f 0.250 4.8402 4.9227 5 21 0.250 5.0572 5.1438 In Table XXV are given the most common diameters and corresponding pitches, and, for given wires used in measuring, the dimension over the wires. If the sizes of wires stated are used, this table will save all figuring in the cases where the diameter and the pitch of the screw or tap to be measured can be found in the table. The dimensions are given for sharp V thread as well as for United States standard thread. Limits for Diameter of Wires Used in the Three-Wire System. — It is evident that there are certain maximum and minimum limits for the sizes of the wire which can be used for measuring the diameters of screws and taps with the three-wire system. The most desirable size of wire would be that which is of the same diameter as the ball points for ball-point micrometers previously referred to. The wires would then tangent the sides of the thread at the points over which the angle diameter is measured. This size of wire, however, is rather small, too small, in fact, for measuring taps with sharp V thread, as the anvil and 84 SMALL TOOLS the point or face of the micrometer screw would be liable to bear upon the top edges of the thread before bearing upon the wire. We can, however, determine the limits between which wires may be selected for each particular pitch. The limits must be such, for the minimum dimension, that the wires extend beyond the top of the thread so as to prevent Fig. 29. Limits for Wires Used when Measuring Threads by the Three-Wire System the micrometer bearing on the threads, as mentioned, and for the maximum limit, that the wires tangent the sides of the thread, and do not bear upon the corners or edges of the top of the thread. These maximum and minimum limits with regard to the United States and V standard threads are clearly indicated in Fig. 29. If we first refer to the minimum size of wire for the United States standard thread, we find that to be reached THREAD-CUTTING — MEASURING THREADS 86 when the line AB (Fig. 29) tangents the wire. The length of the side AB of the triangle into which the circle repre- 7 senting the wire is inscribed equals - X pitch. But O AB X cos 30° = BD, and CD = BD (the radius of the O circle inscribed in an equilateral triangle being equal to one-third the altitude). Consequently CD = \ AB X cos 30° = ^ X \ X pitch X cos 30° 3 3 8 = 0.2526 X pitch. The minimum size of wire would then be twice this, or 0 5052 Minimum wire = 0.5052 X pitch = —- ' —- :—- • No. ot threads per inch The maximum size for the United States standard thread would be a wire which would tangent the thread 7 at E and H, Fig. 29. We have here EH = - X pitch, O EF = - EH, and EG = - • • Consequently 2 cos 30 EG = EH 7 pitch _ ~ 8 X 2 X cos 30° _ 0.5052 pitch. 2 X cos 30 c The maximum size of wire would be twice this, or „ . , . A , 1.0104 Max. wire = 1.0104 X pitch = — -—---;—r • No. of threads per inch In a similar manner we find the minimum and maxi¬ mum wires for the sharp V thread. Min. wire = — X pitch X cos 30° = • 3 0.5773 n *- . pitch Max. wire = - No. of threads per inch 1.155 cos 30° No. of threads per inch 86 SMALL TOOLS While the figures found give the extreme limits, it is evident that the wires used ought not to be near to these limits, particularly not to the larger one, as that gives a poor place for contact with the thread. We may say that if the wires vary between 0.65 X pitch and 0.9 X pitch, that will give us satisfactory results. Allowing these limits, it is evident that the same size wire may be used for a number of sizes, as is the case in Table XXV. Formulas for Whitworth Thread. — When measuring Whitworth threads with the three-wire system the formula used is Diameter of screw — —-- 7 —T + (3.1657 No. of threads per inch X diameter of wire used) = micrometer reading. In other words, if D = diameter of screw, M = measurement over wires, W = diameter of wires, P = pitch of thread = —- -r——:—r > No. of threads per inch then M = D - 1.6008 P + 3.1657 W and D = M + 1.6008 P - 3.1657 W. In Table XXVI are given the values of the constant 1.6008 P for various pitches. The maximum and minimum limits of the wires used for measuring Whitworth threads are determined by the formulas Maximum limit = 0.81 pitch and Minimum limit = 0.51 pitch. THREAD-CUTTING — MEASURING THREADS 87 TABLE XXVI. VALUES OF CONSTANTS USED IN FORMULAS FOR MEASURING ANGLE DIAMETERS OF WHITWORTH SCREWS WITH THE THREE- WIRE SYSTEM. No. of Threads per Inch. 21 2 | 2 * 2f 2 f 2i 3 3 i 3 * 4 4 * 5 Whit¬ worth Thread, 1.6008 P. 0.7115 0.6740 0.6403 0.6098 0.5821 0.5568 0.5336 0.4926 0.4574 0.4002 0.3557 0.3202 No. of Threads per Inch. 5i 6 7 8 9 10 11 12 13 14 15 16 Whit¬ worth Thread, 1.6008 P. 0.2911 0.2668 0.2287 0.2001 0.1779 0.1601 0.1455 0.1334 0.1231 0.1143 ! 0.1067 0.1001 I No. of Threads per Inch. 18 20 22 24 26 28 30 32 34 36 38 40 Whit¬ worth Thread, 1.6008 P. 0.0889 0.0800 0.0728 0.0667 0.0616 0.0572 0.0534 0.0500 0.0471 0.0445 0.0421 0.0400 No. of Threads per Inch. 42 44 46 48 50 52 56 60 64 68 72 80 Whit¬ worth Thread, 1.6008 P. 0.0381 0.0364 0.0348 0.0334 0.0320 0.0308 0.0286 0.0267 0.0250 0.0235 0.0222 0.0200 Measuring Acme Threads with the Three-Wire System. — The three-wire system may also be used for measuring Acme threads in the angle. As there are no standard diameters corresponding to certain pitches in the Acme standard, we cannot make up a table in the same manner as we have done for the V and United States standard threads. In Table XXVII, however, all the figures necessary to facilitate measuring Acme threads with three wires are given. In the second column the size of wire to use for certain pitches is stated. The third column in the table gives the amount which must be added to the root diameter of an Acme tap or screw to find the dimension over the wires. The last column gives the amount which must be added to the standard outside diameter to find the size over the wires. The convenience of this last column is that it makes it unnecessary to find the root diameter of the screw in order to measure the angle diameter. 88 SMALL TOOLS If it should, for instance, be desired to cut a one-inch screw or tap with six threads per inch, the only computation necessary is to add the value found in the last column in Table XXVII, opposite six threads per inch, to the outside diameter of the screw: 1.000 + 0.0521 = 1.0521, which is the size that the screw or tap should measure over wires 0.0916 inch in diameter. In regard to the points of tangency between the wires and the sides of the thread, these points would evidently be most correctly located if they coincided with the points over Fig. 30. Determining Formula for Measuring Acme Threads by Three-Wire System which the angle diameter is measured, that is, the points C and D in Fig. 30. This would be permissible for Acme thread screws, but in the case of taps with fine pitch the wire would be too small to reach above the top of the thread, which on Acme thread taps is 0.010 inch higher than on the screws. For this reason the points of tangency must be located a trifle further toward the top of the thread, say at' 3 AB (Fig. 30) which is — X pitch from the top of the thread. THREAD-CUTTING — MEASURING THREADS 89 The diameter of the wire for measuring will be found as follows. CD = £ if p signifies the pitch, and is located at A a distance of ^ p from the top of the thread, inasmuch as CD is at the location of the pitch line over which the angle diameter is measured. AB = CD + 2 X— v X tg 14J°. AB The diameter of the wire =-— • cos 14£° Consequently \ + f x tg 14i« Diam. of wire = -—-- = 0.5498 v. cos 14^ r The diameter according to this formula is given in Table XXVII. TABLE XXVII. MEASURING ACME THREAD SCREWS BY THE THREE-WIRE SYSTEM. No. of Threads per Inch. Diam¬ eter of Wires Used. Dimen¬ sion over Wires minus Root Diam. (=2 a). Dimen¬ sion over Wires minus Standard Diam. (=26). No. of Threads per Inch. Diam¬ eter of Wires Used. Dimen¬ sion over Wires minus Root Diam. (=2 a). Dimen¬ sion over Wires minus Standard Diam. (=26). 1 0.5498 1.3324 0.3124 5 0.1100 0.2825 0.0625 H 0.3665 0.8950 0.2083 51 0.1000 0.2586 0.0568 2 0.2749 0.6762 0.1562 6 0.0916 0.2388 0.0521 21 0.2199 0.5450 0.1250 7 0.0785 0.2075 0.0446 3 0.1833 0.4574 0.1041 8 0.0687 0.1840 0.0390 31 0.1571 0.3950 0.0893 9 0.0611 0.1658 0.0347 4 0.1375 0.3481 0.0781 10 0.0550 0.1512 0.0312 41 0.1222 0.3116 0.0694 12 0.0458 0.1293 0.0260 90 SMALL TOOLS The formula for determining the distance b is easily found. Let R be the radius of the wire. Then b = (R + EF) -^p. But EF — R x sin 14§°, and R = 0.2749 p, according to our previous formula for the diameter of wire. Consequently b = 0.1562 p. Fig. 31. Measuring Acme Threads by Three-wire System The dimension a in Fig. 31 and Table XXVII is simply b + depth of thread, or, as given in the table, 2 a = 2 b + double depth of thread = 2 b + p + 0.020. The best and most handy tool for measuring the depth of Acme and square threads is the micrometer depth gauge. As this tool is fairly common in the shop, a description seems unnecessary. Sensitive Micvometev Attachment .—AVhcn testing the diameters of taps or other pieces that are handled in great quantities and are all supposed to be within cer¬ tain close limits of a standard dimension, the ordinary micrometer presents the difficulty of having to be moved for each piece, and small variations in diameters have to be carefully read off from the graduations on the barrel. THREAD-CUTTING —MEASURING THREADS 91 Not only does this take a comparatively long time but it also easily happens that the differences from the standard diameter are not carefully noted and pieces are liable to pass inspection that would not pass if a con¬ venient arrangement for reading off the differences were at hand. Fig. 32 shows a regular Brown and Sharpe microm¬ eter fitted with a sensitive arrangement for testing and inspecting the diameters of pieces which must be within certain close limits of variation. The addition to the ordi- Fig. 32. Sensitive Micrometer Attachment nary micrometer is all at the anvil end of the instrument. The anvil itself is loose and consists of a plunger B, held in place by a small pin A. The pin has freedom to move in a slot in the micrometer body, as shown in the enlarged view in the cut. A spring C holds the plunger B up against the work to be measured and a screw D is pro¬ vided for obtaining the proper tension in the spring. The screw and the spring are contained in an extension E screwed and doweled to the body of the micrometer. A pointer or indicator is provided which is pivoted at F and has one extension arm resting against the pin A, which 92 SMALL TOOLS is pointed in order to secure a line contact. At the end of the indicator is a small scale graduated with the zero mark in the center, and as the indicator swings to one side or the other, the variations in the size of the piece measured are easily determined. A small spring G is provided for holding the pointer up against the pin A. The case H simply serves the purpose of protecting the spring mentioned. As the plunger B takes up more space than the regular anvil, the readings of the micrometer cannot be direct. The plunger B can be made of such dimensions, however, that 0.100 inch deducted from the barrel and thimble reading will give the actual dimensions. Such a deduction is easily made in all cases. In other words, the reading of the micrometer should be 0.100 when the face of the measuring screw is in contact with the face of the plunger; the 0.100 inch mark is thus the zero of this measuring tool. When wanting to measure a number of pieces, a stand¬ ard size piece or gauge is placed between the plunger B and the face L of the micrometer screw and the instrument is adjusted until the indicator points exactly to zero on the small scale provided on the body of the micrometer. After this the micrometer is locked and the pieces to be measured are pushed one after another between the face L and the plunger B, the indications of the pointer M being meanwhile observed. Whenever the pointer shows too great a difference the piece of course does not pass inspection. All deviations are easily detected, and any person of ordinary common sense can be employed for inspecting the work. Testing the Lead of Taps and Screws. In cases where there is no necessity of ascertaining the exact error in the lead of a screw or tap, and when only THREAD-CUTTING —MEASURING THREADS 93 a limited number are to be tested, a fairly good test is afforded by simply screwing the thread into a female gauge. The threaded portion of this latter should then, however, be fairly long, so that errors in lead, which are liable to be very small in a short distance, may be detected by tak¬ ing account of the error in the comparatively long length. Ordinarily, however, when quantities of taps are to be tested, the errors in lead are most easily ascertained by some device particularly intended for the testing of the lead of a screw thread alone. Some devices which test both the lead and the diameter within certain limits are 1 ^ 1 ( s' / / \ v ^ L Fig. 33. British Gauge for Simultaneous Testing of Lead and Angle Diameter also in use. Of these latter, two examples are shown in a report on British Standard Systems for Limit Gauges for Screw Threads, presented to the Engineering Standards Committee of Great Britain. Testing the Lead by Gauges. The first of these gauges is shown in Fig. 33. In this gauge, allowance is made for a permissible error in angle diameter and lead. As is plainly shown in the cut, the screw thread enters between three fixed points, shaped like the thread, two of which are located in the lower jaw 94 SMALL TOOLS of the gauge and one in the upper. The distance between the two points on the lower part of the gauge should be equal to about twice the diameter of the screw. The fixed point in the upper jaw should, of course, be placed midway between the points in the lower jaw. At A is shown a ground flat face which is so adjusted that the small cylinder C, of such diameter that it will touch the thread about half way down its depth, will barely enter between the flat face and the thread of the bolt for the minimum permissible diameter, but will “not go” as a general rule. This device then gives a practical test for both diameter and lead. If the lead were out too much, the screw would not enter the gauge, because the two points in the lower jaw would not fit the pitch of the thread, these points being, of course, set to a standard gauge. If, again, it could be conceived that the diameter was so much smaller than the standard that the screw or tap' could be placed in the gauge in spite of the lead being an appreciable amount long or short, then the feeler C would enter so freely between the face A and the screw as to indicate that the screw was not within permissible limits. It will be noticed that provision is made for getting the points entering the threads placed exactly in the center of the screw. In the end view the screw is shown rest¬ ing with one side up against the back of the gauge, the distance from the back of the gauge to the center of the points being equal to half the diameter of the screw. It is evident that gauges of this kind will have to be made for each different diameter and pitch. Another form of gauge intended to deal with shorter lengths of thread than the one just described is shown in Fig. 34. In this case two separate gauges are applied, one minimum and one maximum. The screw is supposed to enter into the one and refuse to enter into the other. THREAD-CUTTING — MEASURING THREADS 95 In this gauge the top plates T are made of hardened steel and contain V teeth set as senting the next even num¬ ber of threads immediately above the number con¬ tained in a length of screw equal to the diameter of the thread, while the distance L x is one thread shorter. The plates are screwed, and preferably doweled, to a base plate, and are, of course, made and adjusted to a standard plug. At s are shown screws which can be so adjusted that the measurement can be made exactly at the center of the screw, the distance from the faces of screws s to the center of the gauge the diameter of the screw. shown, the distance L repre- pi/ ri i ~ \s _f i_ Fig. 34. Maximum and Minimum Gauge for Lead and Angle Di¬ ameter plates being equal to one-half Comparators for the Lead of Taps and Screws. When it is wanted, however, to determine the errors in pitch with some exactitude and not to find out only whether the error is between certain limits, then the instrument termed “thread comparator” is used. This consists, in its simplest form (see Fig. 35), of a fixed block A and a sliding block B provided with ball points. The sliding block operates a pointer C, which on a large scale indexes the errors of lead. The manner of using this instrument is as follows. A standard plug is first placed 96 SMALL TOOLS against the device so that the ball points enter in threads, say one inch apart. The position of the pointer on the scale is noted when the standard plug engages the ball points, the free block B adjusting itself to the thread into which its ball point enters, and carrying with it the pointer C. Next the tap or screw to be tested is placed in position against the device. If the lead of this screw Fig. 35. Simple Form of Comparator for Lead of Screw Threads or tap is correct and is the same as that of the plug, the pointer will evidently occupy the same position in relation to the scale as in the case of the plug. If the tap or screw is long or short in the lead, the pointer will show the amount on the scale by swinging either to the left or to the right. The scale should, of course, preferably be graduated so as to show thousandths of an inch. THREAD-CUTTING — MEASURING THREADS 97 A more elaborate device for measuring the errors in lead of taps is shown in Fig. 36. Here one ball point A, which we may call the fixed, is mounted in a slide D, which latter is operated by a knurled head screw B. Ball point A may be screwed into any of the holes C, which may be one-half inch apart; thus one may with this device measure the lead in one inch, or in any length up to six inches, as may be desired, by moving the ball point A to different positions in the slide D. The ball point E is inserted in a movable block 98 SMALL TOOLS resting on a ball bearing. This block, in turn, is connected through the lever F with the indicator or sensitive gauge G, which should be so arranged and graduated that thou¬ sandths of an inch can be easily read. When the standard plug is placed against this device, the ball points entering between threads in the same way as in the device previously described, the slide D can be so adjusted by the knurled head screw B that the indicator points to zero. When the screw or tap to be tested is placed against the ball points, any error will then be apparent by the motion imparted by too long or too short lead to the movable ball point E. This motion is; of course, carried to the indicator through the lever arm F. If the latter is graduated in thousandths of an inch, the graduations below or above zero will indicate the amount in thousandths of an inch that a tap or screw is short or long in the lead in the distance originally meas¬ ured on the plug, i.e., the distance between the ball points when the plug was placed in position against the device. In the device shown, the length of the lever F, between its pivot and that end which is operated by the movable block, is half of the length between the pivot and the end operating the gauge. Consequently, if the gauge be graduated to show movements of 0.001 inch on its own plunger, it will indicate a motion of 0.001 inch on the movable ball point by moving two graduations on its own scale. Very close measurements are consequently possible. Of course this device is only one modification of the many possible for obtaining the same results. Very likely there are others equally good, but this one is shown as an example of a satisfactory design, and at the same time as an indi¬ cation of the principles involved in the design of compara¬ tors for the lead of screw and tap threads. CHAPTER III THREADING TOOLS. — DEFINITIONS OF TAPS. Simple Forms of Thread Tools. Thread tools for V, United States, and Whitworth Threads. — A threading tool of the simplest form is shown in Fig. 37. This tool is provided with a shank held in the tool-post and ground on the end to the shape of the thread to be cut, in this case a sharp V thread. The tool should be ground flat on the top face AB, and the sides CD and EF should form an angle of 60 degrees. It should be noted that this angle must measure 60 degrees in the plane AB, as the angle in This plane is the one which will be duplicated in the thread-cutting. The angle between the two faces in the section GH, perpendic¬ ular to the line KL, the tool being given clearance, will be slightly more than 60 degrees. In grinding an ordinary tool as shown, it is unimportant what this latter angle is so long as the tool fits the thread gauge measured in the plane AB. When making special thread-cutting tools which are ground in special fixtures or grinding machines, however, the angle in the section GH is the one taken into account. It is, of course, of great importance that the clearance angle KLM should be permanently settled upon in such cases, as the difference between the angle between the faces 99 100 SMALL TOOLS measured in the section GH and the angle measured in the plane AB is directly dependent upon the clearance angle. This clearance angle is usually made 15 degrees. In the case of a United States standard thread tool, shown in Fig. 38, the difficulty of correctly measuring the flat is the one of the greatest importance. In ordinary practice this flat is made in accordance with standard thread gauges, such as are sold for instance by the Brown and Sharpe Company; but if the flat must be fully cor¬ rect, as is required in thread tools manufactured for the market or for making thread gauges, a more complicated method must be resorted to. This method will be treated in detail in connection with single-point cutters used in standard thread tool holders. Thread tools for the Whitworth standard thread form in fact are forming tools. As seen from Fig. 39, the tool is provided with round corners on the sides of the tool to form the round points of the top of the thread, while the point of the tool of course forms the actual groove or thread. Thread Tools for Square Threads. — Tools for cutting _ ,i i , i Fig. 39. Thread Tool for Whit- square threads must be given 6 worth Thre . ld “side clearance” as well as clearance for the cutting edge. The latter is 15 degrees, as commonly used for all threading tools. The former Fig. 38. Simplest Form of Thread Tool for United States Standard Thread THREADING TOOLS — DEFINITIONS OF TAPS 101 depends upon the diameter of the screw to be cut and the pitch of the thread. A tool for cutting square threads is shown in Fig. 40. The angle DCE is the side clearance angle, or the angle which the sides of the tool must make with the vertical line in order to clear the sides of the thread in the cutting operation. This angle should be equal to the helical angle of the thread. In other words, the tangent for the side clearance angle is equal to the D I E Fig. 40. Square-Thread Tool lead divided by the circumference of the screw, or if expressed in a formula, tan DCE = —, 7Ttt if l equals the lead of the thread and d the outside diame¬ ter of the screw. Instead of using the outside diameter of the screw it would be more correct to use the angle diame¬ ter of the screw in the formula, although this is seldom done. In such a case the formula would be transformed into tan DCE = l x(d- ip) ’ in which formula l and d denote the same quantities as 102 SMALL TOOLS before, and p the pitch of the thread. In the case of a single-threaded screw, of course, the pitch and the lead would be the same. This clearance angle can be constructed graphically in a very simple manner. In Fig. 41, draw a line AB equal to the circumference of the screw and at B a line BC at right angles to AB ; the length of BC should be equal to the lead of the thread. Draw a line from A to C. The angle BAC in the required clearance angle, provided the drawing has been made fairly accurate. This angle can be measured by means of a protractor and the tool c Fig. 41. Laying out the Clearance Angle for a Square-Thread Tool ground according to it without the use of trigonometrical tables. Tools for the Acme standard thread are similar to those for square thread, but as a rule do not need side clearance except for steep pitches. The width of the flat is deter¬ mined by a thread gauge, the same as for the United States standard thread. Thread-Tool Holders. Ordinarily, however, it is cheaper to use threading tools held in special holders. The same holder can be used for all sizes of threading tools, and the tools themselves are made with a constant cross section from the beginning, so that all grinding takes place on the top of the tool, the thread form remaining perfect until the thread tool is THREADING TOOLS — DEFINITIONS OF TAPS 103 used up by grinding. A holder which is manufactured by the Pratt and Whitney Company and universally used, is shown in Fig. 42. Threading tools for use with this holder are shown in Figs. 43 and 44. Referring to the holder it will be noticed that the tool is held in position by means of a tongue A, and clamped tightly by a clamp B and the nut C. An elevating screw D is provided by means of which the threading tool proper, which has a thread on Fig. 42. Pratt and Whitney Thread-Tool Holder its back part, may be raised or lowered so as always to be adjusted to its proper height. The screw D is stationary as far as longitudinal movement is concerned, being held in place by the pin E ; consequently the tool will move whenever the adjusting screw is turned. The screw F is for adjusting the height of the clamp B in relation to the body of the holder, so that if the threading tool proper should be either a little too thick or too thin, a perfect bearing can still be obtained by adjusting this screw. 104 SMALL TOOLS Single-Point Cutters. In Figs. 43 and 44 the ordinary thread tool or single¬ point cutters used with this holder are shown. The former cut shows the form of tool for all pitches smaller than 4 threads per inch, while Fig. 44 shows the tool used for coarse pitches, say from to 4 threads per inch. This form for coarse pitches is necessitated by the width of the body of the tool, which is only one-quarter inch, and Fig. 43. Single-Point Cutter used in Pratt and Whitney Thread-Tool Holder for Pitches finer than 4 Threads per Inch it is obvious that the cutting part of the tool itself must at least be equal to the pitch, hence for pitches coarser than 4 threads per inch the front or cutting part is made seven-sixteenths inch wide. Special forms of single-point cutters are shown in Fig. 45. Here the cutting point is offset with regard to the body of the tool in order to make it possible to cut a thread close up to a shoulder. The tool to the left is termed a right-hand offset tool, and the one'to the right is a left-hand offset thread tool. THREADING TOOLS —DEFINITIONS OF TAPS 105 Fig. 44. Single-Point Cutter used in Pratt and Whitney Thread-Tool Holder, 2£ to 4 Threads per Inch Chasers. In Fig. 46 is shown the common form of thread chaser used in the thread-tool holder referred to. While the part of this chaser having provision for being clamped in a holder and adjusted can be of a description to suit any 106 SMALL TOOLS holder, the part containing the thread can in all cases be made according to the dimensions given in Table XXVIII. Fig. 46 TABLE XXVIII. DIMENSIONS OF THREADING CHASERS. No. of Threads per Inch. A. B . No. of Teeth in Chaser. No. of Threads per Inch. A. B . No. of Teeth in Chaser. 3 1.333 i 4 12 0.667 A 8 31 1.231 f 4 13 0.615 A 8 31 1.143 f 4 14 0.571 i 8 4 1.000 1 4 16 0.500 1 8 41 1.111 f 5 18 0.500 I 9 5 1.000 1 5 20 0.450 1 9 51 0.909 1 5 22 0.409 A 9 6 0.833 1 5 24 0.375 A 9 7 0.714 1 5 26 0.385 A 10 8 0.750 ! 6 28 0.357 A 10 9 0.667 t 6 30 0.333 A 10 10 0.700 1 7 32 0.312 1 10 11 0.636 t 7 36 0.278 i 10 HI 0.696 ! 8 48 0.250 i 12 The Making of Threading Tools. United States Thread Tools. — The chief requirements for cutting a correct thread are correct threading tools, a correct setting of the tool, and a lathe with a reasonably THREADING TOOLS — DEFINITIONS OF TAPS 107 accurate lead screw. In making the thread tool a correct 60-degree angle gauge is necessary. To produce such a gauge first plane up a piece of steel in the shape of an equilateral triangle as shown at a in Fig. 47. After hardening this triangle, grind and lap the edges until the three corner angles prove to be exactly alike when meas¬ ured with a protractor. This is now the master gauge. To produce the female gauge make two pieces, one right hand and one left, like that shown at b in Fig. 47; harden Fig. 47. Gauge for Making a 60-Degree Thread Tool them and lap the edges that form the 150-degree angle so that they are straight, and square with both sides. When this is done the two pieces should be screwed, and doweled to a backing plate d as shown in Fig. 47, using the master triangle to locate them, thus producing a practically per¬ fect female gauge. In making up the tool some form of cutter to be used in a holder should be chosen in preference to a forged tool on account of convenience in handling and measuring and the facility with which it may be reground without 108 SMALL TOOLS destroying the shape. The tool should be made so that the top will stand level when in the holder, and the clear¬ ance should be about 15 degrees, which is ample for a single thread unless the pitch is very coarse. With that amount of clearance the included angle between the sides of the tool in a plane perpendicular to the front edge is approximately 61° 44'. The tool should be planed to that angle as nearly as is possible by measuring with a protractor, then, to test its accuracy, it should be placed top down on a flat piece of glass c and tried with the 60-degree gauge as shown in Fig. 47. After lapping the tool until it shuts out the light when tried in this man¬ ner, the angle may be considered as nearly correct as is possible to obtain with ordinary means. To adapt the V thread tool thus made to cut the United States standard form of thread, it is only necessary to grind off the sharp edge an amount equal to one-eighth of the depth of a V thread of the required pitch, or for 20 threads per inch 0.866 20 X i = 0.0054 o inch. To test the accuracy of this grinding, a piece of steel should be turned up to the correct outside diameter and a short shoulder turned down at the end to the correct diameter of the bottom of the thread; then the piece is threaded and the tool fed in until the flat of the tool just tangents the shoulder. Then cut a nick in the edge of a piece of sheet steel with the threading tool. This sheet steel piece is now applied like a gauge to the threaded cylindrical piece. If the nick in the sheet steel fits the thread so that it shuts out the light, the flat of the tool is correct. In preparing a plug gauge for threading it should be made the same as the cylindrical test piece above, with a part turned down to the root diameter of the thread, except that for V thread it is customary to leave the THREADING TOOLS — DEFINITIONS OF TAPS 109 shoulder 0.005 inch large on account of the impossibility of producing a perfectly sharp point on the tool. The thread tool should be set level, with the top at the same height as the center line of the spindle of the lathe, otherwise the correct angle will not be reproduced. After a master plug has once been produced, it is not necessary to turn down a portion to the root diameter of the thread, as the work can be compared with the master plug by means of a micrometer fitted with either ball or V points for measuring in the angle of the thread. It occasionally happens that a tap is to be threaded, or other external threading is to be done, of an odd size or pitch where it is desired to originate a master plug. In such cases it is best to use the three-wire system for measuring the angle of the thread. Measuring Width of Flat on United States Standard Thread Tools. — When making United States standard threading tools, as described, it is comparatively easy to arrange for gauging the angle, but the measuring of the width of the flat is a more difficult task, if by measuring we understand the process of making sure that the flat is fully correct, and not merely comparing the thread tool we make with a manufactured thread gauge, which is a very uncertain test for accurate work. The common method already described is a “cut and try” scheme, first cutting a thread on a cylindrical piece with the tool supposed to be approximately correct, and afterward using the same thread tool with which this thread was cut to plane a groove in a flat piece of steel. The groove in the flat piece of steel is then a duplicate of the thread previously cut and should also be an exact duplicate of the section GACF of the thread cut on the cylindrical piece. (See Fig. 48.) When testing, if the groove proves to be an exact duplicate of the thread form, the flat evidently is correct, 110 SMALL TOOLS inasmuch as the flats at the bottom and at the top of the thread are alike, it being supposed that the angle was previously tested and found correct. However, if the groove in the flat steel piece does not exactly fit the sec¬ tion of the thread on the cylindrical piece, it is necessary to grind the tool again and make another trial, continuing this until a tool with a correct flat is produced. The ideal K Fig. 48. Section of U. S. Standard Fig. 49. U. S. Standard Thread Thread Tool before Grinding Flat method would be to measure the flat by micrometers, if that could be done, in which case there would be no uncertainties, and a correct tool could be produced more directly and with less work. It is, of course, not possible to measure with micrometers the distance AC in Fig. 48, as such a measurement would be at best uncertain for large pitches, and absolutely impossible to make on smaller ones, even when using an eyeglass. If, however, the ver- THREADING TOOLS — DEFINITIONS OF TAPS 111 tical distance BD from the top of the thread down to the flat can be measured, the width of the flat is easily figured, as for a United States standard thread, AO=2BDx tan 30°. This distance cannot, of course, be measured with ordinary micrometers, but a micrometer can be simply Fig. 50. Micrometer for Measuring Flat of Thread Tools designed which may be used for obtaining this distance. Such a micrometer is shown in Fig. 50. If it were only a case of measuring a threading tool without clearance, the angle CBD in Fig. 50 would simply need to be 60 degrees, and the micrometer so graduated that the reading would be zero when the face A of the measuring screw was exactly in line with the point B of the angle CBD. When 112 SMALL TOOLS wanting to measure the width of the flat of a threading tool, the tool would be placed in the angular space pro¬ vided for it and the micrometer adjusted until the face of the measuring screw would touch the flat. The reading should then be multiplied by two times the tangent for 30 degrees, or 1.155. As the threading tool is provided with clearance, the case, however, is not quite so simple, but still presents no actual difficulties. Referring to Fig. 49, where a thread¬ ing tool is provided with 15 degrees clearance, it is evident that the measurement taken by the micrometer will have to be along the line CD in a plane AB at right angles to the line EK. The length of the line CD is equal to Ml multiplied by cosine of 15 degrees, or, reversing the expression, MI = CD cos 15° The width of the flat HG again is equal to 2 X Ml X tan¬ gent for 30 degrees. Thus: HG= 2 X CD cos 15 o X tan 30°, or in other words, the width of the flat of the threading tool equals two times the distance measured by the microm¬ eters in the plane AB divided by cosine of 15 degrees, the quotient multiplied by the tangent for 30 degrees. We naturally would reverse the formula when wanting to produce a threading tool for a given pitch, the width of the flat HG being then given from the beginning and the distance we require to know being CD. Knowing this distance, we can grind down the sharp V tool until we read off on the micrometer the required figure for CD. The formula for determining CD is TfC CD = —- X cot 30° X cos 15°. A THREADING TOOLS — DEFINITIONS OF TAPS 113 For United States standard thread, HG = b _ 1 _ number of threads per inch If N denotes the number of threads per inch, the for¬ mula may be written: CD = cot 30° X cos 15° 16 N In Table XXIX the values of CD are given for a num¬ ber of United States standard pitches when the clearance angle of the tool is 15 degrees. TABLE XXIX. MICROMETER READINGS FOR MEASURING THE FLAT OF UNITED STATES STANDARD THREAD TOOLS. Clearance angle 15 degrees. No. of Threads per Inch. Micrometer Reading. H 0.0465 2f 0.0440 2* 0.0418 2f 0.0398 21 0.0380 n 0.0364 3 0.0349 31 0.0322 31 0.0299 4 0.0261 41 0.0232 5 0.0209 51 0.0190 6 0.0174 7 0.0149 8 0.0131 No. of Threads per Inch. Micrometer Reading. 9 0.0116 10 0.0105 11 0.0095 12 0.0087 13 0.0080 14 0.0075 15 0.0070 16 0.0065 18 0.0058 20 0.0052 22 0.0048 24 0.0044 26 0.0040 28 0.0037 30 0.0035 32 0.0033 No. of Threads per Inch. Micrometer Reading. 34 0.0031 36 0.0029 38 0.0027 40 0.0026 42 0.0025 44 0.0024 46 0.0023 48 0.0022 50 0.0021 52 0.0020 56 0.0019 60 0.0017 64 0.0016 68 0.0015 72 0.0015 80 0.0013 Referring now to Fig. 50, the micrometer consists of an ordinary micrometer head fitted into a block F. This block is provided with an angular groove CBD to receive the tool. The angle to which to plane this block equals 114 SMALL TOOLS 61° 44', which-is the angle between the faces IH and IG in Fig. 49, measured in the plane AB. In the center of the block, where the micrometer head is attached, part of the block is cut away, leaving a free view of the tool and the face of the measuring screw when the former is placed in position for measuring. The micrometer head em¬ ployed may be an ordinary one with regular graduations, in which case the reading of the micrometer must be carefully noted when the face A of the screw is in line with the point B of the angular groove, but it is still better, if one wants to go to the expense, to make the head with a special graduation having the zero mark where the face and point of the angle coincide. In this latter case the graduations would evidently be made in a direction opposite to the one on an ordinary micrometer barrel. In the former case it would be necessary to subtract the measured reading from the reading when A and B coincide in order to obtain the length of the line CD in Fig. 49. To facilitate the holding of the tool when measuring, it is advisable to knurl it on the top at G. This manner of measur¬ ing can be conveniently employed when testing or in¬ specting tools with round points like the tools used for originating the thread tools used to cut the Whitworth or the British Association standard thread. In this case the length of a line CD Thread Tool THREADING TOOLS — DEFINITIONS OF TAPS 115 from the point I to the highest part. M of the radius measured in a plane at right angles to EF as shown in Fig. 51, must be determined. The angle CBD (Fig. 50) of the block must of course be made according to the angle of the thread which is measured. If the angle of the thread is v, the angle CBD is determined from the formula tan CBD 2 cos 15° ’ provided that the clearance angle is 15 degrees. The values for the length of the line CD measured on a tool with 15 degrees clearance angle are given in Table XXX for the Whitworth standard thread and in Table XXXI for the most common pitches of the British Association standard thread. TABLE XXX. MICROMETER READINGS FOR TESTING WHITWORTH FORM OF TOOL. Clearance angle 15 degrees. No. of Threads per Inch. Micrometer Reading. No. of Threads per Inch. Micrometer Reading. No. of Threads per Inch. Micrometer Reading. 21 0.0687 • 9 0.0172 34 0.0045 2| 0.0651 10 0.0155 36 0.0043 21 0.0619 11 0.0141 38 0.0041 2| 0.0589 12 0.0129 40 0.0039 21 0.0562 13 0.0119 42 0.0037 21 0.0538 14 0.0110 44 0.0035 3 0.0515 15 0.0103 46 0.0034 31 0.0476 16 0.0097 48 0.0032 31 0.0442 18 0.0086 50 0.0031 4 0.0387 20 0.0077 52 0.0030 0.0344 22 0.0070 56 0.0028 5 0.0309 24 0.0064 60 0.0026 51 0.0281 26 0.0059 64 0.0024 6 0.0258 28 0.0055 68 0.0023 7 0.0221 30 0.0052 72 0.0021 8 0.0193 32 0.0048 80 0.0019 116 SMALL TOOLS TABLE XXXI. MICROMETER READINGS FOR TESTING BRITISH ASSOCIATION FORM OF TOOLS. Clearance angle 15 degrees. British Micrometer British Micrometer British Micrometer Asso. No. Reading. Asso. No. Reading. Asso. No. Reading. 0 0.0102 9 0.0040 18 0.0015 1 0.0092 10 0.0036 19 0.0014 2 0.0083 11 0.0032 20 0.0012 3 0.0075 12 0.0029 21 0.0011 4 0.0068 13 0.0025 22 0.0010 5 0.0060 14 0.0023 23 0.0009 6 0.0054 15 0.0021 24 0.0008 7 0.0049 16 0.0019 25 0.0007 8 0.0044 17 0.0017 _ Making Whitworth Thread Tools .—While the develop¬ ment of a correct United States or V-thread tool is a thing requiring a great deal of skill and patience, it is easy compared to the task of producing a tool for the round top and bottom thread, of which the Whitworth and British Association standards are the leading examples. In testing for accuracy, threads of this type are not only measured by gauges and micrometers, but the curves must match the angle so evenly that when the male gauge is tried in the female from either end no difference can be detected. The difficulty attending this will be better appreciated when it is known that some of the leading tap and die manufacturers of this country and Europe have failed in producing threads that would pass the British government’s inspection. It may be laid down as a cardinal principle that the best results are obtained by developing the form first with a flat top and bottom as in the United States thread, rounding the corners afterward. The first step of all is THREADING TOOLS — DEFINITIONS OF TAPS 117 to produce a correct angle gauge; assuming that we are to work out the Whitworth thread, this would be a gauge measuring 55 degrees. Make and harden a steel triangle, A, Fig. 52, with the angle x as near 55 degrees as is possi¬ ble by using a bevel protractor; the other two angles are to be equal. Then make an angle iron B, making sure that ab and cd are parallel, and that be is square with ab. Assuming that C and D are accurate two-inch and one- half-inch plugs, we put in the pins E, E in such a position that a line drawn through the centers of C and D, at right angles to their axes, will make an angle of 27| degrees Fig. 52. Making Angle Gauge for Whitworth Thread Tool with ab. This can be done by figuring the distance fg as follows: In the triangle Ihk, hk — 1 — 0.25 = 0.75 inch. 0.75 0.75 tan 27£° “ 0.5206 1.4406 inch. 1.4406 + | diameter of C — £ diameter of I) = 1.4406 + 1 - 0.25 = 2.1906 inch = /g. Set the pin F near enough to D to keep the corner of the triangle from striking the angle iron B. Mount the triangle A as shown, and set up the fixture on surface grinder table, using a toe strap in the small hole in A to 118 SMALL TOOLS hold it in position, and grind first one edge, then the other. This gives us the male angle gauge. A female gauge can now be made from this by the method described in connection with United States standard thread tools. The tools to be used in making the thread tool (see Fig. 53) include an angular tool with a flat point, the width of the point to be such that it reaches to the center of the round in the bottom of the thread, the angle of the tool matching the gauge previously made; a female radius tool for forming the point; and a male radius tool for the side radii. For convenience in measuring and getting the exact form required, these tools should be made with the top square with the face at the cutting edge, i.e., without clearance. The sides and back of all should be ground as well as the top. The tool a can be ground by means of an angular block made in the same manner as the male angle gauge and should be finished by lapping. The tool b can be made in two pieces, one a hardened, ground, and lapped wire, and the other a soft piece made up in such shape that the wire can be soldered or otherwise firmly fastened to it in the correct position. The tool c should be made up first as at c' and hardened. Then lap the hole carefully to size and grind the outside. After measuring the distance from the hole to the back of the tool, the front can be ground off to ef and the THREADING TOOLS — DEFINITIONS OF TAPS 119 bevels ground until the depth of the round part is right. We now require a shaper with an apron made up to hold the tool holder at an angle of 15 degrees, as shown in Fig. 54. The apron should fit the clapper box perfectly. If it does not, it is better to fasten it solid and let the Fig. 54. Method of Planing a Whitworth Thread Tool tools drag back through the cut, sharpening the tools over again before finishing. Otherwise one runs the risk of side shake. With this angular apron we can use the tools made without clearance to produce a tool with correct clearance for the lathe. Two thread-tool blanks, one, a, of tool steel and one, b, of machinery steel, should be set up on the table adapter as shown in the cut with spacing- 120 SMALL TOOLS parallels between to avoid interfering with one while planing the other. The blanks should be planed off to exactly the same height, and all measurements for height should be figured from the line cd, allowance being made for the difference caused by the 15-degree clearance. Then, after carefully measuring the tools previously made to determine where the exact center is, we can start form¬ ing the blanks, setting the tools sidewise successively by positive measurement from the rib of the adapter. The angular tool comes first, and with it we plane down the sides of the tool a and the center of b so that the point of the tool just reaches the center of the radius. Then using the female radius tool we round the point of a and the two points of b, coming down until the circle of the tool is just tangent to the top of the blanks. The male tool will round out the two lower corners of a and the center of b, being fed down to exact depth. We now have the thread tool a, which can be hardened and the machinery steel blank used as a lap to correct errors in it, reversing the lap occasionally, and using oil¬ stone powder or other fine abrasive as the cutting medium. Great care must be used in putting on the abrasive, as in all lapping operations of this kind points and corners are apt to lap faster than wide surfaces. This operation does not really correct the tool, but equalizes the errors due to imperfect matching of the different cuts, and it can be done so effectively that whatever errors of that kind are left cannot be detected. To test the tool, turn up a blank plug with a teat equal to the diameter at the bottom of the thread. When this is threaded, the point of the tool should touch the teat just as the outer corners touch the top of the thread. In the angle, the thread should measure by wires according to the formula THREADING TOOLS — DEFINITIONS OF TAPS 121 Diameter of screw — - - -;rA-—- ;—- number or threads per inch + (3.1659 X diameter of wire used) = micrometer reading. For the final test of the fit of the curves with the angle, a tap must be threaded with the tool, and a female gauge tapped with the tap. The plug made before must screw into this with an equal amount of friction from either end and show a full contact on the thread. If this last test is not successful it shows that the lapping is not good enough and must be done over. If the plug does not measure right it is necessary to go back to the planing and plane up another tool, making such allowances as one judges will correct the error. It is sometimes necessary to do this several times before a perfect tool is produced. In the use of the tool in the lathe great care is necessary to see that it is set at the center of the spindle, and so that the two side curves will scrape the top of the thread at the same time. With the exception of making the angle gauge and tool-grinding block, this whole procedure has to be carried out for every pitch required. Thread Tools with Side Clearance. The tool most commonly used requiring side clearance is the square-thread tool. We have previously referred to the method of determining the amount of this clear¬ ance. Acme thread tools for steep pitches often also require side clearance, and as the matter of determining the exact amount of this is more complicated than in the former case, a more detailed analysis is necessary. In figuring the side clearance as well as the angle to which to plane threading tools, the angle of clearance is, of course, the determining factor. In Fig. 55 a diagram 122 SMALL TOOLS illustrating the planing of thread tools is shown. By means of the formulas on next page the angles to which the planer or shaper head should be set can be easily determined. By reference to the diagram, the formulas are readily understood. The expressions “the leading” and “the following” side of the tool may need a short explana¬ tion. The former indicates the side of the tool which first enters the work when a thread is cut; the latter, of course, is the side which would last leave the work if it is Fig. 55. Tool with Side Clearance supposed that the tool traveled along the full length of the work. The diagrams and the formulas are given with special reference to the tools used in the Pratt and Whitney thread-tool holder, this holder being the one most used in general practice. Evidently the formulas are equally applicable to any thread tool which can be planed or shaped in a similar manner to the one particularly referred to. If we first consider a tool with side clearance, as shown in the cut, we will first find it necessary to determine the THREADING TOOLS — DEFINITIONS OF TAPS 123 angle of the helix of the thread, the same as for square- thread tools mentioned in the first pages of this chapter. In the formulas, a = depth of thread, b = width of flat on offset tool, c = actual width of flat, d = outside diameter of screw, v = clearance angle, w = one-half angle of thread, y = angle of helix, x = normal angle (to which to set planer head when planing tool on side). For finding the angle of helix of the thread we have then , lead of thread tan y = ■——-r-- • y (d - a) it For the normal angle we have cos y ± (cot w X sin t? X sin y) tan x a .. • cot w X cos v Use + for leading side and - for following side. For Acme (29 degrees) thread and 15 degrees clear¬ ance angle, the formula can, for all practical purposes, be written tan x = cos y ± sin y 3.735 The width of flat on the offset tool is figured from the formula b = c X cos y. If the tool has no side clearance, the angle of helix can be considered = 0 degrees, and above formula reduces 1r , , tan w itself to tan x= -. cos v 124 SMALL TOOLS For 60-degree screw thread, United States standard, the formula will thus have this appearance: tan x = = 0.5977; x = 30° 52'. cos 15° In this latter case the width of flat of tool (c) remains unchanged. It will be noticed that formulas are given first for 11 tools with side clearance” and second for “tools without side clearance.” Of course any thread tool ought to be given a side clearance, the amount of which depends on the angle of helix of thread to be cut; but on account of the small angle of helix on fine-pitch threads the necessity of using a tool with side clearance in such cases is reduced to a minimum, and can for practical reasons be dispensed with, the clearance of 15 degrees in the front of the tool being sufficient to carry the parts of the tool not cutting far enough back so as not to interfere with the thread. Threading Tools for Taper Taps. Threading tools for taper taps may, in fact, be said to constitute a class by themselves, particularly if the threading tool be a chaser. The cutting of taper-threaded taps, such as pipe taps, with chasers is more or less com¬ mon in shops where taper taps are manufactured, but the operation usually causes some difficulties. In itself the problem is very simple and the difficulty has probably originated in an insufficient analysis of the subject. We will consider the conditions of cutting a taper thread with a chaser, and particularly consider the case of a pipe tap with a total taper of three-quarters inch per foot, cut with a chaser supposed to be held in a threading tool holder. In Fig. 56 a chaser is shown such as would be held in THREADING TOOLS — DEFINITIONS OF TAPS 125 the threacling-tool holder made by the Pratt and Whitney Company. It is evident that if either a single-point cutter or a chaser used for ordinary straight-thread cut¬ ting were put in a holder and the holder swiveled around so as to present the chaser to the work at right angles to the outside of the tapered blank to be threaded, the thread formed would not be correct, inasmuch as a line drawn through the center of the thread perpendicular to Fig. 56. Taper Tap cut with Chaser made According to the Method shown in Fig. 57 the axis of the tap would not bisect the angle of the thread. This last condition, that the line perpendicular to the axis of the tap should bisect the angle of the thread as shown in Fig. 56, is the main requirement for producing a correct thread on a tapered piece. In order to produce such a thread with a chaser, the chaser must be made in a way specially adapting it for this class of work only. There are two ways in which such a chaser can be made, depending upon the way in which the chaser is to be presented to the work. In the first place, the chaser may 126 SMALL TOOLS be presented to the work perpendicular to the axis of the tap, as shown in Fig. 56, or the chaser may be presented perpendicular to the outside surface of the tap blank, as shown in Fig. 59. We will first discuss the former case. If the chaser were not provided with clearance it is evident that the milling cutter for milling the grooves in the chaser would be a 60-degree angular cutter, being 30 degrees on each side. The chaser would be held in the vise as shown in Fig. 57 and the cutter fed down, for each consecutive Fig. 57 Fig. 58 Two Methods of Milling the Teeth of Chasers for Taper Taps tooth cut, an amount depending upon the taper and the pitch of the thread. The values of a (Fig. 56) for pipe thread and other common taper tap pitches, when the taper is f inch per foot, are as follows: Threads per Inch. a 8.•. 0.0039 Hi. 0.0027. 12. 0.0026 14. 0.0022 18. 0.0017 27 . 0.0012 THREADING TOOLS — DEFINITIONS OF TAPS 127 However, as the chaser must be made with 15 degrees clearance, the milling cutter cannot be made 60 degrees, but must be made 61° 44', this being the angle between the two sides of a single-point cutter with 15 degrees clearance angle, if measured in a plane at right angles to the front face of the tooth. The arrangement for holding the chaser when milling, and the angles required for the milling cutter, are shown in Fig. 57. The feeding down of the cutter will not equal a (Fig. 56) on account of the 15-degree clearance angle, but will be equal to a X cos 15 degrees. This distance is shown as b in Fig. 57. The values of b for various pitches are given below: Threads per Inch. 0 . . 0.0038 1 I . 0.0026 12 .. 0.0025 14 . 0.0021 i 8 ;;;;;. 0.0016 .. 0.0011 While b is theoretically different from a, it will be seen by comparing the two tables that the difference is so small as to be insignificant for all practical purposes. We will now consider the case where the tap is cut with a chaser at right angles to the outside tapered sur¬ face of the blank. We will find that in cutting this chaser with a milling cutter and holding it as shown in Fig. 58, we will not need to feed down the milling cutter for each consecutive tooth to be cut, but the milling cutter itself must be provided with different angles for the different sides of the thread. In Fig. 59 the actual angles of the sides of the thread with a line perpendicular to the outside surface of the blank are given as 28° 13 7 and 31° 47', respectively, the sum of these angles being 60°. The chaser being cut with 15 degrees clearance, these angles 128 SMALL TOOLS in the cutter will be 29° 3' and 32° 41' respectively, the sum of these two angles being 61° 44'. In Fig. 58 the manner of holding the chaser in a vise and the angles of the cutter are plainly shown. In the view to the left in Fig. 59 are indicated the angles to which to plane a single¬ point cutter held in the same manner as the chaser and provided with a clearance of 15 degrees. Care must be taken when making chasers to be used in the manner indicated in the first case that the elevating shown in Fig. 58 screw of the milling machine, by means of which the chaser is raised up toward the milling cutter for each consecutive tooth cut, is correct, and that no back lash enters as a factor in the operation. As this is difficult to insure against, it is advisable to cut the threads according to the second method, as there the chances of error are smaller, it only being required that the milling cutter be ground to the exact angles wanted, and that the chaser afterward be presented to the \york fully perpendicular to THREADING TOOLS — DEFINITIONS OF TAPS 129 the outside surface. The angle which the face of the chaser in the latter case will make with the axis of the tap to be cut is 1° 47'. This angle, however, would be difficult to measure unless the threading tool were held in a tool-post provided with some kind of a graduated swivel. In such a case a chaser could be placed so that its face would be parallel with the axis of the tap, clamped to the tool-post swivel, and this swivel afterward moved around in an arc corresponding to 1° 47k Ordinarily, however, if the tap blank is turned to a correct taper, the chaser can be set from the outside surface of the blank, its face being parallel to this surface in a horizontal plane through the axis of the tap. The Influence of the Thread Miller on Threading Tools. With the advent of the thread milling machine the extreme accuracy of thread forms hitherto scrupulously adhered to was sacrificed for the greater commercial advantages in rapid thread-cutting. The thread milling cutter, while, as a rule, itself ground to the correct form of the thread, is, when in use, swiveled around a horizontal axis at right angles to the axis through the center of the hole of the cutter in order to conform to the angle of helix of the thread to be cut. By swiveling the cutter in this way the exact form of thread is not duplicated in the screw to be cut, inasmuch as the correct angle of the thread will not be measured in a horizontal plane through the axis of the screw as it ought to be, but in a plane at right angles to the direction of the helix of the thread. It is obvious that the inaccuracy is increased in proportion to the angle of helix. For fine pitches the inaccuracy is so small as to be insignificant for practical consideration, 130 SMALL TOOLS but as the pitches grow coarser, the same diameter being retained, the differences between the correct thread form and the one produced become enough pronounced to demand attention. It is particularly when cutting Acme threads that this difference is great enough to cause difficulties, because of the fact that the pitches on Acme screws are usually twice as coarse as those on United States or V standard screws. The head of the thread milling machine carry¬ ing the cutter has to be tilted over so much in cutting the screw that the dimensions of the thread produced differ by measurable amounts from the standard thread, and if a screw with such a thread is placed in a nut cut with a tap having a correct thread, a very poor fit will result. The variations are, of course, even greater in the case of multiple-threaded screws, and the use of the thread milling machine for cutting such screws may be prohibitive in extreme cases unless the taps for the nuts are produced in a manner similar to the one used for the screws. One way would be to mill the taps on screw milling machines. This is also done to a certain extent by man¬ ufacturers of these taps. But if it is desired to cut the taps in a lathe, and there are not enough taps to be made to warrant the making of thread tools to suit all the different angles of helix which may occur, a correct thread tool or single-point cutter may be used and placed in a tool-post or holder capable of swiveling adjustment, so that the tool can be tilted over to the same angle as the milling cutter would be set to in cutting the screw. Such a tool holder is shown in Fig. 60. An incidental advan¬ tage and saving of expense is gained by the use of such a holder, because the tool or single-point cutter, being set over to conform to the angle of the thread, does not need to be provided with side clearance, but can be made THREADING TOOLS — DEFINITIONS OF TAPS 131 as if intended for cutting a circular groove or a thread of very fine pitch. The tool holder shown is provided with a tongue A and a clamp B to hold single-point cutters of the kind manufac¬ tured by the Pratt and Whitney Company. The stem C of the holder is fitted to a cast-iron bracket D, which is clamped to the cross slide of the lathe. The screw E clamps the holder in position. The shoulder F of the holder is grad¬ uated in degrees in order to indicate the angle to which the tool is tilted. The holder, as shown, is of the very 132 SMALL TOOLS simplest construction in order to merely convey the idea of the tool. With a little more elaboration in the design a still more efficient tool may result, but for temporary use the one shown will prove efficient. Square-Thread Tools. The top of the thread of square-threaded screws with coarse lead is always thicker or wider than the thread at Fig. 61. Extreme Example Showing the Difference in Width at Top and Bottom of the Square Thread the bottom. The space between the thread is still of the same square section. The explanation of the difference between the thickness of the thread at the top and bottom is that a thread with a steep lead is approximating a groove cut parallel with the axis of a screw as shown in Fig. 61. We see that in this extreme case, while the groove is of correct square section, the portion between the grooves, or the “thread/ 7 is far wider at the top than at the bottom. Evidently this imperfection in square threads is greater the steeper the pitch is. Where the THREADING TOOLS — DEFINITIONS OF TAPS 133 lead is small compared with the diameter, the difference in width at the top and bottom of the thread is not noticeable. It is clear that if a nut is to perfectly fit a screw having the top of the thread wider than the width at the bottom, the thread in the nut must be cut accordingly. The tool for cutting the thread in the nut must be wider at the point and its sides must be ground convex. The thread in such a case is first cut with parallel sides to the required depth with an ordinary square threading tool; then this special tool is used for widening the thread to the required shape. The exact shape of the square threading tool is obtained by drilling a hole in a piece of steel, which latter is of the same diameter as the screw, inserting a plug in this hole and threading the piece the same as the screw, so that the inserted plug is located in the middle of a thread with the grooves on each side cutting into it. If the plug is then removed, it will show the exact section of the thread in the screw and the shape which should be given to the thread tool for threading the nut. When cutting square threads it is customary to make the screws exactly according to the theoretical standard of the square thread. The width of the point of the tool for cutting screws with square threads is therefore exactly one-half of the pitch, but the width of the point of the tool for cutting taps, which afterwards are used for tapping nuts, is slightly less than one-half the pitch, so that the groove in the tap becomes narrower, and the land or cut¬ ting point wider than the theoretical square thread, thereby cutting a groove in the nut which will be slightly wider than the thread in the screw, so as to provide for clearance. An inside threading tool for threading nuts evidently must be of the same width as the land on the tap would be, or in other words, slightly wider than one- 134 SMALL TOOLS half the pitch. This provides, then, the required clear¬ ance. Table XXXII gives the width of the point of the tool for all ordinary pitches from one to twenty-four threads per inch. The second column gives the width of the point for cutting taps to be used for producing square- thread nuts. The third column gives the width of the point of the tool for cutting screws, which, as we have said, equals one-half the pitch; and the fourth column gives the width of the point for inside threading tools for nuts. While the table has been carried to as fine pitches as those having twenty-four threads per inch, square- threaded screws having so fine a pitch are very seldom used. Some manufacturers of square threading tools, however, make square threading tools for pitches as fine as these, and for this reason they have been included. TABLE XXXII. WIDTH OF TOOL FOR CUTTING SQUARE THREADS. Width of Point of Tool. Width of Point of Tool. No. of No. of Threads For Threads For per Inch. For Taps. For Screws. Inside Thread Tools per Inch. For Taps. For Screws. Inside Thread Tools for Nuts. for Nuts. i 0.4965 0.5000 0.5035 8 0.0615 0.0625 0.0635 n 0.3715 0.3750 0.3785 9 0.0545 0.0555 0.0565 H 0.3303 0.3333 0.3363 10 0.0490 0.0500 0.0510 if 0.2827 0.2857 0.2887 11 0.0444 0.0454 0.0464 2 0.2475 0.2500 0.2525 12 0.0407 0.0417 0.0427 2} 0.1975 0.2000 0.2025 13 0.0375 0.0385 0.0395 3 0.1641 0.1666 0.1691 14 0.0352 0.0357 0.0362 31 0.1408 0.1428 0.1448 15 0.0328 0.0333 0.0338 4 0.1235 0.1250 0.1265 16 0.0307 0.0312 0.0317 41 0.1096 0.1111 0.1126 18 0.0272 0.0277 0.0282 5 0.0985 0.1000 0.1015 20 0.0245 0.0250 0.0255 51 0.0894 0.0909 0.0924 22 0.0222 0.0227 0.0232 6 0.0818 0.0833 0.0848 24 0.0203 0.0208 0.0213 7 0.0699 0.0714 0.0729 THREADING TOOLS — DEFINITIONS OF TAPS 135 In Fig. 62 a diagram is presented which will facilitate the calculation of the clearance angles required by square threading tools. Fig. 62. Diagram of Clearance Angles for Square Thread Tools Referring to Fig. 63, the angle on the leading side is figured to correspond to the root diameter of the screw to be cut, whereas the angle on the following side is determined bj^ the outside diameter of the screw. The use of the diagram, Fig. 62, is best indicated by an 136 SMALL TOOLS example. Suppose it is required to find the angles for the square threading tool for a screw 2 inches in diameter, having 4 threads per inch. The root diameter equals 2 — i = If inches. To find the angle for the leading side of the tool, follow the vertical line from If inches diameter to the intersection with the horizontal line from 4 threads per inch, and from the intersection follow the nearest diagonal line, thus finding the clearance angle of the leading side of the tool equal to 2| degrees. To find the angle for the following side, follow the vertical line from 2 inches diameter to its intersection with the horizontal line from 4 threads per inch. From the intersection follow the nearest diagonal line, finding thus the clear- Fig. 63. Clearance Angles of Square Threading Tools ance angle for the following side equal to 2\ degrees. These angles are the theoretical clearance angles. For practical purposes, slightly greater clearance should be given. Special Thread Tool Holder. The cut, Fig. 64, shows a spring thread tool holder the object of which is to permit the thread tool to spring away from the work if too heavy a cut is taken. This tool consists of a holder A, which is provided with a projection into which a hole is drilled for obtaining the spring effect, and the usual clamp and binding nut. The slot B is cut from the lower side of the holder into the hole, and permits the front part of the holder to recede THREADING TOOLS — DEFINITIONS OF TAPS 137 under a too heavy cut. Proper resistance is given to the tool by the set screw C, which has a spring at the lower end, acting upon the front part of the holder. The part D is an inserted blade or key which keeps the front part of the holder from bending to one side while cutting. A great many designs of spring tool holders have been tried, and the one shown in Fig. 64 is comparatively common. The difficulty with holders of this kind is that it is almost impossible to adjust the screw for each particular pitch to be threaded so that the spring will have proper tension. It is evident that in cutting a coarse thread there is no need of the tool being as sensitive as when cutting a very fine thread, but there is no means for judging when in each particular case the proper springing action has been attained. Another objection to the design shown is that it prevents a full and clear view of the thread being cut, the projecting part extending partly above the work. 138 SMALL TOOLS Of all spring thread tool holders hitherto designed, how¬ ever, this one is about as good as any. A spring tool holder for threading tools which will overcome the objec¬ tions mentioned is greatly in demand, and many attempts have been made to solve the problem, but none have been entirely successful. Definitions of Different Kinds of Taps. Before entering into a detailed discussion of the require¬ ments and qualifications of taps, we will here briefly review the uses of various kinds of taps and define the names for different classes commonly used. In some cases there are doubts as to the proper name for a cer¬ tain tap, and some confusion exists for instance as to the difference between a tapper tap and a machine tap. Per¬ sons not very familiar with the nomenclature of tool¬ making would also easily confuse such names as screw machine tap, machine screw tap, and machine tap. In order to avoid any misunderstandings throughout this treatise we will settle definitely upon the meaning of the terms used. The same names as are used by leading tap-makers and manufacturers of small tools will be adhered to. Hand taps, as the name implies, are taps used for tap¬ ping holes by hand. All taps used in this manner, how¬ ever, are not termed hand taps, the name as commonly used referring only to straight taps used by hand. In fact, not even all taps which would come within this descrip¬ tion are properly termed hand taps. The machine screw tap is nothing but a hand tap, but is not ordinarily termed so, inasmuch as all taps used for tapping holes for standard machine screws are classified as machine screw taps. THREADING TOOLS — DEFINITIONS OF TAPS 139 Tapper taps and machine taps are both used for tapping nuts in special nut-tapping machines. There is, however, a distinct difference between these two kinds of taps, although the names are often confused. The tapper tap is the original and older form used for machine nut tap¬ ping, and is simpler in its construction, consisting simply of a long chamfered and a straight portion, and usually relieved only on the top of the thread of the chamfered part. The construction of the machine tap is more com¬ plex, and will be described in detail later. The latter tap is capable of greater endurance, and is used preferably in tough material and when good cutting qualities are necessary. Screw machine taps, as the name implies, are used for tapping in the screw machine. They are provided with shanks fitting either the turret holes of the machine or bushings inserted in these holes. As these taps ordi¬ narily cut threads down to the bottom of a hole they are provided with very short chamfer. Pulley taps are used for tapping holes which cannot be reached by ordinary hand taps, as for instance the set¬ screw or oil-cup holes in the hub of a pulley which can be reached only through a hole drilled in the pulley rim. The pulley tap, practically, is nothing but a hand tap with a very long shank. Die taps are used for cutting threads in dies. They are provided with a very long chamfer, and, while used by hand, resemble in their construction the machine tap. Hob taps are used for sizing dies. Because of their construction they cannot be used for actual thread-cutting, but can only take a slight finishing chip. A special form is the Sellers hob, which is used with a special guiding arrangement and is provided with a long guide at the 140 SMALL TOOLS end of the thread. The commonly used hob tap, or the short-shank hob tap, is in all particulars similar to an ordinary hand tap, except in regard to fluting. Taper taps, as properly understood, are any taps which have the diameter of the part of the thread nearest the shank larger than the diameter of the point, the inter¬ mediate portion being formed by a gradual taper from the point to the end of the thread at the shank. It is necessary to note this proper meaning of the expression “ taper tap ” because of the fact that the first tap in a set of hand taps is commonly, but not properly, referred to as a taper tap. As this expression is used to denote two widely different things, and as its common usage pre¬ cludes any possible change, we will in the following pages distinctly state which of the two meanings is referred to in any particular case. The most common of all taper taps is the pipe tap, which is used for tapping holes for standard pipe sizes. There is also a particular form of pipe tap termed the straight pipe tap, which, as the name implies, is straight. This latter tap, in fact, is nothing but a hand tap, the name merely indicating the standard sizes in regards to diameter and pitch conforming to which this tap is made. Other less common forms of taper taps, which, how¬ ever, are largely used in boiler and locomotive work, are mud or wash-out taps, sometimes termed arch pipe taps, taper boiler taps, and patch-bolt taps. Pipe hobs are used for sizing pipe dies. They are longer than ordinary pipe taps and fluted in a different manner. Stay-bolt taps are used in locomotive boiler work. Their action is that of a hand tap, but they are usually provided with a reamer portion preceding the threaded part. A special form of stay-bolt taps is embodied in THREADING TOOLS — DEFINITIONS OF TAPS 141 the spindle stay-bolt tap, which revolves on a central spindle provided with a taper guide on the front end. Straight boiler taps are used in boiler work. They differ in construction somewhat from the taper boiler tap, and are provided with a straight portion, which in fact puts them in the same class as ordinary hand taps. A number of taps for special purposes have been named after the persons with whom they originated, or after the devices with which they are used. They embody, how¬ ever, no principles of construction differing from any of those mentioned, in so far as the tap part is concerned. Inserted cutter taps may belong to any of the classes mentioned before, and are in a class by themselves only because of not being solid but having the cutting teeth on blades which are inserted and held in a body in a suitable manner. CHAPTER IV. HAND TAPS. Of all taps, the ones most commonly used are hand taps. While there is a great deal of difference of opinion in regard to the proper way in which to make most machinists’ tools, hand taps have been made so long and in such quantities as to have nearly settled all disputes regarding their necessary qualifications. There is only one point on which opinions differ, and this will be referred to later. Even on this point it is probably not so much a difference of opinion as a difference in common usage. Hand Taps Made in Sets. Hand taps are, as a rule, made in sets of three, the taps being termed taper, plug, and bottoming taps respec¬ tively. When using all three for tapping a hole they are used in the order named. A set of three taps is shown in Fig. 65. As indicated in the cut, the point of the taper tap is turned down to the diameter at the bottom of the thread for a length of about three or four threads. This turned-clown portion acts as a guide and aids in securing a straight tapped hole. From the upper end of this guide the thread is chamfered until it reaches the full diameter of the tap. The length of this chamfered por¬ tion should be from six to seven threads. The remaining part of the threaded portion of the tap is turned straight or parallel. The plug tap is chamfered at the point for a length corresponding to about three threads. The remaining portion of the thread of this tap is then turned 142 HAND TAPS 143 parallel. 'The bottoming tap is made practically in the same way as the plug tap, with the exception that only about one thread is chamfered at the point of this tap. It is understood that the diameter of the straight or parallel portion of the thread of all the taps in the set is the same. The question of the principle according to which hand taps should be made in sets is the point about which --< - WwAAAAAA/WO~ rvWWWWM Plug -< ■^^AAAAAAAiri Fig. 65. Set of Three Taps made According to Prevailing Practice there may be some difference of opinions. It is evident that from a critical point of view this way of making taps intended to be used in sets cannot be considered correct, inasmuch as the work to be done by the taps will be very unevenly distributed on account of the fact that all the taps in the set have the same diameter. The chamfered portion of the first or taper tap will have the bulk of the work to do, while the two following taps practically have no work to do except in a case where a full thread is 144 SMALL TOOLS required at the bottom of a hole; but even then the duties of the different taps in the set are rather unevenly distributed. For this reason it is very obvious that taps intended for use in sets should vary in diameter, as shown in Fig. 66, so that each tap will have a reasonable amount of work to do; of course, the last tap, being a finishing tap, should have less work to do than the first two. The making of Fig. 66. Set of Three Taps made with Gradually Increasing Diameters hand taps in sets, in this manner, although being both for practical and theoretical reasons the only correct and the best way, does not seem to have met with the favor of the tap manufacturers, there being only one leading firm (the Pratt and Whitney Company) which manufactures hand taps made in this manner. Objection to Making Hand Taps in Sets. — The prin¬ cipal objection to making hand taps in sets as described above, and the probable cause for their slow introduction, HAND TAPS 145 must be that when using taps of such description the whole set always has to be used, whereas for a short hole to be tapped clear through a piece the taper tap alone will be found sufficient, if the straight portion of the tap is up to the full diameter; and in fact all three taps, when all made with the same diameter, are seldom used except when a full thread is wanted at the bottom of a hole. However, the cutting of the full thread tapped clear through a piece, by the taper tap in one operation, places an undue stress on this tap, and will not give as smooth a thread as if the hole had been run through by a set of taps of varying diameter, each of which cuts a fair amount of the thread. Proportioning the Work to he Done by Each Tap in a Set. — The question of making the taps in a set with differ¬ ent diameters is of so great importance, and will prob¬ ably be given more or less attention by tap-makers in the future, that it may be well worth to analyze the problem of just how much each succeeding tap should be larger in diameter than the preceding one. We must also remark at the outset that it is not enough that there is a variation in the diameters of the taps as measured on the top of the thread; there must also be a difference in the diameters measured in the angle of the thread. The two diagrams Figs. 67 and 68 show by means of different cross-sectioning the amounts of metal removed by the different taps in a set made as outlined above. The first diagram represents the cutting of a V thread, the second a United States standard thread. The differences in the outside diameters of the taps as well as in the angle diameters are clearly indicated. We will now proceed to express these differences by formulas, and it is, of course, evident that the values will vary with the pitch of the thread. In the formulas given 146 SMALL TOOLS in the following the proportions between the amount of metal removed by each succeeding tap are so adjusted that the first tap cuts the greater part of the thread, the second tap a somewhat smaller amount, and, finally, the last tap in the set a comparatively slight proportion of the total thread. If we first consider the V thread, and take the pitch of the thread as the working factor, the distances from the top of the full thread to the top of the thread of the plug and taper taps respectively will be found according to the following formulas: a = 0.15 X pitch. b = 0.47 X pitch. Fig. 67. Section Showing Relative Amount Removed by each Tap in a Set of Three Taps, Sharp V Thread The relative values of a and b are shown in the diagram of the sharp V thread, Fig. 67. Considering the differences in the angle diameter of the thread, these ought to be the amounts c and d, respectively, smaller than the correct angle diameter, for the plug and taper taps: For plug tap c =0.09 X pitch, For taper tap d =0.17 X pitch. HAND TAPS 147 For United States standard thread the formulas would be e = 0.05 X pitch and / = 0.33 X pitch for the differences on the top of the thread (for the rela¬ tive values of e and / see diagram, Fig. 68). The angle diameter perhaps should, strictly considered, vary differently from that of a sharp V thread, but the variation would be so slight that it can be eliminated in all practical considerations, and the variations between the correct angle diameter and those of the plug and taper tap can be made the same as for sharp V thread, viz., Fig. 68. Section Showing Relative Amount Removed by each Tap in a Set of Three Taps, U. S. Standard Thread 0.09 X pitch for the plug tap and 0.17 X pitch for the taper tap. For convenience, and in order to save the trouble of figuring the values from the formulas in each individual case, Table XXXIII, showing the amounts found from the formulas, is given herewith. The quantities a, b, e, and / are given as 2 a, 2 b, 2 e, and 2 /, thus giving the differ¬ ences for the diameter (a, b, e, and / being the difference on one side only). Only as many decimals are given as are necessary for all practical purposes. The differ¬ ences in the angle diameters, although alike for United 148 SMALL TOOLS States standard thread and sharp V thread, have been repeated in both columns in order to secure uniformity. TABLE XXXIII. DIMENSIONS FOR MAKING HAND TAPS IN SETS. No. of Thread per Inch. Pitch. U. S. Standard Thread. Standard Sharp V Thread. 2 /. 2 e. d. c. 2 b. 2 a. d. c. 3 0.3333 0.222 0.033 0.056 0.030 0.312 0.100 0.056 0.030 31 0.2857 0.190 0.029 0.048 0.026 0.269 0.086 0.048 0.026 4 0.2500 0.167 0.025 0.042 0.023 0.235 0.075 0.042 0.023 41 0.2222 0.148 0.022 0.037 0.020 0.209 0.067 0.037 0.020 5 0.2000 0.133 0.020 0.033 0.018 0.188 0.060 0.033 0.018 51 0.1818 0.121 0.018 0.030 0.016 0.171 0.055 0.030 0.016 6 0.1667 0.111 0.017 0.028 0.015 0.157 0.050 0.028 0.015 7 0.1429 0.095 0.014 0.024 0.013 0.134 0.043 0.024 0.013 8 0.1250 0.083 0.012 0.021 0.011 0.118 0.037 0.021 0.011 9 0.1111 0.074 0.011 0.018 0.010 0.104 0.033 0.018 0.010 10 0.1000 0.067 0.010 0.017 0.009 0.094 0.030 0.017 0.009 11 0.0909 0.061 0.009 0.015 0.008 0.085 0.027 0.015 0.008 12 0.0833 0.056 0.008 0.014 0.008 0.078 0.025 0.014 0.008 13 0.0769 0.051 0.008 0.013 0.007 0.072 0.023 0.013 0.007 14 0.0714 0.048 0.007 0.012 0.006 0.067 0.021 0.012 0.006 16 0.0625 0.042 0.006 0.010 0.006 0.059 0.019 0.010 0.006 18 0.0556 0.037 0.0055 0.009 0.005 0.052 0.017 0.009 0.005 20 0.0500 0.033 0.005 0.008 0.0045 0.047 0.015 0.008 0.0045 22 0.0455 0.030 0.0045 0.0075 0.004 0.043 0.014 0.0075 0.004 24 0.0417 0.028 0.004 0.007 0.004 0.039 0.0125 0.007 0.004 26 0.0385 0.026 0.004 0.0065 0.0035 0.036 0.0115 0.0065 0.0035 28 0.0357 0.024 0.0035 0.006 0.003 0.034 0.0105 0.006 0.003 30 0.0333 0.022 0.0035 0.0055 0.003 0.031 0.010 0.0055 0.003 32 0.0312 0.021 0.003 0.005 0.003 0.029 0.0095 0.005 0.003 34 0.0294 0.020 0.003 0.005 0.0025 0.028 0.009 0.005 0.0025 36 0.0278 0.019 0.003 0.0045 0.0025 0.026 0.0085 0.0045 0.0025 38 0.0263 0.018 0.0025 0.0045 0.0025 0.025 0.008 0.0045 0.0025 40 0.0250 0.017 0.0025 0.004 0.0025 0.0235 0.0075 0.004 0.0025 42 0.0238 0.016 0.0025 0.004 0.002 0.0225 0.007 0.004 0.002 44 0.0227 0.015 0.0025 0.004 0.002 0.0215 0.0065 0.004 0.002 46 0.0217 0.0145 0.002 0.0035 0.002 0.0205 0.0065 0.0035 0.002 48 0.0208 0.014 0.002 0.0035 0.002 0.0195 0.006 0.0035 0.002 50 0.0200 0.0135 0.002 0.0035 0.002 0.019 0.006 0.0035 0.002 52 0.0192 0.013 0.002 0.003 0.0015 0.018 0.006 0.003 0.0015 54 0.0185 0.0125 0.002 0.003 0.0015 0.0175 0.0055 0.003 0.0015 56 0.0179 0.012 0.002 0.003 0.0015 0.017 0.0055 0.003 0.0015 58 0.0172 0.0115 0.0015 0.003 0.0015 0.016 0.005 0.003 0.0015 60 0.0167 0.011 0.0015 0.003 0.0015 0.0155 0.005 0.003 0.0015 HAND TAPS 149 In regard to the chamfer at the point of the thread it is good practice to chamfer 6 threads on the first, 3 on the second, and 1 on the last tap in a set when made as out¬ lined above. What has been said before in regard to making hand taps in sets has special reference to taps with United States standard thread and sharp V thread. It has also bearing upon taps with International or French standard thread. No table, however, can be considered necessary for these stand¬ ards. As the shape of the threads for the latter standards is the same as for the United States standard, the values in the column under “United States Standard Thread,’' if selected for the pitch which comes nearest to a given pitch in millimeter, will give satisfactory working figures. Acme Taps in Sets. — While it has not become the generally adopted custom to make the three taps in a set of hand taps with the United States or V standard thread of. different diameters, so that each tap cuts a certain proportion of the metal to be removed in forming the thread, this construction becomes imperative when mak¬ ing taps with Acme or square threads. The reason for this is that the pitch of the thread of taps with the latter class of threads is usually coarser for corresponding diameters, and the same size tap is therefore required to remove more metal in this case than if it were provided with 60-degree threads. The shape of the Acme and square threads, with their wide flats at the top of the thread, also increases the resistance to the cut, if the full depth of the thread should be produced with one tap. For these reasons Acme and square thread taps, intended for cutting a complete thread from a nut blank, and not intended merely for finishing a thread cut in a lathe, are always made in sets, each tap in the set being smaller in diameter than the one following. 150 SMALL TOOLS While for Acme and square thread taps three taps in a set are undoubtedly the most common, these taps may be made with only two taps in a set for very fine pitches, and with as many as five taps in a set for very coarse pitches. The last tap in these sets is not made on the principle of a bottoming tap, as Acme and square threads are seldom used except in nuts which are threaded straight through. There is, in fact, a more liberal chamfer on all the taps in the set than is common with ordinary taps. In giving formulas and definite data we will first turn our attention to the Acme tap. On account of the clear¬ ance required on the top of an Acme thread between the screw and the nut, the actual diameter of the last or finishing tap in the set must be larger than the standard or nominal diameter of the screw or nut. If A = actual diameter of finishing tap and B = root diameter of the thread, the relations of these values to the nominal or standard diameter of the tap are A = nominal diameter + 0.020 inch, B = nominal diameter — ( - T - ; ——=- . \number of threads per inch + 0.020 inch!. Table XXXIV gives the proportions for the diameters of Acme taps in sets of two up to and including five. Referring to the table, C = the actual diameter of the suc¬ ceeding taps in the sets, D = the diameter at the point of the thread, and E = the length of the straight or parallel portion of the thread in relation to the whole length of the thread L. In order to simplify the expressions in the formulas the difference between the actual diameter of the finishing tap A and the root diameter B is termed G. HAND TAPS 151 TABLE XXXIV. ACME THREAD TAPS IN SETS. No. of Taps in Set. Tap. C D E 2 1st B + 0.65 G B + 0.010 inch L 6 L 2nd A C on 1st tap — 0.005 inch 3 1st B + 0.45 G B + 0.010 inch L 6 3 2nd B + 0.8 G C on 1st tap - 0.005 inch L 4 3rd A C on 2nd tap - 0.005 inch L 3 1st B + 0.4 G B + 0.010 inch L 8 2nd B + 0.7 G C on 1st tap — 0.005 inch L 6 4 3rd B + 0.9 (j C on 2nd tap — 0.005 inch L 4 4th A C on 3rd tap - 0.005 inch L 3 1st B + 0.37 G B + 0.010 inch L 8 2nd B + 0.63 G C on 1st tap - 0.005 inch L 6 5 3rd B + 0.82 G C on 2nd tap - 0.005 inch L 5 4th B + 0.94 G C on 3rd tap - 0.005 inch L 4 5th A C on 4th tap - 0.005 inch L 3 Square-Thread Taps in Sets. — If we now turn to the square-thread tap, and let the letters represent the same dimensions as in the case of Acme taps, we will find our dimensions in Table XXXV. We must, however, take into account that there is no clearance allowed on the 152 SMALL TOOLS top of the thread, and that the depth of a square thread equals one-half of the pitch. Therefore A = the nominal diameter of the tap and B — the nominal diameter — pitch of thread. No. of Taps in Set. Tap. 1st 2nd 1st 2nd 3rd 1st 2nd 3rd 4th 1st 2nd 3rd 4th 5th TABLE XXXV. SQUARE-THREAD TAPS IN SETS. B + 0.67 G A B + 0.41 G B + 0.8 G A B + 0.32 G B + 0.62 G B + 0.90 G A B — 0.005 inch C on 1st tap — 0.005 inch B — 0.005 inch C on 1st tap — 0.005 inch C on 2nd tap — 0.005 inch B + 0.26 G B + 0.50 G B + 0.72 G B + 0.92 G A B — 0.005 inch C on 1st tap — 0.005 inch C on 2nd tap — 0.005 inch C on 3rd tap — 0.005 inch B — 0.005 inch C on 1st tap — 0.005 inch C on 2nd tap — 0.005 inch C on 3rd tap — 0.005 inch C*. r\n ItV* ton n nnc Kqio^iec j | | ^loo^lco HAND TAPS 153 By comparing the tables given for the Acme and the square thread taps it will be noticed that the differences occur in the columns for the values of C and D, for the latter, however, only in the case of the first tap in each set. That the values for C should differ is evident, inas¬ much as there is a decided difference in the cutting action of an Acme and a square thread tap. In a set of square- thread taps each tap is a finishing tap in itself, because the lands of each tap are alike. In a set of Acme taps each tap may be considered as a finishing tap for the preceding one. The last tap in each set has less work to do in order to assure a smooth bottom of the thread in the nut tapped. In regard to the dimension D, this is larger than the root diameter of the tap in the case of an Acme tap, because the nut is supposed to be bored out with a clearance of 0.020 inch, as explained when reference was made to vari¬ ous forms of threads. This, then, still permits the tap to enter into the nut. In the case of a square-thread tap there is no standard as to how much the hole in the nut should clear the root of the thread, and therefore the point of the tap is made below the root diameter on the first tap in each set to insure that the tap can enter the nut. In order to further facilitate the entering of the tap in the nut, there should be, besides the long chamfer referred to above, a slight chamfer at the point of the thread, by means of which the tap will easily find its way into the nut to be tapped. This chamfer should not be lacking on any of the taps in the set. Acme and Square Thread Taps in Sets of Three. — As was mentioned before, the most common way of making Acme and square thread taps is to make them with three taps in a set. The values necessary to obtain C in Tables XXXIV and XXXV have therefore been figured for a set of three taps for the most common 154 SMALL TOOLS pitches and are given in Table XXXVI. it must be understood that the formulas given and the tables figured from them possess a certain degree of flexibility, inasmuch as the making up of the formulas necessarily required some assumed standard to be selected as embodying the best practice. Certain conditions may require deviations from the rules given. While, how¬ ever, the formulas which are given may not suit all pos¬ sible conditions, they are made up to suit ordinary needs, and they are particularly valuable in suggesting the possi¬ bility of systematizing the making of tools too often given up to “guesswork.” TABLE XXXVI. TABLE FOR MAKING ACME AND SQUARE THREAD TAPS IN SETS OF THREE. Acme Thread. Number of Threads per Inch. Amount in Inches to add to Root Diameter of Tap to obtain Diameter of Straight Part of Thread of Square Thread. Amount in Inches to add to Root Diameter of Tap to obtain Diameter of Straight Part of Thread of 1 H 2 3 31 4 4 } 5 5 * 6 7 8 9 10 12 1st Tap. 0.468 0.318 0.243 0.198 0.168 0.147 0.130 0.118 0.108 0.100 0.093 0.082 0.074 0.068 0.063 0.055 2nd Tap. 0.832 0.566 0.432 0.352 0.298 0.261 0.232 0.210 0.192 0.178 0.166 0.146 0.132 0.121 0.112 0.098 1st Tap. 0.410 0.273 0.205 0.164 0.137 0.117 0.102 0.091 0. 82 0.075 0.068 0.059 0.051 0.046 0.041 0.034 2nd Tap. 0.800 0.533 0.400 0.320 0.267 0.229 0.200 0.178 0.130 0.146 0.133 0.114 0.100 0.089 0.080 0.067 HAND TAPS 155 In using Table XXXVI it is necessary first to find the root diameter by subtracting the double depth of the thread, plus the clearance in the case of Acme thread, from the nominal diameter of the tap, and then add the amount stated opposite the pitch for the respective taps in the set. It is difficult to draw a distinct line between hand taps and machine taps when these are provided with Acme or square threads, for while these taps are as a rule used as hand taps, the construction is that of a machine tap. In general practice, however, these taps are generally classified as hand taps. General Construction of Acme and Square Thread Taps. — Before we leave the Acme and square thread taps to return 1 n 1 1 1 LT !^r l 1 . ►t TAPER IN BOTTOM' OF THREAD Fig. 69. General Appearance of Acme and Square Thread Taps to the regular hand taps, we will point out some of the peculiarities in their construction. The first tap in a set should be turned to a taper in the bottom of the thread for a distance of about one-quarter of the whole length of the threaded part as indicated in Fig. 69. The diameter at the root of the thread at the point of the first tap should thus be less than the standard root diameter. If the taper selected is such that the root diameter will be about one- thirty-second inch smaller at the point than the root diame¬ ter proper of the tap, that will be found to greatly increase the ease with which the tap can be started in the nut. The first tap in the set should also be provided with a groove or a secondary thread on top of the ordinary thread. This will aid in preventing the tap from reaming, instead of 156 SMALL TOOLS actually cutting a thread in the nut. This secondary thread may continue the full length of the chamfered por¬ tion of the first tap. The first tap should also preferably be provided with a short pilot as shown in Fig. 70 to guide the tap straight into the nut. When the pitch is very coarse as compared with the diameter of the tap, or when the number of taps in a set is small in proportion to the work they are to perform, the first tap in the set should be provided with spiral flutes, forming a right angle with the angle of direction of the thread. In other words, the spiral of the flutes should be left-hand for a right-hand tap, and vice versa. This will greatly increase the cutting qualities of the tap. In fact, it evidently would increase Fig. 70. Difference between First and Subsequent Taps in a Set of Acme or Square Thread Taps the efficiency of all taps to flute them in this manner, but whenever it is not imperative it is avoided on account of the increased expense and difficulty. When the first tap in a set is provided with a pilot, the diameter of this should be made a trifle smaller than the hole in the nut to be tapped (from 0.002 to 0.005 inch smaller). The length of the pilot should be about equal to the diameter of the tap, or, at least, not shorter than 0.75 times the diameter. The length of the pilot should project from the regular length of the thread of the taps in the set, but in order to make the total length of all the taps in the set the same, the length of the pilot should be subtracted from the length of the shank in the first tap. This is indi¬ cated by the dotted lines in the cut, Fig. 70, where the full HAND TAPS 157 lines show the second and third taps in a set, and the dotted the pilot and the modification in the shank of the first tap. At the end of this chapter we shall return to these taps when giving formulas and length dimensions for all kinds of hand taps. We shall now again take up ordinary hand taps with United States, sharp V, or Whitworth form of thread. What will be said in regard to the fluting of these taps applies of course to Acme and square thread taps as well. The relief of the latter taps will be specially men¬ tioned later. Cutting Taps with Dies. While it is rather common to cut the threads on taps with dies instead of cutting the thread in a lathe, it is a practice which can hardly be recommended. Any inaccuracy in the lead of the thread of the die will be duplicated in the tap, and still further augmented by the change in lead in the tap due to hardening. Sometimes, when the threads on small taps are cut with dies in screw machines, it is found that the taps have a “stretched” thread, or in other words, that the lead of the thread is longer than the standard lead. On examination the die may be found to be properly made, but further investi¬ gation may show that the heavy turret slide of the screw machine was dragged along with the die, and this has caused the thread to stretch, making the lead long. For this reason it is not advisable to cut the thread of taps which are required to have the highest possible degree of accuracy in a screw machine. It is particu¬ larly bad practice in the case of taps with a long threaded portion or taps used for threading long holes, as the inaccuracies in lead will be so much the more pronounced. The opinion that taps stretch or become long in the lead when cut by dies in screw machines is one that is 158 SMALL TOOLS not universally accepted, and it must be admitted that the reason given for this occurrence does not seem entirely plausible. Whatever be the cause, however, the fact that taps cut in screw machines are liable to be inaccurate remains undisputed. It is true that it is the practice with some firms manu¬ facturing taps to cut the thread with dies in a screw machine, but in the case of manufacturing some factors enter which make this permissible. In the first place, the difference in price when threading in a screw machine or cutting the thread in a lathe is so great that a number of taps can be thrown out at the final inspection if their inaccuracy in lead is greater than the limits of error per¬ mitted, and a saving may still be the result of the method employed. It must be understood, however, that such a procedure is applicable only to small taps, where the loss of material is not very significant should a tap not pass the inspector, but this process should not be applied to taps where great accuracy is especially desired. In such cases nothing can compare with a thread cut in a lathe provided with a lead screw which itself has been properly tested as to its own accuracy. For ordinary machine screw taps, however, in manufacturing, the screw machine may answer the purpose and prove economical. Requirements for Correctly Threaded Taps. In correctly threading a tap, there are six distinct points to be taken into consideration. The tap must be pro¬ vided with the correct diameter in the angle of the thread, a correct outside diameter, correct lead, correct angle between the sides of the thread, correct relation of this angle to the axis of the tap, and finally' correct flats or radii at the top and bottom of the threads, as required by the standard thread form. The angle diameter, for HAND TAPS 159 instance, may be correct while the outside diameter would be a trifle large or small, depending upon whether the flat or radius at the top of the thread were either too small or too large. The lead, of course, may be incorrect while the other factors are practically correct. The angle of the thread may be larger or smaller than the standard angle, and if the lead, the outside diameter, and the angle diameter were still approximately correct, the tap would produce a very poorly fitting thread. The angle between the sides of the thread may be correct in itself, but the thread¬ cutting tool may have been presented to the work at an oblique angle, thus producing a thread that would not be symmetrical about a line through the center of the thread at right angles to the axis of the tap. It is evident that all these requirements in regard to threading must be filled in order to make a perfect tap. In manufacturing, where tools and holders specially made for the purpose are used in threading taps, there is little danger of inaccurate or unsymmetrical angles of the thread. It is therefore the practice simply to inspect the angle diameter and the lead of the tap. If these two prove correct within the prescribed limits, and if the out¬ side diameter of the tap blank was inspected before threading, there is little danger of any serious inaccuracies in respect to the other details of the thread. It must, however, be understood that the threading tools and the alignment of the threading lathes must be subject to inspection at certain intervals, if the chances of error are to be guarded against as much as possible. Fluting. The flutes of a tap serve two purposes. They provide for cutting edges for the threads and form channels for the carrying off of the chips. The form of the flute is 160 SMALL TOOLS very important, as it determines the cutting qualities of the tap as well as the ease with which the chips will be able to pass away from the cutting points. The main qualities looked for in a tap are strength and ease of working, provided the tap is otherwise correct. In order to obtain strength a shallow flute 'with no sharp corners is the first requirement. An easy-working tap, again, requires a considerable amount of chip room, and con¬ sequently a comparatively deep flute. The correct flute therefore is a compromise between a flute which will give the greatest amount of chip room and the greatest Fig. 71. Common Forms of Tap Flutes strength to the tap. Besides, the flute must be of a shape easily produced, so as to limit the cost as far as con¬ sistent with good results, and must carry away the chips from the cutting edges in a manner offering the least resistance. The present practice is to provide hand taps with deep straight-sided flutes having a small round in the bottom, as shown to the left in Fig. 71. This method, while it provides an abundance of chip room, is accompanied by some very grave disadvantages. The tap will crack more easily in hardening, it will not carry away the chips from the cutting edges as readily, and is not as strong as a tap fluted in the manner shown in the section HAND TAPS 161 to the right in Fig. 71. The making and maintenance of the cutters for producing this latter flute, however, are more expensive, and as the present practice of fluting is becoming fairly universal it is evident that the objections, while of a serious nature, do not outweigh the advantages gained. The radius at the bottom of the flute ought, however, not to be less than one-quarter of the diameter of the tap. Some persons well familiar with this kind of work claim that a radius of one-eighth of the diameter of the tap would serve the purpose equally well, besides giving a larger space for chips. It has been proven beyond doubt, however, that this slight difference in the radius at the bottom of the flute influences the endurance qualities of the tap very materially. Fluting Cutters. — The cutter used for cutting the straight-sided flute is shown in Fig. 72. The included angle between the sides is 85 degrees, 55 degrees on one side and 30 degrees on the other. The thickness of the cutter should be approximately equal to *^ D + T 5 g inch if D equals the diameter of the tap. The radius, as men¬ tioned before, ought to be equal to — , but should not 162 SMALL TOOLS exceed T 7 g- inch. The diameter of the cutter depends, of course, not only upon the diameter of the tap to be fluted but also upon the size of the hole in the cutter for the milling-machine arbor. If we assume that we use a three- quarter-inch hole in the cutters for the smaller diameters of taps, say up to and including three-quarter-inch, and one-inch hole in cutters for large-diameter taps, we can make Diameter of cutter = ~ + 2 inches, in which formula D, as before, equals the diameter of the tap to be fluted. TABLE XXXVII. DIMENSIONS OF FLUTING CUTTERS FOR HAND TAPS. (See Fig. 72 for form of cutter.) Diameter of Tap. Diameter of Cutter.' Thickness of Cutter. Radius. Diameter of Hole in Cutter. A B C D 1 4 2 I A f f 21 1 A f 1 21 1 1 f f 21 t A f f 21 f A f I 21 ! A 1 1 21 f 1 1 H 21 1 A 1 2f 1 f 1 if 2f n A 1 2 3 n A 1 2f 3 H A 1 21 31 if A 1 2f 31 ii T6 1 3 31 if A 1 31 3f if ' A 1 4 4 2 A 1 HAND TAPS 163 Table XXXVII is figured from the formulas given. The figures given in the table are, however, practical working figures and are only approximately the values figured from the formulas whenever these values give dimensions unnecessarily fine and in too small fractions. Of course the nearest quarter of an inch is near enough for the dimension in regard to diameter, and the nearest one-eighth inch in regard to thickness. The radius, how¬ ever, must be given in finer subdivisions, as one-thirty- second or even one-sixty-fourth inch makes a considerable difference in this respect. The cutter for the flute shown to the right in Fig. 71 is shown in Fig. 73. The curve forming the cutting edge is composed of two arcs tangent to each other with their centers at A and B respectively. The radius for the large arc should be about equal to the diameter of the tap. The radius of the small arc should be about one-sixth of the diameter. It must be plainly under¬ stood that when formulas and rules like the above are given they are intended only for guidance. It is evidently impossible to have cutters conform to these formulas for each different diameter of tap, as it would require more cutters than necessary. The ri g< 73 . formulas merely express a good average working practice. The lands of the tap when fluted with the cutter last described may be somewhat narrower than the lands in taps fluted with straight-sided flutes, inasmuch as the latter tap requires wide lands in order to make up for the loss of strength due to the deep, more sharp cornered flute. Fluting Taps for Brass. — In the case of either flute it Form Special of Tap Fluting Cutter 164 SMALL TOOLS is the practice to make the cutting edges of the taps radial as in Fig. 71. This is, at least, the common practice in regard to taps for steel and cast iron. In regard to taps for brass there is some difference of opinion. The general practice, however, if a tap is to be used entirely for brass, is to provide a cutting edge which is slightly in advance of the radial line, or in other words, parallel to the radial line, but ahead of the center, as shown in Fig. 74. This way of cutting the flute gives a slight negative rake, and causes the tap to cut more smoothly and with less liability of chattering. The dimension a in Fig. 74 should be from one-sixteenth to one-tenth of the diameter of the tap. However, a tap with the cutting edges radial will cut brass fairly well if otherwise properly made. Number of Flutes. — Lastly, we have to consider the number of the flutes in hand taps. The formula Number of flutes = ^ + 2f, O in which formula D equals the diameter of the tap, will give approximately the correct number of flutes. Figur¬ ing a table from this formula, we will find the number of flutes for various diameters as stated in Table XXXVIII. It will be noticed that the numbers of flutes for hand taps as given in Table XXXVIII are 4, 6, and 8, the odd numbers 3, 5, and 7 not being used. The reason for this is that an even number of flutes enables one to measure the diameter of the tap in all cases with ordinary micrometers. If an odd number of flutes is used the for Brass hand taps 165 measuring of the diameter is rather complicated and requires a gauge to which to fit the tap. Even then there will still be more or less uncertainty unless the tap is of a standard diameter. TABLE XXXVIII. DIAMETERS OF HAND TAPS AND CORRESPONDING NUMBER OF FLUTES. Diameter of Tap. Number of Flutes. Diameter of Tap. Number of Flutes. \ 4 H 6 ! 4 2 6 h 4 2i 6 t 4 2i 6 ! 4 2i 6 l 4 3 6 l 4 3 * 8 H 4 4 8 H 4 It must also be remarked, in connection with the flut¬ ing of hand taps, that the width of the lands does not depend only upon the necessary strength of the tap. As a hand tap, as a rule, receives all its guidance from the lands resting against the walls of the nut it is necessary to have the lands wide enough so that they steady the tap during the tapping operation. In regard to the number of flutes there is, however, some difference of opinion. There are those who con¬ sider four flutes the proper number to use on all sizes of hand taps with the land about one-fourth the diameter of the tap. However, on large taps the land will be rather wide if made according to this rule, and better results will be obtained by increasing the number of flutes in accordance with the formula previously given. 166 SMALL TOOLS Convex Fluting Cutter. — Sometimes a regular convex cutter is used for fluting taps. This is merely a way of providing a flute similar to the one shown to the right in Fig. 71, but avoiding the expense of a special cutter. In selecting half-round (convex) cutters for taps the formula below can be used for determining the proper thickness of the cutter: rn 8 D t =Ja’ in which formula T = the thickness of the cutter, D = the diameter of the tap, A = the number of flutes. If, for instance, we wish to flute a one-inch tap with four flutes, the thickness of a convex cutter for the purpose would be ||ri = J 2 =0.667, or || approximately. Grinding Fluting Cutters. In the case of formed cutters with regular milling cutter teeth it is, of course, necessary that the teeth be ground around the edges, instead of being ground only on the faces as is always the case on cutters with eccentrically relieved teeth. In Figs. 72 and 73 are shown two types of milling cutters which may be ground with devices working on the principles indicated and described below, the cutter in Fig. 72, as mentioned above, being a regular fluting cutter for taps, and the cutter in Fig. 73 a special fluting cutter. In Fig. 75 is shown the device used for grinding a regular tap fluting cutter. The angle included between HAND TAPS 167 the two faces on the fluting cutter is 85 degrees, and the angle between the two faces G and D in the device for grinding the teeth of these cutters is also 85 degrees, one Fig. 75. Device for Grinding Tap Fluting Cutter Shown in Fig. 72 side making 30 and the other 55 degrees with a line at right angles to the axis of stud A on which the cutter is mounted while grinding. The device consists of a base plate G having three feet which rest on a special table on the grinding machine, shown in Fig. 76, which will be more 168 SMALL TOOLS Fig. 76. Grinding Device for Fluting Cutters, on Table of Grinder HAND TAPS 169 fully described later. On this base plate G slides a cutter holding slide H, which has a groove in the bottom fitting a tongue projecting from the base plate. An oblong slot is provided in the base plate as shown at P, so that the slide H can be clamped to the base plate by the screw L at any place within the length of the slot. The screw K passing through the lug R driven into the base plate G, and acting upon the slide H, permits the necessary adjust¬ ment. The slide H holds a stud or spindle A passing through a projecting standard F of the slide. The cutter to be ground is mounted on this stud. It will be evident, upon explanation of the action of this device, that when grinding the cutters these must be so mounted upon the stud A that the apex of the included angle between the two angular faces (that is, the point where the angular sides would meet if extended) shall be on, the same center line as the point N of the grinding fixture, where the two sides C and D meet (see Fig. 75). In order to obtain the fine adjustment necessary to bring these two points on the same center line, that end of stud A which enters into the bearing in the standard F is provided with threaded portions on which adjusting nuts are mounted. Collars are placed on the smaller diameter of A against the shoulder M, so that the adjustment necessary to be made by the nuts will be comparatively small, the 1 collars taking up the main difference in width of the various cutters to be ground. On the outside end of the stud A is a collar B and a set screw having a large round slotted head, which is used for binding the collar against the cutter. It will be noted that this collar is cut off on one side to an angle. This is done in order to permit the collar to clear the emery wheel of the grinder when the side of the cutter tooth next to the collar is being ground. 170 SMALL TOOLS As shown in Fig. 72, the cutters to be ground have their two faces connected with the small radius, different for different kinds and sizes of fluting cutters. This radius is obtained by permitting the faces of the cutter teeth to project slightly outside of the faces C and D of the base plate G, Fig. 75, when the cutter is in position on the stud A, the point of the cutter, however, still being in line with the point N of the device, as mentioned above. When in use, the grinding device is placed on the table of the grinding machine, as shown in Fig. 76. This table is mounted directly on the grinding-machine knee, and is provided with a guide strip E. The hardened shoe N in Fig. 75 slides against this guide strip E in Fig. 76, and by swinging the device around so that first the face G comes along the guide strip E, and then turning it around the point N until the face D rests against the guide strip, the cutter is ground to the same angle as that of the base plate G in Fig. 75, and a radius. will be formed at the point of the cutter, depending upon how far the faces of the cutter teeth project outside of the faces C and D of the base plate G. Different angles may be obtained by put¬ ting tapered strips along the sides C and D, the angle included between the face of the strips being the same as the angle between the faces of the teeth of the cutter. The base plate for this device should be made of machine steel, and the faces C and D should be case-hardened. If tapered strips are screwed onto the faces G and D to accommodate other angles than the ones referred to, these strips should also be made of machine steel and case-hardened. Slide H is made of cast iron. Referring now to Fig. 76, in which the special table on the cutter grinding machine is shown, this table consists of a cast-iron body, being provided with two tool-steel plates S on the top, forming the table surface. These plates HAND TAPS 171 are hardened and ground to prevent too rapid wear, as the feet of the grinding device constantly slide on their top surface. The guide strip E is also made of tool steel and hardened. At T in Fig. 76 a stud is shown projecting up from the top of the table. From this stud projects an arm W, which is used for setting the cutter tooth, as shown, the cutter being indicated by dotted lines. It is, of course, necessary that each tooth be exactly at the same height as the others, when ground, so that the diameter of the cutter measured over any two teeth will be exactly the same. The cutter is held simply by frictional resistance, and the indexing around is done by hand by the operator. The table can be fed out and in by means of a feed screw with a knurled head V, thereby permitting a greater or less amount to be ground off from the teeth of different cutters. In Fig. 77 is shown a device which is used for setting the slide H in Fig. 75 to such a position that the correct radius will be ground at the apex of the angle of the cutter teeth. The stud C Fi g- 77 - is screwed into the top of any kind of a base or surface plate. This stud has a slot or groove cut in its top surface, and a regular 4-inch machinist’s scale, pref- U - m - d 1 'Mil 1 ,1,1.1. TCIt FT if tv'IN „i, M r 'I' M' 3 - ( 3 TUT t 1 Device for Setting Grinding Fixture to Grind a Certain Eadius at Point of Cutter 172 SMALL TOOLS erably graduated in lOOths or 64ths of an inch, is laid in this slot at the top and held by means of the set screw B, the upper part of the round stud C being split so that the scale can be gripped in the slot cut for it, as if placed in a split chuck. When the device in Fig. 75 is to be set so as to grind a certain radius, the pin A , Fig. 77, is placed against the edge of the point N of the base plate G, Fig. 75, and the slide H is adjusted so that the cutter touches the end D of the scale in Fig. 77. When the scale is so set that m equals n, the cutter to be ground will have no radius but will get a sharp edge at the point. When m is shorter than n, the difference between n and m will give a rela¬ tive measure of the radius that will result between the faces of the cutter teeth; but it must be understood that this difference does not give the exact actual radius. This would be measured from the side D of the plate G to the side of the cutter. Of course, the arrangement in Fig. 77 may be used for measuring this length also, by placing the face D against pin A and the angular side of the cutter tooth against the end of the scale. The device in Fig. 78, finally, is used for inspecting the cutters when ground. The cutter is placed on the stud A, the stud entering the hole in the cutter, and the gauge pin B, having a large head ground flat, is pushed up against the ends of the teeth in the cutter. This permits not only the length of the different teeth in the same cutter to be gauged, but in cases where several cutters are used in a set for fluting taps, all the cutters in the set can be gauged to find out if they are of exactly the same diam¬ eter. The gauge stud B is fed in and out by means of the micrometer screw C which has a graduated head as shown. When the stud B has been set to the size of one cutter in the set of cutters, it is clamped in place by the clamp HAND TAPS 173 screw D. If, however, the other cutters in the set should prove to be smaller or larger than the first cutter, the gauge screw D can be loosened and the micrometer screw adjusted so as to move B in the desired direction, and the amount that the cutters are smaller and larger than Fig. 78. Gauge for Fluting Cutters 174 SMALL TOOLS the size of the other cutters in the set can be determined by reading off the number of thousandths directly on the graduated head of the micrometer screw C. This head should be graduated so that each graduation reads 0.001 Fig. 79. Device for Grinding Formed Fluting Cutter Shown in Fig. 73 inch. A pointer E is screwed to the. end of the gauge stud B, to insure correct reading of the graduations. Collars may be put on stud A to accommodate smaller or larger thicknesses of cutters, or the binding screw F may be loosened and the stud A moved up enough to accommo¬ date thinner cutters, the cutters resting on the shoulder G. HAND TAPS 175 In Fig. 79 is shown a device used in conjunction with the grinding table in Fig. 76 for grinding formed fluting cutters, with an outline similar to the one shown in Fig. 73. The principle of this device is practically the same as that in Fig. 75. It will be noticed, however, that in order to permit the device to be swung around so as to grind the complete form of the cutter a slot T cut on a circular arc has been provided in the base of the device, and the top portion is swiveled around the stud A. At Pig. 80. Side View of Formed Fluting Cutter Grinding Device the front end of the slide B a threaded hole D is provided for the screw which holds the former for the various formed cutters to this slide, the slide being adjustable to take care of the different diameters of the cutters. In Fig. 80 is shown a side view of this device, which plainly shows the design of the cutter-holding slide, the arbor, and its adjustment. It will be noticed that in this case, instead of adjusting the cutter arbor by means of two nuts on each side of standard F, the stud C has the smaller end threaded directly into the upright F and the nut E simply acts as a binding or check nut. A slot is 176 SMALL TOOLS provided for a screw-driver in the end of the stud C to facilitate adjustment. It will be noticed that in the device in Fig. 79 the former is not attached directly to the base of the device but is placed on an independent slide. On account of this there is no need of having any sliding adjustment between the base H of the device and the standard F, all adjustment being taken care of by the slide B, having the formers attached at D, as mentioned. The general shape of the formers used is shown at K, Fig. 79. The device last described may also be used for grinding cutters for fluting drills when these cutters are made with regular milling cutter teeth. In fact, the former, shown in place in Fig. 79, is one which in form most nearly corre¬ sponds to the form of a drill fluting cutter. Relief of Taps. In the next place we must turn our attention to the proper relieving of hand taps. The question of proper relief is one of the most serious and particular met with in tap-making. The old and until recently the most common method was to give all the teeth a relief on the top as well as in the angle of the thread; i.e., the heels of the teeth were made of smaller diameter than the diameter measured over the cutting edges, both at the top and at the root of the thread (as shown in Fig. 81). However, this has been found to be wholly unnecessary, and taps of this kind are now made without any relief at all in the angle of the thread; but the top of the thread of the chamfered part only is slightly relieved. To further improve upon the cutting qualities of the tap, it should be made smaller in diameter toward the shank than at the point. This difference in diameter should, of course, vary for HAND TAPS 177 different diameters, and the limits in variation of size permitted must, of course, also be taken into consider¬ ation. It may be said that in general practice it answers the purpose if the tap is about 0.0015 inch smaller at the shank end of the thread for taps up to one-half inch diameter, and from 0.002 to 0.003 inch smaller at this end than at the point for taps from one-half up to two inches diameter. It may be added that although this is an essentially good point in tap-making, most manufac¬ turers do not make their taps that way, probably because it would increase the expense in the manufacture and require greater care in making. Fig. 81. Section of Tap Relieved Fig. 82. Section of Tap Relieved both on Top and in Angle of in Center of Land Thread Another improvement upon a hand tap, seldom seen in taps manufactured for the market, is to give to the angle of the thread a relief in the center of the land, as shown in Fig. 82. The reason for so doing is obvious. The tap gets the same support along its periphery as if not relieved in the angle of the thread, because it retains its bearing at the heel of the thread, but as can be clearly 178 SMALL TOOLS seen a good portion of the resistance is eliminated, the bearing surface of the tap thread which is presented to the nut being considerably smaller. Acme and square thread taps should be relieved on the top of the thread on the chamfered portion on all the taps in a set, and the finishing tap should be given relief in the center of the land on its straight or parallel por¬ tion. In cases where the taps are used as machine taps rather than as hand taps, they should be relieved in the angle of the thread as well as on the top on the chamfered portion. Change of Pitch in Hardening. As is well known, the pitch of a tap as well as its diam¬ eter will change in hardening, the pitch as a rule becom¬ ing shorter and the diameter larger. This tendency of change can be minimized by slow and even heating, com¬ bined with hardening at as low a heat as is possible to obtain the desired result in the tap, but it can never be fully eliminated. For this reason it is necessary to cut the thread of taps on lathes having lead screws slightly longer in the pitch than the standard. The tap will then also have a pitch slightly in excess of the standard before hardening, and if the excess length is properly selected, the tap will have a nearly correct pitch when hardened. The amount that the pitch should be longer before hardening varies, of course, according to the makes and grades of steel. To give definite rules in this matter would be impossible, more particularly so because the result of hardening may not always be shrinkage in the length of the piece to be hardened. Practical experi¬ ments have proved that in some cases, although rare, even when working with a most uniform grade of steel and handling it with the utmost care, there is no sure way of telling whether the result will be shrinkage or expan- HAND TAPS 179 sion. However, it has been found that most kinds of steel have an invariable tendency to contract lengthwise when hardened, and if this contraction has been found to be within certain limits in a few experiments, the steel may be fairly well depended upon to vary in the same way in so great a number of cases as to permit neglecting those in which unexpected results are obtained. It is of interest to note, however, that exceptional cases have been observed where different parts of the same pieces have shown considerable difference in the amount of shrinkage. While, as stated before, definite rules cannot be laid down, it may be given as a guide that most steels have an average shrinkage of from 0.016 to 0.020 inch per foot, when the ratio between the diameter and the length of the work does not exceed say 1 to 10. Wlien, however, the threaded piece is very long compared with the diameter, as for instance in stay-bolt taps, the contraction is pro¬ portionally greater. For very large diameters a pro¬ portionately smaller value of shrinkage between the limits given above can usually be assumed. Jessop’s steel changes about the least and is the most uniform of any kind of ordinarily used steels. The average shrinkage of this steel is so small that it gives it a great range of use¬ fulness in cases where other steels make trouble. The amount of change is only from about 0.004 inch to 0.006 inch per foot, these values being in proportion to smaller or larger diameters of work, as remarked above. Of course many conditions will have to be taken into consideration to obtain satisfactory results. The amount of change depends not only upon the grade of steel but, as said before, upon the uniformity and amount of heat used when hardening, the rapidity and manner of cooling, and also upon the number of times the work has been 180 SMALL TOOLS through the fire. In regard to the effect upon steel of repeated annealing, a few interesting remarks might be made. If after having been through the fire once the pitch of a tap is correct, and it is annealed and hardened again, each consecutive repetition of this process will invariably bring about a growing error. Again, if a cer¬ tain kind of steel should be too long in the lead after the first hardening, a second or, if necessary, a third harden¬ ing is likely to bring about a satisfactory result so far as the pitch is concerned, though this is not advisable, as tool steel generally loses its good qualities by being put through the fire too many times. Lead Screw for Cutting Taps Long in the Lead. — In this connection it may be appropriate to give some attention to the process of producing a lead screw intended for cutting a thread which is a certain amount longer in the lead than the same thread would be if regularly pitched. If such a lead screw is to be cut on a lathe pro¬ vided with a standard screw there are some difficulties in finding the change gears with which to obtain the results desired. The following formula will aid in find¬ ing the ratio of the gears to be used. In this formula a = amount thread is longer in one foot than the same number of threads would be if regularly pitched. n = nominal number of threads per inch on work to be threaded. I = threads per inch on lead screw of lathe. r = ratio of gears in head of lathe. PI = ratio of change gears to cut a thread a certain amount, a , longer in one foot than same number of threads regularly pitched. I X r (12 + a) ' Then HAND TAPS 181 The ratio of change gears having been thus obtained, the proper gears to use must be found by trial calculations. The most common amount to cut hand taps long in the lead in one foot is about 0.018 inch. Stay-bolt taps and taps of a similar kind are often cut from 0.030 to 0.034 inch long in the lead in one foot. If we assume that we wish to cut a lead screw which is 0.018 inch long in the lead in one foot, and that the nominal number of threads per inch in this lead screw is to be 8, that the correct lead screw in the lathe used for cutting the screw has 6 threads pei inch, and finally that the ratio of the gearing in the head-stock of the lathe is 2, then the ratio of change gears required to cut the lead screw in question would be 6 X 2 (12 + 0,018) 12 X 8 1.50225. The trials which will give the gears which most nearly produce this ratio are more or less lengthy, but no definite rule can be given except for finding the ratio according to the above formula. Fig. 83. Effect of Difference in Lead in Nut and Screw Provision for Differences in Lead of Tap and Screw. — The lead of a tap cannot, however, be depended upon to be exactly correct even when the precautions referred to above are taken, but it will be within very close limits. If the tap is long in the lead the nut tapped will, of course, also be long in the lead, and will not correctly fit a stand¬ ard screw. The resulting fit is shown exaggerated in Fig. 83. As this difficulty cannot be in any way elimi- 182 SMALL TOOLS nated, the only way possible to arrange so that a screw of standard diameter and correct lead will go into a nut of incorrect lead is to make the diameter of the nut, and consequently the tap for tapping the nut, a ceitain amount over-size, as is evident from Fig. 83. This amount depends upon the length of the nut to be tapped and upon the unavoidable error in the lead of the tap. As these quantities are difficult to determine particu¬ larly when making taps for general purposes in great quantities, some standard figures must be assumed which will fill the requirements in all ordinary cases. Table XXXIX gives the values of over-size near which the angle diameter of hand taps ought to be after hardening. In other words, the angle diameter must be between the standard angle diameter and the standard plus the limits of over-size stated in the table, and preferably near the larger value. TABLE XXXIX. LIMITS OF OVER—SIZE IN DIAMETER OF HAND TAPS. Size of Tap in Inches. Limit of Over-size. V5 0.00075 i 0.001 i 0.00125 t 0.0015 h 0.00175 f 0.002 1 0.00225 l 0.0025 i 0.0025 0.00275 Size of Tap in Inches. Limit of Over-size. 11 0.00275 11 0.003 2 0.003 21 0.0035 21 0.0035 2f 0.004 3 0.004 3i 0.0045 4 0.005 Swelling of Taps in Hardening. — Table XXXIX is, of course, only of value for inspecting taps after harden¬ ing unless some data are given in regard to the amount HAND TAPS 183 a tap is likely to increase in diameter in the hardening process. If such data are given, it will make it possible to determine the angle diameter of the tap before harden¬ ing, the only figure which is of use in making the tap. It is extremely difficult to state anything with certainty in this respect. Experiments with taps made from the same kind of steel and under the same conditions prove that there may be very great variations in the swelling or increase in diameter of taps due to hardening. In Table XL are given such values as may be considered correct for average cases. TABLE XL. INCREASE OF TAPS IN DIAMETER DUE TO HARDENING. Diameter of Tap. Increase Due to Hardening. Diameter of Tap. Increase Due to Hardening. A H 0.0025 I 0.00025 if 0.0025 1 4 0.0005 2 0.003 i 0.001 21 0.003 1 4 0.0015 3 0.0035 1 0.002 H 0.0035 H 0.002 4 0.004 As the amount of over-size necessary for a tap depends on the pitch rather than upon the diameter, the data given in Table XXXIX should be applied only to taps with standard threads. The relationship between the pitch, the length of the nut, and the error in lead on the one hand, and the excess in angle diameter on the other, is approximately expressed by the formula A - A = A X N X L tan 30° 184 SMALL TOOLS in which formula D x = the theoretical angle diameter, D 2 = the actual angle diameter required in the tap to compensate for the error in the lead, A = the error in lead per each thread, N = the number of threads per inch, and L = the length of the nut in inches. Diagram of Relation between Lead and Excess Diameter. — The relationship expressed by the formula above is shown in the diagram Fig. 84. This diagram gives the excess in angle diameter required over the standard angle diameter in taps to compensate for given errors in the pitch of the thread due to shrinkage in hardening. If the error in the pitch in a certain length T is given, the diagram will give the excess in pitch diameter necessary to compensate for this error, assuming that the length of the piece to be tapped equals T. If the length of the piece to be tapped does not equal T, the amount of excess in pitch diameter required is obtained from the formula j, X E = excess in pitch diameter necessary to permit a correct screw to go into the tapped piece. In this formula L = the length of the piece to be tapped and E = the excess in pitch diameter required for a piece to be tapped, the length of which equals T. Let us assume that the given error in the pitch of the thread in a length of 3 inches is 0.001 inch. Suppose the nut. to be tapped is 1^ inches long. Then T = 3; L= 1J; E= 0.00175 (found from the diagram), and according to our formula li j X 0.00175 = 0.00075 (approx.) = excess in angle diameter required. 0055 HAND TAPS 185 GIVEN ERRORS IN PITCH OF THREAD,CAUSED BY EXCESS IN PITCH DIAM. REQUIRED TO COMPENSATE FOR GIVEN ERRORS IN PITCH OF THREADS 186 SMALL TOOLS The value of E is found from the diagram by finding 0.001 on the horizontal line AC; then follow the vertical line from 0.001 to the line AB; from the intersecting point on this line follow the horizontal line to BC and read off the nearest graduation on the scale on this line. The value obtained is E, or the excess in angle diam¬ eter required, provided the length of thread in which the error in lead is measured equals the length of the nut. Otherwise the amount of excess is found by the formula previously given, in the manner already explained. It is common practice that the length of nut taken as the basis for various taps, when they are to be used on general work, is assumed to equal the diameter of the tap. It is evident, however, that this will be correct only for taps with standard threads, because when threads finer than standard are used for a certain diameter, the length of the nut is usually shorter. The excess in angle diameter should therefore properly be determined rather by the pitch than by the diameter of the tap. This is done by several firms when inspecting taps made for them by other manufacturers. The Westinghouse Electric and Manufacturing Company makes use of a formula: Excess in angle diameter = s/ pitch X 0.01. By means of this formula values a trifle larger than those given for limits of over-size in Table XXXIX are obtained. In this formula the excess angle diameter is made directly dependent upon the pitch of the thread. In Table XLI the values of the excess for a number of pitches are given. The corresponding diameters of United States standard screws are also stated. This will permit comparison to be readily made with the values in Table XXXIX. It HAND TAPS 187 must be remembered that these values refer to the sizes of the taps after they are hardened. TABLE XLI. LIMITS OF OVER-SIZE IN DIAMETERS OF HAND TAPS. No. of Threads per Inch. Correspond¬ ing Diameter, U. S. Standard. Limit of Over-size = y /pitch X 0.01 No. of Threads per Inch. Correspond¬ ing Diameter, U. S. Standard. Limit of Over-size = a/ pitch X 0.01 3 3f-4 0.0058 18 A 0.0024 4 2f-2f 0.0050 20 i 0.0022 5 iMi 0.0045 22 0.0021 6 if-H 0.0041 24 0.0020 7 14-H 0.0038 26 0.0020 8 l 0.0035 28 'h 0.0019 9 l 0.0035 30 0.0018 10 0.0032 32 Id! 0.0018 11 t 0.0030 36 $2 0.0017 12 A 0.0029 40 i 0.0016 13 I 0.0028 50 A 0.0014 14 0.0027 56 0.0013 16 t 0.0025 64 T5 0.0012 Hardening Taps. As mentioned before, the amount that a tap will change in dimensions in hardening depends greatly upon the manner in which it is hardened. The heating must be made evenly throughout the tap, and it should be heated slowly; the water used for dipping should not be very cold; the tap, when dipped, should be held in a vertical position. The amounts given in the preceding tables were obtained from actual experience in the manufacturing of taps. But it must be clearly understood that the rules for hardening are all very indefinite. It is easy to say: “Heat slowly and uniformly/’ but not so easy to do it; and only by experience is it possible to attain 188 SMALL TOOLS uniform results in the hardening of a tap or any other tool. Mr. E. R. Markham in Machinery, May, 1904, described a method of hardening taps by means of which, he claims, the original pitch and diametrical measurements can be maintained. This method is termed “pack hardening.” Mr. Markham says: “It is a well-known fact that small, thin pieces of steel can be hardened by heating red hot and dipping in oil, with little or no tendency to spring; but as steel is hard¬ ened by rapid cooling from a red heat and as large pieces of steel cool very slowly in oil, it is generally considered advisable to cool them in water, brine, or some bath which takes the heat quickly from the steel. Now it has been ascertained by experiment that steel can be treated in a manner that insures its hardening when dipped in oil, thus eliminating the danger of cracking or breaking, and reducing to the minimum the liability of springing. This is accomplished by packing the articles with some car¬ bonaceous material in an iron box which should be covered with a flat piece of iron. The space between the edges of the box and cover should be luted with fire clay which has been mixed with water until it is of the consistency of dough. This should be allowed to dry before placing in the furnace, or the rapid drying will cause it to crack. Should it crack when drying the cracks may be filled with clay and this allowed to dry. “The carbonaceous material used must not contain any elements that are injurious to tool steel. For this reason do not use bone in any form. Bone contains phosphorus, and this is extremely injurious, as it causes the steel to become brittle when it is in com¬ bination with carbon. Burned bone does not contain as high a percentage of phosphorus as the raw bone, but HAND TAPS 189 will not give as good results as other material we can use. “If the steel used in making the tool does not con¬ tain over per cent carbon, ‘charred leather’ is an excellent material to use when packing in the iron box. If steels of higher carbon are used, charred leather does not act as well as charred hoofs, or a mixture of charred hoofs and horns; for charred leather has a tendency to give high-carbon steels a grain that resem¬ bles steel made by the cementation process, when it is subjected to heat for a considerable time. But there is no such effect when charred leather is used in con¬ nection with steels that do not contain more than per cent carbon.” The box containing the articles is heated in the fur¬ nace, and when heated throughout, the taps are taken out and immersed in a bath of raw linseed oil, work¬ ing the taps up and down and around in the oil while cooling. In drawing the temper, it is of course evident that a certain temperature can hardly be settled upon, inasmuch as various kinds of steel would not require to be drawn to exactly the same temperature. It may be said, however, that temperatures varying from 430 to 460° F. will not prove to be far from the correct ones. The lower tem¬ perature mentioned is commonly employed for the oil baths used for drawing the temper in manufacturing plants. If preference should be given to any exact tem¬ perature, it would be correct to make a rule of drawing large taps to 430 degrees and smaller ones, say up to seven-sixteenths inch inclusive, to 460° F. When hardening in the ordinary way the tap can be heated to the greatest advantage in a crucible of molten lead heated to a red heat. There is, however, some 190 SMALL TOOLS difficulty in regard to the lead sticking to the tap. While there are some tool-makers who do not take any pre¬ cautions to prevent this, it may be avoided by dipping the tap in a mixture of two parts charred leather, three parts fine flour, and four parts table salt, all thoroughly mixed while dry, and converted into a fluid by slowly adding water until the mixture has the consistency of varnish. The ingredients should be finely pulverized. This mixture will prevent the lead from sticking to the tap, and facilitates the hardening of the tap because of its carbonaceous composition. After dipping, the tap must be allowed to dry thoroughly, as otherwise, when plunging the taps in the hot lead, the latter will fly and endanger the operators. Dimensions of Ordinary Hand Taps. It has been a very common thing among manufacturers of taps, and still more among persons who only occasion¬ ally have been called upon to make these tools, to pro¬ duce taps without following any definite rule as to the proportions of the various details. Little attention has been given to the possibility of expressing the relation between the diameter and the total length, for instance, by a single formula. For this reason it is very common to find that the dimensions of taps, or of any other tools of a similar character which are made in a great number of sizes, do not follow any definite rule in their propor¬ tions, except the one that a larger size has most of its dimensions a trifle larger than those of the preceding one. Various manufacturers also differ widely as to the pro¬ portions of their tools. It is, however, not impossible to express in simple formulas the rules according to which taps of proper proportions could be made. The formulas which follow are all worked out so that all the length HAND TAPS 191 dimensions of the tap stand in a certain relation to the diameter of the tap. This insures a tap which will be well proportioned and at the same time be well adapted for its work, even if the pitch of the thread should vary for the same diameter. The formulas are worked out with particular regard to taps with standard threads, either United States standard or sharp V thread, but will be equally serviceable for finer pitches. The formulas, as has been said, are based upon the tap diameter, this being the most convenient working factor, as, of course, the diameter is always given from the beginning. At the first glance an observer might infer that the working factor ought to be the number of threads per inch, but as that number in all standard systems is dependent upon and stands in a certain relation to the diameter, this latter factor is just as correct to work from, and gives simpler and more universal formulas. It is obvious that formulas cannot be made up that would suit the whole range of diameters from the very smallest up to the very largest, and therefore it has been necessary to divide the series into two groups in order to obtain correct proportions, the one group including taps from three-sixteenths inch up to one inch diameter; the second from one inch up to four inches diameter. In the formulas the following letters are used to denote the dimensions: A = the total length of the tap, B = the length of the thread, C = the length of the shank, D = the diameter of the tap, E = the diameter of the shank, F — the size of the square, G = the length of the square. 192 SMALL TOOLS For sizes up to and including one inch in diameter the formulas are: A = 3.5 D + If inches, B = D + 1J inches, C. = 1.25 D + If inches, E = root diameter of thread — 0.01 inch, F = 0.75 E, G = 0.75 D + inch. For sizes one inch and larger the formulas will be: A = 2.25 D + 2} inches, B = D + 1% inches, C = 1.25 D + If inches, E = root diameter of thread — 0.02 inch, F = 0.75 E, G = 0.33 D + \ inch. Table XLII contains figures for the dimensions of hand taps with standard threads based on these formulas. Of course, where no necessity for close fractional dimensions exists, the dimensions are only approximately those obtained from the formulas, and are given as practical working dimensions. As seen in the table the shanks for the three- sixteenths-inch and the quarter-inch diameter taps are made equal to the diameter of the tap, according to the usual custom in manufacturing these taps. Dimensions of Acme and Square Thread Taps. It has been mentioned previously that Acme and square thread screws are usually made with coarser pitches than used for the V form of thread. For this reason the length dimensions given for ordinary hand taps do not suit those provided with the former kinds of threads. The Acme HAND TAPS 193 TABLE XLII. DIMENSIONS OF HAND TAPS. Diam¬ eter of Tap. Number of Threads per Inch. Total Length. Length of Thread Length of Shank. Diameter of Shank, E. Size of Square. Length of Square. D. U. S. St’d. V St’d. A. B. C. U. S. St’d. V St’d. F. G. 32 24 21 1 If % V Wi A 1 20 20 21 1 11 1 1 A A 18 18 2t5 H i A 0. 23 0. 21 A A f 16 16 211 11 itt 0 28 0. 25 A f A 14 14 31 If if 0 33 0 30 1 f 1 13 12 3f H H 0 39 0 34 A A A 12 12 3 A it iff 0 44 0 40 A 1 1 11 11 3ff U 2A 0 49 0 45 M A a 11 11 4 11 21 0 56 0 52 A A f 10 10 41 2 21 0 61 0 56 A t A 10 10 4A 21 2A 0 67 0 62 1 A 1 9 9 4A 21 2A 0 72 0 67 1 f A 9 9 41 2f 21 0 78 0 73 A f l 8 8 51 21 2f 0 82 0 77 t A 7 8 51 2A 2A 0 86 0 83 f 1 1 F 7 7 5A 2f 2A 0 92 0 86 A 1 7 7 5A 2A 21 0 98 0 92 A 1 U 7 7 5A 2f 915 L 16 1 04 0 98 f. A 1A 6 7 5A m 3 1 08 1 05 A A if 6 6 6 21 31 1 14 1 07 A A 1 A 6 6 61 2A 3A 1 20 1 13 1 l il 6 6 61 3 31 1 26 1 19 A l if 51 5 6A 31 3A 1 37 1 26 l i A if 5 5 6A 31 3A 1 47 1 38 i A i A U 5 41 71 3f 3f 1 59 1 46 il il 2 41 41 7f 31 31 1 69 1 59 H i A 21 41 41 7H 3f 4A 1 81 1 71 i A i A 21 41 41 7A 3f 4A 1 94 1 84 i A il 2f 4 41 81 31 4f 2 03 1 97 il i A 21 4 4 81 4 41 2 15 2 04 i A i A 2f 4 4 8jf 41 4A 2 28 2 17 1A if 2f 4 4 9A 41 4 If 2 40 2 29 if i A 2f 31 4 9f 4f 5 2 .48 2 42 1A i A 3 31 31 9f 41 51 2 .60 2 48 H H 31 31 31 10A 4f 5A 2 85 2 .73 2A i A 31 31 31 lOf 5 5f 3 08 2 .95 21 1A 31 3 3 DA 51 6A 3 .29 3 .15 2A if 4 3 3 111 51 6f 3 .54 3 .39 2f 1A 194 SMALL TOOLS and square thread taps should also be made in sets, usually in sets of three. These conditions necessitate a separate set of dimensions for taps with these systems of thread. When the dimensions for the diameter of each tap in the set have been ascertained in accordance with Table XXXVI ; Table XLIII may be used for finding the length dimensions for Acme taps, in sets of three taps, from one-half to 3 inches diameter. The dimensions in this table apply to single- threaded taps. For multiple-threaded taps, or taps with very coarse pitch relative to the diameter, it is advisable to lengthen the dimensions for the chamfered part of the thread, leaving the other dimensions as given in the table. The size of the square of these taps is not given, depending as it does upon the varying diameters of the shank, which in turn depend on the depth of the thread. The square should, however, always be made equal to f X diameter of shank. Square-thread taps are made according to the same table as Acme taps, with the exception of the figures in column K in Table XLIII, representing the full diameter of the last tap in a set of Acme-thread taps. In the case of square- thread taps column K should be equal to the nominal diameter of the tap, because, as has already been mentioned, no over-size allowance is customary in making these taps. Machine Screw Taps. As has been previously said, machine screw taps are only a special form of hand taps, used for tapping holes for standard machine screws. These taps are known by numbers from one to thirty. A certain outside diameter corresponds to each number, but there is no rigidly recog¬ nized number of threads corresponding to the various diameters. The form of the thread is the V shape, with an angle of 60 degrees, sharp at the bottom of the thread, HAND TAPS 195 TABLE XLIII. LENGTH DIMENSIONS OF ACME TAPS IN SETS. —1- 1 1ST TAP IN SET --- -- - < 2nd tap in set <-Fu¬ rnishing TAP Fig. 86 Nom¬ inal Diam. A B C D E F G H I K 1 41 H 2t 1 It t It t 11 0.520 A 4| 2* 2t A 2A t 2 1 It 0.582 t 51 2t 3t t 21 t 21 H 2 0.645 tt 6 21 31 A 2 It It 2 A 11 21 0.707 t 61 211 3H H 3t 1 2 It It 2 A 0.770 it 6* 2 It 4A t 3A Its 3 i A 2f 0.832 i 71 3 41 t 31 It 3t il 2! 0.895 A 7A 3t 4 A It 3t i A 31 i A 2t 0.957 l n 31 4# It 3H il 3t it 3 1.020 it 81 3A 4 M t 4A i A 3t it 3 A 1.145 H 9 3t 51 It 4A it 3t it 3t 1.270 it 91 4 51 l, 41 i A 4A 2 31 1.395 H 10 41 51 l 4t il 41 2t 3f 1.520 if 101 41 6 l 5 il 41 21 31 1.645 it 11 4t 61 LA 5A i A 4ti 21 4 1.770 H HI 4t 61 i A 5A i A 4 It 21 41 1.895 2 Ht 5 6t it 5t it 5t 2t 4f 2.020 21 121 51 71 it 6t it 51 21 4t 2.270 21 131 51 7f i A 6A it 5J 2f 51 2.520 2f 14 5t 81 il 7 2 61 2t 51 2.770 3 15 61 8f H 71 2 6t 3 5t 3.020 196 SMALL TOOLS but provided with a considerable flat at the top of the thread. There is no standard adopted for the size of this flat. It varies with the different pitches and diameters, and the only guidance in making these taps is to fol¬ low the standards adopted by the tap manufacturers. A list of sizes with a number of different pitches is given in Table XLIV. The outside diameter, which is con¬ stant for each size or number of tap, and the angle diam¬ eter, upon which the width of the flat depends, are given in the table. The root diameter of the thread is easily found by subtracting the depth of the sharp V thread from the angle diameter. In regard to the making of these taps there is little to say which has not already been touched upon in con¬ nection with ordinary hand taps. They are made in sets of three, on the same principles as are used in the common method of making hand taps, that is, with the diameter of all three taps in a set the same on the straight or parallel portion. As these taps are very small, they cannot be provided with female centers, excepting on the larger sizes, particularly not at the threaded end. It is custo¬ mary to provide all these taps one-quarter inch in diame¬ ter and smaller with male centers. Machine screw taps are fluted in the same manner as hand taps. The form of the fluting cutter, its size, thickness, and the radius between the angular sides which produces the fillet in the bottom of the flute are all dimensions which may be figured from the same formulas as for regular hand taps. The radius of the cutter is perhaps the most important of these dimensions. It will be found that according to the formula Radius = —, 4 HAND TAPS 197 in which D = the diameter of the tap, the radius for sizes Nos. 1 and 2 should be about one-sixty-fourth inch, for No. 3 to No. 7 about one-thirty-second inch, for No. 8 to No. 11 about three-sixty-fourths inch, for No. 12 to No. 18 about one-sixteenth inch, for No. 19 to No. 26 about three-thirty-seconds inch, and for No. 28 and No. 30 about one-eighth inch. The number of flutes should properly be three for sizes smaller than five-thirty-seconds inch in diameter, and four for larger sizes. Dimensions of Machine Screw Taps. — The various length dimensions of machine screw taps may be ex¬ pressed by simple formulas the same as in the case of regular hand taps. The general appearance of the former taps is shown in Fig. 87. The shank on the smaller sizes is larger than the diameter of the tap itself, and on the larger sizes equal to the diameter of the tap. On the larger sizes there is a neck between the threaded portion and the shank, but on the smaller the thread runs directly into the shank part. In the formulas for machine screw taps, A = the total length of the tap, B = the length of the thread, C = the length of the neck, D = the diameter of the tap, E = the length of the shank, F = the diameter of the shank, G = the size of the square, H = the length of the square 198 SMALL TOOLS TABLE XLIV. SIZES, PITCHES, AND ANGLE DIAMETERS OF MACHINE SCREW TAPS. No. of Tap. No. of Threads per Inch. Outside Diameter. Angle Diameter. No. of Tap. No. of Threads per Inch. Outside Diameter. Angle Diameter. 1 72 0.071 0.0670 6 48 0.141 0.1291 1 64 0.071 0.0620 6 44 0.141 0.1250 1 60 0.071 0.0650 6 40 0.141 0.1290 1 56 0.071 0.0612 6 38 0.141 0.1245 H 56 0.081 0.0710 6 36 0.141 0.1230 n 52 0.081 0.0715 6 34 0.141 0.1235 2 64 0.089 0.0800 6 32 0.141 0.1230 2 60 0.089 0.0790 6 30 0.141 0.1155 2 56 0.089 0.0795 6 28 0.141 0.1195 2 48 0.089 0.0785 6 26 0.141 0.1160 2 40 0.089 0.0747 6 24 0.141 0.1150 2 36 0.089 0.0710 7 48 0.154 0.1415 3 64 0.101 0.0912 7 40 0.154 0.1375 3 60 0.101 0.0925 7 36 0.154 0.1360 3 56 0.101 0.0957 7 32 0.154 0.1377 3 52 0.101 0.0875 7 30 0.154 0.1320 3 50 0.101 0.0895 7 28 0.154 0.1314 3 48 0.101 0.0870 7 26 0.154 0.1310 3 44 0.101 0.0910 7 24 0.154 0.1249 3 40 0.101 0.0890 8 48 0.166 0.1535 3 36 0.101 0.0860 8 44 0.166 0.1520 3 34 0.101 0.0840 8 42 0.166 01525 3 32 0.101 0.0812 8 40 0.166 01549 4 56 0.113 0.1035 8 38 0.166 0.1530 4 52 0.113 0.1005 8 36 0.166 01510 4 50 0.113 0.1003 8 34 0.166 0.1520 4 48 0.113 0.1045 8 32 0.166 01480 4 46 0.113 0.0975 8 30 0.166 01457 4 44 0.113 0.1000 8 28 0.166 0.1455 4 42 0.113 0.0992 8 26 0.166 0.1435 4 40 0.113 0.1031 8 24 0.166 0.1385 4 38 0.113 0.0960 8 22 0.166 0.1432 4 36 0.113 0.1000 8 20 0.166 0.1387 4 34 0.113 0.0965 9 40 0.180 0.1625 4 32 0.113 0.0970 9 38 0.180 0.1600 4 30 0.113 0.0970 9 36 0.180 0.1652 5 50 0.125 0.1117 9 34 0.180 0.1630 5 48 0.125 0.1135 9 32 0.180 0.1630 5 44 0.125 0.1108 9 30 0.180 0.1603 5 40 0.125 0.1140 9 28 0.180 0.1590 5 36 0.125 0.1120 9 26 0.180 0.1535 5 32 0.125 0.1199 9 24 0.180 0.1515 5 30 0.125 0.1070 10 48 0.194 0.1805 HAND TAPS 199 TABLE XLIV — Continued. No. of Tap. No. of Threads per Inch. Outside Diameter. Angle Diameter. No. of Tap. No. of Threads per Inch. Outside Diameter. Angie Diameter. 10 40 0.194 0.1753 14 24 0.246 0.2221 10 38 0.194 0.1792 14 22 0.246 0.2160 10 36 0.194 0.1760 14 20 0.246 0.2113 10 34 0.194 0.1780 14 18 0.246 0.2140 10 32 0.194 0.1710 14 16 0.246 0.2035 10 30 0.194 0.1730 15 28 0.261 0.2390 10 28 0.194 0.1685 15 26 0.261 0.2325 10 26 0.194 0.1680 15 24 0.261 0.2309 10 24 0.194 0.1680 15 22 0.261 0.2345 10 22 0.194 0.1610 15 20 0.261 0.2270 10 20 0.194 0.1592 15 18 0.261 0.2225 10 18 0.194 0.1575 16 40 0.272 0.2530 11 40 0.206 0.1927 16 36 0.272 0.2520 11 36 0.206 0.1890 16 32 0.272 0.2512 11 32 0.206 0.1925 16 28 0.272 0.2504 11 28 0.206 0.1820 16 26 0.272 0.2500 11 26 0.206 0.1800 16 24 0.272 0.2450 11 24 0.206 0.1780 16 22 0.272 0.2421 11 22 0.206 0.17G4 16 20 0.272 0.2370 11 20 0.206 0.1740 16 18 0.272 0.2326 12 48 0.221 0.2095 16 16 0.272 0.2295 12 44 0.221 0.2065 16 14 0.272 0.2232 12 40 0.221 0.2048 17 24 0.285 0.2570 12 36 0.221 0.2025 17 22 0.285 0.2540 12 34 0.221 0.2035 17 20 0.285 0.2520 12 .32 0.221 0.2035 17 18 0.285 0.2435 12 30 0.221 0.2013 17 16 0.285 0.2397 12 28 0.221 0.2015 18 26 0.298 0.2735 12 26 0.221 0.1970 18 24 0.298 0.2710 12 24 0.221 0.1940 18 22 0.298 0.2680 12 22 0.221 0.1900 18 20 0.298 0.2686 12 20 0.221 0.1858 18 18 0.298 0.2608 13 32 0.234 0.2140 18 16 0.298 0.2550 13 28 0.234 0.2112 19 24 0.312 0.2850 13 24 0.234 0.2080 19 20 0.312 0.2803 13 22 0.234 0.2048 19 18 0.312 0.2762 13 20 0.234 0.2005 19 16 0.312 0.2704 13 18 0.234 0.1938 20 24 0.325 0.2970 14 44 0.246 0.2307 20 22 0.325 0.2940 14 40 0.246 0.2330 20 20 0.325 0.2980 14 36 0.246 0.2310 20 18 0.325 0.2886 14 32 0.246 0.2272 20 16 0.325 0.2830 14 30 0.246 0.2220 22 24 0.350 0.3235 14 28 0.246 0.2245 22 22 0.350 0.3200 14 26 0.246 0.2231 22 20 0.350 0.3155 200 SMALL TOOLS TABLE XLI M — Concluded. No. of Tap. No. of Threads per Inch. Outside Diameter. Angle Diameter. No. of Tap. No. of Threads per Inch. Outside Diameter. Angle Diameter. 22 18 0.350 0.3150 26 16 0.404 0.3592 22 16 0.350 0.3065 26 14 0.404 0.3560 24 24 0.378 0.3495 28 18 0.430 0.3905 24 22 0.378 0.3462 28 16 0.430 0.3883 24 20 0.378 0.3425 28 14 0.430 0.3826 24 18 0.378 0.3420 30 18 0.456 0.4175 24 16 0.378 0.3340 30 16 0.456 0.4166 24 14 0.378 0.3305 30 14 0.456 0.4096 26 18 0.404 0.3660 The following formulas will apply to all sizes of machine screw taps: A = 5 D + 1 ye inches, B = 3 D + | inch, G = 0.75 F, H = 0.67 D + | inch. F, the diameter of the shank, is 0.125 inch up to and including No. 5 machine screw tap, and equal to D for larger sizes. Up to and including No. 7 machine screw tap there is no neck between the shank and the thread. For larger sizes, G = 0.75 D. For sizes up to and including No. 7, E = 2 D inch. For larger sizes, E = 1.25 D + inch. The values in Table XLV are figured from these for¬ mulas, but it must be remembered that here as in the case of hand taps dimensions are only approximately HAND TAPS 201 those obtained from the formulas, whenever no necessity for close fractional dimensions exists. TABLE XLV. DIMENSIONS OF MACHINE SCREW TAPS. —H—>J K- I—-- , Root Diameter 1 J T -\ 1_ i L i / -M*- -c- -»t*- - -A--- -a— " 1 . Fig. 87 No. of Tap. Diam. of Tap. St’rd No. of Threads. Total Length. Length of Thread. Length of Neck. Length of Shank. Diam. of Shank. Size of Square. Length of Square. D A B C E F G H . 1 0 071 64 i* A 1A 0 125 A A 0 081 56 itt t i A 0 125 A A 2 0 089 56 li f li 0 125 A A 3 0 101 48 i+t ii H 0 125 A A 4 0 113 36 n xi i A 0 125 A A 5 0 125 36 in t 1A 0 125 A A 6 0 141 32 2 n 111? 0 141 A 7 0 154 32 2tS n 0 154 A A 8 0 166 32 2i * i 0 166 i A 9 0 180 30 2A n i li 0 180 i i 10 0 194 24 2i a A IA 0 194 A i 11 0 206 24 2A i A IA 0 206 A i 12 0 221 24 2j5 ia A iA 0 221 A A 13 0 234 22 2£ 1x5 3 T6 H 0 234 A $2 14 0 246 20 2A li A H 0 246 A A 15 0 261 20 2 s' i A A ii 0 261 A A 16 0 272 18 2H IA A IA 0 272 ire 18 0 298 18 2tfi li A m 0 298 A A 20 0 325 16 2+ft n A Hi 0 325 i ii 22 0 350 16 3x5 1t5 i If 0 350 i ii 24 0 378 16 3A 4 A 1M 0 378 A f 26 0 404 16 3A 1 A A 1A 0 404 A f 28 0 430 14 3A 1+i A i A 0 430 A ii 30 0 456 14 3A if A 0 456 A 202 SMALL TOOLS The limits of over-size in diameter of machine screw taps after hardening should be made as indicated by Table XLVI. TABLE XLVI. LIMIT OF OVER-SIZE IN DIAMETER OF MACHINE SCREW TAPS AFTER HARDENING. Diameter of Tap. Inches. Limit of Over-size. Diameter of Tap. Inches. Limit of Over-size. Diameter of Tap Inches. Limit of Over-size. A A-i 0.00075 0.001 5HS" 1 1 0.00125 0.0015 i i 0.002 0.0025 A. S. M. E. Standard Machine Screws. We mentioned in Chapter I the standard for machine screws, approved and adopted by the American Society of Mechanical Engineers. The dimensions for the thread quantities, according to this standard, are given in Tables XLVII, XLVIII, XLIX, and L, for both taps and screws, regular and special. STANDARD MACHINE SCREWS. HAND TAPS 208 w § 02 < OOOMt'NWMNNt'OMHfflNIMOlOOOOCOOO NCOMKlTtlrtl-^lOlOlOSDtOt^NOOXOOWOlOO OOOOOOOOOOOOOOOOOOO-—It-I ooooooooooooooooooooo ooooooooooooooooooooo WONOOOxnflOlOJ^NtOOlOOOOOOOOtlNN Tj(iofflN 00 OJOH(MC 0 '>Jt® 00 O(Nl 0 t' 01 r-lKH 0 O O O O O O r-4 t— l t— t t—h »—l t— t C-IOO-iOOTt<--iI>.OO ^ujot'OoaooNm^tocooiM^eoooiN') 1 OOOOOO'-H’—l '—i -i—iif *' ffiOHIM-■ CO <0®NOO®HN»^«3n00M^9 oooooi-H'-H’-i'-ii- lCO HCOcOCOHTt-Aei-O^C^r-lC s ^C^COCO^t | CO-^’^OCOOOOOOOOOOOT-HOO r _ < ^_< T -H(MC^C^l r~*i <****•) Q o cO O O^ 05 O <0 l O> 05 05 '05 t O ) 0000000000000000000000005050505 ooooooooooooooooooooooooooo 35 ^>O 00 O 00 OONN'^N^CC 05 NO 305 »O‘O 0505 , ^ 05 CO’^'^ M^ICIO^OONONOC 5 CO(N» 00505 INCOO)^NCOIOIO S !>- OO O O O o C* -“ -- OOOOO-H’-H’-H i(M(N(N(NCOCOCOCO^ ooooooooo oooooooooooooooooo nstDNoot-oooot^o^ooimTfcomNNOO^o^^^ hNCOCOhCO^NiOOONhO(NNNOCOO(NiO O t>» GO O O O O *” OOOOOr-lr-HT- ^ ^ *___— • I(MCOOOOCO M^^IO^CDCDCOOWIOCOOCO^COO KNWtNtNCOCOCOCO^ ooooooooooooooooooooooooooo ^lOOON^W^^NNOONOOCOlNMNNOCDOOOOOCONOO ooooooooooooooooooooooooooo 00000000000000000000000050050 ooooooooooooooooooooooooooo COCDOJININiOinoOOOHH^^hNOOONCOjOONCO^O N0005HH(N(NC0C0i0L0C0ONN0305H'J^ON^NgCJ2 0 00’-Hr-lT—<1—|HHHHHHHHHHMN(N(MfOCCCOCO^^ o o o o o o ooooooooooooooooooooo OOIO(NCX)COOOCDCOCOCCNCO(N(NOOCOCOOO^^^(NOINOOOO 05 (NIONNOOWCOCOCD 0505 (NHIO^O'DINCO '^00 cOoOOiOOfNNWfO^^iO^NNOOCOHCOCOCO _ OO ^ . . __ I^CD 05 HtJ< i(N(N(N(NCOCOCOCO^Tf< OOOOOOOOOOOOOOOOOOOOOOOOOOO tFCOOOOOOcOCOC s * P Q OOOOOOiOiOlOOOiOlOlOlOOlOOOOOOOmmo ^ OncCOOOCO^OCINOlOONNIMINW ^H(MM^CTlO^!DOOO«lONHrHii i-irtHrtrtrtrtrtHrt«iNiMNcococO WNtoNiHoomto intoNooooosooo OOOOOOOr-1 r—i OOOOOOOOOOOOOOOOOOOOOOO' rtmiOCCO)COO)ffirtrt(NrtlMNlOrtiI5lot'NO)OSOO)rtO oj(M(MrONNMNMCOrtrHiflrtloiOffqr-i!NIN<0(D(0c —^^^^oooooooooooooooooooooo OOOOOOOOOOOOOOOOOOOOOOOOOO' C0MC0i003iO03an0i000i000G0Oi0OO OOCON-N-OOCO^t^-N-OOCOiOCOOO^ _ „ NOOHHWCO^^IOIONNOOCOOO^IONOWIOOOOWCC' ^^ rHrHtHrH.HTHfHr-MMCqiMCOCOCOCO'^^^ 00000000000000000000003000300 HO5CO^IO^IOIOCDCOCOCOCO0OOCOOOOOO3O3O3O3OO3HOO ^NOCOWCOcOt^OitNCNiOiOooOOHnNCOQiOHOOCOOCOlN t^OOOf-HT-HC^CMCOCOiOLOOOt^t^cOOr-H^cOOCMT^t^OcMiO OOhhhhhhhhhhhhhhh(^WW(MCOCOCO^^^ OOOOOOOOOOOOOOOOOOOOOOOOOO' ^S22222 COCO(:<,C ^ CiW00 ^ (:S, '^ , ^OOCOCOCOOOt}'COCD CDiO’^'^fOTjHrocOCOfOCOCOCOCOtNCOCNtNtNC^ o o cq io ob Jh 4< N-OOOt— i c<| CO tO CO OOOr-) H r-H H i-H ^ 1 V. N I - < T—I 1—I 1—1 1—1 T—I 1—H 4 77, 2£> + 3 Table LV is based upon the formulas given. All dimen¬ sions are given in convenient working sizes, and are approx¬ imate in cases where the formulas give values which cannot be expressed in even fractions, or give fractional values inconvenient for working figures. The diameter of the extreme end or point of the cham¬ fered portion should be equal to the root diameter less the depth of the thread, or in other-words, equal to the full diameter of the tap minus three times the depth of thread. 224 SMALL TOOLS TABLE LV. DIMENSIONS OF MACHINE TAPS. Root Diameter-0.015 k- -»**- -A--- Root Diameter -=1 X- -P Zp\r 1 1 i i_f- Fig, 96 Diam. of Tap. Total Length Lengtl of Thread Lengtl of Shank. Lengtl Full Thread Lengt of Taper in Angle. 1 T Lengtl below Root Diam. Size of Square Length of Square. D A B C E F G H K 1 5A If 3A f A A 1 f A s| 2 3f A 1 A A f 1 6A 2A 31 1 A i A A A 6f 2A 4A 1 A i 1 f 1 6f 21 41 A f A A f A 7 A 2f 4A f A A A 1 7f 21f 4A ft f A A f A 7ff 2A 41 ft f f A f 1 8A 3f 5A f A f A A A si 31 51 ft 1 f 1 l i Sff 3A 51 1 A A 1 l A 91 3A 5ft 1 A A A 1 9f 3f 51 A l A f if if 10f 4A 6A i A U i A 1A if n A 4f 6A H i A A f il if HA 411 7* il i A A A if if 121 5 71 1A if t A 1A if 131 5A 7If i A il A l il if 13M 5f 8A il i A A l A if if HA 5ff 8f if 1A f it 1A 2 15f 61 91 ift if f A if 21 151 6A 9A if 1A f 1A if Zf rsf 6f ' 91 iff H A i A if 2f 161 6ft 9ft iff 1A A a 1A 2f 16f 7 91 H 2 f 1A 1A 2f 171 7A 10A iff 2A I 1A 1A 2f 17f 7f 191 2 21 t if 1A 2f 18 7A ioA 2 2A A 1A if 3 18f 7f 19f ZA 21 A if if 3f l9f 81 li 2A 2f l 2A if 31 19f 81 nf 21 21 i A 21 1A 3f 20f 81 nf 2f 2f i A 2A 1A 4 21f 91 ' 12f zA 2f it 2f 2 TAPS 225 Screw Machine Taps. Definition and General Appearance. — Screw machine taps, as the name indicates, are used for tapping in screw machines. The thread to be cut is usually short and the taps therefore are essentially different from other taps used for nut tapping in machines. It is difficult to establish a standard for this kind of taps, as in many cases the length of the thread, the length of the chamfer, and the diameter of the shank largely depend upon special conditions. When manufactured in quantities, however, either for shop use or for the market, there is a necessity for establishing a standard which will be correct in most cases. The chamfered end of the thread of these taps is usually very short, as in most cases the tap is required to tap down to the bottom of a hole. A neck is provided between the tap and the shank, as the latter is usually larger in diameter than the tap itself. In regard to the diameter of the shank, manufacturers making a specialty of this kind of taps recommend that this diameter be made to corre¬ spond with the outside diameter of a spring screw die for cutting the same size of thread as that for which the screw machine tap is intended. This makes it possible to use the same kind of holders for both tap and die. In Table LVI the diameter of the shank is given in accordance with this recommendation, but it must be understood that this diameter depends in many cases upon the size of the turret or the bushings which the tap shank is to fit. The shank should be ground true with the thread, as otherwise the resulting thread cut with the taps may be out of true. A flat is milled on the shank for the turret binding screws. This prevents the ground surface of the shank from being spoiled by the burr that would result from binding directly upon the circular surface. The 226 SMALL TOOLS flutes of a screw machine tap are cut with double angle cutters of 85 degrees inclusive angle, 55 degrees on one side and 30 on the other. The thread is relieved only on the top of the thread of the chamfered portion. The straight portion ought not to be relieved, as the screw machine tap must always be reversed at the end of the cut, and if relieved, there would be danger of chips get¬ ting in between the back of the threads on the lands of the tap and the threads in the nut, which might result in damaging not only the thread already cut but the tap also. Dimensions of Screw Machine Taps. — The following formulas may be used for determining the dimensions of screw machine taps for general use. In these formulas, D = diameter of tap, A = total length of tap, B — length of thread, C = length of neck, E = length of shank, G = width of flat on shank. The dimensions in Table LVI are approximately figured from the following formulas: , 5 D + 20 p D + 4 sy D + 3 <7 “ — 8“’ p 2 D + 9 E= ~r~ ■ The diameter of the shank cannot be determined by any formula, as it should conform to the diameters most com¬ monly used for spring screw threading dies. The width of TAPS 227 the flat, G, depends of course upon the diameter of the shank and should be made approximately according to the formula 2 F + 1 G= 8 ' The dimensions given must, of course, be deviated from in many cases, inasmuch as they would not suit all special purposes but are intended only for taps made for general use. Screw machine taps should have four flutes in all sizes smaller than 1| inches, and six flutes for larger diameters. TABLE LVI. DIMENSIONS OF SCREW MACHINE TAPS. Fig. 97 Diameter of Tap. Total Length. Length of Thread. Length of Neck. Length of Shank Diameter of Shank. Width of Flat. D A B C E F G 4 2f 1A f i A 4 \ A 2H i A A i A 1 4 A f 2 if i A A 1A f A A 2 if 14 A H 1 f 4 2tf 14 A 14 1 f A 2tt 14 A 14 14 A f 2H 14 A 14 14 A tt 2 n i A A i A 14 A f 2 If i A A i A 14 A A 3 i A 4 i A if 4 f 3 i A 4 i A if 4 if 34 14 4 if if 4 l 34 14 4 if if 4 n 34 14 4 if 2 f H 34 i A 4 i A 2 f if 3 A i A A i A 24 f if 3A if A 14 24 f if 3 A if A 14 24 i if 3A 1A A i A 34 if if 3f i A f i A 34 if 2 3f if f if 34 if 228 SMALL TOOLS Hobs and Die Taps. Ordinary Hob Taps .—Hob taps are, as a rule, only intended for final finishing or sizing of the thread in dies. For this reason their construction differs widely from that of ordinary hand taps. They are not primarily intended for actual cutting, being used merely for burring a thread already cut with ordinary taps. Straight hob taps are not relieved either on the top or in the angle of the parallel portion of the thread. Two or at most three threads, however, are chamfered at the point of the tap, and these chamfered threads are relieved on the top of the thread the same as ordinary hand taps. A taper hob, of course, should be slightly relieved on the top as well as in the angle of the thread. The flutes of a hob tap constitute the essential difference between this tap and the hand tap. The number of flutes is greater, and the cutters used are usually regular angular cutters of 50 degrees inclusive angle, 25 de¬ grees on each side, or 45 degrees inclusive angle, 22J degrees on each side. They should have a very slight round joining the angular sides. The dimensions of ordinary hob taps are made the same as for regular hand taps. These were given in Table XLII in the preceding chapter. The number of flutes will be found from Table LVII of Sellers hobs, the number of flutes being made the same for these latter hobs as for regular ones. Sellers Hobs. — The Sellers hobs are a special kind of hob taps, differing from the ordinary hob tap in that they are provided with a guide at a point of the thread. The diameter of this guide or pilot is given in Table LVII according to the ordinary method in practice. The other dimensions are TAPS 229 given approximately according to formulas below, in which D = diameter of hob, A = total length of the hob, B = length of the pilot, C = length of the thread, E = length of the shank, G = the size of the square, and H = the length of the square. Formulas for hobs up to two inches in diameter are: A = 5f D 4- 3f, * 2 + 8> C — - + 5 ^ - 2 + s, E = 3D + 17 G = | X diameter of shank, u _ 3D + 5 For sizes of Sellers hobs two inches in diameter and more, use the formulas: A = 3f D + 7|, B-f + 2 |, C=f + 2f, E = 3 D + 17 8 G = f X diameter of shank, g _ 3Z) + 5 _ 230 SMALL TOOLS The diameter of the shank should be made about one- sixty-fourth smaller than the diameter of the root of the thread. The guide or pilot should always be hardened and ground. Die Taps. — Die taps are used for cutting the thread in the die in one single operation from the blank and are sup¬ posed to be followed by the hob tap. The die tap is pro¬ vided with a long chamfered portion and a short straight or parallel thread. If to be followed by a hob tap, the parallel portion should be slightly under the standard size so as to leave enough metal for the hob tap to remove to insure the correct size of the die. This difference in size should be not only on the top of the thread but in the angle of the thread as well, so that any inaccuracy in the lead of the thread may be taken care of. On the other hand, it must be remembered that the difference must be very slight, as the hob cannot remove very much stock, having a very short chamfer and very small chip room for the stock removed. II this is not taken into consideration, the dies may be injured in the sizing operation. It may not be out of the way to point out that one should never try to cut the full thread in the die with a hob, as this is purely impossible if any satis¬ factory results are expected. There are cases known where persons, supposedly well informed as to the use of tools, have bought hob taps for the pur¬ pose of cutting dies with these taps in one operation, and after having met with failure in accomplishing this, have complained that the tools supplied were not satis¬ factory. Returning to die taps we may say that they are very similar to machine taps and are made in almost exactly the same way. The flutes are cut with the same fluting cutters as are used for machine taps. The die taps are TAPS 231 TABLE LVII. DIMENSIONS OF SELLERS HOBS. Fig. 98 Diam. of Hob. Total Length. Length of Pilot. Length of Thread. Length of Shank . Diam. of Pilot. Size of Square. Length of Square. No. of Flutes. D A B C E F G H \ 4f 11 11 21 A i f 6 A 5 If If 21 1 A f 6 ft 5* i A i A 21 A A f 6 A 5H Hi i+A 2A A 1 If 6 1 6A if if 2A f A A 8 A 6A 2 2 2A f A A 8 4 6f 2A 2A 2f 1 M f 8 tt 7 2A 2A 2f 1 M f 8 ft 7* 21 21 2f 1 A f 8 « 7H 2f 2f 2A 1 1 A 8 1 8A 2A 2 A 2A A 1 A 8 A 8* 2A 2A 21 A A l 10 l 8f 3* 3* 21 A ft l 10 H 9 A 3A 3A 2A f A i A 10 H 10 A 3f 3f 2A f f i A 10 if lOf 4A 4A 2f i A If H 10 H ii A 4f 4f 2H i A If i A 10 if 12* 4A 4A 2f 1A l il 12 if 12f 5 5 2f i A i A H 12 if 13A $A 5A 2A il H l* 12 2 14f 5f 5f 2f H H if 12 2* 14A 5A 5M 2A 11 i A i A 12 2f 14ff 6 6 2A 11 i A i A 12 2* 15f 6A 6A 3 11 U il 12 2i ISftft 6f 6f 3A 11 i A i A 12 2f 161 6 A 6A 3* 11 m if 14 2* 161 6f 6f 31 11 if if 14 2f 17* 6A 6A 3A 11 in Hi 14 3 171 7f 7* 31 H if if 14 3f 18* 71 71 3A 2f 2A lift 16 3* 19* 7f 7f 3A 2f 21 lift 16 3f 20 81 81 31 2f 2A 2 16 4 201 8f 8f 3f 2f 2ft 2f 16 232 SMALL TOOLS relieved both on the top of the thread and in the angle of the thread on the chamfered portion, and they are threaded on a taper for a short distance from the point of the tap the same as machine taps. On the end of the die tap a straight pilot may be provided with advantage. This will help in guiding the tap straight when starting the thread. Some manufacturers do not provide their taps with this straight pilot; they simply chamfer them all the way down to the point, but make the diameter of point below the root diameter of the thread for a dis¬ tance .equivalent to the length of the guide. This, of course, serves no other purpose than to aid in facilitating the point of the tap to easily enter the hole in the die blank but does not guide or start the tap straight. When these taps are to be used for threading dies which have already been provided with clearance holes, they should be fluted with somewhat narrower flutes than otherwise, leaving the lands fairly wide, and preferably be given a greater number of flutes than usual. This will permit the tap to pass through the die without deviating from its true course. Dimensions of Die Taps. — Table LVIII gives com¬ plete dimensions for these taps. The dimensions are figured from the formulas below. In these formulas, D = diameter of the thread, A = total length of die tap, B — length of the thread, C = length of the shank, E = length of the straight thread, F = length of the pilot, G = size of the square, and H = length of the square. TAPS 233 TABLE LVIII. DIMENSIONS OF TAPER DIE TAPS. Diam. of Tap. Total Length. Length of Thread. Length of Shank. Length of Straight Thread. Length of Pilot. Size of Square. Length of Square. No. of Flutes. D A B C E F G H i 5* 2* 2} } f f * 5 * 5f 3* 2* * * * ft 5 1 5ft 3* 2* I f * ft 5 * 6f 3} 2} * * } ft 5 f 6ft 3f 2} f ft * f 5 * 6ft 4f 2* * ft * * 5 5 s 7* 4} 2* ft ft ft * 5 ft 7 ft 4* 3 * ft ft f 6 1 8* 4* 3} 4 f * f 6 if 8# 5* 3* * f f * 6 ft 8f 5* 3* 7 8 * f 1 6 if 9f 5} 3} JJ> 16 * * 1 6 l 9f 6 3f l f ft 1* 6 if 10* 6f 3* if 15 16 ft 1} 6 H 10* 7* 3} 1} 1 f 1* 7 if Ilf 7* 4* if l* * 1* 7 if 12ft 8ft 4} if * If 7 if 13* 8ft 4* if * 1 1* 7 if 13* 9* 4} if i* 1* If 8 if 14f 9* 4* if * If 1ft 8 2 15} 10} 5 2 i* 1} 1ft 8 2f 15* 10f 5* 2} i* 1* If 8 2f 16* 11* 5} 2} * 1* 1* 9 2f 17} 11* 5* 2} i* If 1* 9 2f 18} 12} 5} 2f * 1* 2 9 2ft 18* 12ft 5* 2ft * 1ft 2 9 2f 19 12} 6} 2f i* If 2 10 2f 19* 13} 6* 2f * 1* 2* 10 3 19} 13} 6} 3 is If 2* 10 3f 20f 13} 6} 3} i* 2* 2* 10 3f 21ft 14} 7} 3f * 2} 2} 10 3f 22} 14} 7ft 3f i* 2* 2} 10 4 23} 15} 8 4 * 2ft 2* 10 >iameter 234 SMALL TOOLS For diameters below 2\ inches the following formulas are used: A = 5f D + 3f, B = ±\D + If, 0 = l\D + 2, E=D, F=VD - ff = |X the diameter of shank, #=!£> + tV For sizes 2^ inches and larger the following formulas are used: A = 3| D + 9f, B=2D + 7f, C= l^D + 2 , E=D,_ F=VD - §, G = f X diameter of shank, H= ID + lii It must be plainly understood that the formulas given are for guidance only, and that no hard and fast rule TABLE LIX. LIMIT OF OVER-SIZE IN DIAMETER OF HOBS AND DIE TAPS AFTER HARDENING. Diameter of Tap. Inches. Limit of Oversize. Diameter of Tap. Inches. Limit of Oversize. Diameter of Tap. Inches. Limit of Oversize. A 0.00025 f 0.002 H 0.003 i 0.0005 1 0.00225 3 0.003 i 0.00075 H 0.00225 31 0.0035 f 0.001 H 0.0025 31 0.0035 i 0.00125 if 0.0025 3f 0.004 f 0.0015 2 0.00275 4 0.004 f 0.00175 21 0.00275 TAPS 235 could be made in regard to the dimensions. Formulas are given for so insignificant a dimension as the length of the squared portion of the shank only in order to facili¬ tate a systematic arrangement of the values in the tables. The limits of over-size in diameter permissible in hobs and die taps after hardening are given in Table LIX. Hobs and die taps are made to somewhat closer limits in regard to the excess diameter. The figures given in Table LIX should not be exceeded under any circum¬ stances, as a hob with an error in lead so great as to require a larger excess in diameter than given should not pass inspection. CHAPTER VI. TAPER TAPS. — MISCELLANEOUS TAPS. Taper Taps in General. ■ Taper taps, if the expression be properly understood, are taps which have the diameter of the thread nearest the shank larger than the diameter of the full thread at the point, the intermediate portion being formed by the gradual taper from one end of the thread to the other, as has already been said when defining different kinds of taps in Chapter III. It may be well to call attention again to this proper meaning of the expression “ taper tap ” because of the fact that the first tap in a set of hand taps is com¬ monly but not properly referred to as a taper tap. As this expression is used to designate two widely different things, and as its common usage as the name of the first tap in a set of hand taps .prevents any possible change, it is always well, when speaking of taper taps, to state which of the two meanings is referred to in any particu¬ lar case. In the present discussion we are referring to the taps properly termed taper taps, that is, those with the diameter of the full thread at the point smaller than the diameter of the thread at the end nearest the shank as shown exaggerated in Fig. 100. There are three particular points to take into considera¬ tion when making taper taps. In the first place, the threading tool must be presented to the tap at right angles to the axis of the tap, and not at right angles to its tapered surface, unless the tool is specially made for taper threading of taps with a definite taper; in the second place, taper 236 TAPER TAPS — MISCELLANEOUS TAPS 237 taps should, if possible, be turned on lathes provided with taper attachments, and not by setting over the tail- stock of the lathe; and, finally, proper relief should in all cases be given a taper tap. The first of these questions Fig. 100. General Appearance of Taper Taps was treated at length in the chapter on threading tools, under the heading “Cutting Taper Threaded Taps with Chasers.” The second and third questions will now be taken up. Effect of Setting Over Tail-Stock when Threading Taper Taps. — The second consideration of importance when threading taper taps is that, if possible, the thread should not be cut by means of setting over the tail-stock but by means of a taper attachment. If the old method of setting over the tail-stock is used, two errors will be introduced, and these errors will increase as the taper of the taps increases. The first error consists in the pitch of the thread becoming finer than the standard, which is readily seen by referring to Fig. 101. The length of the work shown between the centers of the lathe is a if measured along the 238 SMALL TOOLS axis of the work. If measured along the tapered surface the length is b ; but 6 = —^—. If the piece is threaded cos v with a certain number of threads per inch, c, the number of threads when threading by means of a taper attachment Fig. 101. Effect of Setting Over Tail-Stock when Threading Taper Taps would be a X c; but if the threading is done with the tail- stock set over, as shown by the dotted lines, the number of threads would be-- ■ X c, or a greater number of threads, cos v ’ and consequently a finer pitch than in the first case. An example will plainly demonstrate the case. Let the length a, measured parallel to the axis, be 12 inches. Assume that we wish to cut 10 threads per inch and that the angle v is 8 degrees. The number of threads on the whole length of the piece, when cut in a correct way by means of a taper attachment, will be 120. Now, the length b, or the length of the piece measured parallel to 12 the outside, is = 12.121, or 12| inches approximately. In this length we would get 121f threads instead of 120. It is thus evident that for steep tapers the difference is quite considerable and cannot be overlooked. ‘Drunken” Thread .—-The second error due to setting over the tail-stock when cutting a taper thread is that the thread, instead of becoming a true, continuous helix, TAPER TAPS — MISCELLANEOUS TAPS 239 becomes “ drunken. ” An exaggerated drunken thread is shown in Fig. 102. The drunken thread is due to the fact that in taper turning with the tail-stock set over, the work does not turn with a uniform angular velocity, while the cutting tool is advancing along the work longitudinally Fig. 102. Exaggerated Appearance of Drunken Thread with a uniform linear velocity. The change in the pitch and the irregularity of the thread are so small as to be imperceptible to the eye if the taper is slight, but as the tapers increase to say one-half inch or three-quarters inch per foot the errors become pronounced. While the setting- over of the tail-stock for cutting taper threads should be discouraged as much as possible, in cases where it is neces¬ sary the evil effects of the method may be partly overcome, at least so far as the cutting qualities of the taps are con¬ cerned, by relieving the threads liberally. Obviously this will not correct the errors of incorrect pitch and imperfect helix of the thread, but it will cause the tap to cut freely. Amount of Error Due to Setting Over the Tail-Stock. — In Table LX figures are given stating the amount a tap will be short in the lead in one inch for various tapers if threaded with the tail-stock set over. When used in con¬ nection with taps and reamers, “amount of taper ” is meant to express the difference in diameter per foot of length measured along the center line or axis of the tool. From the table given it is easily seen whether the inaccuracy 240 SMALL TOOLS produced will be of consequence in a particular case or not. The amount of the error in one inch equals 1 — cos v, if v is figured from the formula tanr = t 2 X 12 in which formula t is the taper per foot of the piece to be threaded. A numerical example will make the formulas more easily understood. Suppose the taper per foot of a partic¬ ular piece of work is five-eighths inch. The angle v is then first determined: tan v = 0.625 2 X 12 v = 1° 30'. 0.026, The amount the lead of the thread will be short in one inch if threaded with the tail-stock set over equals 1 - cos 1° 30' = 0.00034, or about 0.004 per foot. Being a fairly small taper we see that the amount of the error is comparatively slight. If the taper' is increased, however, the error will soon assume such proportions as to be negligible only in very rough work. TABLE LX. AMOUNT OF SHORTAGE IN LEAD IN ONE INCH OF TAPS THREADED BY SETTING OVER THE TAIL-STOCK. Taper per Foot. Error in Lead per Inch. Taper per Foot. Error in Lead per Inch. * 0.00001 B 0.0019 1 0.00005 n 0.0026 0.00012 2 0.0035 0.00022 21 0.0054 t 0.00034 3 0.0078 i 0.00048 31 0.0105 l 0.0009 4 0.0137 0.0014 TAPER TAPS — MISCELLANEOUS TAPS 241 Relief of Taper Taps. — The third and perhaps the main consideration in regard to making taper taps is the question of a proper relief. This question has caused much perplexity, particularly in the case of taps with steep tapers. It is evident that a taper tap not relieved, either on the top or in the angle of the thread, will refuse to cut altogether, or if forced through a hole will either leave a very rough and irregular thread or break off its own teeth. This depends upon that, as the tap is continuously tapering upward, the heels of the teeth are always located in a circular section of a larger diameter than the cutting edges of the corresponding teeth. Con¬ sequently, if forced to cut a thread, the tap, if not relieved, will squeeze the metal back of the cutting edge in order to find room for the increasing diameter. While the edge cuts, the space produced by the cutting point of the thread is not large enough for the increasing diameter of the part of the thread immediately following. On account of this it is imperative that taper taps be relieved the full length of the thread, on the top as well as in the angle of the thread, for the full width of the land. The relief should also be greater on the side D than on the side E of the thread. (See Fig. 103.) This will lessen the friction and the resistance while cutting a thread, inasmuch as it is obvious that the greater pressure on the thread of the tap created by the cutting process comes on the side D. Thus, if this side is properly relieved, so as to permit only 242 SMALL TOOLS the cutting edge to come in contact with the material to be cut, the friction is reduced to the smallest possible amount at the same time as the keenness of the cutting edge is increased. With the exception of the previous remarks there is nothing, to be added concerning taper taps which has not already been discussed in relation to straight taps. As a rule there is not the necessity for the extreme accuracy in taper taps that is sometimes expected in hand taps, because, with incidental exceptions, of course, taper taps are usually employed on work of rougher character. Besides, being tapered, there is never any requirement for a working fit between the stud and the nut, and taper taps are used mainly for tapping holes where a steam- or air-tight fit is required. Pipe Taps. The most common of all taper taps is the pipe tap. The number and form of threads for this tap were given in Chapter I. The pipe tap tapers three-quarters inch per foot, or one-sixteenth inch per inch measured along its axis. The taps are known by the nominal size of the pipe for which they are intended. Consequently a pipe tap is a great deal larger than the size by which it is designated. The largest diameter of a half-inch pipe tap, as seen from Table LXII, is 0.887 inch. Fluting. — Pipe taps are fluted with the same kind of cutters as are used for hand taps. As there is consider¬ able difference in the manner in which a hand tap and a pipe tap cut, there is also some difference in regard to the required chip room. In the case of a hand tap, as soon as the thread has been cut by the chamfered portion, the straight part of the thread does not cut or produce any chips. The pipe tap, again, being tapered, is constantly cutting, no matter which part of the tap is in contact with TAPER TAPS —MISCELLANEOUS TAPS 243 the work, and therefore there is necessity for large chip room, and the flutes should be made as deep as possible without impairing the strength of the tap. The number of flutes for pipe taps may be approximately determined by the formula N = 1.75 A + 3, in which N is the number of flutes and A the diameter of the tap at the size line. This formula gives the following number of flutes for sizes up to 4-inch pipe tap. Nominal Size of Tap. Number of Flutes. Nominal Size of Tap. Number of Flutes. \ 4 11 6 i 4 2 7 t 4 2J 8 i 4 3 9 i 5 31 10 1 5 4 11 H 6 The formula given for the number of flutes makes the distance from cutting edge to cutting edge at the size line larger as the sizes grow larger, thereby making possible deeper flutes in the larger sizes. Testing Lead of Taper Taps. — In testing or inspecting the lead of taper taps, it must be remembered that the correct lead should be on a line parallel to the axis of the tap, and the lead of the thread cannot be measured in the same manner as with straight taps, unless due allow¬ ance is made for the differences in length along the axis and the tapered surface. In Table LX I the values are given which should be measured along the tapered surface to correspond to one inch along the axis for dif- 244 SMALL TOOLS ferent tapers. In other words, if a tap is tapered three- quarters inch per foot, and is provided with 8 threads per inch, the distance covering 8 threads on the surface of the tap is not one inch but 1.0005 inch, as seen from the table opposite three-quarters taper per foot. If the lead of the thread is tested by comparing it with a standard plug, this need not, of course, be taken into consideration, as then any device for comparing the lead of straight taps is equally applicable to taper taps. TABLE LXI. AMOUNT MEASURED ALONG THE TAPERED SURFACE CORRESPONDING TO 1 INCH ALONG THE AXIS. Taper per i Foot. Amount Measured along the Tapered Sur¬ face Corre¬ sponding to 1 Inch along the Axis. Taper per Foot. Amount Measured along the Tapered Sur¬ face Corre¬ sponding to 1 Inch along the Axis. i 1.0000 H 1.002 i 1.0001 if 1.0025 f 1.0001 2 1.0035 1.0002 2} 1.0055 f 1.0003 3 1.008 f 1.0005 31 1.011 1 1.0009 4 1.014 n 1.0015 The distance on the tapered surface corresponding to one inch along the axis is —— > if v is determined by the cos v formula tan v t 2 X 12’ where t is the taper per foot. TAPER TAPS —MISCELLANEOUS TAPS 245 Thus, if a tap tapers If inches per foot and has 8 threads to the inch, if 16 threads were measured at the surface of the taper, the length, if the lead be correct, should not be 2 inches but 2.003 inches, which we find from tan ” = 2^12 = °-° 521: v = 3° (approximately), and —= 1.0014; COS O 2 X 1.0014 = 2.003 (approximately). In Tables LX and LXI figures have been given for tapers as steep as 4 inches per foot. Of course, such steep tapers are very seldom used. Dimensions of Pipe Taps. — The dimensions of pipe taps are given in Table LXII. Referring to Fig. 105, a diameter A is given at the distance B from the point of the tap. This diameter is the essential diametrical measure of a pipe tap, and the circular line which may be imagined to be drawn around the tap at this place is termed the size line. The two smallest sizes are provided with a neck between the threaded part and the shank. On the remaining sizes the shank is made small enough to come below the root diameter of the thread, and a neck is therefore unnecessary. As pipe taps must be made according to the established manufacturing standard, formulas for the dimensions cannot be given, excepting for those measurements which are unessential, like the dimensions for the shank and square; but Table LXII gives all necessary information in regard to all standard sizes, and formulas, even if they could be given, would consequently be superfluous. Limits of Accuracy. — The accuracy usually demanded of taper pipe taps in regard to the exact location of the size 246 SMALL TOOLS line is given below. The method of testing or measuring taper taps in order to insure that they are within the per¬ mitted limits of variation in this respect is by means of a ring gauge, as shown in Fig. 104, the diameter L at the large end of which is the dimension at the size line; the diameter S at the small end of the hole is the diameter at the point of the tap, and the length M of the ring gauge equals the dimension B in Fig. 105, representing the distance from the Fig. 104. Gauge for Testing Taper Pipe Taps size line to the point of the tap. Thus, in testing the tap with this ring gauge, if the end of the tap comes exactly flush with the gauge, the location of the size line is exactly correct. If the end of the tap projects through or comes short of the face of the ring gauge at the small end of the hole, such projection or shortage represents the error in the location of the size line. Error Permitted in theLoca- Pipe Sizes. tion 0 f g, ze Lj ne . 1-1 .± h 11-3.± ts 31 and up.±1 Plus in the above table signifies a projection of the tap through the ring gauge, and minus, failure of the tap to reach the end of the gauge. TAPER TAPS —MISCELLANEOUS TAPS 247 TABLE LXII. DIMENSIONS OF BRIGGS STANDARD PIPE TAPS. -T— —h~4 i—M—H — B —*1 --H -«l Fig. 105 S . A ■w oi t-. Nominal Pipe Size. Diameter i Size Line. Distance frc End to Size Line Diameter e Large Enc Length oi Thread. I Length oi 1 Shank. Total Lengt Diameter < Shank. Length oi Square. h cr 02 *4—< o O) 55 Diameter c Neck. Length of Neck. A B C D E F G H X L Af 1 0.405 n 0.443 A 1# 2# A A A f f 1 0.540 A 0.575 u, 11 21 11 A f f t 0.675 A 0.718 U 31 A A 1 0.840 1 0.887 If* 2 31 1 A A 1 1.050 1 1.104 Iff 21 31 A 1 A o 1 1.315 if 1.366 If 21 41 11 A A o u 1.660 H 1.717 a 21 4f 1A A l 3 3.500 1A 3.605 31 41 71 2# il 1A C3 .a 3* 4.000 if 4.125 3f 4A 8A 2B i A 21 CO CO 4 4.500 1A 4.629 31 41 8f 3 ift 21 si S3 4* 5.000 1 7 1 8 5.125 31 4B 8A T?6 A* 2f CO CO 5 5.563 2 5.687 4 41 81 31 il 21 O) CO CD CO 6 6.625 21 6.766 41 41 91 31 A 2A 0) 43 7 7.625 2f 7.773 41 5 91 41 2 3A H H 8 8.625 n 8.773 41 51 91 41 21 3f 9 9.625 2i 9.781 5 51 101 41 21 3ft 10 10.750 2* 10.906 5 51 10f 51 2| 3 A English Taper Pipe Taps. English taper pipe taps constitute a special class of taper taps. Most tap manufacturers in this country make them exactly like the Briggs standard pipe taps in regard to dimensions, the only difference being that the English taper 248 SMALL TOOLS pipe taps are provided with the Whitworth form of thread and with such a number of threads per inch as is called for by the standard for Whitworth standard gas and water pipe thread. It appears, however, that in England these taps are made with 1 inch taper per foot, instead of three-quarters inch, and at least one firm in this country follows the English practice. The last statement is made on the authority of Mr. Charles E. Smart of Greenfield, Mass., who in a communication to Machinery in June, 1908, wrote as follows: “Mechanical hand-books give nothing on the subject of the taper of Whitworth pipe taps, and for that reason it is highly de¬ sirable that the question of correct taper be brought up in the discussion of this subject. The dimensions of these taps should be based upon standard Whitworth pipe tap gauges, which are made in England by the Whitworth Company. These gauges all taper 1 inch to the foot and are so marked upon the gauge. “The accompanying table [LXIII] shows the dimensions of Whitworth pipe taps as made by the A. J. Smart Manu¬ facturing Company. It will be noticed by comparing this table with the one for regular Briggs pipe taps, that the diameters at the small end are not the same for the same nominal sizes. This is because English pipe is smaller than American pipe, according to all tables, so that the ends on the Whitworth pipe taps should be made correspondingly smaller. It is believed by the A. J. Smart Manufacturing Company that the proper way to make the taps, therefore, is to make the diameter at the smaller end correspondingly smaller. The lengths of the pipe taps in the table will also be found to be shorter, because it has been found that all users of pipe taps, especially plumbers, prefer the shorter lengths, and many of the tap manufacturers are now making the lengths of the threaded part of pipe taps the same as those given in the table. The A. J. Smart TAPER TAPS — MISCELLANEOUS TAPS 249 TABLE LXIII. WHITWORTH PIPE TAPS. (A. J. Smart Manufacturing Company’s Standard.) Taper per foot = 1 inch. Nomi¬ nal Size. Diam. at Large End of Thread. Total Length of Tap. Length of Thread. Length of Shank. Diam. of Shank. Length of Square. No. of Threads per Inch, Whit¬ worth Form. No. of Flutes. Size of Steel. £ 0.435 2£ 1 H- 0.328 M 28 4 M 0.570 2f If U 0.438 T6 19 4 ff £ 0.718 2f 1A 1* 0.563 t 19 4 i i 0.888 3 Irk 1A 0.703 & 14 4 59 I 0.964 31 m 1 25 0.781 f 14 4 l** 1 1.103 3f H U 0.906 a 14 4 lft 1 1.382 3f if 2f 1.125 if 11 4 iff if 1.725 H if 2f 1.453 R 11 6 if if 1.958 4f U 2f 1.609 i 11 6 iff if 2.130 41 iff 2 A 1.766 Its - 11 6 2* 2 2.430 4f 2 2f 2.063 if 11 6 m Manufacturing Company also only makes 4 or 6 flutes in its taps. The company has found that customers do not like an odd number of flutes, as the taper with the odd number of flutes can never be measured by microm¬ eters after the flutes have been once milled. This is a great disadvantage (or, to some people, an advantage) in cases of disputes as to the sizes of the taps. In the table given there will be found a column giving the size of the steel used for the different taps. This information is given for the convenience of the purchasing agent, the superintendent, the foreman, etc., and has often been found exceedingly useful.” In paragraph 7, page 6, of the “Report on British Standard Pipe Threads for Iron or Steel Pipe and Tubes,” of April, 1905, issued by the Engineering Standards Com- 250 SMALL TOOLS mittee, however, the taper of Whitworth pipe is given as three-quarters inch per foot. Before this report was issued it was the custom in England to make these taps with a taper of one inch per foot. Pipe taps and taper taps in general are often made with the interrupted thread shown in Fig. 92, Chapter V. This form of thread is very well adapted for taper taps, and in case of a very steep taper is, in fact, almost essen¬ tial if a smooth and perfect thread is to be cut. In hardening, pipe taps should be drawn to a somewhat higher temperature than ordinary hand taps of the same sizes. The correct temperature is about 470° F. Pipe Hobs. Pipe hobs are used for sizing pipe dies after the thread has been cut nearly to size either in a lathe or by a pipe tap. The threaded portion of a pipe hob is made longer than that of pipe taps, but there is no good reason why this should be so, excepting that it has become customary, and established custom is as unyielding in tool-making as in anything else. Outside of the longer threaded portion, the only essential difference from the pipe tap is the number and the form of the flutes. These latter are cut with a 50-degree double-angle cutter, 25-degree angle on each side, which is the same kind of a cutter as is used for ordinary straight hob taps. The number of flutes may be approximately determined by the formula 8.5 B = N, in which B = diameter at large end of thread of hob and N = the number of flutes. This formula gives the width of each land as about three- sixteenths inch, and the width of the space or flute the TAPER TAPS — MISCELLANEOUS TAPS 251 same amount. According to this formula the number of flutes for various sizes of pipe hobs is as follows: Size of Pipe Hob. Number of Flutes. Size of Pipe Hob. Number of Flutes. i 5 2 22 i 6 21 26 t 6 3 32 8 31 36 I 10 4 40 1 12 41 44 H 16 5 48 i£ 18 6 58 Dimensions of Pipe Hobs. —• The dimensions for lengths and diameters of pipe hobs are given in Table LXIV. The dimension A is given according to the established standard of the manufacturers of taps. This is the essen¬ tial diameter and is located 1J inches from the large end of the thread of the hob. The limit of error for the loca¬ tion of this diameter is the same as the limit for the loca¬ tion of the size line of pipe taps which has been previously stated, and the gauging is done in the same manner. It is evident that a separate set of ring gauges is required, and that the length of the gauge in this case should always be 1§ inches, the large diameter of the hole in the gauge being diameter B in Fig. 106, and the small diameter the dimen¬ sion A. The taper of pipe hobs is, of course, the regular pipe thread taper, three-quarters inch per foot. The more important dimensions in Table LXIV are figured from the formulas: „ N + 16 ^ 5 VN + 11 4 F — A - tV for pipe sizes up to and including 3 inches, N F = — + 3| for 3J-inch pipe size and larger. o 252 SMALL TOOLS In these formulas, A = size of the hob 1J inches from the large end of the thread, N = nominal size of hob (pipe size), O = length of shank, D = length of thread, and F = diameter of shank. TABLE LXIV. DIMENSIONS OF PIPE HOBS. Nomi¬ nal Size. Actual Size. Diameter at Large End. Length of Shank. Length of Thread. Length Over All. Diam. of Shank. Size of Square. Length of Square. A B C D E F G H 1 0.445 0.539 2 3A 5fk t A 1 1 0.573 0.667 2 31 5f 1 1 1 t 0.719 0.813 2A 31 5A * A 1 1 0.885 0.979 2A 31 5H 11 1 1 1.104 1.198 21 31 6 1 A A 1 1 1.363 1.457 21 4 61 i A l U H 1.721 1.815 2 A 41 6A if il 11 H 1.955 2.049 2A 41 6A 11 i A If 2 2.460 2.554 21 41 6f 21 11 21 2.963 3.057 2A 441 7 21 2A If 3 3.620 3.714 21 41 71 3 A 21 11 31 4.062 4.156 2A 5* 71 3+i m 11 4 4.485 4.579 21 51 71 31 2A 11 41 5.000 5.094 2A 51 m 3H 21 11 5 5.565 5.659 2f 51 81 31 2t§ 2 6 6.620 6.714 2f 51 81 4 3 2 TAPER TAPS — MISCELLANEOUS TAPS 25 B Relief. — Pipe hobs, being provided with a taper thready must be relieved both in the angle and on the top of the thread. In this respect they differ from straight-thread hobs, which are relieved only on the top of the thread of the short chamfer at the point. Taper Boiler Taps. Taper boiler taps, as the name indicates, are used in steam boiler work, and, like the pipe tap, are used in this work where a steam-tight fit is desired. The taper of these taps is the same as the pipe tap taper, three-quarters inch per foot. In regard to their construction there is nothing to say that has not already been said either in connection with pipe taps or about taper taps in general. The size by which these taps are designated is located one-quarter inch from the large end of the thread. The permissible limits of error in the location of the size line are the same as for pipe taps. In Table LXV dimensions are given for taper boiler taps. The most important of these are approximately figured from the following formulas: A = 3 D + 2| inches, B = + If inches, C = -p + f inch, E = 2 D + | inch. In these formulas, A = total length of tap, B = length of thread, C = length of neck, D = diameter of tap, measured one-quarter inch from the large end of the thread. 254 SMALL TOOLS These taps are provided with 4 flutes up to 1| inches diameter, and with 5 flutes for sizes from If to 2 inches. If made in sizes larger than 2 inches, 6 flutes should be given to the tap. Boiler taps are always provided with 12 sharp V threads per inch, irrespective of the diameter of the tap. TABLE LXV. DIMENSIONS OF TAPER BOILER TAPS. Diam. Total Length Length Length Diam. Length Size of of of of of of of Tap. Length. Thread. Neck. Shank. Neck. Square. Square. D A B C E F G H 1 4| 21 1 11 4 1 f 4 44 24 1 If M 4 4 i 4f 2f 1 U 4 f fi 4 44 2f 4 U If 4 1 l 5 24 4 2 If 1 4 4 54 21 4 21 M 4 f f 5f 24 4 21 H f 4 4 54 24 f n n 4 4 l 51 2f f 21 ff 1 1 111) 54 Oil Z T6 f 2f ft 14 4 if 6f 21 f 21 11 if f 1 A 64 21 4 2f 14 14 f H 61 24 4 3 14 4 l* 64 21 4 31 14 14 1 if 6f 24 4 31 14 if 14 1 -16 24 1 3* 14 14 14 4 71 3 1 31 14 il if if 7f 31 1 31 iff il il if 8 34 4 4 41 il T4 4 8f 34 4 41 1 23 1 3 2 il 14 2 81 3f 1 41 1 2 7 il • il TAPER TAPS — MISCELLANEOUS TAPS 255 Patch-Bolt Taps. Patch-bolt taps are practically only a modified form of taper boiler taps. The taper is the same, but the threaded portion as well as the total length is shorter than the corresponding lengths of a taper boiler tap. The taps are used for similar purposes in boiler construction. TABLE LXVI. Fig. 108 Diam. of Tap. Total Length. Length of Shank. Length of Neck. Length of Thread. Diam. of Neck. Diam. of Shank. Size of Square. Length of Square. D A B C E F G H K 4 21 4 li t 4 f 4 A 3 1A 4 1A A A A 4 1 3A H 4 i A 4 t If A A 34 l* 4 i A A A 4 A 1 3A it 4 1 A t f A I it H 11*6 1 1 A A A t f * 31 11 4 it I 1 li A it 3ts l* 4 it it A A A 1 3* if 4 it i l 1 1 1* 3A lli 4 it it !A A 1 1* 3* H 4 it l H II A 1A 31 lit 4 1 TS i A i-A 4 A li 3ft it 4 i A it A A i 1A 3* 144 4 i A iA i A l 1 n 3 it 2 4 ii A 1A A 1A 4 2 A 4 i A i A i A i A A 1* 4* 24 4 i A it li i| l 256 SMALL TOOLS The dimensions for patch-bolt taps are given in Table LXVI. The essential dimensions are approximately figured from the formulas: A = 1-ft D + 2/s inches, B — D + f inch, E = x 3 s D + IfV inches, F = D — l inch. In these formulas, D = diameter of tap (measured five-eighths inch from the large end of the thread), A = total length of tap, B — length of shank, E = length of thread, and F = diameter of neck. The diameter of the shank equals the diameter of the tap. Patch-bolt taps are always provided with 12 threads per inch, V form, irrespective of diameter. All sizes are fluted with 4 flutes up to 1J inches diameter. Patch-bolt taps are not manufactured in larger sizes. Mud and Wash-out Taps. Mud and wash-out taps are used in boiler work the same as the taps previously referred to. These taps are some¬ times referred to as arch pipe taps, but the former name is by far the more common. They are made in six sizes, usually known by numbers as stated in Table LXVII. These taps taper 1| inches per foot, and have 12 sharp Y threads per inch. The dimensions as given in Table LXVII conform in all essential details to the practice of manufacturers of taps. Number 0 tap is provided with 5 flutes, No. 1 with 6, No. 2 with 7, and the others with 8 flutes. TAPER TAPS — MISCELLANEOUS TAPS 257 TABLE LXVII. DIMENSIONS OF MUD OR WASH-OUT TAPS. Fig. 109 Number of Diameter at Diameter at Diameter of Size of Tap. Small End. Large End. Shank. Square. A B C D 0 1A If if H 1 If 2ts if If 2 2t$ 2f 2 3 2f 2B 2 If 4 2ii 3 2 5 3 3t$ 2 If Blacksmiths’ Taper Taps. There is but one more class of taper taps generally manufactured, the blacksmiths’ taper tap. This tap has a long taper thread and a very short shank, only suffi¬ ciently long for a square and a collar to prevent the tap wrench from slipping from the square down upon the body of the tap. The taper of the thread is three-quarters inch per foot; the size by which the tap is known is measured five-eighths inch from the large end of the thread. These taps are generally made with the standard number of V threads per inch corresponding to their nominal diameter. The sizes given in Table LXVIII are the sizes generally made; all these sizes have four flutes. 258 SMALL TOOLS TABLE LXVIII. DIMENSIONS OF BLACKSMITHS’ TAPER TAPS. ,H = sqi ARE % INCH TAPER PER FT. 1 -1- t 1 V, TT t- - ^liiiwi { iimr 1 U_ F , 1 1 D ^ L „ L —e -d -=► Fig. 110 Nomi¬ nal Diam. of Tap. Length of Shank. Length of Neck. Length of Thread. Total Length. Length of Square. Diam. of Shank. Size of Square. A B C D E F G H i h f F 2f f i A A A 1ft 2ft f f A 8 f A If 2ft A A A A t A 2A 3* A i f 1 if h 2* 3A i A A A 1 i 2A oil 1 f ft f if i 2ft 3 if A IF h A if $ m ft A A 1 i A 3 4ft f if ft if if A 3A 4ft I I if i l A 3f 4ft if if if if l f 3A 5ft if l f l Fre f 3f 5ft f i A if if 1 A if 4f 6 if i A f ft ft if ft 6ft f 1A l if if i ft 7 if i A 1A ft i A i 5i 7A l 1 A ift Pipe Taps and Drills Combined. Pipe taps are sometimes provided with a drill point as shown in Fig. Ill, for drilling the hole previous to tapping. Instead of a square for a wrench, they are then usually provided with square taper shank for a taper drill socket. The dimensions of the shank must of course suit the TAPER TAPS—MISCELLANEOUS TAPS 259 requirements. The threaded portion is an exact dupli¬ cate of the threaded part of a pipe tap. The drill part has two flutes like a twist drill, and the point is ground to the same angle, 59 degrees with the center line, as are ordinary twist drills. The diameter and the length of the drill point are the only dimensions necessary to state in this connection. Pipe Tap Length of Diameter of Size. Drill Point. Drill. I 1 H A i 1 I H 37 1 n ft 1 it 2 9 3T 1 ii i& B . if 11 li H iff 2 If 2^ 21 2 2f Stay-Bolt Taps. Stay-bolt taps are extensively used in locomotive boiler work. The ordinary or radial stay-bolt tap is shown in Fig. 112; in Fig. 113 is shown the spindle stay-bolt tap, which has derived its name from the guiding spindle upon which the tap proper revolves. Radial Stay-bolt Taps. — If we first give our attention to the radial stay-bolt tap as shown in Fig. 112, the length 260 SMALL TOOLS C represents the threaded portion. Of this part, the portion F is straight or parallel, and the part G is cham¬ fered. The part E is a taper reamer which reams the hole previous to tapping. The taper of this reamer is usually three-thirty-seconds of an inch per foot. The diameter at H is equal to the root diameter of the thread. The diameter of the shank is about 0.005 inch below the root diameter. Stay-bolt taps are usually made with 12 threads per inch of the sharp V form. Although practice has almost universally favored the employment of the sharp V thread, the main advantage (and perhaps the only real advantage) of a thread of this sort is that it can be made tight in the boiler sheets and kept tight without any great diffi¬ culty. On the other hand, the use of the V thread violates one of the fundamental principles of machine design — the principle, namely, of avoiding all sharp angles and of filleting every place where such angles tend to occur. This must have occurred many times to engineers and designers, and yet no general movement has been made to discard the V thread and substitute for it a form that shall not be open to the same objection. The Whitworth thread is receiving considerable attention at the present time, however, for use upon stay-bolts, and it is regarded with favor by certain builders of large experience, notably by the Baldwin Locomotive Works, who are now using this thread upon locomotive stay-bolts. If experience shows that stay-bolts can be made tight and kept so when fitted with this thread, it is probable that its adoption will extend to other builders. Stay-bolt taps receive very rough treatment, and are exposed to hard usage, and should therefore be made of an extra good quality of steel. The thread should be TAPER TAPS—MISCELLANEOUS TAPS 261 relieved both on top and in the angle of the thread on the chamfered portion. In order to prevent the existence of too wide cutting edges toward the smaller end of the chamfered portion, the tap is threaded taper about one- half of the chamfered part. This prevents the tap from reaming instead of cutting. In order to gain the same end it is advisable never to make the chamfer any longer than 6 inches. The interrupted thread shown in Fig. 92, Chapter V, is particularly of value in the case of stay-bolt taps, and is probably used more on this class of taps than on any other. In Table LXIX the dimensions for standard radial stay-bolt taps as made by a prominent tap-manufactur¬ ing firm are given. However, stay-bolt taps are made in a variety of sizes and designs for special requirements ; but the two kinds given in the table are the most com¬ monly used. All stay-bolt taps of sizes given in the table should have 5 flutes. The over-size limit of variation in diameter from the correct size, is commonly assumed in stay-bolt taps to be 0.002 inch for taps smaller than 1 inch in diameter and 0.003 inch for larger sizes. It is evident that it is not permissible for the tap to be under the correct size ; con¬ sequently the diameter is required, after hardening, to be between the standard diameter and a diameter 0.002 or 0.003 inch respectively, above the standard. Sometimes stay-bolt taps are provided with a threaded guide at the upper end of the thread. This guide is not fluted and should be made slightly smaller in diameter than the cutting size of the tap. The amount which the diameter is smaller is usually about 0.010 inch, and should apply to the angle diameter as well as to the top of the thread. While not fluted, this threaded guide ought 262 SMALL TOOLS still to be grooved by a small convex cutter for oil pas¬ sages to the flutes. TABLE LXIX. DIMENSIONS OF REGULAR STAY-BOLT TAPS. Fig. 112 Total Length of Tap. Diameter of Tap. Length of Shank. Length of Thread. Length of Reamer. Length of Parallel Thread. Length of Chamfer. Root Diameter. Diameter of Shank. Size of Square. Length of Square. ' A D B C E F G H K L M f 7 71 51 11 6 0.606 0.601 M f if 7 71 51 11 6 0.668 0:663 5 l 7 71 51 11 6 0.731 0.726 A i $ H 7 71 51 11 6 0.793 0- 788 M \ 43 o 1 7 71 51 11 6 0.856 0. 851 iff 1 .£ 1* 7 71 51 U 6 0.918 0.913 If 1 o H 7 71 51 11 6 0.981 0.976 I 1 7 71 51 11 6 1.043 1.038 ij 1 if 7 71 51 11 6 1.106 1.101 82 n l* 7 71 51 11 6 1.168 1.163 i u U 7 71 51 11 6 1.231 1.226 H H f 9 8 7 2 6 0.606 0.601 M 3. 4 tf 9 8 7 2 6 0.668 0.663 I 3 4 9 8 7 2 6 0.731 0.726 A I If 9 8 7 2 6 0.793 0.788 9 2 . 4 $ l 9 8 7 2 6 0.856 0.851 H 1 o d l* 9 8 7 2 6 0.918 0.913 A 1 if 9 8 7 2 6 0.981 0.976 i 1 csr 1A 9 8 7 2 6 1.043 1.038 25 3? 1 if 9 8 7 2 6 1.106 1.101 U H 1A 9 8 7 2 6 1.168 1.163 i H if 9 8 7 2 6 1.231 1.226 II 11 Spindle Stay-Bolt Taps'. — The spindle stay-bolt tap, as shown in Fig. 113, is not provided with a reamer, and with but a short chamfer. It is fluted about half way of TAPER TAPS — MISCELLANEOUS TAPS 263 the threaded part. The remaining part of the thread acts as a guide and should be made in the same way as threaded guides for radial stay-bolt taps. The guide E on the end of the spindle holds the tap in place in rela¬ tion to the inner tube sheet while the outer one is threaded. The standard dimensions for these taps are given in Fig. 113 and in Table LXX. TABLE LXX. DIMENSIONS OF SPINDLE STAY-BOLT TAPS. Fig. 113 Diameter of Tap. Diameter of Shank. Size of Square. Diameter of Neck. Diameter of Guide. D A B C E ! 1 1 4 0.601 f H l 1 1 f f 0.663 0.726 A f • if A 1 I 0.788 l i A id 0.851 | Its if f 0.913 A 1 A J 0.976 l *A n A 1.038 !A U 1A l 1.101 H 1A i A if 1A 1.163 if i A 1A 1.226 Straight Boiler Taps. Straight boiler taps are, strictly speaking, only a special class of hand taps. They have a long chamfer and a 264 SMALL TOOLS straight guide at the point. The chamfered portion is relieved on the top of the thread. These taps are fluted in the same way as hand taps. In Table LXXI the dimensions for these taps are given. TABLE LXXI. DIMENSIONS OF STRAIGHT BOILER TAPS. Tig. 114 Diam. of Tap. Total Length. Length of Shank. Length of Neck. Length of Thread. Length of Full Thread. Length of Cham¬ fer. Length of Pilot. Length of Square. Size of Square. D A B C E F G H I K f 4f H f 2 f I •f f A 4A Iff f 2f A i A f A A I 4f Iff f 2A f H A f ff ff 4x1 Iff A 2A ff i A A ff f 1 5 If A 2A I i A f 1 A If 5A Iff A 2fs ff if f ff S i 5! 2 A 2ff 8 1A f f ff if 5 A 2 f 2ff ff H f ff ff l 5f 2 f H 1 i A A l 1 Its If 5 If 2fs I 31 i A if A 1A ff 6f 2A I 3A 4 iff f if i 1A 6A 2fs ff 3A i A if I 1A I If 6f 2f ff 3 if ii il ff il ff 1A 6tt 2A ff 3ff i A iff ff i A l If 6f 21 ff 3ff if if ff if 1A i A 7A 21 if 4| i A iff 1 i A i A if 71 21 1 41 if 2 1 if H if 7f 2A 1 4A if 2* ff H if i! 8 2f ff 4 if if 2A f if 4A if 8f 2f ff 5A if 2A f if i A 2 81 2f f 5f 2 2A ff if if TAPER TAPS — MISCELLANEOUS TAPS 265 The most important of these dimensions are determined from the formulas: A = 3 D + 2f inches, E — 2\ D + | inch, F=D, H = | D + t\ inch, in which formulas, A = total length of tap, D = diameter of tap, E = length of threaded portion, F = length of full or parallel thread, and H = length of guide. In making these taps the same limits in regard to over¬ size diameters as are employed for regular hand taps should be adopted. Straight Pipe Taps. Straight pipe taps, as was mentioned in a previous chapter, are only a variation of hand taps, having the same number of threads per inch as the corresponding sizes of taper pipe taps, and a diameter arbitrarily adopted by the manufacturers of these taps. Table LXXII gives the dimensions for taps up to and including three-quarters inch nominal diameter. The larger sizes are given in Table LXXIII. It will be noticed that the difference in appearance between the larger and smaller sizes is simply that the latter is provided with a short neck, turned down below the root diameter, while on the larger sizes the whole shank is turned down below the root of the thread. 266 SMALL TOOLS TABLE LXXII. STANDARD STRAIGHT PIPE TAPS. |-P= SQUARE - % t X T 1 ? t A 1 J ■ t-" ! — ^ r-° rnl Fig. 115 Nomi¬ nal Size. Diam. of Tap. Total Length. Length of Thread. Length of Neck. Length of Shank. Diam. of Neck. Diam. of Shank. Size of Square. Length of Square. D A B C E F G H / 1 0.398 2f 1 A Ifk 0.335 f A A 0.531 2* n f If 0.440 1 f i 1 0.672 3A ii f i A 0.575 f if A 1 0.828 31 if A 1A 0.705 f A f f 1.041 3f if 1 4 0.915 1 1 i TABLE LXXIII. STANDARD STRAIGHT PIPE TAPS. P= SQUARE - * —i—’ -/•' T- v . . in jnimiiiiii- _ S' Q 1 3 1 iiu.Jiii.ilmu i "im nrnC _ Fig. 116 _ Nomi¬ nal Size. Diam. of Tap. Total Length. Length of Thread. Length of Shank. Diam. of Shank. Size of Square. Length of Square. D A B C E F G 1 1.293 4 If 21 11 If If 11 1.645 4A HI 21 11 If If 11 1.880 41 21 2f If i A 1 2 2.359 5ff 2A 31 If il iA 21 2.836 61 2f 3f H i A i A 3 3.461 71 31 41 21 if il 31 3.971 8A 3A 4f 2f Hf ill 4 4.398 9 H 51 2f iff iff TAPER TAPS — MISCELLANEOUS TAPS 267 These taps are chamfered the same as plug hand taps, and relieved only on the top of the thread on the cham¬ fered part. The number of flutes may be made the same as for corre¬ sponding sizes of Briggs standard pipe taps; if it is considered that fewer flutes would be more advisable, approximately the same number of flutes as is given to regular hand taps will be satisfactory. In cases like this the number of flutes, within reasonable limits, is largely a matter of judgment. The straight pipe tap, being actu¬ ally a hand tap, should evidently be fluted like a hand tap. But inasmuch as the tap has a greater number of threads per inch than corresponding sizes of ordinary hand taps, there is a reason for providing it with a greater number of flutes. English straight pipe taps having Whitworth form of threads and made according to Whitworth’s thread system for gas and water piping are given in Tables LXXIV and LXXV. TABLE LXXIV. ENGLISH STRAIGHT PIPE TAPS. (See Fig. 115 for meaning of letters in table.) Nomi¬ nal Size. Diam. of Tap. Total . Length. Length of Thread. Length of Neck. Length of Shank. Diam. of Neck. Diam. of Shank. Size of Square. Length of Square. D- A B C E F G H / £ 0.385 2f 1 A 1 A 0.335 t A A 0.520 2£ 4 4 if 0.448 h i £ 1 0.665 3A 4 1 1 A 0.593 f M A * 0.822 3i if A i A 0.726 ! A f f 0.902 3 A 4 A 4 0.806 1 4 f£ 4 1.034 3f If h 4 0.938 l 4 4 268 SMALL TOOLS TABLE LXXV. ENGLISH STRAIGHT PIPE TAPS. (See Fig. 116 for meaning of letters in table.) Nomi¬ nal Size. Diam. of Tap. Total Length. Length of Thread. Length of Shank. Diam. of Shank. Size of Square. Length of Square. D A B C E F G 1 1 189 31f 111 21 1A If If 1 1 302 4 11 21 11 If 13 T6 4 1 492 41 If 2f IA 1 1 H 1 650 4A Ilf 21 11 If If If 1 745 4ti 2A 2f i A 1 tf H 1 882 4f 2f 21 if 1A l if 2 021 5A 2A 21 i A iA 1A if 2 160 5A 2t% 3 il il i A if 2 245 51 2f 31 i A i A il 2 2 347 5 A 2A 31 if il 1A 21 2 467 5f 21 3f i A il 1A 21 2 587 61 2f 31 if i A il 2f 2 794 6A 2A 3f ill if i A 2j 3 001 61 21 31 il i A 1A 2f 3 124 61 2f 31 1 15 1 16 i A if 2f 3 247 611 2 If 4 2 il i A 2 i 3 367 71 3 41 2A i A i A 3 3 485 7f 31 41 21 if il 31 3 698 71 31 41 21 1H 31 3 912 &A 3A 41 2f i+f i A 3f 4 125 8f 3f 5 21 U il 4 4 339 9 31 51 2f iff iA Adjustable Taps. Purpose and Kinds of Adjustable Taps. — Adjustable taps are made for the purpose of permitting adjustment to a correct standard size. As the solid tap, on account of changes in hardening, cannot be depended upon to meas¬ ure exactly the diameter for which it was intended, and because of the impossibility of preventing a solid tap from decreasing in diameter through wear, the adjustable tap has a wide field of usefulness where correct-sized nuts TAPER TAPS — MISCELLANEOUS TAPS 269 must be produced. The adjustable tap may either be made from a solid piece, split in a suitable manner to permit adjustments, or may be provided with inserted blades or cutters, which are so held in the tap body that a slight movement of these blades in the longitudinal direction of the tap moves the cutting points of the thread nearer or further from the axis of the tap, thus decreasing or increasing the diameter as the case may be. Another cause for inserted blade taps besides adjusta¬ bility may also be mentioned. The efforts constantly made by progressive manufacturers to decrease the cost of tools without impairing their efficiency have resulted in the designing of a number of taps of this type which permit cheaper grades of material to be used in the tap body, while the best quality steel may be used for the inserted blades, the total cost, especially in the case of large taps, being smaller than if the tap were made solid of ordinary tool steel throughout. Incidentally another advantage is also gained, in that, as the wear of the cutting portion of the tap is the only reason for discarding the tap, the inserted blade design makes it possible to retain the body proper and replace the cutters only. In the case of large taps and coarse pitches the adjust¬ able tap does not give very good satisfaction if a thread is cut by one passage of the tap, because the strain on the tap is so great as to spring it to a certain extent. It is evident that an adjustable tap cannot possibly be made quite as rigid as a solid tap. But in such cases the tap still retains its superiority as a “sizing” tap, used to finish the thread after it has been roughed out by means of an ordinary tap cut somewhat under size. Examples of Adjustable Taps. — The form of adjustable taps, previously referred to, which is cut from a solid piece and split, is shown in Fig. 117. The body is split 270 SMALL TOOLS straight through; a nut with a taper thread serves to hold the tap together at the end, and a screw with a taper head is used to expand the tap, as shown. As the expansion is Fig. 117. Adjustable Tap Made from Solid Stock effected by bending the cutting lands as the tapered head of the screw travels inward, the thread form is not accu¬ rately retained and the tap is not to be recommended. When accurate work is required the inserted blade form of adjustable taps is the preferable form. The requirements for a good inserted blade tap are that the blades when bound in place shall be practically solid with the body; that the design shall permit a liberal adjust¬ ment in regard to size; that this adjustment shall be easily accomplished; and that the means employed for binding and adjusting the blades shall not be of such a kind as to prevent the use of the tap in any case where the solid tap could be used. This latter requirement involves the possibility of tapping clear through a hole as well as the tapping down to the bottom of a hole. A tap which fills fairly well all these requirements with the exception of the one mentioned last is shown in Fig. 118. The blades are held in place by nuts, beveled on the inside to fit the tapered ends of the blade. In this manner the blades are prevented from longitudinal motion as well as from moving out or in in relation to the center line of the tap. The blades fit into slots in the tap body and are thus prevented from moving sideways. The adjustment is provided for by the tapered bottom of the slots in the TAPER TAPS — MISCELLANEOUS TAPS 271 body, by means of which the cutting size of the tap increases when the blades are moved upward toward the shank end of the tap. The adjustment is easily accomplished, it only being required to loosen the upper nut and push up the blades, and then tighten the lower as well as the upper nut solidly upon the blades. It is, however, not possible with the design shown to tap down clear to the bottom of a hole, Fig. 118. Adjustable Tap with Inserted Blades nor is it possible to tap straight through a hole. This latter requirement could, of course, be easily obtained by making the slots deeper and the blades wider, thus making it possible to decrease the outside diameter of the upper binding nut so that it would be less than the root diameter of the thread. This would permit the tap to pass clear through a threaded hole. There is, however, a more serious objection to this design. The backing of the blade by means of a, tapered surface in the nut is not very positive, and the blades are liable to be a trifle incorrect in their relative position in regard to lead. It is evident that if that is the case the thread cut will be incorrect in its shape, the space cut being wider than the thread itself in the nut. A tap which over¬ comes the objections raised in regard to the tap in Fig. 118 is shown in Fig. 119. Pratt and Whitney Company Adjustable Tap. —This tap consists of body, blades and binders, and a thrust nut and a check nut mounted on a threaded part of the body. 272 SMALL TOOLS On comparatively small sizes of taps the end of the body is turned down to fit a hole in the shank, as shown in the lower view, Fig. 119. The shank is then driven into place and secured by a taper pin. On larger sizes the shank is made solid with the body as shown in the upper view. This difference in design is necessitated by the construction of the tap. The shank if made solid with the body must Fig. 119. Pratt and Whitney Company’s Design of Adjustable Tap obviously be below not only the root diameter of the tap itself but also below the root diameter of the portion on the body threaded for the thrust and check nut, as other¬ wise these nuts could not be put in place. On small taps this would require a diameter of shank altogether too small compared with the diameter of the tap. In such cases, therefore, the body is driven into a shank of larger diameter than would otherwise be possible to use. The body is slotted longitudinally to receive the blades, and has a circular groove all around to receive the binders. The latter are, by means of small screws threaded into the body, pressed firmly against a shoulder formed by a small groove in the blades, as shown plainly in the enlarged view of the binding arrangement in Fig. 120. The hole shown at the front end of the tap extending at the center of the TAPER TAPS—MISCELLANEOUS TAPS 273 tap for some distance inward is for providing clearance for the taps when tapping the binder screw holes. The blades are squared off at the upper end to rest solidly against the thrust nut. As it is important that each blade be placed in a correct position in relation to the others, each blade being a certain amount ahead of the next preceding one in regard to lead for the purpose of securing a continuous thread around the tap, it is customary to replace all the blades at once, prefer¬ ably threading them in the tap body itself or in a master holder similar to the tap. It is evident that it would be difficult to replace single blades, as the replaced blade would hardly come in such a position in relation to the others as to produce a Fig. 120. Method of Binding the Blades in the Tap in Fig. 119 perfect continuous thread all around the tap. As the thrust nut only locates the blades longitudinally, the binders are relied upon altogether for holding the blades down. For this reason the binder is placed near the center of the blade. In the case of a reamer constructed on this same principle the binder is placed nearer the front end, as in a reamer there is no objection to beveling the thrust nut on the inside in a manner similar to that used for the inserted blade tap formerly described. This beveling of the nut and tapering of the upper end of the blade will, of course, hold the blade very securely in place, but cannot, for the reasons previously given, be adopted in a tap of good design. The binders are made from a solid ring which is turned, 274 SMALL TOOLS chucked, reamed, and has the screw holes drilled and counterbored before the ring is cut into pieces. This tap fills all the requirements mentioned at the beginning of the discussion of inserted blade taps. When the binders are tightened against the shoulder in the blade, and the nuts are screwed tightly up against the end of the blades, the blade at the same time fitting the slot in the body snugly, there is no possible chance for the blade to move. The tapered bottom of the slots in the tap body provides for the adjustment the same as in the case of the inserted blade tap previously described. When the tap is to be expanded, the binder screws are loosened and the nuts at the upper end of the blades are screwed back. The blades can then be moved upward as far as necessary for obtaining the desired size, and the nuts and binders are again tightened. The ease of accomplishing this adjust¬ ment is apparent. No parts of the tap used either for binding or adjustment project outside of the tap at the end. Nor does any detail project beyond the root diam¬ eter of the thread in the tap. Thus the tap can pass entirely through a hole as well as tap clear down to the bottom of a hole, provided only a short chamfer is given to the thread. Very few taps of the adjustable or expan¬ sion type fill the given requirements as well as does this one. Of course, this is not intended to mean that the design which we have described to some extent in detail is the only one possible which will fill the requirements outlined. There can, of course, be a great deal of vari¬ ation in the design, and the example chosen is selected simply because it embodies all the features which are of importance. Taps of this construction are manufactured by the Pratt and Whitney Company. Inserted blade taps do not adapt themselves to very small sizes of taps. As a rule, it should not be attempted to make such taps of TAPER TAPS —MISCELLANEOUS TAPS 275 sizes smaller than inches or at least not below 1J inches in diameter. Other Examples of Inserted Blade Taps. — In Fig. 121 an inserted blade tap of a design common for pipe taps is shown. Here the chasers are held in place by means of taper pins which wedge the metal of the body firmly against the blade. The correct location of the blades in a longitudinal direction is obtained by means of a ring held to the body by screws. It is plainly seen from the construction that this tap is not intended to be adjust¬ able, but is simply made with inserted blades from an economical point of view. This design being most com¬ monly used for large taps affords a considerable saving in material. The tap shown in the cut is provided with interrupted thread as commonly used on pipe taps and taper taps in general. Another form of inserted blade tap is shown in Fig. 122. The blades are here held in place by means of a ring threaded on the inside to fit the thread of the blades or chasers, and split and provided with binding screws so as to make possible a positive grip over the blades. The advantage of this design is that the threads of the vari- 276 SMALL TOOLS ous chasers must necessarily be so located as to form a continuous helix all around the tap, inasmuch as the threaded ring fits upon the thread in the chasers. But the design is open to the objection that the ring prevents threading as far down in a hole as may sometimes be Fig. 122. Burritt’s Design of Inserted Blade Pipe Tap required, and the ring may interfere with lugs or pro¬ jections in the piece to be threaded. In this respect the former of the two taps last described is superior, as it is free from any outside incumbrance and takes up no more room than a solid tap. Kind of Steel Used for Taps. Ordinary carbon steel or tool steel should be used for all kinds of taps. It is advisable to use a higher grade, or at least a tougher kind, of steel for machine taps and stay-bolt taps than for other kinds as they are subjected to heavy twisting strains. While high-speed steel has proven itself to be of great usefulness for cutting tools of general description such as lathe and planer tools, drills, etc., it has not as yet proven practicable to make such tools as taps, threading dies, and chasers, which cannot be ground after hardening, of this material. The reason for this is that most grades of high- TAPER TAPS — MISCELLANEOUS TAPS 277- speed steel have to be heated to such a high temperature when hardening that the sharp edges of the tools to be hardened are practically melted away, and as a rule, unless the tool is of such a construction that it can be ground after hardening, it is almost useless for cutting purposes. It is not to be inferred from this that it is impossible to make taps and threading dies from high-speed steel, but the difficulties encountered in trying to successfully harden these tools are such that prominent manufacturers hesitate to undertake the making of tools, that cannot be ground after hardening, from this material. The substitution of machine steel for purposes for which carbon steel was formerly employed is one of the improve¬ ments about which little is heard. Nevertheless, some large concerns use it almost exclusively for dies, taps, and other cutting tools which require toughness as well as hardness. A machine-steel tap when skillfully case-hard¬ ened will cut as freely and is said to wear practically as well as one of carbon steel. Besides being cheaper to make, it will not snap off suddenly when subjected to undue .stress. It is said that the Singer Manufacturing Company use little carbon steel in their Elizabethport works, and that all punches, dies, taps, etc., are generally made from machine steel, case-hardened. CHAPTER VII. THREADING DIES. It is undoubtedly true that there is, as a rule, a great deal more said in the technical press as well as in text¬ books on tool-making about making taps than there is about making threading dies. The reason for this is probably that while the principles governing tap-making are fairly well settled and agreed upon, those appertaining to the making of threading dies are-not so well defined. Besides, dies are not made in such variety as are taps, nor do they differ from one another very materially, pro¬ viding we except the spring screw threading die. How¬ ever, the die is used for external thread-cutting just as often as the tap is used to thread the corresponding nut, and for this reason threading dies ought to be given a place equally prominent with taps in the manu¬ facture of shop tools. Spring Screw Threading Dies. At present no thread¬ ing dies are used to such a great extent as are spring screw threading dies, Fig. 123. The in¬ creasing importance of automatic screw ma- Fig. 123. Spring Screw Threading Die chines has been the one great factor which has added most to the demand for this class of dies. There is, however, still a great deal to wish 278 THREADING DIES 279 for in regard to the making of these dies, as at present they are not manufactured exactly as they ought to be. A simple analysis will bear out this statement. Requirements of a Threading Die. — There are in general three main requirements for a threading die. The cut should be smooth and clean, the thread should be of a perfect form, and the threaded piece should be of the exact diameter required. In order to obtain this there are several points to be taken into consideration. In the first place it must be observed that a die with a thread cut perfectly straight or parallel would act exactly the same as a tap without back taper, that is, a tap having the same angle diameter at the shank end as at the point. This question in relation to taps was mentioned in a previ¬ ous chapter in connection with the relief of taps. The trouble encountered in using taps made without back taper will also appear in dies made in the same manner. To overcome the difficulties arising, and in order to give to the die a certain amount of back taper, usually called clearance, dies for the market are generally made a certain amount over the size required, and then the size to be cut is obtained by means of an adjusting collar, forcing the prongs of the die down sufficiently to produce the.correct diameter required on the piece to be threaded. This will, of course, give the die a certain back taper, the amount of which will depend upon the amount over the actual size the die was originally made. The collar being applied at the front end of the die, will evidently spring the prongs more at the point, where it is applied, than further up, nearer the solid part of the die. This is the general pro¬ cedure of making spring screw dies for the market, and we will now analyze the results, and see whether this die fills our three main requirements mentioned above. The die has ample clearance and will almost invariably 280 SMALL TOOLS produce a smooth, cleancut thread. The size of the thread on the threaded piece can also be exactly correct, as the adjusting collar, usually called clamp collar, can be so adjusted as to give any size wished for within certain limits. Shortcomings of the Commercial Spring Screw Die. — The form of the thread, however, will not be perfect, as can Fig. 124. Distortion of Thread Form in Spring Screw Dies of Usual Design when Adjusted readily be seen from the cut, Fig. 124, where the case is shown exaggerated. By bending the prongs inward the thread will evidently not move inward at right angles to the axis of the die, but will move along an arc, thus causing the thread to be of incorrect angle in the piece cut, one side of the thread making an angle of more, and one an angle of less than 30 degrees with the axis. That this inaccuracy is of importance is even more evident if we refer to a die with a thread form such as shown in Fig. 125. Here the angle of the thread is very slight, and consequently, the bending of the prongs is distorting the thread-form still more. The piece threaded THREADING DIES 281 by adjusting a die of this class in this manner can never be expected to fit very well into a nut provided with a correct thread. Fig. 125. Spring Screw Die with Special Threads, and Result of Adjustment Preferable Method of Making • Spring Screw Dies. — In order to eliminate the error produced by the closing in of the prongs for adjustment by means of a clamp-collar and still maintain the necessary back taper or clearance, the correct size should originally be at the front end of the die, and the diameter of the thread in the die should gradually increase backward, that is, the die should be made with back taper from the beginning. On large sizes this is, of course, very easily accomplished by setting over the taper bar of the machine where the die is chased out an amount equal to the amount of back taper desired. On small sizes, however, this is impractical, and on very small sizes absolutely impossible. Therefore, in order to obtain a die made in a way that will produce the results required, the die must be tapped out from the back end with a tap that has been cut with the taper required in the die. The amount of the clearance mentioned should vary according to the kind of metal the die is to be used upon, the clearance being greater for brass than for steel. Opinions vary as to what is the best amount of back 282 SMALL TOOLS taper to give to a die. While some consider that a clear¬ ance of 0.003 inch per inch is ample for cutting steel or iron, and 0.005 inch per inch for brass, others claim that one might give even as much as 0.010 inch per inch clearance for steel and iron, and 0.015 inch per inch for dies cutting brass, copper and metals of similar structure. It may be safe to say that any figure between the extreme limits given above will prove satisfactory, and that the exact amount of clearance is comparatively unimportant. A die made according to the last mentioned method would, when new, cut a perfectly correct thread. Sup¬ pose now that the die should wear, and in order to obtain the correct size of the thread the adjusting collar had to be tightened. In such a case a slight error in the form of the thread would occur, on the grounds mentioned pre¬ viously, but considering the way in which this die is made, the error is reduced to a minimum. In fact, it is easily seen, that the maximum error, when a die of this kind is almost worn out, cannot be any greater than the minimum error occurring in a new die with the same length of thread cut straight, and made a sufficient amount oversize to produce the same amount of back taper by forcing the prongs in at the point. The reason for continuing to manufacture spring screw dies in the old manner, when the superiority of dies made according to the system outlined is well known by manu¬ facturers, is one merely of expense. It would make the die more expensive to grind on the outside, true with the thread, as a taper arbor would be more difficult to make than a straight arbor, but it is unquestionable that the increase in expense is very slight if compared with the superior qualities of the die. The grinding of the outside of the die should never be overlooked by those desiring a good die, especially if a solid holder is used. It must, THREADING DIES 283 however, be admitted that most dies made for the market are not ground on the outside, a fact of which most users probably are painfully aware, as it takes a great deal of experimenting and attention to produce desirable results with dies where the thread is not true with the outside. It also seems unnecessary to spend so much time and care in producing a good thread in the die, and then to over¬ look a factor equally important to accomplish perfect results. Objections to the Method Described. — It has been objected that it is rather difficult to grind the outside of spring screw threading dies, particularly the outside of small dies. • It is true that it is difficult to grind some sizes of dies, but certainly not impossible even under manufacturing conditions. The advantages gained would be fully worth the cost of trying to conquer the difficul- Fig. 126. Spring Screw Die Mounted on Threaded Arbor for Grinding ties. As shown in Fig. 126, the die should be held on a taper threaded arbor, corresponding to the taper in the die, but the whole length of the die should not be ground at once. There would, however, be no difficulty in grinding the die from the point upward for a length about equal to the length of the thread in the die, as the arbor and the die for that distance are practically one solid piece and are well supported by the centers of the arbor, which of course should not project outside of the die more than necessary. When this is done the die should be taken — with the arbor still in place in the die 284 SMALL TOOLS — and put into a machine equipped with a drawback mechanism and a spring collet or step chuck (Fig. 127). The die is then, of course, held by the outside of the already ground portion of same, and the back can if neces¬ sary be supported by the center of the arbor. Any one making a business of manufacturing spring screw thread¬ ing dies would find this operation very inexpensive. The matter of cost is particularly pointed out in this con¬ nection, as it has been claimed that it would be too expen¬ sive in ordinary manufacturing to grind spring screw dies on the outside. But if we consider that a die not ground on the outside after hardening must be made from Fig. 127. Grinding the Outside of Spring Screw Dies either drawn wire of the correct required size or made from rough stock, which before being made into die blanks had to be turned and ground, the question gets a different aspect. A die ground on the outside after hard¬ ening is made from rough stock, rough turned and ready for grinding after hardening. Right here we have a sav¬ ing of either the difference in price of drawn wire and rough stock or the saving of the cost of grinding the soft blanks. If we add to this saving the time saved in not having to be so extremely particular in maldng the tapped hole run perfectly true with the outside of the die as we have to be if the die is not to be ground on the outside after hardening, we have quite an item to deduct from our grinding expenses after the dies are hardened. As regards the difference in the expense in making the die taps and THREADING DIES 285 hobs there is none. The only increase is the expense of making the arbor used when grinding the outside of the die, but when considering that this arbor is made exactly the same and at the same time as the hob, the expense is reduced to a minimum. Clamp Collars. — Another point of great importance in making spring screw dies cut correctly is the way in which the prongs or lands of the die are being adjusted to cut the proper size. The clamp collars generally used for this are nothing but split steel rings. The adjustment is secured by means of a screw, and it is readily seen from the cut, Fig. 128. Usual Form of Clamp Collar for Spring Screw Dies Fig. 128, that the action of the steel collar on the prongs of the die is not uniform, that is, it will not give an equal pressure to the various prongs. The prongs A and B will be forced in more than the prongs C and D. The result of this will be a die with its thread out of round, and all the care and precautions taken in making a perfect die have become useless by the use of improper means for adjusting the prongs. Being out of true the die cannot have all the prongs cutting, which of course is essential in producing good results. The only correct principle to apply for adjusting the 286 SMALL TOOLS prongs is a solid ring which will evenly torce all the prongs equally toward the center. This can be accomplished by making a solid steel ring with the hole tapered, and tapering the fluted end of the die to suit the taper in the ring. Fig. 129. Taper Collar tor Adjusting Spring Screw Dies (See Fig. 129.) The amount of taper in the ring and on the prongs will be directly dependent upon the adjustment wanted in the die. As, however, this taper ring would require all dies to be Fig. 130. Special Types of Clamp Collars tapered towards the point it has not met with general acceptance. There have been, instead, attempts to improve upon the old style of clamp collar. In Fig. 130, two such improvements are shown. The one to the left actually does embody a decided improvement on the old form, but THREADING DIES 287 whether the one shown to the right is-superior in any respect may be open to discussion. Fluting. — Spring screw dies are generally made with four flutes, but experience has taught that a die of this kind will almost invariably have only two lands cutting. A die with three flutes, however, will, even if slightly out of true on account of spring in the hardening, have the three lands cut evenly, and three flutes are therefore to be recommended. There is also another advantage gained by giving a die only three flutes. The lands become wide and stiff, while the chip-room may still be equally large or even larger. It may be said as an objection to wide lands that they will necessarily produce more friction between the die and the piece to be cut. This can easily be over¬ come by milling the prongs as shown in Fig. 131. When fluting, the kind of material upon which the die is to be used should also be considered. If the die is to be used on soft metals, such as brass, the cutting face of the prongs is usually made to come a small amount back of the center, while on dies used for steel or iron the cutting face is radial. Fluting Cutters. — If the die is made with three flutes, these should be cut with a 60-degree angular cutter. If made with four flutes, however, the cutter should be 48, 45 or 40 degrees according to the size of the die, the 48-degree cutter being used for the smallest dies, and a 45-degree cutter for all ordinary sizes. Dies one-half inch in outside diameter or smaller are usually never made with more than three lands. Hardening Spring Screw Dies. — The principal troubles encountered in the manufacture of spring screw threading Fig. 131. Three-fluted Die with Lands Re¬ lieved to Reduce Fric¬ tion 288 SMALL TOOLS dies are due to difficulties in hardening. In the fir^t place the lead is liable to be incorrect, due to the shortening of the prongs in hardening. This difficulty is so much the more pronounced as the prongs may alter differently from one another, in which case the die may be perfectly useless. In the second place the prongs may spring out of shape in the form of a curve outward, as shown exaggerated in Fig. 132. In the third place they may twist, as shown in Fig. Pig. 132. Exaggerated View of Prong of Die Sprung Outward in Hardening 133. That in either case a good thread cannot be cut with the die is obvious. In the case of the prong springing out in a curve all the beneficial effect of the back taper would be lost. In the case of the prong twisting, the contact with the piece to be threaded is not on the cutting edge of the teeth, but back of it, causing a drag which always makes a rough thread and is very likely I to break off the screw to be 133, Prongs I)ie Twistec * threaded. in Hardening In order to eliminate as much as possible these effects of hardening it is well to take care not to heat the die back of THREADING DIES 289 the line ab in Fig. 134, and not to heat it any more than so that it will harden only to the line cd at the end of the thread. It is, however, even more effective for preventing the die from springing out of shape in hardening not to flute right through the metal into the hole, but to leave a small amount to be removed when grinding the flutes after the die has been hardened and finish ground on the outside. The temper should be drawn to about 430° F. Chamfer of Threads. — The only point now remaining to be considered is that of the chamfer, which is, of course, greatly dependent upon the class of work to be done. It Fig. 134. Directions for Hardening Spring Screw Dies is evident that the longer chamfer, or taper on the top of the threads, one can allow in a die, the better results will be obtained, as it is obvious that a greater number of teeth will then do the cutting, and each tooth will have less to remove. The result will be a smoother thread. For general use one must, of course, settle upon a certain length of chamfer. The practice is to chamfer about three threads, if the die is not expected to cut close to a shoulder. In the latter case, one, or at most one and one-half thread of chamfer must suffice. Dimensions. — The length of the threaded part of a spring screw die should be directly depending upon the 290 SMALL TOOLS pitch of the thread. It is common practice to make the length of the thread equal to about 7 times the pitch. In Table LXXVI, the length of thread for various pitches is given. TABLE LXXVI. LENGTH OF THREAD IN SPRING SCREW DIES FOR VARIOUS PITCHES. No. of Threads per Inch. Length of Thread. No. of Threads per Inch. Length of Thread. No. of Threads per Inch. Length of Thread. 40 16 16 T6 8 i 36 7 TZ 14 i 7 1 32 4 13 16 6 1A 28 A 12 1 51 1 * 24 A 11 5 i A 20 I 10 i 41 i A 18 M 9 A The outside diameters of spring screw dies are made in certain standard sizes. It is difficult to say what outside diameter should correspond to a certain diameter of thread, as practice differs quite widely. In Table LXXVII dimensions are given for spring screw dies which will be found to embody the average practice very accurately. The length of the flute should be about three-fifths of the length of the die. Sizes of Hobs for Spring Screw Dies. — It has been pre¬ viously mentioned that while a superior die is produced by threading the die with a taper hob from the back, the general practice is still to tap the dies with straight taps a certain amount oversize. The amount which the die taps should be made oversize for different pitches when the dies are produced in the latter manner is stated in Table LXXVIII. THREADING DIES 291 Diameter Outside Length. Diameter Outside Length. of Cut. Diameter. of Cut. Diameter. A B C A B C 1 H 1 If 21 A 1 H 1 2 3 1 1 U 1 2 3 1 1 U 1 2 3 A 1 if U ' 2 3 1 1 il H 2 3 1 l 2 U 21 31 A l 2 H 21 31 1 l 2 11 21 31 1 if 21 11 31 4 A if 21 2 31 4 t U 21 21 31 4 Dimensions of Clamp Collars. — As has been said al¬ ready, the clamp collar shown in Fig. 136, although not the best, is the one most commonly used. In Table LXXIX dimensions for these clamp collars are given correspond¬ ing to the diameters of dies given in Table LXXVII. In order to facilitate the design of intermediate sizes a set of approximate formulas for determining the relation between the dimensions is given below. The various dimensions denoted by the letters are seen from Fig. 136. 292 SMALL TOOLS TABLE LXXVIII. OVERSIZE OF TAPS FOR HOBBING SPRING SCREW DIES WHEN CUT STRAIGHT. No. of Threads per Inch. Oversize. No. of Threads per Inch. Oversize. No. of Threads per Inch. Oversize. 4* 0.015 12 0.006 28 0.004 5 0.013 13 0.006 30 0.004 5 * 0.012 14 0.005 32 0.004 6 0.010 16 0.005 36 0.004 7 0.008 18 0.005 40 0.003 8 0.007 20 0.005 48 0.003 9 0.007 22 0.005 56 0.003 10 0.006 24 0.004 64 0.002 11 0.006 26 0.004 72 0.002 TABLE LXXIX. DIMENSIONS OF CLAMP COLLARS FOR SPRING SCREW THREADING DIES. Fig. 136 A B C D E F i I is ft A is i 1 h 8 ■h ft 1 i If is II 1 f if 1ft IS *1 ft i 2 2f ft If ft 1 2* 31 ft If 1 1ft THREADING DIES 293 The formulas are: B = 1M + * G = \ A + ^ D = % A + 3 3 2 Roughing and Finishing Spring Screw Dies. In order to obtain uniform and well-finished threads when cut with spring-screw threading dies it is well known that it is necessary to use two dies, one for roughing and one for finishing the thread. In general practice the roughing die is obtained simply by adjusting a regular spring screw die of standard size to cut a certain amount oversize. This, of course, answers the purpose well enough for most classes of work for which this kind of die is used. It is evident, however, that there is no great certainty as to the relative amount of metal removed by each die, and it is most probable that the roughing die, at least on larger sizes, is doing far more than its fair portion of the work, leaving but a small amount of metal for the finishing die to remove. The latter die should, of course, not perform as heavy a duty as the former, but it is considered as a fair proportion to let the roughing die remove two-thirds and the finishing die one-third of the total amount of metal to be removed. In order to obtain such a proportion some firms who perform very close work by means of spring-screw dies make special roughing dies, enough over size to permit the finishing die to cut the predetermined amount of the thread. These roughing dies are provided with perfectly-shaped threads, simply hobbed out with a tap which is the desired amount oversize on the top as well as in the angle of the thread. In this manner the finish¬ ing die will remove a certain amount of metal both on the E — fV A + xV F = | A + \ 294 SMALL TOOLS top and in the angle, thus finishing the whole thread per¬ fectly smooth and to the correct form. It must, of course, be determined how much oversize the roughing die is required in order to leave one-third of the metal to be removed by the finishing die. This can be expressed in a simple formula with the pitch of the thread as the variable. In Fig. 137 the relative amounts of metal removed by the respective dies are shown in a diagram; we have here a United States standard thread where the V Fig. 137. Diagram of Metal Removed, United States Standard Thread amount of metal represented by the area ABDC is to be removed by the roughing die and the area BEFGHACD by the finishing die. The derivation of the formula we wish to obtain is as follows: Formulas for U. S. Standard Thread. — The area, of a section of a full V thread with the pitch p is Subtracting from this the amounts 1 X ^ 4 ^ 2Xcos 30°; an d | X ^j-p 2 Xcos 30°+-^ p 2 X cos 30°, THREADING DIES 295 which represent the areas deducted from a full V thread in order to obtain the area of a section of a United States standard thread, we find this latter area to be |p 2 Xcos 30°. O Consequently the amount of this sectional area to be removed by the roughing die is ^p 2 Xcos 30°, 4 and the amount to be removed by the finishing die ~p 2 X cos 30°. 8 Referring to Fig. 137 we therefore arrive at the following equation: | ft p - 2x X tan 30°^cos 30° - | X -^p 2 X cos 30° = X cos 30°. 4 Solving this equation gives x = 0.135 p approximately. The diameter of the tap with which the roughing spring- screw die is to be produced should thus equal the standard diameter plus two times 0.135 p. This refers to United States standard threads. Formulas for Sharp V thread. — For the same pro¬ portions between the amount of metal removed by each die, if a full V thread is to be cut, the formulas are, of course, derived in the same manner, but have a different aspect. The area of a section of the thread is ^ p 2 X cos 30°. A 296 SMALL TOOLS The amount of sectional area to be removed by the roughing die is consequently |-p 2 X cos 30°. Referring to Fig. 138 we arrive at the following equation ; | (p -2 x x tan 30°^ cos 30° = ^ p 2 x cos 30°. Solving this equation gives x = 0.160 approximately. Using this value, the diameter of the roughing die is now easily determined. Fig. 138. Diagram of Metal Removed, Standard Sharp V Thread If we wish to give formulas for the results obtained, we can express them in the following manner: For the United States standard thread, R = D + 0.27 p. For sharp V thread, R = D + 0.32 p, in which formulas R = diameter of roughing die, D = standard diameter of finishing die, and p = pitch = _ 1 _ number of threads per inch THREADING DIES 297 It is, of course, of no great importance if the amount removed by each die is somewhat different from the values given, the amounts to be removed being arrived at in a purely arbitrary way from the beginning. But the pro¬ portions given conform to the practice of a prominent tool¬ manufacturing firm, and the calculations are given to show that even in a domain largely given over to “guesswork” there can be exact calculations made and adhered to. In tool-making, as a rule, calculations form a very small part, and altogether too often is “a few thousandths over” or “a few thousandths under” considered the only way to determine certain values which, if once settled upon, could be formulated by simple figuring so as to serve as a permanent guide for the tool-maker. It is a mistake to think that tool-making is so widely different in its nature from other fields of industrial progress that here no-strict rules can be followed. It must be admitted that there is perhaps no field of mechanical achievement where opinions differ so widely as they do in regard to tool-making. But that is no reason for continuing to consider tool-making as a business in which no principles or rules can be concen¬ trated in simple formulas arrived at in a logical and common-sense manner. Various Classes of Threading Dies. We have in the preceding pages given particular atten¬ tion to one class of dies in the same manner as in the case of taps we devoted ourselves most particularly to one class of taps, hand taps. The same fundamental prin¬ ciples, of course, hold good for all kinds of dies as were pointed out with reference to spring screw threading dies. We can therefore in the following summarize our state¬ ments, and shall only dwell upon the more important points in regard to other classes of dies. 298 SMALL TOOLS The remaining kinds of dies may be divided into three general classes — solid dies, which may be either square or round as shown in Fig. 139; adjustable split dies, which usually are round; and inserted chaser dies, where the blades, provided with the cutting teeth, are inserted in a body and secured in some suitable manner. Solid Dies. The solid die is used to a great extent on general work, either in cases where a correct size is not essential or for roughing a thread before taking a finishing cut with an Pig. 139. Square and Round Solid Dies adjustable die. The solid die is not preferable to use when threads are to be cut requiring a high degree of accuracy. In the first place, the size when the die is hardened cannot be depended upon to be exactly the size wanted, as dies are very apt to “ go ” more or less in hardening, and, on account of their construction, to “ go ” in an irregular manner, one land closing up or departing more from the true axis of the thread than the others. In the second place, even if the die were correct from the beginning, there are no provisions for adjusting it to size when worn. Solid Square Dies. — The solid die, as a rule, is of a square form. It is used principally for threading in bolt THREADING DIES 299 cutters, and for work of this kind answers its purpose well. It is also used for pipe dies. In this case the thread evidently must be tapered. As a tapered thread in order to cut a thread smoothly and correctly requires to be relieved in the angle, and as the difficulties of relieving an internal thread like that of a pipe die are very great and it is not customary to do so, pipe dies, and, of course, also all other taper dies, cannot be used for cutting the threads of taps, but can only be used for rough work on pipes and similar soft metal where a perfect thread is not essential. Lands and Clearance Holes. — Solid square dies are always provided with four lands excepting if very large, when five lands may be preferable. The width of the land should be about one-twelfth of the circumference of the screw to be cut with the die, or approximately one-fourth of the diameter of this screw. The clearance holes should be laid out so as to provide for this width of land. The center of the clearance holes should be located a trifle outside of the circle which measures the diameter of the screw to be cut. Some makers of dies locate the center of the clearance holes exactly on this circle, but the clear¬ ance holes then become rather small and are easily clogged with chips which may tear the threads of the screw being cut and occasionally break the teeth of the threads in the die. In very large dies it is not possible to make circular clearance holes, as these would be required to be of too large a diameter in order to make the lands of the correct width. In such cases two clearance holes are drilled between each two of the lands and connected with a straight surface as shown in Fig. 140. The chamfer on the top of the thread should extend for about three to four threads. It is necessary to relieve the 300 SMALL TOOLS dies on the top of the thread of the chamfered teeth in order to make the die cut. If the die should be expected to cut a thread close up to a shoulder, the chamfer, of course, would have to be made propor¬ tionally shorter, the same as in the case of spring screw dies already mentioned. As the clearance holes when drilled do not produce a desirable cutting edge on the face of the teeth, the front face must be filed after the holes are drilled. They are as a rule filed radial as shown in Fig. 141. When the dies are used wholly for threading brass castings and various other alloys of copper, it is common in many shops Fig. 140. Large Size Square Solid Die, showing Form of Clearance Holes Fig. 141. Cutting Edges as Ordi¬ narily made Fig. 142. Cutting Edges with Negative Kake to give the face of the cutting edges a negative rake as shown in Fig. 142. However, opinions differ widely as to the proper rake to give to the lands of threading dies, and it is probably as well to make the faces radial in all cases. As a matter of fact the dies will cut all metals THREADING* DIES 301 ordinarily used in a machine shop to full satisfaction if made in this manner. Dimensions of Solid Square Dies. — In regard to the sizes in which solid square dies should be made, the outside dimensions evidently depend upon the size of the holders in which the dies are used. The thickness of the die should preferably be made not less than one and one- quarter times the diameter of the screw to be cut with the die, but manufacturers of dies do not as a rule make their dies quite so thick. The general rule is to make the thick¬ ness about equal to the diameter, at least for sizes of screws larger than three-quarters inch diameter. In Tables LXXX and LXXXI are given the general dimensions of dies as commonly manufactured, both for regular sizes and pipe sizes. These dimensions are, of course, given only as a guidance, there being no particular reason for making the dies in these sizes excepting that the outside dimensions being standardized, the number of holders necessary to use with the dies is reduced to a minimum. TABLE LXXX. DIMENSIONS OF SQUARE SOLID BOLT DIES. Diameter of Thread. Size of Square. Thick¬ ness. Diameter of Thread. Size of Square. Thick¬ ness. \ 2* i 21 f TS 21 i 1 21 i f 21 i n 21 i 21 i n 21 i 1 21 i if 21 i 1$ 21 I H 3 i 1 21 f if 3 i 21 I if 3 H f 21 I H 31 il if 21 1 2 3f 2 302 SMALL TOOLS TABLE LXXXI. DIMENSIONS OF SOLID SQUARE PIPE DIES. Nominal Pipe Size. Size of Square. Thick¬ ness. Nominal Pipe Size. Size of Square. Thick¬ ness. 1 2 i 1 3 f 1 2 i H 3 1 I 2 i h 4 1 t 21 i h 4 1 1 2i i 2 4 1 1 21 f 21 5 11 I 3 l 4 3 5 11 It is, however, necessary to call attention to the fact that on account of the clearance holes the size of the out¬ side square must have some minimum relation to the diameter of the thread to be cut, so that the metal where the clearance holes are drilled will not become too thin. Even if strong enough to stand the strain incident to the thread¬ cutting operation, a die with too thin metal at the clearance holes will spring badly out of shape in hardening and will become a very poor tool for its purpose. The outside size of the square ought not to be less than double the diameter of the thread to be cut. Number of Lands. — While four cutting edges or lands are sufficient, at least for all dies up to four inches diameter which cut a full thread, it is necessary to provide more than four cutting edges in a die used for threading work in which part of the circumference is cut away. A greater number of cutting edges is here needed in order to steady and guide the die and prevent the work from crowding into the side where the metal is cut away. When more than one-sixth of the circumference is cut away, it is not advis¬ able to try to use dies for cutting the thread. The number of cutting edges is proportional to the amount of the THREADING DIES 803 circumference of the work cut away and should be as follows: Fraction of Circumference Cut Away. Number of Cutting Edges. A 5 12 6 1 7 * 8 Split Adjustable Dies. Split adjustable dies, as said before, are usually round, as shown in Fig. 143. The split permits the die to be Fig. 143. Round. Split Adjustable Die Fig. 144. Die with Grooves for Adjusting Screws opened or closed up for adjustment. The countersink A at the split is for the point of the adjusting screw. The countersinks B are for the binding screws, which close up the die to bear upon the point of the adjusting screw. Instead of countersinking at A and B as shown in Fig. 143 it is cheaper when making these dies in quantities to mill grooves as shown in Fig. 144. The groove as well as the 304 SMALL TOOLS countersink for the adjusting screw is usually made 60 degrees inclusive angle, and those for the binding screws 90 degrees. In order to make the dies more easily adjustable a small hole is often drilled outside of the clearance hole opposite the split, as shown at C in Fig. 143. If the dies made are few they may be split before hardening, as shown in Fig. 145, with a saw or narrow file, but should not be split all the way through until after hardening in order to prevent springing due to this process. When made in large quantities, a hole Fig. 145. Manner of Splitting Fig. 146. Another Method of Round Adjustable Die before Splitting Round Adjustable Hardening Dies before Hardening may be drilled outside of the clearance hole where the split is to come and the groove for the adjusting screw milled so as to leave a narrow bridge of metal between the hole and the bottom of the groove as shown in Fig. 146. This bridge of metal is then removed after hardening by means of grinding with a thin emery wheel or a bevel wheel with an acute angle. Round split dies for sizes up to and including three- sixteenths inch are given only three lands. All other sizes are provided with four lands. When hardening these dies, draw to a blue back of the clearance holes, in order to insure a good spring temper. THREADING DIES 305 About three threads should be chamfered and relieved on the top of the chamfer on the leading side of the die. Such dies as are intended for use in die stocks should be chamfered on both sides or ends, in order to permit the turning of the die and its cutting close up to a shoulder. In such cases the chamfer on the leading side should be about three threads as before and on the back side from one to one and one-half threads. The thread which is to be cut close to a shoulder should, however, always be started with the leading side of the die, both because this side is provided with a longer chamfer and consequently Fig. 147. Comparison between Common Ways used for Locating Adjusting Screws possesses better cutting qualities, and also because of the guide with which the die stock is provided on the leading side which is necessary to insure a straight thread. There is some difference of opinion as to the best man¬ ner of arranging the binding screws for adjustable split dies. The common arrangement, with two screws, has been referred to; but an arrangement for four screws, as shown in Fig. 147, evidently will close up the various lands more uniformly and the die will cut more freely. If adjusted so that the lands do not come at a uniform distance from the true axis of the die, all the lands will not 306 SMALL TOOLS eut; or, if they cut, will produce a thread that will be out of true. Dimensions. — The outside dimensions of round split dies are usually made to certain standards to fit a few holders. Dimensions commonly used are stated in Table LXXXII. TABLE LXXXII. DIMENSIONS OF ROUND SPLIT ADJUSTABLE DIES. Diameter of Thread. Outside Diameter of Die. Thick¬ ness. Diameter of Thread. Outside Diameter of Die. Thick¬ ness. A II i 4 1 2 f 1 « 1 vs 2 1 A H 1 1 2 f i H 1 t! 2 1 A l 1 f 2 t 1 l t 11 21 11 TS l I I 21 11 l I n 21 H VS l 1 1 21 H 1 u 1 1 21 H ■A 1 11 21 ti 1 ii 1 H 21 H If there is no necessity of adhering to certain outside diameters in order to fit holders, the dimensions for these dies published in the American Machinist, issue of June 29, 1905, answer the purpose very well. These dimen¬ sions are given in Table LXXXIII. There is no necessity, of course, to use as many die-holders as there are different outside diameters of dies. A couple of holders may be used, and intermediate sizes which do not fit the holders may be held by using a split bushing or collar in the holder. In Fig. 148 two circles C and D are shown. On these circles are located the centers of the clearance holes, the three holes having their centers on the inner circle, and the fourth hole, the one opposite the split, on the outer circle. This THREADING DIES 307 provides for the springing qualities of the die, and saves the drilling of an extra, small hole to give necessary adjusting possibilities. The last mentioned (fourth) hole is also larger in diameter than the others. TABLE LXXXIII. DIMENSIONS OF ROUND SPLIT DIES. Diameter of Screw. Diameter of Die Blank. Diameter of Large Center Circle. Diameter of Small Center Circle. Thickness, of Die. Diameter of Large Clearance Hole. Diameter of Small Clearance Hole. A B C D E F G 1 n lit If f ft if It 2f HI m ft n i 2A li 1A M ft ft t§ 2A if 1A t A f i 2 H if A It ft ft lit 1A 1A II ft A t m i* It M A 25 S? A i* It II A 2 5 6? ff f i A 2 7 3T 1 f fi A A 1A 23 3? n A if A f l t A A ft A It i M A A A i n ft f A tf A Approximate formulas may be given to express the relation between the various dimensions. In these for¬ mulas, 308 SMALL TOOLS A = diameter of the screw to be threaded, B = diameter of the die blank, C = diameter of outside circle locating clearance hole opposite split, D = diameter of inside circle locating other three clearance holes, E = thickness of the die, F = diameter of clearance hole opposite split, and G = diameter of the remaining three clearance holes. The approximate formulas are: B = 2.62 A, C= 1.68 A, 1.5 A, E = 0.75 A, F = 0.69 A, 0.62 A. Die Holders. An ordinary lathe die holder is shown in Fig. 149, and dimensions for holders of this design for the dies in Table LXXXII are given in Table LXXXIV. A holder for a smaller size is also specified, as dies for small machine screw sizes are often made with an outside diameter of five-eighths inch and a thickness of one-quarter inch. The dimensions cannot always be adhered to perhaps, but they will be of value as guidance when proportioning holders of this or similar kinds. It will be noticed that the center line of the binding screws does not fully coincide with the center of the die in the longitudinal direction, but that the screws apparently THREADING DIES 309 are located 0.010 inch too far in. This is for the purpose of forcing the dies solidly toward the bottom of the recess, the screws exerting a wedge action on the dies in the countersinks or milled grooves provided for the point of the screws. Approximate formulas may be found from which well- proportioned holders for other sizes than those given in the table may be made. In the formulas, d = outside diameter of die, A = diameter of recess, B = depth of recess = thickness of die, C = outside diameter of holder, D = diameter of hole in shank, E = diameter of shank, F = length of body, G = length of shank, H = total length, I = size of adjusting and binding screws, and K = distance from end of holders to center of screws. The following formulas give results approximately as stated in Table LXXXIV. A = d + (0.004 d + 0.005), ~ lld + 1 C= 8 ’ G = 3 B, D = —, 16 „ 9 B H T’ jy, 3 d + 1 E = 4 ’ r —d , 3 I ~8 + 32’ » f_ 3.14D P P Suppose we wish to obtain the number of teeth in a cutter 6 inches in diameter with the teeth spaced for finish- \ZJ)X8 ing according to the formula P = ——— previously given. We first find the pitch, vd) X 8 _ V48 16 “ 16 7_ 16 (approximately). We now apply this value of the pitch to our formula for the number of teeth: IV = 3.14 X 6 _7_ 16 301.4 7 43 (approximately). The number of teeth selected would, of course, be an even number, that is 44. It may be well once more to remark that this fine spacing, while it may be all right and even desirable for smooth finishing cuts, is not well suited for general prac¬ tice. Besides, experiments have proven that less power is required to drive coarsely pitched cutters than those of fine pitch. The result of these experiments shows that for two four-inch cutters the one having 30 and the other only 15 teeth to the circumference, the ratio of the power required to drive the cutters, all conditions being equal, was 13.5 : 10.5, or in other words, the finely pitched cut- 330 SMALL TOOLS ter required nearly 30 per cent more power to perform a certain amount of work than did the coarsely pitched one. This certainly is evidence that ought to prove conclusively that fine pitches on milling cutters should be avoided. TABLE LXXXVII. LEAD OF SPIRAL FOR PLAIN MILLING CUTTERS. Spiral = 9 X diameter + 4. Diameter of Cutter. Lead of Spiral in Inches. Diameter of Cutter. Lead of Spiral in • Inches. 2 22 51 531 21 241 6 58 21 261 61 621 2| 281 7 67 3 31 71 711 31 351 8 76 4 40 9 85 41 441 10 94 5 49 Spiral-cut Milling Cutters. — The teeth of plain milling cutters should preferably be cut spiral.* While all cutters ought to be cut spiral, whatever be the width of the face, it has become a practice among manufacturers of cutters to cut the teeth straight on narrow cutters, that is, cutters up to about three-quarters inch thickness. The amount of spiral is commonly expressed by stating the distance along the axis of the cutter corresponding to one com¬ plete turn of the spiral. If we denote this amount by S and the diameter of the cutter by D, we may write the formula _ S = 9 D +4. * “ Helical” is, of course, the more correct expression, but as the word “spiral” is commonly used to express the helix of milling cutters, this word will be used. PLAIN AND SIDE MILLING CUTTERS 331 Thus, if a cutter is six inches in diameter, the spiral should make one turn around the cutter in 9 X 6 -f 4 = 58 inches. The amount of spiral for various diameters figured from this formula is given in Table LXXXVII. Nicked Milling Cutters. — In some cases it is preferred to have cutters with the teeth cut straight, no matter what width of face. One reason for this is that a spiral cutter necessarily produces a certain amount of end thrust, and when used in special machines not properly designed to take up a great deal of pressure in the longi¬ tudinal direction of the spindle it may be desirable to use a cutter with the teeth cut straight. Of course there would be no need for this in any modern, standard milling machine. When the teeth are cut straight, in order to break up the length of the cut, small grooves are cut at proper intervals in the lands of each tooth in such a manner that the grooves in one tooth come in the center of the cutting portion between the two grooves in the next tooth, as shown in the upper and lower cutting edges in Fig. 161. Cutters, the cutting edges of which are notched by this 332 SMALL TOOLS method, are generally termed “cutters with nicked cut¬ ting edges.” Very often the cutting edges of spiral-teeth cutters are also nicked, particularly when the face is wide; but whether this actually improves the cutting qualities of the cutter may be open to question inasmuch as the cut is continually broken up anyway owing to the spiral of the cutting edge. Fluting Cutters for Plain Milling Cutters. — Plain milling Fig. 162 Fig. 163 Fluting Cutters for Plain Milling Cutters cutters, with the teeth cut spiral, should be fluted with a cutter having 60 degrees included angle, 12 degrees on one side and 48 degrees on the other, as shown in Fig. 162. Most manufacturers of small tools make for the market cutters for fluting spiral mills having an inclusive angle of 52 degrees only, 12 degrees on one side and 40 on the other. These cutters, however, produce too weak and unsupported a tooth and as a matter of fact the manufacturers themselves use a 60-degree cutter for PLAIN AND SIDE MILLING CUTTERS 333 cutting the teeth of the cutters of their own manu¬ facture. When cutters are provided with straight teeth a grooving cutter as shown in Fig. 163 should be used. This is a regular 60-degree angular cutter. The angular cutter for producing the teeth should have the corners of the teeth slightly rounded rather than sharp. The amount of round need be but slight, Fig. 164. Cutting Radial Fig. 165. Cutting Teeth Teeth in Milling Cutter with Negative Rake but it makes a stronger cutter when the grooves are cut a trifle rounding in the bottom and it also reduces the ten¬ dency to crack when the cutter is hardened, sharp corners being an invitation to crack. Cutting the Teeth of Plain Milling Cutters. — While the teeth of all ordinary milling cutters are cut radial as shown in Fig. 164, some persons very familiar with the best shop practice claim that a certain amount of negative front rake, as shown in Fig. 165, is sometimes desirable, 334 SMALL TOOLS particularly when the cutter is to be used on brass. There are, however, differences of opinion in this respect, because on the other hand there are good reasons why milling cutters should be given a slight positive front rake in order to improve their cutting qualities. This has not been the practice so far, but it may become rec¬ ognized , that here is an opportunity for improvement. Mr. A. L. De Leeuw in Machinery for May, 1906, calls attention to the fact that the use of a positive front rake in milling cutter teeth is not as common as it ought to be. He says that while it is true that not every cutter can be used with front rake, a great number that ought to have front rake are not provided with it. There are two main reasons why the rake for a milling cutter may not be advisable; one is that a cutter ground with rake is liable to produce a rather poor surface; the other is that the spaces between the teeth are liable to be filled up with chips. It is generally easy to avoid trouble on the latter score by providing means for washing the chips away. As far as the first reason is concerned, this is not quite so bad as it looks. In the first place, where one operation is done on a great number of parts it would be easy to have two cutters, one for roughing and one for finishing. This is something which, for some reason, is too much neglected in milling practice, perhaps for the reason that not so long ago most shops had only one or two milling machines, which were mainly used for tool work, or such operations as could not possibly be done on any other machine. As a consequence, there was a very great number of costly milling cutters for only one or two machines. It was quite natural, then, that this large number of cutters was not doubled again so as to get one cutter for roughing and one for finishing. As a rough surface was positively inadmissible, it followed that the cutter had to be made in PLAIN AND SIDE MILLING CUTTERS 335 such a way that a good surface was produced. That the cutter was not a decided success as a roughing cutter was only regretted (if it was noticed at all). Now that the milling machine is beginning to be recognized as a factor in the rapid production of work in manufacturing shops, it seems that the time is past when people can be satisfied with a slow cut, because the same cutter which takes a fast cut will not make a good surface. Fig. 166 shows a cutter milled with positive front rake. It / must be understood that such / cutters are not suited for finish- j ing cuts, but only for roughing. \ In milling the teeth it is neces- \ sary to leave a slight portion \ at the top of the tooth flat; this portion is termed “land,” and is ground after hardening to the with p ositiTe Front Bake required angle to give keenness to the cutting edge. The width of the land varies for different pitches of teeth, and consequently for different diameters. The values for the dimension of the width of the land are given in Table LXXXVIII. TABLE LXXXVIII. WIDTH OF LAND OF PLAIN AND SIDE MILLING CUTTERS. Diameter of Cutter. Width of Land. Diameter of Cutter. Width of Land. 2 3*2 5 A 21 3*2 6 A 3 F2 7 A 31 A 8 A 4 10 A 336 SMALL TOOLS Allowance for Grinding. — The hole in the cutter should be left about 0.005 inch under size before hardening and ground to size when hardened. In order to facilitate this grinding it is advisable to recess the hole as shown in Fig. 167. The ends of the cutter must also be ground so as to offer true surfaces for the ground clamp collars to bear against. A considerable saving when grinding the ends is afforded by recessing as shown in Fig. 168, thereby Fig. 167. Cutter with Hole Fig. 168. Ends of Cutter Recessed Recessed to Facilitate Grind- to Save Grinding more than ing Actual Hubs producing a hub, which is the only portion of the end requiring to be ground. The diameter of the hub should not be less than the diameter of the hole in the cutter plus three-quarters inch. All corners should be care¬ fully rounded when recessing, as any sharp corners are liable to produce cracks in hardening. Key-ways .— In commenting upon the diameter to select for milling cutters, one of the conditions governing the size was the strength of the metal between the key-way and the bottom of the groove between the teeth. This key- PLAIN AND SIDE MILLING CUTTERS 337 way causes a great deal of confusion to users as well as to makers of cutters, as there is not as yet any universally adopted standard as to the size of the key-way. Manu¬ facturers of cutters are trying to establish a standard for square as well as for half-round splines, which, if adopted by all users, would save a great deal of expense and diffi¬ culty and add to the interchangeability of the cutters. These standards are given in Tables LXXXIX and XC. TABLE LXXXIX. STANDARD KEY-WAYS FOR MILLING CUTTERS.—SQUARE. D = Diam. of Hole. A = Width of Key-way. B = Depth of Key-way. C — Radius of Corners. j to ^ inch. A Wi 0.020 f to l inch. i A 0.030 ft to If inch. A Wi 0.035 1A to If inch. A A 0.040 1A to If inch. i i 0.050 Iff to 2 inch. A A 0.060 2A to 2f inch. 1 A 0.060 2A to 3 inch. A A 0.060 Hardening. With regard to the hardening of milling cutters a great deal has been written, but there can be very little said that is definite enough to actually benefit any one who is trying to learn hardening theoretically. Experience and 338 SMALL TOOLS TABLE XC. STANDARD KEY-WAYS FOR MILLING CUTTERS. — HALF ROUND. D = Diam. of Hole. A = Width B = Depth of Key-way. of Key-way. | to f inch. 1 A U to if inch A A | to 1A inch. i i It to 1A inch. A A It to 2 inch. 1 A 2^5 to 2A inch. A A 2t to 3 inch. .... _ i i acquaintance with the steels used are essential for success¬ ful hardening. Slow heating is, of course, necessary. For quenching bath some hardeners advocate the use of raw linseed oil, some brine, and some nothing but water. The bath should not be very cold. A brine bath of a temper¬ ature of about 70° F. will prove satisfactory if the hardener knows his business in other respects. Small cutters, say those below 2 \ inches in diameter, should be dtawn to a temperature of 430° F. The temper of large milling cutters is usually not drawn. It may be remarked that when quenching milling cutters, after having heated them, the general principles to be borne in mind are that long cutters should be plunged •vertically and thin ones edgewise. This will in both cases tend to counteract distortion of the cutter. PLAIN AND SIDE MILLING CUTTERS 339 Grinding. The grinding of the teeth of plain milling cutters is done in either of two ways. By the first and oldest method it is done by an emery wheel of the disk type, the wheel grinding the land of the tooth to the desired angle of clearance. The principal objection to this method is that Fig. 169. Comparison between Action of Disk Wheel and Cup Wheel when Grinding Milling Cutter Teeth the surface ground will become slightly concave, as shown by the dash-dotted line in Fig. 169. Another difficulty in this method, particularly, is also to be found in the care necessary to so adjust the grinding wheel that the proper degree of clearance will result. In this respect the tool- maker is entirely dependent upon his own judgment. It may, of course, be said that the angle of clearance should be from 5 to 7 degrees, that is, the land of the tooth should be in a plane making 5 to 7 degrees angle with the tangent 340 SMALL TOOLS f-c— 5 to 7 Degrees to the outside diameter of the cutter at the edge of the tooth as shown in Fig. 170. In other words, if the teeth are cut radial, the included angle between the top of the tooth and the front face should be from 83 to 85 degrees. This, however, does not help the tool-maker much, as it is very hard to measure the angle referred to with any degree of accuracy. The common method of finding out whether enough clearance has been given to the tooth is to place a straight edge or a regular scale on top of the ground teeth as shown in Fig. 171. If the straight edge, when rest¬ ing on adjacent cutting edges either coincides with the plane Fig. 170. Angle of Clearance Cutter Teeth Fig. 171. Gauging the Clearance by Means of a Straight Edge of the land of the tooth or shows a slight clearance between the straight edge and the top of the tooth as shown in Fig. 171, then the angle of clearance may be considered approximately correct. PLAIN AND SIDE MILLING CUTTERS 341 Grinding Clearance with Cup Wheel .—The second method of grinding the relief or clearance of plain milling cutters is by means of a cup wheel. This method was originated in Germany, and is at present gaining ground everywhere. The difference in the surface produced by this wheel and by the disk wheel is easily seen in Fig. 169. The cup wheel produces a longer lasting tooth, as the latter is not provided with so keen and unsupported a cutting edge. This method of grinding is to be recommended in all cases where it is possible to use it. By this method Center li ne of Cutter Fig. 172. Cup Wheel Inclined to the Angle of Clearance of Cutter it is also possible to gauge the angle of clearance in a more satisfactory manner. The grinding head may be made so that the cup wheel spindle inclines say 6 degrees to the horizontal. This of course gives the face of the cup wheel an inclination of 6 degrees to a vertical plane. If now the cutter is presented to the wheel so that the front face of the tooth to be ground is in the horizontal plane going through the center of the cutter, as shown in Fig. 172, then the clearance angle of the tooth will evidently be 6 degrees. The advantages of the method referred to are a flat top surface and a uniform clearance angle on all the teeth. 342 SMALL TOOLS In order to diminish the disadvantage of the concave form of the land of the tooth when the grinding is per¬ formed with a disk wheel, it is necessary to select a wheel of as large a diameter as possible, as then evidently the concavity will become less pronounced. Precautions in Grinding. — When grinding it is also necessary to get the length of all the teeth as nearly equal as possible, so that one tooth does not project further from the common center than do the others. If one or a few teeth project beyond the others, they will cut deeper into the metal to be cut, and a surface of an uneven and wavy appearance will result. In order to get the teeth ground to an equal length they should all be ground with a stop resting against the face of the tooth operated upon. It is evident that in such a case they must all be identically the same when ground. If the cutter were indexed around by an index head when grinding, in the same way as when the teeth are cut, an uneven length of teeth would result, because no index head is so perfect as to bring every tooth to the very same position in relation to the grinding wheel as was occupied by the former tooth. Every indexing head will cause slight irregularity in the spacing of the teeth. If, however, the teeth are all one after another brought up against the same stop, which is held in a fixed relation to the grinding wheel, every tooth will be ground correctly, irrespective of slight irregularities in the spacing of the teeth. When a special grinding head with the spindle inclined as mentioned previously cannot be had, the clearance angle can be secured by using a cup wheel with a vertical face and setting the stop pin or guide for the tooth some¬ what below the center of the cutter to be ground, as shown in Fig. 173. Evidently this will fill the purpose equally well. PLAIN AND SIDE MILLING CUTTERS 343 Setting the Tooth Guide .— The amounts to set the guide below the cutter center are given in Table XCI for 5- and 7-degree angles. This table is as given by the Cincin¬ nati Milling Machine Company. When grinding with a disk wheel the center of the wheel must be set a certain distance above the center of the cutter, the guide pin in this case being set at the same height as the cutter center. The amounts to set the wheel center above the cutter center for various cutter diameters are given in Table XCII. It is evident that if too large a wheel is selected it may cut Fig. 173. Setting Stop Pin for Grinding Clearance on Milling Cutter Teeth into the tooth nearest to the one ground. In such a case a smaller wheel must be used. In regard to the clearance angle it may be added that where special roughing and finishing cutters are made 5 degrees should be used for the latter and 7 degrees for the former cutters. Side or Straddle Milling Cutters. The next class of cutters to be considered are side or straddle milling cutters, Fig. 174, the latter name having originated through the use of these cutters in pairs or gangs. 344 SMALL TOOLS TABLE XCI. TABLE FOR SETTING TOOTH REST BELOW CUTTER CENTER TO OBTAIN 5 AND 7 DEGREES CLEARANCE WHEN GRINDING MILL ING CUTTER TEETH WITH CUP WHEEL. Diameter of Cutter. 5 Deg. Clearance. 7 Deg. Clearance. Diameter of Cutter. 5 Deg. Clearance. 7 Deg. Clearance. 1 0 Oil 0 015 3 0 132 0 180 t 0 015 0 022 3} 0 143 0 195 1 0 022 0 030 3i 0 154 0 210 § 0 028 0 037 3i 0 165 0 225 1 0 033 0 045 4 0 176 0 240 i 0 037 0 052 4} 0 198 0 270 1 0 044 0 060 5 0 220 0 300 H 0 050 0 067 51 0 242 0 330 H 0 055 0 075 6 0 264 0 360 H 0 066 0 090 61 0 286 0 390 if 0 077 0 105 7 0 308 0 420 2 0 088 0 120 n 0 330 0 450 2i 0 099 0 135 8 0 352 0 480 21 0 110 0 150 9 0 396 0 540 2* 0 121 0 165 10 0 440 0 600 . TABLE XCII. TABLE GIVING DISTANCE TO SET CENTER OF GRINDING WHEEL ABOVE THE CUTTER CENTER WHEN USING DISK WHEEL. Diameter of Emery Wheel. 5 Deg. Clearance. 7 Deg. Clearance. Diameter of Emery Wheel. 5 Deg. Clearance. 7 Deg. Clearance. 2 A 1 41 21 A A 41 a ifa 21 A 41 u 19 21 & 5 ~h 3 ' i A 51 M 11 31 & M 51 M H 31 A -h 51 1 If 31 ifa a 6 1 7 1 4 a i PLAIN- AND SIDE MILLING CUTTERS 345 These cutters can be considered as a combination of a plain milling cutter and an end mill, and consequently, as far as the face is concerned, whatever has been said about plain milling cutters applies also to side milling cutters. As these cutters are very seldom made of any considerable width of face, they are almost always cut straight. Milling the Teeth on the Sides. — When milling the teeth on the sides of a side milling cutter, the cutter to use and the angle to which to set over the mill when being cut must be selected with a great degree of judgment and care. It would be almost impossible to give any definite rules or figures, but for general guidance it may be said that a cutter of the same form as for milling the teeth on the face should be used except that the angle of the cutter should be about 75 degrees instead of 60 degrees. The formula for finding the angle to which to set over the cutter while 346 SMALL TOOLS the teeth are being cut on the side can, however, easily be derived. If N be the number of teeth in the cutter to be cut, v the angle of the cutter with which the teeth are cut, and w the angle to which to set over the index head of the milling machine on which the mill to be cut ts mounted, then 360° cos w = tan —— X cot v. N This formula is proved as follows: Let it be assumed that the number of teeth in the mill to be cut and the angle of the angular cutter with which the teeth are to be milled are given. The angle sought is the one to which to set the index head of the milling machine. In Fig. 175 the problem is shown diagrammatically, the cutter angle ADB and the number of teeth, N, being given, while the angle to which the index head is to be set (which is to be determined) is BEC. In order to simplify the calculations, assume the radius of the side mill to equal 1. Evidently the length of the radius has no influence on the final result, or on our formula, anyway. The angle BCM represents the angle of one tooth of the side mill. Now produce CM to A and draw AB. The line CE represents the bottom of the tooth, and the plane in which the angle of the cutter for milling the teeth must be measured is at right angles to CE, or in the plane BD (lower view of Fig. 175). A A Tig. 175. Deriving Formula for the Setting of Side Milling Cutter when Milling Teeth on Side PLAIN AND SIDE MILLING CUTTERS 347 We can now arrive at the following equation: Angle ACB = • But BC = radius of side mill = 1, and consequently (1) The triangle ABD, shown at the right in Fig. 175, is in a plane perpendicular to the bottom CE of the tooth, the angle ADB being the cutter angle, as mentioned. Then QAA° BD = AB X cot ADB = tan X cot ADB. (2) The line BD, however, also lies in the plane containing the right triangle CDB. We have, therefore, ( 3 ) But BC = radius of side mill = 1, and consequently, from (2) and (3), qao° cos CBD = BD = tan—— X cot ADB. (4) The angle CBD equals the angle BEC, or the angle to which to set the index head; therefore cos BEC = tan —— X cot ADB, or, expressed in words: The cosine of the angle to which to set the index head equals the tangent of the tooth angle multiplied by the cotangent of the angle of the cutter hy which the teeth are cut. This proof was contributed by Irving Banwell in Machin¬ ery, February, 1908. Assume as an example that we wish to cut the teeth on the side of a side milling cutter having 18 teeth with an 348 SMALL TOOLS angular cutter of 75 degrees. Then the cosine for the angle to which to set the index head in which the milling cutter is held, or cos w = tan 20° X cot 75° = 0.364 X 0.268 = 0.0975. w = 84° 25'. Number of Teeth. The number of teeth in a side milling cutter may be a trifle greater than that of a plain milling cutter, because the former class of cutters usually are very much narrower than the latter. If N is the number of teeth and D the diameter of the cutter, the following formula for number of teeth corresponds with the practice of the Pratt and Whitney Company: N =3.15 + 11. Thus the number of teeth in a cutter 5 inches in diameter would be 3.1 X 5 + 11 = 15.5 + 11 = 26.5, which of course must be 26 teeth. The number of teeth figured from this formula is given in Table XCIII. TABLE XCIII. NUMBER OF TEETH IN SIDE MILLING CUTTERS. No. of teeth =3.1 diara. + 11. Diameter of Cutter. Number of Teeth. Diameter of Cutter. Number of Teeth. 2 18 51 28 21 18 6 30 21 18 61 32 n 20 7 32 3 20 71 34 31 22 8 36 4 24 9 38 41 24 10 42 5 26 PLAIN AND SIDE MILLING CUTTERS 349 Relief of Teeth. — What has been previously said about the relief of plain milling cutters is equally applicable to side milling cutters. The relief on the side of these cutters need not, however, be as large as the relief on the face of the tooth. In fact, some manufacturers do not relieve their side milling cutters at all on the side, but that cannot be considered good practice. A slight relief is evidently called for if the tooth on the side is to be able to cut at all. Fig. 176. Comparison between Relief of Teeth on the Cylindrical Surface and the Side of Cutter The reason why the relief on the side of the cutter may and should be smaller than that on the face is very obvious if one considers the difference in the relationship of the tooth to the surface to be cut when this tooth is located on a circular and on a plain surface. Referring to the cut, Fig. 176, where the case is shown in exaggerated scale, it is easily seen that if the same angle of relief is given to the tooth A on a circular surface and to the tooth B on a flat surface (the side of the cutter) the actual relief C will be con¬ siderably larger on the tooth B and will be larger than the 350 SMALL TOOLS relief on the tooth A according to the diameter of the circle on which the tooth A is located. The same angle of relief gives a smaller actual relief C on a smaller diameter than on a large one. Even if we do not consider this theoretically, there are practical reasons why the relief on the sides need not be as large as on the face; in fact, the main reason why a side milling cutter is preferable to a narrow, plain milling cutter for cutting slots is that the former has more chip room on the sides because of having teeth and consequently space for chips between them, thus making the sides of the slot smoother, whereas, when using the plain milling cutter, the chips will clog between the sides of the cutter and the sides of the slot, producing rough places in the work. It is well known that the actual cutting of a side mill is per¬ formed by the face; this is proven also by the fact that these cutters have to be ground more often on the face than on the sides. It may be inferred that no relief at all on the sides is necessary if the teeth on the sides are not doing any actual work. However, there are occasions when these cutters will have to do actual work, and that is when no other cutter than a side milling cutter with the teeth relieved on the sides will produce desirable results, as, for example, when an absolutely straight slot is required to be cut. When cutting a slot a plain milling cutter will never cut its way straight through the work, because when once out of the straight line it has no means of correcting its path, but must follow the direction in which it started to cut, whereas a straddle milling cutter with its teeth relieved on the sides will, even if started wrong, have an opportunity of correcting its path by being able to cut with its sides. It may be said that if the cutter or cutter arbor is running out, the slot will obviously be wider than the cutter, but PLAIN AND SIDE MILLING CUTTERS 851 the slot will in all cases be straight. In this connection it is appropriate to mention various ways of making cutters that will maintain standard widths. This is accomplished by interlocking the cutters in such a manner as to permit adjustment after the cutters have been reduced in width by grinding on the sides or through wear. Interlocked Cutters. There are three different ways of interlocking cutters in common use, viz.: (1) A straight slot through the center Fig. 177. Simplest Form of Interlocked Cutters across one end of one cutter and a corresponding tongue on one end of the other cutter fitting loosely in the slot (Fig. 1 7 7); (2) Two or more sectors on one end of each of the two cutters cut away in such a manner that the remaining high sectors in the one cutter fit loosely into the spaces cut away in the other cutter (Fig. 178); (3) Oppo¬ site every other tooth on one side of each of the two cutters is cut away a portion, leaving a space into which the high portions of each of the cutters fit (Fig. 179). Referring to the first kind of interlock mentioned, it must be remarked that this interlock is poorly adapted for maintaining a standard width and is mostly used where 352 SMALL TOOLS cutters of unusual lengths are required which would be impractical, if not entirely impossible, to make in one piece. This interlock is to be recommended for such purposes because of its being very simple and inexpensive to make. It will be noticed from the cut that there ought to be a clearance of 0.010 inch between the bottom of the slot in one cutter and the top of the tongue in the other cutter, thus giving a resting surface between the two cutters at A and B, which faces ought to be ground. It Fig. 178. Interlocked Cutters for Maintaining Standard Width may also be remarked that between the sides of the slot and the tongue there does not need to be a perfect fit and consequently these sides do not need to be ground. As mentioned above, this kind of interlock is not to be recom¬ mended for maintaining a standard width, although it could be used for such purpose by inserting thin pieces between the ground faces A and B. For maintaining a standard width, interlocks such as are shown in Figs. 178 and 179 are the most desirable. In these cases the cutters are provided with ground hubs, PLAIN AND SIDE MILLING CUTTERS 353 the width being maintained by inserting thin washers between these hubs. Between the hubs and the interlock¬ ing sections there should be an annular recess of sufficient width and depth to permit clearance for the milling cutter when milling out the sections for the interlock. If such a recess is not provided, or if it is not wide enough, the cutter will cut into the hub, causing an unfinished appearance as well as a poor surface for a good contact with the hub in the other cutter with which it is interlocked. Fig. 179. Interlocked Cutters with Every Other Tooth Recessed Cutters for Maintaining Standard Widths by Means of Beveled Faces. — In the February, 1905, issue of Machin¬ ery, Mr. E. R. Markham showed a method of making cutters for maintaining a standard width which he claims to be very satisfactory, and which has, he says, in many shops superseded the cutter with interlocking teeth for the pur¬ pose mentioned. This cutter is shown in Fig. 180. To make this form of cutter use an eccentric mandrel like that in Fig. 181. This mandrel has two sets of centers; the 354 SMALL TOOLS eccentric centers are located, equidistant from the regular centers but on opposite sides, on the opposite ends, as shown. Half of the cutter is placed on the mandrel so that the end to be cut at an angle shall be halfway between the ends of the mandrel, as shown in Fig. 182. After facing the end a by running the mandrel on the concentric centers, the eccentric centers are placed on the lathe centers and the end b is faced as shown. The two parts are then put together on a stud and the hole drilled and reamed for the dowel pin, a, Fig. 180. The cutter is then placed in the vise of the shaper or planer and the key-way cut, after which the teeth are milled. The necessary adjustment for width of the slot is obtained by blocking apart by means of collars of tin, thin sheet steel, or paper. Gang Cutters. — When two milling cutters, for instance, one plain and one side milling cutter, are used together in PLAIN AND SIDE MILLING CUTTERS 355 a gang, as it is usually termed, one should always let the teeth of the larger cutter project outside of the hub, as shown in Fig. 183, so that when cutting no ridge in the metal cut will result. When the cutters are of equal or nearly equal diameter, the common methods of interlock¬ ing evidently provide against any ridge being left in the surface milled. It is very important, whenever arrang¬ ing milling cutters in a gang to finish a continuous width of surface, that all the cutters either interlock or project inside one another. In Fig. 184 U pi lilt kmmm Hill mm Slllllilll jjjp W Fig. 184. Gang of Milling Cutters is shown a gang of four cutters thus arranged. No ridge can be left at any place when this gang is put together in the manner shown. High-speed Steel for Milling Cutters. In regard to the material which can most advantage¬ ously be used for milling cutters, opinions differ as to the Fig. 183. Plain and Side Milling Cutters in Gang 356 SMALL TOOLS higher efficiency gained by making the cutters from high¬ speed steel. Mr. Robert Grimshaw of Hannover, Germany, in Machinery , February, 1907, stated that his experience with high-speed steels has shown that while they would rough out about three to five times as fast as the carbon steels, they were not to be recommended either for finish¬ ing cuts on the lathe or for milling cutters, and that his own rather expensive experience was backed up by the results obtained by others in Germany. It should hardly be necessary to say that the reason why we should not expect proportionately as good work in finishing as in roughing is that the new steels, almost without exception, require to be almost, if not quite, red hot in order that their molecules may arrange them¬ selves in mechanical grouping or in chemical combination so as to give the maximum hardness, and that in conse¬ quence of the high speed required to get this temperature, and the tearing rather than cutting action, the surfaces obtained are not so smooth as those produced with the carbon steels. The experiments of Prof. Haussner of Brunn, Germany, go to show that a slight increase in specific power required to produce turnings accompanies an increase in the speed of cutting; and this is at once the cause of the new tools getting hot when roughing and the reason why they cut so fast. But in finishing on the lathe or planer there is less heat developed than in roughing. In milling there is, in the first place, no machine that will give the speed required to make the tool red hot; and in the second place the weight and cross-section of the body of the mill, in proportion to the cutting portion proper, is so great that in any case the slight heat developed by the work is rapidly carried away from the point of application of the cutter. Further, the teeth are not constantly at PLAIN AND SIDE MILLING CUTTERS 357 work, as is the case with the point of a lathe tool; and each tooth has a chance to cool off “between bites.” This being the case, we have not the combination of cir¬ cumstances tending to produce that high temperature of the cutting point, or points, necessary in the case of the new steels to do fast work. In a paper before the Ameri¬ can Society for Testing Materials, Mr. Metcalf said in effect: “As far as we know, the users of high-speed steel have not been able to make tools that will finish satis¬ factorily; therefore they use for this purpose carbon- steel tools, after they have done the heavier, rougher work with the high-speed steels.” Although this was said about finishing in the lathe, it applies equally well to all milling operations, roughing and finishing alike, as the conditions encountered are in principle the same, as has already been pointed out. While these experiences, of course, have their value, and while the reasoning underlying the opinions is undoubt¬ edly correct, yet both in this country and in England a number of the leading manufacturers, who are users of milling cutters, find that although the cutting speed can be only slightly increased, so that the saving in time does not in itself outweigh the increased expense of material for cutters of high-speed steel, such cutters retain their cutting edges much longer than those made of ordinary tool steel; and this fact, when considering the question of economy, is nearly as important as that of high cutting speed. In large shops, where several hundred milling cutters are in constant use, their grinding is a very important item in the expense account, and as high-speed steel cut¬ ters have to be ground less frequently, that is a distinct saving. The labor cost in the making of milling cutters is considerable, in many cases so great that the cost of 358 SMALL TOOLS material is small in comparison; and the greater the labor cost the more important it is to use material which adds to the cutter’s life. The greater cost of high-speed steel becomes a heavy item in tools where the labor cost of making the tool is comparatively small; but in the case of a formed milling cutter, where the labor cost is large, the difference in the total cost between ordinary carbon steel and high-speed steel becomes insignificant. In a discussion regarding the manufacture and up-keep of milling cutters, at a meeting of the Institution of Mechan¬ ical Engineers of Great Britain, one of the speakers called attention to one valuable property of high-speed steel, which he had not seen referred to, namely, that of withstanding shocks. In one of the railway shops in England the output of the crank-turning lathes had been practically doubled by the use of high-speed steel tools. The forgings were never very accurate, there being perhaps one-quarter inch to take off one side of the diameter, and 1J inches off the other, and a tool suited to such wide variation was greatly appreciated. If the high-speed steel tool dug in, it did not break, as invari¬ ably happened with ordinary carbon steel. Another speaker called atten¬ tion to an important factor affecting the life of high-speed steel milling cutters. The teeth, besides being correctly relieved at the back, should have a front rake of 5 degrees, as indicated in Fig. 185. The number of teeth in milling cutters, particularly when made of high-speed steel, plays a very important part. A cutter made of this material with a large number of teeth has Fig. 185. Method of Making High-Speed Steel Cutters to Insure Long Service PLAIN AND SIDE MILLING CUTTERS 359 a considerably shorter life than one with fewer but deeper teeth. In a certain case two milling cutters, one with 16 teeth and one with 32 teeth, had been made. The one with the coarser teeth, of helical shape, would finish an article with as good a finish as the one with the finer pitched teeth, but the cost of making the coarse-pitched cutter was 35 per cent less than the cost of making the one with the fine-pitched teeth and the life of the coarse- pitched cutter was four or five times as long as that of the other. CHAPTER IX. MISCELLANEOUS MILLING CUTTERS End Mills. The end mill, as the name indicates, is a cutter having teeth on, and cutting with, the end rather than by the face as in the case of face or side mills. However, the end mill is provided with teeth on the face as well as on the end, as shown in Fig. 186. This kind of cutter is usu- Eig. 186. End Mill with Taper Shank ally made with a solid shank, but is also made with a hole through it to fit a removable shank and is then termed shell end mill. Such a mill is shown in Fig. 187. -. $ ::..A ^. . \ - .. \ Eig. 187. Side View and Section of Shell End Mill The end mill is a combination of a plain and side milling cutter, and can be used for milling surfaces parallel to the axis of the cutter as well as surfaces, perpendicular to the 360 MISCELLANEOUS MILLING CUTTERS 361 axis. The teeth on the end are almost always radial, and without front rake. The teeth on the cylindrical surface are usually cut straight, but may be cut spiral as well. The object of the spiral is the same as in the case of face mills, viz., that the cut may be broken up into a number of smaller portions. The amount of spiral should not exceed 20 degrees. Direction of Spiral. — The direction of the spiral in end mills is more important than in the case of plain mills, where the spiral may be in either direction. In Fig. 188 are shown two end mills, both cutting in the right-hand direc- Fig. 188. Right- and Left-hand Spiral Cut End Mills. tion, but one with right-hand and one with left-hand spiral flutes. At first thought it seems as if a right-hand end mill should be given a right-hand spiral, the same as a twist drill. This would tend to force the chips out of the grooves, while a left-hand spiral would tend to force them down toward the cutting edges. The right-hand spiral, however, tends to draw the whole mill into the piece to be cut, the spiral acting as a thread of steep pitch. This is a very grave objection in that it loosens the mill shank, if tapered, from its socket, and may result in injury to the work in hand. Manufacturers of end mills, there¬ fore, as a rule use a left-hand spiral for right-hand mills, 362 SMALL TOOLS and vice versa, notwithstanding that this produces a poorer cutting mill. Not only is there an obstruction to the chips freely moving out of the flutes, which is very important in taking deep cuts, but the teeth on the end get a negative front rake, as seen from the cut, and for this reason the mill is not suited to cut with the end, but will cut freely only with the teeth on the cylindrical sides. The fact that the left-handed spiral pushes the mill firmly into the socket is, however, considered to out¬ weigh the disadvantages mentioned. If the mill is to be used as end mill only, then the spiral on a right-hand mill should be right hand, because the teeth can be given posi¬ tive front rake. For ordinary use the end mill with teeth cut straight is preferable, as it does not cause any trouble of the kind referred to above. Size of Shank. — Solid-shank end mills are usually pro¬ vided with either Brown and Sharpe or Morse taper shank. In Table XCIV are given the different numbers of stand¬ ard shanks corresponding to the ordinary sizes of end mills. In some cases two numbers are given, indicating that it is usual to make the mills in question with either of two sizes of shanks. The numbers of the shanks given for various sizes of mills correspond to the practice of end- mill manufacturers. Dimensions. — The only dimension necessary to give in relation to end mills, besides the size of the shank, is the length of the cut, or the length of the cylindrical portion provided with cutting edges. This dimension is also given in Table XCIV, together with the number of teeth ordinarily cut in these mills. The length of the neck between the cutting part of the mill and the shank is unimportant, and should only be long enough to prevent the fluting cutter from cutting into the shank when the teeth are milled. MISCELLANEOUS MILLING CUTTERS 863 TABLE XCIV. DIMENSIONS OF END MILLS. Diameter of Mill. Length of Cut. Number of Teeth. Number of Morse Taper Shank. Number of B. and S. Taper Shank. 1 f 6 1 4,5 A f 8 1 4, 5 t f 8 1 4, 5 A 1 8 1, 2 4, 5 1 If 8 1, 2 5,7 A U 8 1, 2 5,7 f If 10 2 5,7 tt If 10 2 7,9 i If 10 2, 3 7,9 i If 10 2, 3 7,9 l 10 2, 3 7,9 n 2 12 3 7,9 u 2 12 3, 4 7,9 n 21 12 3, 4 9 h 21 14 3,4 9 if 21 14 4 9 if 2f 14 4 9 if 21 16 4 11 2 21 16 4 11 Milling the Teeth on the End of End Mills. — The milling of the teeth on the end of end milling cutters, and the selection of a cutter with a proper angle, require a great deal of judgment and care. It is almost impossible to give any definite rules or figures for the cutter to select, as this varies with the size and the number of teeth in the mill, as well as with the clearance it is wanted to give back of the cutting edge. The angle of the angular cutter used should, however, be selected between 55 and 75 degrees. If the cutter is settled upon, the proper angle to which to set over the index head in which the end mill is held (see Fig. 189) can be found by the rule already referred to in connection with the milling of the teeth on the sides of side milling cutters. This was given by Mr. George G. Porter in Machinery, April, 1904. 364 SMALL TOOLS If N = number of teeth in end mill, V = angle of cutter with which teeth are cut, and W = angle to which to set the index head in which the mill is held, then qao° cos W = tan X cot V. N The use of this formula is best explained by an example. Suppose that an end mill is to be made having 10 teeth, and that a 70-clegree cutter will be used for cutting the teeth. We have then cos W = tan 36° X cot 70° = 0.727 X 0.364 = 0.264. From this we have W = 74° 40'. MISCELLANEOUS MILLING CUTTERS 365 End Mills With Center Cut. — When it is necessary to cut into the surface of a piece of work with the end of the mill and then feed along, as in die work, internal cams, etc., the teeth are sharpened or given clearance on the inside, and so are able to cut a path from the point where the mill is sunk into the work. The teeth, being very coarse, allow of heavy cuts. This is especially the case when cast iron is the material being machined. After cutting the teeth on the end of the mill a thin metal splitting saw of comparatively small diameter should be run through close to the face of each tooth, making the cut shown in Fig. 190 at A. This cut is to permit back¬ ing off the inner edge of the tooth, which gives the mill a -t :z ' “7 Jj / / / 7 Fig. 190. End Mill with Center Cut cutting tooth on the inside as well as on the outside, and allows it to cut away the projection made when the mill is fed into the work. As mentioned, the number of teeth in end milling cut¬ ters with center cut is smaller than that in ordinary end mills. It is customary to put in four teeth for sizes smaller than one-half inch, six teeth for sizes from one-half to 1J inches inclusive, and eight teeth for sizes up to 2 inches. In ordinary end mills there is a recess in the end the same as in end mills with center cut, but the teeth are not sharpened on their inside edge. The object of recessing the end in that case is to furnish a cavity for the entrance of the cutter that is used to cut the teeth on the end. It also facilitates the operation of grinding the teeth on the end. 366 SMALL TOOLS Shell End Mills. — Shell end mills, Fig. 187, do not differ in principle from ordinary end mills. They are mounted on arbors such as are shown in Fig. 191. The head of the screw in the end of the arbor fits into the recess in the end of the mill. The keys A fit into the key-ways at the upper end of the mill, and constitute the drive. The important dimensions of shell end mills are given in Table XCV. The number of teeth in these mills is larger for the same diameters than the number in solid Tig. 191. Arbor for Shell End Mills end mills, because the coarser teeth of the latter would require a deeper flute than would be permissible in the thin shell of shell end mills. TABLE XCV. general dimensions of shell end mills. Diam. of Mill. Total Length. i Diam. of Hole. No. of Teeth. Diam. of Mill. Total Length. Diam. of Hole. No. of Teeth. H H 16 2f 2 f 18 H i 16 2f 2 f 18 If H 16 2 f 2 f 18 n i 16 2* 2 1 18 A H f 16 2f 2 1 20 if H f 18 2f 2 1 20 if if f 18 2f 2 1 20 if H f 18 3 2 1 20 2 H f 18 . MISCELLANEOUS MILLING CUTTERS 367 Angular Milling Cutters. Angular milling cutters are provided with teeth on the angular face and on one side as shown in Fig. 192. They are usually made with the angle A 45, 50, 60, 70, or 80 degrees for regular purposes. They are used mainly for fluting milling cutters. They are designated by the angle A, so that a 60-degree angular cutter means one having this angle 60 degrees. Angular milling cutters are orcii- Fig. 192. Angular Milling Cutter narily made in three sizes, 2\, 2f, and 3 inches in diameter, all one-half inch thick, with 1-inch hole in the two smaller sizes and 1 J-inch hole in the largest. A recess B is turned in the side of the cutter provided with teeth. The depth of this,recess may be made five-sixty-fourths inch and the diameter If, If, and 2J respectively, according to the diameter of the cutter. The number of teeth in angular cutters is made 20, 22, and 24 respectively for the three different sizes of cutters. 368 SMALL TOOLS The cutter shown in the cut is termed right hand. The cutter is ordinarily mounted on the milling-machine arbor with the side without teeth toward the milling-machine head. Cutters for Fluting Spiral-teeth Milling Cutters. Cutters for fluting spiral-teeth milling cutters, usually termed cutters for spiral mills, are ordinarily made with a Fig. 193. Cutter for Fluting Spiral Teeth Milling Cutters 52-degree inclusive angle, as shown in Fig. 193, 12 degrees on one side and 40 degrees on the other. However, this cutter produces a rather weak tooth, and it is preferable to make the 40-degree angle on the one side equal to 48 degrees, the inclusive angle then being equal to 60 degrees. These cutters are, of course, nothing but double angle cutters. The one shown in the cut is termed a left-hand cutter; that is, when mounted on the arbor of a milling machine the MISCELLANEOUS MILLING CUTTERS 369 side with the larger angle, the 40- or 48-degree angle, should be toward the machine. The manner in which these cutters are used is shown in Fig. 194, where C is the cutter being milled and A the cutter for cutting the spiral grooves. Cutters for spiral mills are usually- made in three sizes only, 2\, '2f, and 3 inches diameter; the width is made one-half inch in all, and the hole 1 inch in the two smaller sizes and li inches in the largest. The num¬ ber of teeth is made 18, 20, and 22 respectively for the three sizes. The teeth are cut with angular cutters, the 40- or 48-degree side with a 60-degree cutter and the 12-degree side with a 75-clegree cutter. Fixture for Grinding Angular Milling Cutters. Fig. 195 shows a little device which has proved itself very useful in grinding angular milling cutters when a perfect angle is required. This device was shown in Machinery, January, 1908, by Mr. P. Yorgensen. A radius at the point of the angle can also be ground, radius and angle being ground at one setting. This fixture consists of a base plate C, which is clamped to the grinder table so that it can be fed to and from the wheel by the feed arrange¬ ment on the grinder. On this base plate rests a triangular plate D, carried on three feet. This latter plate is free to move in all directions, simply sliding on its feet on the plate C, and is guided only by the hands of the operator. In this triangular plate D there is a slot E, into which a tongue Fig. 194. Setting Cutter in Fig. 193 when Fluting Milling Cutter 370 SMALL TOOLS of the bracket F is fitted, this bracket then being movable back and forth on the plate D, and having arrangement for clamping in any position. The cutters A are clamped to this bracket F by a suitable screw and washer. For dif¬ ferent widths of cutters, either different brackets must be employed or washers may be interposed between the Fig. 195. Simple Fixture for Grinding Angular Milling Cutters bracket and the cutter, because it is evident that the center line of the cutter must always coincide with the center fine of the triangular plate D. The cutter can be set to any given radius between the two angular faces by placing a gauge block, having the same thickness as the radius wanted, against the side of the triangular block, and placing a square against the gauge, and adjusting the cutter so that MISCELLANEOUS MILLING CUTTERS 371 the blade of the square just touches the angular face of the teeth of the cutter A. If, for instance, we have a cutter that we want to grind to a 60-degree angle, and want one- sixteenth-inch radius at the point, we simply set the cutter central with the triangular block and place a one-sixteenth- inch gauge block between the square and the side of the block, and then adjust the cutter until it touches the blade of the square. The cutter is then clamped in place. The grinding itself is performed by sliding the plate D first to one side and then to the other, so that the sides G and H alternately rest against the guide K on the bed plate C, the side of the teeth of the cutter being meanwhile moved back and forth across the face of the grinding wheel. The turning around of the triangular block from one side to the other with the point B against the guide K evidently produces a radius at the point of the cutter between the two angular sides. The height of the cutter tooth in a horizontal direction, when setting, is determined by a gauge block of such a height that the tooth face is in a horizontal plane with the center line of the cutter. The cutters are formed closely, before hardening and grinding, to the desired shape, so that there is but a few thousandths inch left to be removed when grinding. Formed Cutters. While “ formed ” cutters may be provided either with reg¬ ular milling cutter teeth or with eccentrically relieved teeth, the common usage of the term is for cutters with eccentri¬ cally relieved teeth only. Such a cutter is shown in Fig. 196. The formed cutter is intended for milling surfaces of irregular form, and the teeth are so constructed that their form is exactly the same all the way from a to b. In order to give clearance to the cutting edge the tooth is 372 SMALL TOOLS backed off along the periphery of a circle which is eccentric with the outside periphery of the cutter itself, hence the name eccentrically relieved. Owing to the peculiarity in the construction of the cutter tooth, the face c can be ground off, in order to sharpen the tooth, without changing the form cut by the cutter. This grinding may be con¬ tinued until only a very small part of the tooth remains. A well used up cutter is shown in Fig. 197. Formed milling cutters are first turned up in an ordinary lathe to the simple outlines of the form. A forming tool Fig. 196. Eccentrically Relieved Milling Cutter is then applied, by means of which the cutter is shaped to the desired form. This forming tool must be of the exact form wanted on its top face, but must be provided with clearance, usually 15 degrees. The cutter is then fluted, or the teeth cut. After this the cutter is brought back to the lathe and relieved. The lathe should be provided with a relieving attachment for the performance of this oper¬ ation. Of course, by elaborate devices a cutter may be relieved in any lathe, but the time consumed in doing the work under such difficulties as present themselves is too great to be contemplated at the present time when MISCELLANEOUS MILLING CUTTERS 373 there exist excellent facilities for performing this opera¬ tion. Manufacturers of eccentrically relieved cutters employ special machines for this work, which are suited for performing this operation only. After hardening, the cutters are ground on the front faces of the teeth only. In making or laying out formed cutters care should be taken, as far as possible, not to have any part or surfaces of the teeth at right angles to the axis of the cutter, as Fig. 197. Formed Milling Cutter having been used nn t.il but a Small Part of the Tooth remains shown at a, Fig. 198. It is evident that this part would not be relieved, because the width of the forming tool used for relieving is constant. And even if this portion a were relieved by filing or in some other manner, when the tooth were ground, the space between the faces a and b would become wider and the exact form would be lost. Whenever possible, all surfaces should be given an inclina¬ tion of at least 5 degrees to the line perpendicular to the axis of the cutter. This will permit the forming tool to 874 SMALL TOOLS slightly relieve the whole tooth form; the cutter will con¬ sequently cut easier, and at the same time retain its shape when ground. Interlocking Formed Cutters. — At times formed cutters must be provided with surfaces which are perpendicular to the axis of the cutter. In order to make these cutters cut freely the perpendicular face is relieved by means of filing. As said before, the grinding on the face of the Fig. 198. Undesirable Construction Fig. 199. Interlocked Formed of Formed Cutter Cutter tooth will then widen the form or lengthen the distance a, Fig. 199. In order to overcome this difficulty, such cutters are often interlocked so that the hubs which rest against each other may be ground off at the same time as the faces of the teeth are ground, thus bringing the dis¬ tance a back to the original dimension. But it must be remembered that this way of overcoming the difficulty is permissible only when the width a is the most essential MISCELLANEOUS MILLING CUTTERS 375 dimension and the form otherwise can stand slight changes, because the grinding off of the hubs at 6 will evidently bring the curved parts c and d closer together, and thus slightly change the shape of the cutter, while a standard width a is maintained. This is often overlooked, but unless it is taken into consideration interlocking of formed milling cutters of the kind mentioned for retaining a standard width is not permissible, and shows an incomplete concep¬ tion of the principles involved in and the purpose of eccen¬ trically relieved cutters. Number of Teeth. — The spacing of the teeth in eccen¬ trically relieved cutters is far coarser than in ordinary milling cutters. The reason for this is obvious. The tooth itself is so much wider than the ordinary milling- cutter tooth, and the space required between the teeth should be fairly wide, although not necessarily as wide as required for ordinary teeth. The formed cutter cannot cut as heavy chips as the regular milling cutter, and con¬ sequently there is no need for quite as much chip room between the teeth. There can be no exact rule given for the number of teeth, as this must, to some extent, vary with the form of the cutter, that is, whether the difference between the largest and smallest cutting diameters is large or .small, and also with the diameter of the cutter. In this particular there is no way of determining the correct number but by judgment and experience. The cutters used to mill the grooves in eccentrically relieved cutters of all kinds vary according to the diam¬ eter of the cutter and the number and depth of the teeth. In general an angular cutter of 35 degrees inclusive angle is used, but this angle may vary from 30 to 45 degrees. Concave, Convex, and Corner-rounding Cutters. — The most common of all formed cutters, outside of gear-teeth 376 SMALL TOOLS cutters, which form a class by themselves, are concave, convex, and corner-rounding cutters, as shown in Figs. 200, 201, and 202. The corner-rounding cutter may be of two kinds, single or double. It is a distinct improve¬ ment on this cutter not to let the rounded part be a full quarter of a circle, but to let it be made with a tangent 5 degrees to a line perpendicular to the axis of the cutter as shown in Fig. 200. This permits the whole cutting edge of the cutter to be relieved, and at the same time prevents any ridge being visible in the piece worked Figs. 200, 201, and 202. Single and Double Corner-rounding Cutters, Concave Cutter, and Convex Cutter upon by the cutter, as the side of the tooth gradually recedes from the work instead of being perfectly parallel to it. Approximate dimensions for the common sizes of these cutters are given in Tables XCVI, XCVII, XCVIII, and XCIX. The diameters as given are for cutters with one-inch hole. If the hole is larger or smaller than one inch, the diameter of the cutter must vary accordingly. For sizes not given in these tables the following formulas will give correct proportions for cutters with one-inch holes. MISCELLANEOUS MILLING CUTTERS 377 Corner-rounding cutters: B = + 2 inches, G = \ + \ inch, ^4 D = - + i inch for single, and ^4 D = — + % inch for double corner-rounding o cutters. Concave and convex cutters: B = ~ + 2 inches, 4 11 A C = —— + \ inch (concave cutters only), 3 A D = — + l inch (concave cutters only). For the denotation of the letters in these formulas see Figs. 200, 201, and 202. TABLE XCVI. SINGLE CORNER-ROUNDING CUTTERS. (See Fig. 200.) Size of Diam. of Width of Total No. of Size Diam. Width Total No. of Radius. Cutter. Flange. Width. Teeth. Radius. Cutter. Flange. Width. Teeth. A B C D A B C D A 21 A A 16 1 31 1 1 10 A 21 A A 16 A 31 M tl 10 i 21 A A 16 ft 31 A llV 8 a 21 A i i 12 tt 3f M 8 A 21 : A M 12 1 31 1 11 8 A 21 1 A 12 A 4 1 i A 8 1 21 1 1 12 1 41 A Ilk 8 A 2f A H 10 H 41 A il 8 t 3 A H 10 l 41 f if 8 A 3 H 2 5 10 378 SMALL TOOLS TABLE XCVII. DOUBLE CORNER-ROUNDING CUTTERS. (See Fig. 200.) Size Diam. Width Total Width. No. of Teeth. Size Diam. Width Total Width. No. of Teeth. of of of of of of Radius. Cutter. Flange. Radius. Cutter. Flange. A B C D A B C D A 2ft A A 16 ft 3ft ft 1ft 10 A 2i A 1 16 A 3ft A Aft 10 ft 2ft A A 16 ft 3ft A 1A 8 A 2i A ftft 12 A 3f A ifl 8 A 2ft A ftft 12 1 31 ft 2 8 A 2i ft A 12 A 4 ft 2ft 8 ft 2ft ft 12 ft 4ft A 2A 8 A 2\ A 29 10 A 4ft A 2A 8 ft 3 A i A 10 l 4ft ft 2ft 8 A 3 ftft i A 10 TABLE XCVIII. DIMENSIONS OF CONCAVE CUTTERS. (See Fig. 201.) Diam. of Circle. Diam. of Cutter. Width of Cutter. Width of Flanges. No. of Teeth. Diam. of Circle. Diam. of Cutter. Width of Cutter. Width of Flanges. No. of Teeth. A B C D A B C D ft 2ft A A 16 ft 3 i A A 10 A 2ft ft A 16 A 3ft i A A 10 ft 2ft A A 16 l 3ft A A 10 A 2ft A A 12 A 3ft 1A A 10 ft - -2ft 1 - A 12 ift 3ft 1A ftft 8 A 2ft ft A 12 A 31 2ft ft 8 ft 2ft A A > 12 ift 31 2A ft! 8 A 2ft l A 10 A 4 2ft A 8 ft 21 ift ft 10 A 4ft 2ft A 8 A 21 i A ft 10 ift 4ft 2A ftft 8 1 3 ift ft 10 2 4ft 3 ft 8 A 3 if A 10 MISCELLANEOUS MILLING CUTTERS 379 TABLE XCIX. DIMENSIONS OF CONVEX CUTTERS. (See Fig. 202.) Diameter Diameter Number Diameter Diameter Number of Circle. of Cutter. of Teeth. of Circle. of Cutter. of Teeth. A B A B 1 21 16 1 3 10 21 16 M 31 10 1 21 16 l 31 10 A 21 12 U 31 10 ■ t 21 12 U 31 8 ts 21 12 U 31 8 1 21 12 il 31 8 A 21 10 if 4 8 f 21 10 U 41 8 H 21 10 U 41 8 1 3 10 2 41 8 3 10 Importance of Grinding Eccentrically Relieved Cutter Teeth Radially. A leaflet calling attention to the need of grinding eccentrically relieved cutter teeth radially in order to secure satisfactory results was issued in 1907 by the Union Twist Drill Company, Athol, Mass., and from it is reproduced the accompanying illustration, Fig. 203, for the sake of conveying some elementary instruction in the art of grinding formed cutters. The cut shows, diagram- matically, how the teeth should be ground to secure the best results; it also illustrates improper grinding. The teeth A and B, of course, are ground correctly. The lines AC and BC, lying in the plane of the cutting face, are radial; that is, the faces of the teeth would pass directly through the center of the cutter if projected to 380 SMALL TOOLS the center. Tooth D, however, shows an entirely differ¬ ent condition, and one which, unfortunately, is not un¬ common in gear-cutting practice. The top of the tooth is ground back faster than the base, thus throwing the face of the cutter into the plane indicated by the line DE; consequently the shape of the tooth space cut is distorted, and a gear with badly shaped teeth must necessarily be produced by it. Tooth correctly ground, Fig. 203. Correctly and Incorrectly Ground Teeth of Eccentrically Relieved Cutter The expression “may be ground without changing the form” has evidently been taken too literally and without the necessary qualification that it is necessary to grind in a plane radial with the center of the cutter in order that the form shall not be changed. It is evident to any one who will give the matter a little thought that if a gear is cut with a gear cutter having teeth ground like D the resulting tooth space will be too wide at the top if the cutter is carried to MISCELLANEOUS MILLING CUTTERS 381 the correct depth. Moreover, such a gear cutter works badly, as the cutting faces of the teeth have a negative rake. The importance of correct grinding of all formed cutters cannot be too strongly emphasized. Unfortunately, formed cutters that can be ground without changing the form do not always have sufficient clearance to work well with all classes of work, and if such cutters are carelessly used there will be heating and rapid wearing away of the tops of the teeth. If hard pressed and ignorant, the tendency of the grinding operator, in order to hurry the sharpening of such cutters, is to incline the wheel away from the radial plane. On account of this defect in formed cutters, one large concern making small tools has found it profitable in the use of certain formed cutters to make them the same as an ordinary milling cutter, with the same rake and clearance as is the usual practice. When the cutters require sharpening, the teeth are ground on top, using a fixture which preserves the correct tooth shape. This concern has found the practice good, for the cutters are much more effective in action, and notwithstanding the increased cost of grinding, the increased efficiency more than makes up for the differ¬ ence. Of course in grinding eccentrically relieved cutters it is equally important that all teeth be ground to the same length as that they' be ground off radially. Forming Tools. In connection with formed cutters it will be appropriate to give some attention to forming tools. These are used either in the lathe or screw machine for duplicate work, or for forming and relieving formed milling cutters, which in turn are used to produce a great many pieces of exactly the same shape. When made for use in lathes or 382 SMALL TOOLS screw machines, they may be either flat or circular, but when used for forming and relieving milling cutters they are always made flat. For screw-machine work the circular form is the most common. Flat forming tools may either be made solid with the shank, like an ordinary lathe tool, or the tool may be merely a cutter formed to the desired shape and held in a holder. The tool is made solid with the shank only in the case of very simple forms. Where forms are more com¬ plicated, the tool should be made in a separate piece, and provision made for holding it securely in a tool holder or tool clamping device. MISCELLANEOUS MILLING CUTTERS 383 The flat forming tool is first laid out on the piece from which it is to be made, and machined to the desired form without giving any clearance to the tool. In order to obtain a tool with clearance, this first tool made, termed master tool, is used to produce a second tool. The clear¬ ance in this second tool is secured by the process shown in Fig. 204. The master tool is held at an angle in the tool- post of a shaper, and the blank from which the second forming tool is to be made is clamped to the shaper table, being held in a vise at the same angle of incline as the master Fig. 205. Circular Forming Tool with Clearance for Cutting Edge tool. When the master tool, No. 1 in Fig. 204, commences to form the tool No. 2, it is evident that the face of the latter will become an exact duplicate of No. 1, but being held in an angular position, a clearance corresponding to this inclination is produced. The common angle of clear¬ ance on forming tools is 15 degrees. Forming tools used for relieving formed milling cutters are frequently made with a clearance of 25 degrees. This is necessary in order to prevent the tool from interfering with the following tooth of the cutters when the one opposite the tool is being relieved. 384 SMALL TOOLS Circular Forming Tools. — Circular forming tools are used to a great extent in screw machines, as mentioned. They are easily made either by a forming tool, being formed in the same manner as a milling cutter, or by ordinary turning if the shape of the finished tool is not too com¬ plicated. In order to provide for a cutting edge the tool must be milled as shown in Fig. 205. If the piece to be formed should be a true duplicate of the forming tool it would be necessary to mill down the forming tool to a radial line only, as shown in Fig. 206. But the tool in such a case does not receive a proper amount of front rake or clear- Fig. 206. Forming Tool without Clearance ance to cut freely. For this reason the tool is milled down from one-quarter to three-eighths inch below the center, and in making the forming tool the dimensions must be so adjusted that when the tool is milled and ground as men¬ tioned, the desired form is reproduced in the pieces to be made. The allowance to be made must be determined in each case by calculation. In Fig. 207, BC represents the actual distance to be reproduced in the piece of work to be made. But it is evident that the difference between the radii OC and OB is less than BO. As the radii OC and OB determine the shape of the forming tool, these dimensions must stand in an exact relation to the actual distance BG to MISCELLANEOUS MILLING CUTTERS 385 be reproduced. This relationship is expressed by the formula BC = VOC 2 -OA 2 - VOB 2 - OA 2 . This relationship may be better expressed by a general formula. The distance A, Fig. 208, in a piece to be formed must equal the dis¬ tance a on the forming tool, but as this latter distance is measured in a plane a cer¬ tain distance b below the horizontal plane through the center of the forming tool, it is evident that the differ¬ ences of diameters in the tool and the piece to be formed are not the same. A general formula may, however, be deduced, by the use of elementary geometry, by means of which various diameters END VIEW OF PIECE FORMING TOOL TO BE FORMED Fig. 208 of the forming tool may be determined if the largest (or smallest) diameter of the tool, the amount that the cutting edge is below the center, and, of course, the diameters of the piece to be formed, are known. 386 SMALL TOOLS If R = the largest radius of the tool, a = difference in radii of steps, and b = amount cutting edge is below center, then, if r be the radius looked for, r = V- b s - ay + b\ If the smaller radius r is given and the sought, the formula takes the form R = V 7 (V r 2 — b 2 + a) 2 + b 2 . Suppose, for an example, form the piece in Fig. 209. Assume that the largest di¬ ameter of the tool is to be 3 inches, and that the cut¬ ting edge is to be one-quarter inch below the center of the tool. Then the next diam¬ eter below 3 inches is found from the formulas given by inserting the given values: R = 1| inches, b = J inch, ference between 4 and Then larger radius R that a tool is to be made to and a = l inch (half the dif- 3| inches; see Fig. 209). r = V'(V (1|)’ - (i)» - i)» + (})’ = vVH - i)*+ * = = 1.254 inches. 4 While the formula looks complicated, by means of a table of squares the calculations are easily simplified and can be carried out in three or four minutes. The value r being 1.254 inches, the diameter to make the smaller step of the forming tool will be 2.508 inches, instead of 2£ MISCELLANEOUS MILLING CUTTERS 387 inches exact, as would have been the case if the cutting edge had been on the center line. Sometimes forming tools are made in sections, as shown in Fig. 210, so that all diameters, sides and angles can be easily ground after hardening. This design is of value especially when forming tools are made from high-speed steel, as the finished surfaces and the edges are likely to be impaired by the high heat necessary when hardening high-speed steel. Fig. 210. Forming Tool Made in Sections Making Concave and Convex Forming Tools in the Milling Machine. — A method for making the concave forming tools used for forming and relieving convex cutters in a milling machine was described by Mr. J. J. Lynskey in Machinery, December, 1903. Referring to Fig. 211, B represents the tool which is held in the holder A at an angle of 75 degrees with the table of the milling machine, this giving a 15-degree angle of clearance to the finished tool. When the tool blank is placed in the holder the top is milled off parallel with the table of the machine. A half circle of the desired radius is then drawn on the back of the tool and a semicircular groove milled nearly Fig. 211. Making a Concave Forming Tool in the Milling Machine MISCELLANEOUS MILLING CUTTERS 389 to the line scribed. For finishing the tool a plug C is made, the end of which is hardened and ground. This plug is held in a special holder D in the spindle of the milling machine, and set so that the axis of the plug is perpen¬ dicular to the face of the tool to be finished. The spindle is then firmly locked, and the table of the machine moved forward and backward by hand until the tool has got the required shape. By using the concave tool as a planing tool as shown at G a convex tool can be formed, but both tools must be held at an angle of 75 degrees to the milling-machine table. Of course, this example is given only to suggest what can be done in a milling machine if a shaper is not at hand. The latter machine is the one used whenever possible. T-Slot Cutters. The T-slot cutter has gradually and successfully out¬ classed the old-style method of planing T slots in milling- machine tables and other machine tool parts where T slots are regularly used. The old method was far more expensive, and the quality of the work obtained was in no way superior. T-slot cutters, therefore, at the present time constitute an important tool in the machine shop, particularly where machine tools are manufactured. The general appearance of the cutter is shown in Fig. 212. The cutting portion, A, is provided with teeth on its face as well as on both sides. A long neck, B, per¬ mitting the cutter to advance in the narrow portion of the T slot, which is already milled with a side milling cutter before the T-slot cutter is presented, combines the cut¬ ting portion with the shank, which latter as a rule is either a Brown and Sharpe or a Morse taper shank. In making the cutter, after having been turned all over, 390 SMALL TOOLS the teeth on the face are first cut. Then the teeth are cut on the end of the cutter, and finally on the back side at the neck. In order to provide a cutter that will cut more easily than would be the case if all the teeth were full, every other tooth is cut away at the ends as indicated in Fig. 213, but it should be observed that where a tooth is cut off at the end face it is left full at the back face and vice versa. Some makers prefer to leave one tooth full at both ends to facilitate measuring the thickness of the cutter. In order to permit the grinding of T-slot cutters with¬ out making the slot cut by them too small, they are origi- Fig. 213. Teeth of T-slot Cutter Cut Away at Opposite Ends nally made one-thirty-second inch larger in diameter and one-sixty-fourth inch greater in thickness than the nominal size. It is advisable to harden mills of this description the entire length of the necked portion marked B, Fig. 212, especially if the neck is of small diameter. Draw the MISCELLANEOUS MILLING CUTTERS 391 neck to a blue color when tempering, and the cutting portion to a straw color. The teeth of T-slot cutters should be coarse and of a form that insures the greatest strength possible, allowing of course sufficient space between the teeth to accommodate chips. TABLE C. DIMENSIONS OF T-SLOTS. A B c D A B c D i i A A f i A 1 4 A f A f ! 1A is 1 t if A A i if if i A A ft if A A l 1J if i A A A TABLE Cl. SIZE OF SHANKS OF T-SLOT CUTTERS. Nominal Actual Nominal No. of No. of Size of Size of Thickness Thickness Morse B. and S. Cutter. Cutter. of Cutter. of Cutter. Taper Taper Shank. Shank. h n A u 1 4, 5 f H A tt ff 1 5, 7 if ff A 2 5, 7 if 2 7 A ff 2 7, 9 if If A 1 9 Tf 2 7, 9 i A 1A M 2 7 6 4 3 9 1A iM 1 7 ff 3 9 if iff if 4 5 6? 4 9 G 1 29 1 32 if 5 3 ¥¥ 4 9 392 SMALL TOOLS The dimensions of standard T slots for which these cut¬ ters are made are given in Table C. As mentioned, the cutter is originally made one-thirty-second inch larger in diameter and one-sixty-fourth inch greater in thickness than these dimensions. The numbers of Morse and Brown and Sharpe taper shanks with which these cutters are com¬ monly provided are given in Table Cl. Metal Slitting Cutters. Thin cutters intended for cutting off or slitting pur¬ poses are termed metal slitting cutters. The sides of these cutters are ground to run true, and made slightly thicker at the outside edge than at the hole or center, in order to provide for proper clearance and prevent binding in the slot cut. For cutting steel the number of teeth used in these cutters is as follows: Diameter of Cutter. Number of Teeth. Diameter of Cutter. Number of Teeth. 24 30 51 56 3 36 6 60 31 40 61 64 4 44 7 68 4* 48 74 70 5 52 8 72 For brass and very deep slots the pitch of the teeth should be coarser in the proportion of about 2 to 3; that is, if a 4J-inch cutter for steel has 48 teeth, one for brass should have only two-thirds this number, or 32. In case very heavy work is required of a metal slitting cutter the teeth are eccentrically relieved; this permits the teeth to be wider and stronger. For light slotting, like screw slotting, etc., a cheaper MISCELLANEOUS MILLING CUTTERS 393 grade of cutters with very fine teeth, and not ground on the sides, is used. These are commonly termed screw slotting cutters. The number of teeth in these for the most common diameters is as follows: Diameter of Cutter. Number of Teeth. i! 52 2 56 21 60 21 64 2f 68 3 72 Inserted-blade Milling Cutters. Large milling cutters, say from 6 to 7 inches in diameter and upward, are usually made with inserted teeth. The advantages gained nre decreased cost, because the cutter body may be made of either cast iron or machine steel, and the elimination of loss due to the liability of cracking in hardening. The cutter body is generally made from cast iron and the blades from ordinary tool steel. Whether high-speed steel blades are actually greatly superior to carbon steel blades for these cutters some manufacturers doubt. Many users of milling cutters, however, use high¬ speed steel cutters, which then should be inserted in machine steel bodies. The latter material is also used for the body of all inserted-blade cutters smaller than 6 inches in diameter, or where the body is less than 1| inches thick. The blades are inserted in slots milled in the body either parallel with the axis of the cutter or at an angle thereto. When the cutter is to be used as a plain milling cutter the blades are usually set at an angle. When the cutter is 394 SMALL TOOLS used for side or straddle milling or for end milling the blades are not set at an angle with the axis. One of the most common methods for holding the blades in the body is the one shown in Fig. 214. This method combines simplicity and cheapness with strength and durability. This method is employed by the Pratt and Whitney Company. Whether set parallel with or at an angle to the axis of the cutter, the method of holding the SECTION B-B Fig. 214. Method of Securing Blades in Body of Axial Cutter blades is the same. As seen from the cut, the blades are set into rectangular slots in the body and held in position by means of taper pins which wedge the metal of the body firmly against the sides of the blades. There is only one taper pin for every other blade, the pin spreading the metal equally on each side of a narrow slot A located halfway between the slots for the blades. Attention must be called to the fact that the distances between the teeth must be such as to insure on the one hand perfect MISCELLANEOUS MILLING CUTTERS 395 holding qualities (that is, the metal between the slot A and the slots for the blades must not be so heavy as to prevent good springing action when forced sideways by the taper pin), and on the other hand a strong and durable body. In making these cutters the slots for the blades are first milled. The taper-pin hole between every other pair of teeth is then drilled, and reamed to receive the taper pin. After reaming the holes the narrow slots A are cut with a thin metal slitting cutter. When the blades are in position Fig. 215. Section of Inserted Blade End Milling Cutter the taper pins are driven into the taper holes, closing up the stock, as mentioned, and holding the cutters securely. When removing the blades, the taper pins are driven out, and the stock springing back into its normal position leaves the cutter free. The blades are, of course, turned and ground in position in the body. They are backed off so that the backed-off surface makes an angle of from 75 to 80 degrees with the front of the blade. The angle which the slots into which the blades are inserted should make with the center line when not milled parallel with the axis should be between 12 and 15 degrees. 396 SMALL TOOLS In cutters for end milling, the blades should project a considerable amount on the back side, as shown in Fig. 215, in order to allow for adjustment when the cutting faces of the blades by frequent grinding have been worn down near to the body of the cutter. Simple Method of Holding Blades. — One very simple method of fastening the inserted blades to the body is shown in Fig. 216. This form has been long in use in the Armstrong Manufacturing Company’s shops. While not the very best construction, for narrow inserted-blade cutters it Fig. 216. Simple Method of Securing Blades in Inserted Blade Cutter will prove satisfactory, particularly because of being a com¬ paratively inexpensive method of fastening. The body is slotted as usual, the blades C are provided with a shoulder, and against this shoulder bears the head of screw B. In order to prevent side slip, the inner end of the blade is notched so as to engage with the body as shown in the sectional view, Fig. 216. This class of cutter does not recommend itself for end milling, because the blades are hardly held securely enough for heavy strains from the sides or ends. Fig. 217 shows an English method of securing the teeth of inserted-blade milling cutters to the body. This arrange- MISCELLANEOUS MILLING CUTTERS 397 ment is the joint patent of H. S. Moorwood of Onslow House, Brocco Bank, Sheffield, and J. M. Moorwood of Millhouses Lane, Millhouses, Sheffield, England. The body A of the cutter is provided with slots B to receive the cutter blades as usual, but the lower ends of the cutter blades, as well as the portions of the body between the blades, are grooved to receive the annular projection D of two disks E which are screwed tightly to the body, thus holding the blades in place. The groove in the blades as well as the annular projection on the side plates is slightly tapered on the inside, so that the inserted blades are drawn Fig. 217. English Method of Securing Blades in Milling Cutter inward and held firmly against the bottom of the slots for the blades in the body when the bolts are tightened. While, without modification, this method may have its difficulties, and may be rather expensive, the idea involved is commendable, and may serve to suggest something of better practical application. Inserted-Tooth Formed Milling Cutter. Fig. 218 shows an inserted-tooth milling cutter, designed to manufacture the brake shoes shown at A, in which it is necessary to keep both the form and the radius of the cut to gauge. This cutter was shown in Machinery, January, 398 SMALL TOOLS 1908, by Mr. S. A. McDonald. The principle of the inserted teeth is the same as that of the circular forming tools used on screw machines, the teeth being sharpened radially. The taper studs are used to secure the teeth in place by forcing the slots open and binding the body of the cutter on the teeth. The cutter-holding body is grooved in the center to reduce the body of metal to be sprung out in order Fig. 218. Inserted-Tooth Formed Milling Cutter to bind on the outer edges of the teeth or cutters. As the teeth become dull they can be ground while in place a few times before being loosened and again set radially. The advantage of this form cutter is that the teeth can be ground to shape after being hardened (because they are circular), which is impossible with the ordinary form cutter, but often very necessary when the pieces milled have to be correct within small limits. This permits the use of Novo or other high-speed steel, which ordinarily cannot be used MISCELLANEOUS MILLING CUTTERS 399 for form cutters, as the outside is burned in hardening. Broken teeth can be easily replaced. No backing-off machine, or fixture, is needed for making the formed teeth, which will appeal to small shops. The cost of material is considerably reduced as compared with a solid form cutter. Within its limits different kinds of teeth can be used in the same body, but this is only recommended when the removed cutters are of no further use. One weak point in this design of cutter seems to be the' cutting of the central groove B, which naturally permits the outer edges of the cutter body to bend inward when the nut on the tapered pins is tightened for binding the blades. Another objection is the projection of the nuts outside of the cutter body, as it is never good practice to have pro¬ jections of this kind on rotating bodies if it can be avoided. These objections, however, are mere details, and can easily be overcome. The principle of the cutter itself is very commendable, and may also be of value as suggestive of similar adaptations for a multiplicity of work. Dimensions of Inserted-blade Milling Cutters. Definite dimensions for the various quantities in inserted- blade milling cutters are difficult to give, as opinions differ considerably. Each type, of course, would require a different set of dimensions. Table CII gives dimensions for guidance in laying out cutters of the type shown in Fig. 214. Special Form of Milling Cutters. The Hess Machine Company, Philadelphia, Pa., in 1903 brought out a new form of milling cutter working on a different principle from the ordinary cutter. 400 SMALL TOOLS TABLE CII. DIMENSIONS OF INSERTED-BLADE MILLING CUTTERS. Diameter of cutter. Number of blades. Thickness of blades. Width of blades. Size of standard taper pin.. . Diameter of cutter body.... A B C D E F 3 8 } i 4 2* 4 10 1» 4 3} 5 10 A 1 5 4f 6 12 A H 5 5f 7 14 A H 5 6| Diameter of cutter. A 8 9 10 11 12 Number of blades. B 16 16 18 20 20 Thickness of blades. C A I I I A Width of blades. D H li 1} 1} If Size of standard taper pin .. E 5 6 6 6 6 Diameter of cutter body.... F 7f 8} 9} 10} 11} The action of the ordinary milling cutter produces chips that are comparatively wide and thin. Each successive tooth removes a chip having a length equal to the full width of the cut. The feed per revolution of the cutter is MISCELLANEOUS MILLING CUTTERS 401 divided into as many chips as there are teeth in the cutter. While it is true that if the teeth are nicked the continuity of the chip is broken, still the action is substantially the same. Cutting the teeth on a spiral, although it makes the turning moment uniform and preserves a constant thrust in one direction, which means a more even cut, does not change the principle of the cutting action. In order to avoid the consequent heavy thrust at right angles to the work the Hess milling cutter removes the metal in a series of narrow chips, the cut of each tooth being narrow and deep, similar to that of a planer roughing Fig. 220. Hess Machine Company’s New Type Milling Cutter tool. The cutter is not mounted on a keyed mandrel, but instead the outer end of the cutter body is formed into a journal, supported in an outboard bearing, and the other end carries a plug fitting into the spindle. The end of the spindle of the milling machine is provided with a flange, and a corresponding flange is provided on the cutter oody, these flanges being united by bolts. Fig. 220 shows a cutter made on this principle. The teeth are made of high-speed steel, working successfully at a cutting speed of 60 feet per minute. They are cast or fused into the cast-iron body by being placed in the mold and the metal poured around them. 402 SMALL TOOLS The teeth are arranged in a double right-hand helix having a lead of 3 inches. Since there are two rows or threads of teeth there are only two teeth in the same trans¬ verse plane, and each tooth takes a cut whose thickness in the direction of feed is one-half the feed per revolution of the cutter. Since the paths of adjacent teeth overlap it gives each following tooth a finishing action so far as its overlapping Fig. 221. Teeth of Cutter in Fig. 220 shown in half Actual Size portion is concerned. The thickness of the chip taken by the overlapping part of a tooth is thin as compared with the principal chip. The cutting action is very similar to that of a gang planer tool, each tooth having more of a side-cutting than an end-cutting action. Consequently the thrust at right angles to the work is proportionately reduced. The teeth reduced to one-half actual size are shown in Fig. 221. Here are also shown the angle of relief and clearance. CHAPTER X. REAMERS. Introductory. Reamers, in the narrowest sense of the word, include only tools intended for producing a hole that is smooth and true to size. In a wider sense, however, the word is applied to any solid circular tool with a number of cutting edges, used for enlarging cored or drilled holes, little or no account being taken of whether the resulting hole is strictly true to size or not. With reference to the manner in which reamers are made, we may distinguish be¬ tween solid and inserted-blade reamers. The latter are usually adjustable for size. With reference to the pur¬ pose of reamers and the manner in which they are used, we distinguish mainly between hand reamers, chucking reamers, shell reamers, and taper reamers. The latter class of reamers is mostly, perhaps, used by hand, the same as the hand reamer, but the hand reamer is considered to mean only a straight reamer, and the taper reamer forms a class by itself. On the boundary between reamers and drills is the grooved chucking reamer, which is used for roughing cored holes, and is fluted with spiral grooves like a twist drill. Center reamers constitute a special class of reamers, which are used for reaming the centers in pieces to be held between the centers in the lathe. Hand Reamers. The ordinary hand reamer, provided with guide, is shown in Fig. 222. As seen from the cut, it consists of a 403 404 SMALL TOOLS cutting portion, a shank, and a square by which it is turned when in use. As is also shown, the end portion of the shank on which the square is formed is turned down below the diameter of the shank proper. The purpose of this is to prevent any burrs that may be raised on the edges of the square by the wrench by which the reamer is turned from projecting outside of the diameter of the shank, thus either preventing the reamer from being drawn clear through the hole reamed or causing scratches in the hole if the reamer be pulled through. Between the cutting portion and the shank there is a short neck, the purpose of which is, primarily, to provide for clearance for the grinding wheel when grinding the cutting edges as well as Tig. 222. Regular Hand Reamer the shank of the reamer, and also to permit the cutter by which the flutes are cut to clear the shank so as to give a more finished appearance to the tool. Requirements Placed on a Hand Reamer .—Hand reamers are probably among the most difficult and particular tools to make and manufacture. In many reamers manu¬ factured by firms considered to be leaders in the making of small tools no regard or attention seems to have been given to some of the most essential points in the making of these tools. As of course everybody knows, it is abso¬ lutely necessary when making a good hand reamer to take into consideration that the reamer is expected to produce (1) a smooth hole, (2) a straight hole, and (3) a round hole. REAMERS 405 If we now consider first what means are generally used for making reamers that will produce a smooth hole, we will find that three ways have been tried with more or less success. The first and earliest method used to prevent chattering was making an odd number of flutes in the reamers, but this has been almost entirely discarded on account of the difficulty in measuring the diameter of such reamers, it being possible to gauge this diameter only with ring gauges. At present some manufacturers, in order to overcome the vibrations which mar the smoothness of the hole, make their reamers with spiral flutes. This, although partly overcoming the difficulty referred to, has several serious disadvantages. In the first place, such a reamer is more difficult and more expensive to flute, not to mention the difficulty of giving such a reamer the proper relief. In the second place, a reamer fluted in such a way has the disadvantage of either working forward or resist¬ ing, depending on whether right-hand or left-hand spiral flutes have been given to the reamer in question. It may be noted that it is preferable to make regular right-hand reamers of this description with left-hand spiral flutes, which will prevent the reamer from working forward. Some one might think that the working forward of the reamer (to a certain extent depending upon the amount of spiral given to the flutes) would rather be an advan¬ tage, and so it would provided that the forward motion could be on the one hand perfectly uniform and on the other hand small enough to advance the reamer a very limited distance for each revolution. This result, however, can be obtained in a very much simpler and cheaper way by using straight flutes and threading the reamer on the point for a short distance. The advance of the reamer in this case will of course be governed by the pitch of the thread. The outside diameter of the threaded portion must obviously 406 SMALL TOOLS be slightly smaller than the diameter of the reamer itself. Returning to our original consideration in regard to the means employed to prevent vibration, the third way used is to “break up the flutes,” which means that the cutting edges are not equally spaced, although the reamer then is given an even number of flutes. This ununiformity in spacing need not be greater than to permit a gauging of the diameter of the reamer over two opposite cutting edges that will be correct for all practical purposes. The “break¬ ing up of the flutes” is the simplest and most effective way to obtain the result wanted, viz., a smooth hole. Leading manufacturers are commencing more and more to manu¬ facture their reamers in this manner. The second consideration which was mentioned above as necessary in a good reamer is its capability of producing a straight hole. This is the principal point referred to in the beginning of this chapter which seems to have been wholly disregarded by manufacturers of reamers. No reamer will produce a straight hole unless it is properly started, and no reamer will start properly unless it is properly guided. It is obvious that even with the most extreme care, and handled by the most experienced man, a reamer without a guide will make the hole slightly tapered, and too large at the end where the reamer first enters the work. The way hand reamers are generally made for the market is to simply taper the point for a certain distance up, leaving nothing to steady or guide whatsoever. This is not right. Instead a fluted cylindrical portion of the end of the reamer should be left without relief, and this part should be as much less in diameter than the reamer itself as is practical for various metals to be cut with the reamer. As this amount is very small and is left entirely REAMERS 407 to the judgment of the manufacturer, the practice of making reamers with guides slightly smaller than the diameter of the reamer would prevent the user from mis¬ using and abusing the tool, as he cannot use it to remove a greater amount of metal than the reamer is intended for, because the guide will not enter a hole that is not roughed out sufficiently large before hand reaming. When using a reamer with a tapered point it is usually possible to enter and start the reamer in holes so much smaller than the finished size as to seriously injure and even spoil it by trying to make it perform a duty for which it was not intended, this being possible because the taper is made so large by most manufacturers as to permit it. The third consideration, previously referred to, and essential in a good reamer, is its capability of producing a round hole. Most of the reasons set forth in treating the possibilities of getting'a smooth and a straight hole apply here also, and it may well be repeated that unevenly spaced (broken up) cutting edges and a guide nicely fitting the hole to be reamed are the most essential requisites for obtaining the desired results. Relief. It will also be necessary to remark that giving too much or too little relief to a reamer will tend to produce unsatis¬ factory results. Too much relief invariably causes a reamer to chatter. Too small relief, again, will wear the reamer more, as the shavings get in between the cutting edges and the work to be reamed and slowly grind away the land; besides, there is a tendency to bind the reamer in the hole, and as a consequence to injure the hole as well as the reamer, and cause the expenditure of more exertion in performing the reaming operation. 408 SMALL TOOLS In this connection it may be mentioned that the flat relief, although mostly used, is not the most desirable nor the ideal one, because the cutting edge is not properly supported. The best results are obtained by a relief as shown in Fig. 223. The difference between this relief and the flat is very obvious from the cut, where the latter relief is shown in dotted lines. This special relief, usually termed the eccentric relief, is used by only two prominent tool manufacturers, but it is to be strongly recommended because it adds greatly to the . reamer’s Fig. 223. Comparison between Eccentric and Flat Relief capability of producing a smooth hole. The relief is pro¬ duced by placing the reamer in a grinding machine, as usual, but not on centers in line with the spindle but on auxiliary centers, provided with adjustment sideways, so as to enable them to be set at different positions for differ¬ ent relief wanted on different sizes and kinds of reamers. The reamer is thus held eccentrically. A rocking motion is then imparted to the spindles holding the auxiliary centers, and in this manner the grinding wheel, traveling back and forth along the reamer, produces an eccentric relief. This eccentric relief, however, is not in favor with all REAMERS 409 users of reamers. The eccentrically relieved reamer is purely a finishing reamer, and cannot with advantage be used to remove any considerable amount of metal, because it has practically a negative rake. When hand reamers are used merely for the purpose of removing stock, or in other words, simply for enlarging holes, the flat relief will undoubtedly prove to be superior to the eccentric. The primary use of straight hand reamers, however, is for producing holes true to size and smoothly finished, remov¬ ing meanwhile but a small amount of stock. For this purpose nothing excels the eccentric relief. That there is a distinct difference between the relief required, accord¬ ing to the use to be made of the reamer, is best proved by the fact that, while some manufacturers of tools always relieve their reamers eccentrically, intending them to be used as finishing reamers, some of their customers, after receiving the reamers, place them in a grinding machine and replace the eccentric relief with a flat one, because they find this relief better for their purpose, viz., simply enlarging holes, irrespective of the requirements of accuracy and smoothness. Reamers with Helical Flutes. Although the advantages of helical or, as they are com¬ monly called, spiral cutting edges are somewhat doubtful for straight reamers for ordinary use, they are recom¬ mended for work where the hole reamed is pierced crosswise by openings. A right-handed reamer should have left-hand spiral flutes, in order to prevent the tool from drawing into the work. The angle of spiral should be such that the cutting edges will make an angle of 15 degrees with a plane passed through the axis of the reamer. The number of flutes may be the same as if the 410 SMALL TOOLS reamer were provided with straight cutting edges, and the same kind of fluting cutters are employed. Threaded-end Hand Reamers. As has already been mentioned, hand reamers are some¬ times provided with a thread at the extreme point in order to give them a uniform feed when performing the reaming operation. The diameter on the top of this thread at the point of the reamer is considerably smaller than the reamer itself, and the thread tapers upward until it reaches a dimension of from 0.003 to 0.008 inch, according to size, below the size of the reamer; at this point the thread stops, and a short neck, about one-sixteenth inch wide, separates the threaded portion from the actual reamer, which is provided with a short taper from three-sixteenths to seven- sixteenths inch long, according to size, up to where the standard diameter is reached. In fact, the reamer has the appearance of the regular reamer in Fig. 222, excepting that the guide is threaded and tapered. The length of the threaded portion and the number of threads per inch with which to provide the point are given below. Size of Reamer. Length of Threaded Portion. Number of Threads per Inch. From ^ to A inch. 1 32 From 52 to ^ inch. A 28 From to | inch. i 24 From §f upward. A 18 The kind of thread employed is the sharp V thread, as this thread gets a better grip on the metal, and thus feeds the reamer in a more certain manner. REAMERS 411 The diameter measured over the top of the thread at the end of the point of the reamer should be as follows. Size of Reamer. Diameter of Thread at Point of Reamer. From J to \ inch. Standard size—0.006 inch From to 1 inch. Standard size—0.008 inch From to 1$ inches. Standard size—0.010 inch From 1$| to 2 inches. Standard size—0.012 inch From 2 A to inches. Standard size—0.015 inch From 2^| to 3 inches. Standard size—0.020 inch Breaking up of the Flutes. — As has been previously mentioned, the best way to obtain a good hand reamer is to have the cutting edges irregularly spaced. This dif¬ ference in spacing may in fact be made very slight. The manner in which it is usually done is to move the index head, in which the reamer is fixed, a certain amount more or less than would be the case if the spacing were regular. In Table CIII a chart is presented which will serve as a guide in fluting reamers with irregular spacing. This chart gives the amount that the index head should be moved more or less than would be the case for even spacing. The figures designate the number of holes to move in a certain index plate used in each special case. It is, of course, understood that this table is given only as an example of how tables of this kind may be worked out, as there evidently is an unlimited number of variations. Dimensions. — In Table CIV the principal dimensions for hand reamers are given. These dimensions are figured from the formulas which are given below. No figures are given in the table for the diameter of the shank, as on any size reamer the general rule to make the shank very slightly below (0.001 to 0.002 inch) the diameter of the reamer may be adopted. The part of the shank which is squared should REAMERS 413 be turned enough smaller in diameter than the shank itself so that when applying a wrench no burr may result which eventually would interfere with the reamed hole if the reamer were passed clear through. Figures for the diameter of the guide will not be found in the table, as here no definite rule can be given. For different metals it is obvious that different amounts should be left for the reamer to remove. As a guidance for all- around work it may be said that the guide should be made from 0.005 to 0.010 inch smaller than the standard size of the reamer for diameters up to 1 inch, and from 0.010 to 0.015 inch smaller for diameters from 1 to 3 inches. At the upper end of the guide there is a tapered portion (shown F=Size p of Square -;-II- < < - B- > Fig. 224 exaggerated in Fig. 224) extending from about three- eighths to five-eighths inch for the smaller and from three-quarters to l j inches for the larger sizes mentioned. In all the formulas the diameter of the reamer is con¬ sidered as the fundamental factor. In the formulas A = the diameter of the reamer, B = the total length, G = the length of the flute, D = the length of the shank, E = the length of the square, F = the size of the square, G = the length of the guide. TABLE CIV. PROPORTIONS OF HAND REAMERS. (See Fig. 224.) Diameter. Total Length. Length of Flute. Length of Shank. Length of Squared Part. Size of Square. Length of Guide. A B C D E F G A 2 A 1 1* A A A t 2 f H If 1 A A A 3A If Iff A A 1 1 3f If If A A A A 3ff If 2 A ti If I I 4f 21 21 t A ft A 4ft 2 f 2 A ft tl A f 51 2 f 2 f A t f A 5ft 2 f 2ft ft If A t 61 3f 3 f ft M ft 6A 3f 3* If ii t 1 7 3f 3! A A A ft 7* 3f 3A 1 9 31? 3 9 6? f i 7f 41 31 I It 25 33 ft 8A 4f 3ft 2 1 33 If ft 1 8f 4f 41 A I 1 Its 9A 4f 4A ft tl 29 33 H 9f 4 ft 4* 1 2 7 33 A 1* 9 A 5* 4f M tl If H 9f 5* 4A ft A l ift 9ff 5* 4f 2 7 33 6 3 3? i* i! 10f 5f 4f f i A i* i A io A 51 4ft 29 32 i* i* if 101 5f 4f ft if if 1* ion 5f 4ft If iff i* if 101 5ft 5A l i* i A iff 11A 5ft 51 i* m i* if nf 6A 5* i A i* H iff ii A 6* 51 i* At i* if nf 61 5f if in i A iff nff 6t 5* i* 12 9 * 6 * iff 2 12 61 5f i A if if 2 A 12A 6f 5 A i* iff iff 2 1 12f 6* 5ft if iff l A 2 A 12A 6ft 51 i* iff iff 2 i 12f 6ft 5ft i A iff if 2 A 12ft 7A 5f iff iff iff 2 I 131 71 6 if iff l A 2 A 13* 71 6A iff m iff 2 i 131 7f 61 i A H if 2 A 13U 71 6* in if! iff 2 f 13f 7A 6* a iff iff 2fi 14A 7* 61 in 2 A 1 23 1 33 2 f 141 7ft 6* i A 2 A it 2ft 14* 7ft 6f iff 2* 12 5 *33 2f 14f 8 6f if 2 A 1ft 2ff 14f| 81 6 ft iff 2ft 12 7 1 33 3 15 8f 61 iff 21 if REAMERS 415 For reamers from one-sixteenth to 1 inch diameter the following formulas are used: P 7(4A + 1) B= 4 : ’ G = iA +f, D= 3 A + 1 E = - +—, 2 16 F- 3A F ~1 ’ _ 6 A + 1 8 For reamers from 1inches to 3 inches the following formulas are used: B = 3 A + 6, „ 7 A + 12 c =—~' ^ 5A + 12 D = ~~ 4 ? E = - + —, 2 16 F 3A f= T’ 4 A + 3 8 In Table CIV some dimensions are given in even six¬ teenths when the formulas give uneven values. Number of Flutes. — The following table gives the number of flutes with which hand reamers should be provided. It will be noticed that even the smallest sizes are provided with six flutes. It is not considered good practice to make hand reamers with a smaller number of flutes if good results are expected from the use of the tool. Size of Reamer. Number of Flutes. From | to £ inch... 6 From 3^ to 1| inches. 8 From 1^ to If inches. 10 From 1|| to 2f inches. 12 From to 2f inches. 14 From 2§i? to 3 inches. 16 416 SMALL TOOLS From this table it will be seen that the pitch of the teeth, or the distance from cutting edge to cutting edge around the circumference of the reamer, increases from about one-eighth inch for a one-quarter-inch reamer to about nine-sixteenths for a three-inch reamer. The pitch of the cutting edges for a one-inch reamer is about three- eighths inch and for a two-inch reamer slightly more than one-half inch. Fluting Cutters for Reamers. — Often the same kind of fluting cutters as are used for hand taps are employed for reamers also. The reamer, however, does not remove the same amount of metal as does the tap, and conse¬ quently there is no need for the same amount of chip room. The radius in the bottom of the flute is made smaller, because the flute, being made shallower, does not take away so much of the strength of the reamer, and consequently the reenforcement in the form of a liberal round in the bottom of the flute is not necessary. Besides, the flutes on very small reamers are so shallow that a comparatively large radius on the fluting cutter would give a too great negative front rake to the teeth. Figs. 225 and 226 give the usual forms of reamer fluting cutters. Fig. 225 shows a cutter of the same kind as used for taps, but with a smaller radius, D. This class of cutter is used for smaller size reamers, say up to If inches diameter inclusive, while the cutter Fig. 226 is used for larger sizes. The inclusive angle between the cutting faces of the cutters is 85 degrees in both cases, the same as for tap fluting cutters, but while the cutter Fig. 225 has one face making 55 and the other 30 degrees with a line perpendicular to the axis of the cutter, in the cutter Fig. 226 these angles are 15 and 70 degrees respectively. In Table CV are given the dimensions commonly REAMERS 417 employed for these cutters and the corresponding sizes of reamers for which they are used. TABLE CV. FLUTING CUTTERS FOR REAMERS. Diameter of Reamer. Diameter of Fluting Cutter. Thickness of Fluting Cutter. Diameter of Hole in Cutter. Radius between Cutting Faces of Cutter. A B C D i 3 3 ( sharp corner, ^ 4 T6 i ( no radius. A If A f j sharp corner, 1 no radius. 1 If A f A 1 2 1 f A 1 2 A f A % 2 I f A f 2 A f A l 2f 1 1 A n 2f A 1 A H 21 t 1 A if 21 f 1 A 2 21 f 1 A 2f 21 f 1 A 21 21 1 1 A A 2f 21 1 1 3 21 l 1 A 418 SMALL TOOLS Setting the Cutter for Fluting. — When setting the cutter for fluting hand reamers, it should be set so that the tooth gets a slight nega¬ tive rake, that is, the cutter should be set “ ahead ” of the center as shown in Fig. 227. The amount to set the cutter ahead should be so selected that the angle included between the front face of the tooth and the tangent to the circumfer¬ ence of the reamer at the point representing the cut¬ ting edge will be 95 degrees. (See Fig. 227.) A reamer will cut more smoothly if the cutting edge of the tooth has a negative rake than it will if the front face of running to the center. Fig. 227. Setting the Cutter for Fluting Reamers the tooth is radial, that is, TABLE CVI. AMOUNT TO SET CUTTER AHEAD OF RADIAL LINE (see Fig. 227) TO OBTAIN NEGATIVE FRONT RAKE. Size of Reamer. a Size of Reamer. a 1 0.011 n 0.066 t 0.016 n 0.076 0.022 2 0.087 t 0.027 2} 0.098 i 0.033 2} 0.109 l 0.038 2f 0.120 i 0.044 3 0.131 0.055 REAMERS 419 In Table CVI the dimension a, Fig. 227, or the amount to set the fluting cutter ahead of the radial line, is given. The figures in this table give the angle ABC approxi¬ mately 95 degrees as mentioned. There may be objections raised to setting the fluting cutter as much as one-eighth inch ahead of the radial line for three-inch reamers, but inasmuch as the angle of nega¬ tive rake remains the same as for smaller sizes, there is no good reason why this amount should be made any smaller than given in the table. The depth of the flute should be such that the width of the land of the tooth is about one-fifth of the average distance from the face of one tooth to that of the next. Should it not be as deep, there will not be room in the grooves to hold the chips; should it be deeper, the teeth will not be sufficiently strong, and will spring out into the stock being cut, producing a very unsatisfactory hole which will in all probability be larger than the reamer. The width of the land will, of course, vary somewhat, due to the breaking up of the flutes, which makes some of the lands wider than the others. Special Reamer Fluting Cutter. — The difficulties encoun¬ tered in milling the flutes on unequal distances, or break¬ ing up the flutes, as it is commonly termed, are, as mentioned, that if all the grooves are milled to the same depth the remaining land will evidently be wider in the case where the distance from cutting edge to cutting edge is larger than it will be in the case where this distance is smaller. To overcome this it would, of course, be possible to mill the flutes deeper between the cutting edges, which are further apart to insure that the width of the land would be equal in all cases. That this is impracticable when fluting reamers in large quantities is easily apprehended, as it would necessitate raising or lowering the milling- 420 SMALL TOOLS machine table for each flute being cut. In Fig. 228 is shown a method employed by the large machine-tool firm of Ludwig Loewe & Co., Berlin, Germany. The principle of this method is clearly shown in the cut. A formed cutter, eccentrically relieved, is employed, which instead of forming only the flutes, forms the actual land of the reamer, thus insuring that every land will be equally wide with the others. The depth of the flute is deter¬ mined by the depth of the portion of the cutter in front of the cutting edge of the reamer, and it is easily seen that all the flutes will be equally deep. Fig. 228. Special Formed Ileamer Fluting Cutter That this method will be more expensive than the one commonly employed, in which the lands are permitted to become wide or narrow according to the amount the flutes are broken up, is evident, but it cannot be disputed that the general appearance of the reamer will be greatly improved. The greater expense in making reamers in this manner will depend on two factors. In the first place, the eccentrically relieved cutter will cost more to produce than the ordinary fluting cutter. In the second place, the cutting speed cannot be as high with a cutter of this descrip¬ tion as it can be with an ordinary milling cutter. On the other hand, it is possible not only to gain the advan- REAMERS 421 tages mentioned above in regard to width of land and depth of flute, but incidentally there is also gained the possibility of giving to the flute a more accurate form to answer the requirements of strength as well as chip room, which are often by necessity overlooked on account of the straight sides forming the flutes which must be adopted when using the ordinary straight-sided fluting cutter, with milling cutter teeth of the common shape. While it cannot be expected that this method will be used to any great extent on account of its drawbacks from a commercial point of view, it is ingenious and well worth attention. In Fig. 228 the fluting of a shell reamer is shown, but what has been said applies, of course, equally as well to hand reamers. Precautions in Hardening Reamers. If the reamers to be hardened are larger than three- quarters inch in diameter they should be held over the fire immediately after being taken from the hardening bath, in order to remove as much as possible the strains caused by the hardening process. Another method is to remove the reamer from the water bath as soon as it stops “ singing’ 1 and plunge it immediately into an oil bath, allowing the tool to stay in the oil until its temperature has been reduced to that of the oil. The temper should be drawn to 370° F. If reamers spring in hardening they are heated slightly and pressure is applied to the convex side, the reamer being held between centers in the same manner as in a lathe. This same method is applied to long taps and to counterbores and drills. Principles of Grinding Reamers. When grinding reamers, whether they be given an eccentric or a flat relief, it is necessary to rest the face of the tooth being ground against a guide finger which can 422 SMALL TOOLS be adjusted to give any desired amount of clearance. Fig. 229 shows an end view of a reamer being ground. A represents the emery wheel, which should run in the direction of the arrow, so that the tooth of the reamer may be pressed down on the finger B. If the wheel were running in the opposite direction, it would have a ten¬ dency to pull the tooth of the reamer away from the guide finger; the cutting edge of the tooth would then be ground away, and the reamer would be spoiled. It is claimed that when using a dry grinder, that is, one where water is not used on the emery wheel, the danger of heating the tooth and drawing the temper is greater when the wheel is run in the direction shown in Fig. 229; but if the face of the wheel is kept free from glaze, and ordinary care is exercised, there is little danger of drawing the temper, provided a cutting wheel that is not too fine is used. In order to give the tooth the proper clearance, the guide finger is adjusted to bring the cutting edge below the center line. It should not be attempted to remove too great an amount of stock at one cut; it is better to take a number of suc¬ cessive cuts, going around the reamer several times. When grinding reamers it is absolutely necessary to rest the face of the tooth being ground' on the guide finger, otherwise the teeth, particularly when irregularly spaced, REAMERS 423 would not be ground with an equal amount of clearance, nor would all the cutting edges be at an equal distance from the center line of the reamer, and some of the teeth, consequently, would not cut when such reamers were used. Figs. 229 and 230 show, respectively, the correct and in¬ correct ways of applying, the guide finger, it being in Fig. 230 applied to the tooth below the cutting edge being ground. Care should be taken not to give the cutting edge of a reamer any more clearance than is necessary to permit K— -G-—-2 ■■■ * >b Fig. 231. Fluted Chucking Reamer with Straight Shank Fig. 232. Fluted Chucking Reamer with Taper Shank it to cut freely. Too much clearance produces a weak edge which is liable to chatter, and the reamer soon loses its size. Fluted Chucking Reamers. Fluted chucking reamers are used in machines for en¬ larging holes and finishing them smooth and true to size. They are usually provided with either straight or standard taper shank as shown in Figs. 231 and 232. They are not intended for removing any large amount of stock, 0.005 to 0.010 inch being all that should be 424 SMALL TOOLS required. The cutting edges are along the lines ab, and at the front end there is a slight round, as shown at b. In cases where a very accurate hole is desired it must be remembered that reamers held rigidly at the end of the shank are liable to cut holes somewhat larger than their own size. In such cases the reamers used for chucking purposes should be somewhat smaller than the final size of the hole to be reamed, and after having reamed the hole by the chucking reamer it should be finished by a hand reamer. Number of Flutes. — The number of flutes with which fluted chucking reamers should be provided is given in the following table. It will be noticed that the pitch of the cutting edges, or the distance from cutting edge to cutting edge around the circumference of the reamer, is in some cases a trifle smaller than in the case of hand reamers. The same fluting cutters as are used for hand reamers are used for fluted chucking reamers also. Size of Reamer. Number of Flutes. 6 8 10 12 14 16 The slight rounded corners at the end of the flutes b, Figs. 231 and 232, should have a radius of one-thirty-second inch for sizes up to and including three-quarters inch, and one-sixteenth inch for larger sizes. Dimensions. — The only two dimensions of conse¬ quence are the over-all length and the length of the cut, denoted 0 and D, respectively, in Figs. 231 and 232. reamers 425 The over-all length of the straight-shank and the taper- shank chucking reamer are usually the same. The taper- shank is nearly always a Morse standard taper. The size of reamer and the corresponding Morse taper shank with which this reamer is provided are as follows: Size of Reamer. Number of Morse Taper. From | to 1 inch . 1 From H to £ inch. 2 From §f to if inches. 3 From i^- to if inches. 4 From 11| to 3 inches. 5 The length of the cut, C, and the total length, D, Figs. 231 and 232, may be determined from the formulas: C = E + | inch and D = 4 E + 5 inches, in which formula E denotes the diameter of the reamer. Dimensions figured from these formulas will be found in Table CVII. The diameter of the neck between the fluted part of the reamer and the taper shank, Fig. 232, should be about one- thirty-second inch smaller than either the diameter of the reamer or the diameter at the large end of the shank, depending upon which of these two diameters is the smaller, so that the grinding wheel will clear the necked portion when both the reamer part and the shank part are ground. The diameter of the straight shank should be from one- sixteenth to one-quarter inch below the size of the reamer for sizes up to one and one-half inches diameter. For larger sizes the shank may be proportionally smaller, so 426 SMALL TOOLS that the shank for a two-inch reamer is one and one-half inches and for a three-inch reamer one and three-quarters inches. TABLE CVII. DIMENSIONS OF FLUTED CHUCKING REAMERS. (See Figs. 231 and 232.) Diameter of Reamer. Length of Flute. Total Length. Diameter of Reamer. Length of Flute. Total Length. E C D E C D 1 1 6 1! 21 101 A 1 TS 61 H 21 11 I H 61 If 2f HI A i A 6f 11 21 12 * il 7 11 2f 121 A 1A 71 2 2f 13 f if 71 21 21 131 tt 1 T6 71 21 3 14 1 il 8 21 31 141 i if 81 21 31 15 1 if 9 2f 31 16 n il 91 3 31 17 11 2 10 Rose Chucking Reamers. The rose chucking reamer is used for enlarging cored holes, and is so constructed as to be able to remove a con¬ siderable amount of stock. As shown in Fig. 233, the cutting edges are on a 45-degree bevel on the end of the reamer. At every other cutting tooth there is a groove cut the full length of the reamer body. This groove serves the purpose of providing a way for the chips to escape, and forms a channel for lubricants to reach the cutting edges, but does not have any cutting edge itself. Rose reamers were formerly made without the grooves. The body of the REAMERS 427 reamer was solid, with the exception of the cuts made to form the teeth at the end, and for this reason they caused a vast amount of trouble, which has been done away with, however, by cutting grooves for every other tooth as mentioned. In fact, there is no reason why this groove should not be cut for every tooth, excepting that it would increase the expense of making the tool, and not being imperative, this expense is, of course, properly avoided. Rose chucking reamers are slightly back tapered on the i cylindrical body, that is, the diameter at the point with the beveled cutting edges is slightly larger than the body where it joins the shank. This provision also aids to pre¬ vent the tool from binding in the hole being reamed. The back taper ought properly not to exceed 0.0005 inch per one inch, although it is usual in the manufacture of these reamers to make this taper as much as 0.001 inch per one inch. The length of the beveled edge, F, Fig. 233, should in¬ crease with the size of the reamers. The length for various sizes should be as follows: 428 SMALL TOOLS Size of Reamers. Length of Beveled Cutting Edge, F, Fig. 233. From | to f inch. IT? From to f inch. A From f | to f inch. A From -|f to l| inches. A From 1^ to If inches. From Iff to If inches. From Iff to 2 inches. i From to 2f inches. A From 2f§ to 2f inches. A From 2|f to 3f inches. From 3^ to 3f inches. i From 3ff to 4 inches. A This form of reamer will usually produce holes slightly larger than the size, and should always be made from 0.005 to 0.010 inch smaller than the finished size, and be followed by a fluted reamer for finishing. In cored holes these reamers, however, are of great advantage, firstly, be¬ cause they can take a heavy cut, and secondly, because they will cut a hole that is nearer parallel than will a fluted reamer if there are blowholes or hard spots in the walls of the surface being worked upon. Fluting Rose Reamers. — The grooves with which rose reamers are provided along their cylindrical surface, not being intended to produce cutting edges, are not of the same shape as those cut in fluted reamers. A convex cutter, having a width equal to from one-fifth to one- fourth the diameter of the rose reamer itself, should be used for cutting the groove. The depth of the groove should be from one-eighth to one-sixth the diameter of the reamer. The cylindrical part of the reamer between the grooves should not be relieved but should be left circular. Rose reamers smaller than one-quarter inch in diameter may be made without grooves, but in such a case they REAMERS 429 should have only three teeth on the end, and fairly deep cuts between the teeth to take care of the chips. The best practice is, however, to provide rose reamers of all sizes with grooves on the cylindrical part. The number of cutting edges on the 45-degree beveled end of the reamer is as follows: Size of Reamer. From i to ^ inch. From y to 1 inch.... From to 1J inches From iy to 2 inches. From 2^ to 2J inches From 2y to 3 inches Number of Cutting Edges. 6 8 10 12 14 16 The number of grooves is evidently equal to half the number of cutting edges, there being one groove on the cylindrical part for every second cut at the end. The cuts at the end are milled with a 75-degree angular cutter. The width of the land at the cutting edge should be about one-fifth the distance from tooth to tooth. If an angular cutter is preferred rather than a convex for cutting the grooves on the cylindrical surface because of the higher cutting speed permissible when milling the grooves, an 80-degree angular cutter with a slight round at the point may be used. Dimensions. — Rose chucking reamers, like fluted chuck¬ ing reamers, are made with both straight and taper shank. The same dimensions for the total length as were given for the fluted reamers apply to the rose reamers also, but the length of the grooved portion of the reamer, or the body, is longer. If E is the diameter of the reamer and C the length of the grooved part (see Fig. 233), then C = + 1| inches. Li 430 SMALL TOOLS In Table CVIII are given the dimensions for rose chucking reamers in accordance with this formula. What was said in regard to the straight and taper shank of these reamers, and the diameter of the neck in the latter class, in connection with fluted chucking reamers applies to rose reamers also. TABLE CVIII. DIMENSIONS OF ROSE CHUCKING REAMERS. (See Fig. 233.) Diameter of Reamer. Length of Body. Total Length. Diameter of Reamer. Length of Body. Total Length. E C D E C D 1 H 6 If 3^ 101 A If 6 f H 3f 11 1 i ft if 6 i If 3& 111 16 6 f If 3f 12 1 if 7 If 3ff 121 16 2 7f 2 4f 13 f 71 2 f 4A 131 ti 2 f 7f 21 41 14 I 21 8 2 f 4 ft 141 I 2 fs 81 21 4f 15 1 2 f 9 2 f 51 16 2 ff 91 3 5f 17 H 3 10 . Jobbers’ Reamers. The jobbers’ reamer, Fig. 234, constitutes a class of reamers by itself. It is provided with a long fluted body and taper shank for use in machine. The corners at the point of the reamer are slightly rounded as shown at a. The radius for this rounded part should be about one- thirty-second inch for reamers smaller than three-quarters inch in diameter, and one-sixteenth inch for larger sizes. REAMERS 431 Between the fluted portion and the shank a neck is pro¬ vided in order to permit the shank and the cutting edges to be ground. The length of this neck varies according to the size of the reamer. It is customary to make it about one-half inch long for quarter-inch reamer, 1 inch for a 1-inch, 2 inches long for a 2-inch, and 3 inches long for a 3-inch reamer. The shank is nearly always a Morse stand- A- Fig. 234. Jobbers’ Reamer ard taper shank. The sizes of shanks to use for various sizes of reamers are as follows: Size of Reamer. Number of Morse Taper Shank. From f to | inch. 1 2 From H to f inch. From || to if inches. 3 From 1^2 to If inches. 4 From Iff to 3 inches. 5 Jobbers’ reamers are fluted with the same kind of cutters as hand reamers. The number of flutes is also the same as given for hand reamers. Dimensions. — The length of the neck having already been given, and the number of Morse taper shank deter¬ mining the length of the shank part of the reamer, the only additional dimensions necessary are the length of the flute and the diameter of the neck. The latter should be about one-thirty-second inch smaller in diameter than either the reamer itself or the largest diameter of the taper shank, depending upon which of these dimensions is the smaller, 432 SMALL TOOLS so that the grinding wheel will clear the neck when grinding the teeth as well as the shank. The length of the flute may be determined from the formula A = 4 D + 1 inch for sizes up to and including 1J inches, and from the formula A = + 4| inches 4 for larger sizes. In these formulas A = length of cut and D = diameter of the reamer. Dimensions for the length of the flutes, approximately figured from these formulas, are given in Table CIX. TABLE CIX. DIMENSIONS FOR THE LENGTH OF FLUTES OF JOBBERS’ REAMERS. (See Fig. 234.) Diameter Length Diameter Length Diameter Length of of of of of of Reamer. Flute. Reamer. Flute. Reamer. Flute. D A D A D A i 2 rl 41 11 6R A 2i 1 41 U 61 f 2} A 4f 2 7 A 2f 1 5 21 n 1 3 n 51 21 7A A 31 H 6 21 71 f 3* it 61 21 7f tt 3f l* 6f 21 7R 1 4 it 61 3 81 Shell Reamers. In order to save the amount of stock which goes into the shank, shell reamers, having a hole through the center by means of which they are mounted on arbors, are quite REAMERS 433 largely used. As one arbor can be used for a number of reamers the saving is quite considerable. An ordinary fluted shell reamer is shown in Fig. 235. The arbor on which it is used is shown in Fig. 236. The reamer has a key-way A which fits the key B on the arbor freely; the reamer, when at work, is rotated by means of this key and key-way. The hole through the reamer tapers, the taper being one-eighth inch per foot. Manufacturers of reamers have adopted certain standard sizes of arbors, and each arbor corresponds to a certain number of different sizes of reamers. Thus several sizes of reamers are provided with the same size hole through them, and can be used with the same arbor. The arbor as well as the hole in the reamer must be ground after hardening to insure that the reamer will run true. When hardening, if the reamer is larger than 1| inches in diameter, it should be removed from the hardening bath, the same as large hand reamers, when it ceases “singing,” and be plunged into a tank of oil, where it should remain until cool. When the tool is removed from the oil bath, or, in the case of smaller reamers, from the water bath, it should be held over a fire and slowly revolved until at least partly relieved of the internal stresses, tending to crack the tool, which are due to the hardening process. 434 SMALL TOOLS The outside of the reamer is provided with flutes and cutting edges for the greater part of the length of the reamer. A short distance at the end provided with the key-way is turned down below the diameter of the cutting edges. This is done in order to prevent any burr which 1 ^Taper % pet' foot -3-a- -©- t -1 D I F . —1 — 1 p- : 1 T -h- Fig. 236. Arbor for Shell Reamers may be set up by the driving key on the arbor from inter¬ fering with the hole reamed or spoiling the cutting edges of the reamer. Besides, this turned-down portion pro¬ vides space for marking the reamer with its size, and gives a finished appearance to the tool. Fig. 237 shows a shell reamer fluted in the same manner as the rose chucking reamer. This reamer is termed a rose shell reamer. The cutting edges, fluting, and back taper are the same as described before under rose chuck¬ ing reamers, but in all other particulars the tool is the same as an ordinary shell reamer. REAMERS 435 Arbors for Shell Reamers. — The arbor used for driving shell reamers when at work consists of a stem or arbor proper, C, Fig. 236, provided with a collar D which is fastened to the arbor by means of a taper pin. On the end of this collar is milled a tongue B so as to provide for a key to fit the key-way in the reamer, as mentioned. Precaution must be taken in milling this tongue so that it will be exactly in the center of the collar. The same care must, of course, be used in milling the key-way in the reamer which must be exactly in the center. When grinding the outside of the reamer to size it should be ground on an arbor similar to that on which it is to be used, and the edge at the front end slightly rounded as at b, Fig. 235. TABLE CX. DIMENSIONS OF SHELL REAMER ARBORS. (See Fig. 236 for dimensions denoted by letters.) Diameter at Size Line. Length from Size Line to End of Arbor. Total Length. Diameter at Size Line. Length from Size Line to End of Arbor. Total Length. E F H E F H i 11 6 1 31 12 if 7 11 3f 13 1 2 8 11 4 14 t 21 9 If 41 15 1 21 91 2 5 16 t 2f 10 21 51 17 1 3 11 21 6 18 Arbors as well as driving collars should preferably be made out of tool steel. The collars should be hardened. The arbors, as manufactured, are made in 14 sizes, the diameter of each being measured at E, halfway between the end of the key and the solid part of the body of the 436 SMALL TOOLS collar D. The arbor is provided with a flat milled on the shank for the set screws by which it is clamped when held in position for work. In Table CX are given, the most important dimensions for these arbors. Fluting Shell Reamers. — The cutters used for fluting regular shell reamers are the same as for hand reamers. Rose shell reamers are fluted with the same kind of cut¬ ters as rose chucking reamers. The number of flutes in shell reamers must necessarily be greater in the smaller sizes than in corresponding sizes of solid reamers, because the flute cannot be cut so deep owing to the thin walls of the shell. The numbers of flutes for regular shell reamers are as follows: Size of Reamer. Number of Flutes. From i to f inch. 6 From H to § inch. 8 From to 11 inches. 10 From ill to 2\ inches. 12 From 2-fa to 2f inches. 14 From 2§§ to 4 inches. 16 From 4^ to 5 inches. 18 The number of cutting edges on the beveled end of rose shell reamers is equal to the number of flutes in the regu¬ larly fluted kind. The number of grooves on the cylindri¬ cal part of the rose reamer is, of course, half that of the number of cutting edges, there being one groove for every second cutting edge. Dimensions of Shell Reamers. — The over-all length of the shell reamer must evidently be the same as the length F on the arbor (Fig. 236) from the size line to the extreme end. As the same arbor is used for a number of different sizes of reamers, these arrange themselves in certain groups with the same total length. The length of the fluted REAMERS 437 portion in each such group is, of course, also the same, as well as the dimensions for the key-way. The only dimension which varies in each group besides the size of the reamer itself is the diameter of the turned-down neck. This dimension should be as much less than the diameter of the reamer as stated below. Diameter of Reamer. Amount Diameter of Recess should be Less than Diameter of Reamer. f-f inch fW inch 1$-1 inch ItT-H inches 1^ inches and upward 0.006 inch A inch A inch xb inch 1 inch In Table CXI are given the dimensions for the various groups of shell reamers corresponding to the different arbors. TABLE CXI. DIMENSIONS OF SHELL REAMERS. (See Fig. 235.) Diameter of Reamer. Diameter of Hole, Large End. Total Length. Length of Turned- down Portion. Length of Flutes. Width of Key-way. Depth of Key-way. I K L M N 0 P A H I n A 1 A~A A If f it A 1 M-A 1 2 I H A A 1 9—Tl t 2f 1 if is A M-it I 21 1 2 n 1 M-H 1 2f t 21 M i i*-if f 3 f 2f 1 A iy-2 1 31 1 21 i A 2&-2I H 3f f 3 A t 2H-3 il 4 f 3f A 1 if 41 1 31 A f sy-4 2 5 1 4 A f 21 5i 1 41 A I 4||-5 21 6 1 5 A f 438 SMALL TOOLS Taper Reamers. Taper reamers are used for reaming holes for standard taper pins and for taper sockets. A special kind of taper reamer is made for locomotive work. The reamers for standard taper-pin holes are usually always finishing reamers, whereas for reaming taper sockets or other work with large tapered holes usually both a roughing and a finishing reamer are employed. The roughing reamer is simply intended to remove enough stock so that the finishing reamer can produce a smooth hole true to size, without being exposed to excessive wear, and thus retain its correct size so much the longer. Roughing Taper Reamers. — Roughing taper reamers, Fig. 288. Roughing Taper Reamer. such as are used for reaming Morse and Brown and Sharpe standard taper sockets, are made exactly like the finish¬ ing reamers, except that they are made about 0.010 inch smaller in diameter, and are provided with a spiral groove cut like a thread all around the cutting edges, as shown in Fig. 238. This thread or groove breaks up the chips in the same manner as the nicks in the cutting edges of plain milling cutters. The thread is cut left-hand, with a tool similar to a square-thread tool but with the corners slightly rounded. The width of the tool should vary from about one-thirty-second inch for the smallest size reamer for Morse taper sockets to three-thirty-seconds inch for the largest sizes. The depth of the groove should be slightly more than one-half of the width of the took REAMERS 439 After being hardened and drawn to a temperature of about 370° F., the roughing reamer should be ground with a somewhat greater clearance than the finishing reamer. The pitch of the thread should be one-fifth inch for the smallest sizes of roughing taper reamers up to one- third inch for the largest sizes; that is, there will be from three to five threads per inch, according to size, along the cutting edge. The cutting edges of roughing taper reamers are some¬ times cut spiral. The spiral may be a right-hand one in this case, as there is no danger of the reamer drawing into the work too suddenly on account of the taper. How¬ ever, most manufacturers make both roughing and finish¬ ing reamers with straight flutes whenever there is not an exceptionally steep taper or a long tapered hole to be reamed. In such a case the roughing reamers are con¬ structed upon a different principle from the one just described. The reamer is turned somewhat over-size, and ground to the correct diameter desired before being fluted. It is then returned to the lathe and a thread cut on the surface with a square-nosed tool one-quarter inch wide. The pitch of the thread is one-quarter inch, and the depth such that the ground surface at the end of the cut nearest the point of the reamer is barely touched, as shown in Fig. 239. In the cut the dash-dotted lines indi¬ cate the ground tool blank before the thread is cut, and the full lines the appearance of the blank with its thread. This latter is left-handed, and each step is slightly back tapered, say 0.002 inch in the distance of one-quarter inch; that is, the point a of each step is 0.002 inch further away from the axis of the reamer than the point b. After threading, the reamer is fluted with left-hand spiral flutes, the spiral being so selected that the angle which the cut- 440 SMALL TOOLS ting edges make with a plane through the axis of the reamer is 15 degrees. Some tool-makers also advocate an odd number of flutes for these reamers, but as long as the reamer is provided with spiral flutes there seems to Fig. 239. Method of Making Steep Taper Roughing Reamer be no valid reason why an odd number of flutes should add any advantages. Fig. 240 shows another form of roughing taper reamer for steep tapers. This form is known as a step reamer. In fact, this tool is a kind of multiple counter bore; each step together with the previous one forms a com¬ plete counterbore, the smaller step being the guide, the larger the body. All the cutting is done at the front end of each step. The cylindrical portion of the step should not be relieved, but it is preferable to slightly back taper these portions the same as in the case of the threaded REAMERS 441 taper reamer. The flutes may be straight or spiral; if the latter, the same angle of spiral as mentioned previ¬ ously should be selected. The number of flutes for this kind of reamer is usually four. Finishing Taper Reamers. — Finishing taper reamers, as shown in Fig. 241, are similar to ordinary hand ream¬ ers, except that the cutting edges taper. The flutes are almost always cut straight, but spiral flutes are of advan¬ tage in porous metal or in work pierced crosswise by other holes or openings. The spiral should be right-handed, there being no tendency to draw the reamer into the hole on account of the taper of the hole. Fig. 241. Finishing Taper Reamer Taper-pin Reamers. — Taper-pin reamers, as mentioned, are intended for reaming holes for standard taper pins. The taper is one-quarter inch per foot. The diameter of the small end of the reamer should be such that the reamer will project at least one-sixteenth inch, or, on larger sizes, one-eighth inch, through the hole reamed for the longest standard taper pin of the size in question. The cutting edges should be enough longer than the long¬ est pin to permit the reamer to be ground a number of times without being too "small in diameter at the upper end of the flutes for the size pin for which it is intended. In Table CXII are given the standard dimensions for taper pins as adopted by the Pratt and Whitney Company, and in Table CXIII the dimensions for corresponding sizes of taper-pin reamers. These reamers are provided with a 442 SMALL TOOLS square on the end of the shank for a tap wrench. The length of the square • should be about one and one-half times the diameter of the shank. The size of the square should be three-quarters the diameter of the shank. TABLE CXII. STANDARD TAPER PINS. Diam. Approx. Frac- Length of Diam. Approx. Frac- Length No. of at tional No. of at tional Taper- Large Size at Longest Pin of this Size. Taper Large Size at Longest Pin of this Size. pin. End of Large Pin. End of Large Pin. End of Pin. Pin. End of Pin. 000000 0.0715 A f 3 0.219 A If 00000 0.092 A t 4 0.250 1 2 0000 0.108 f 5 0.289 if 2f 000 0.125 1 f 6 0.341 M 3f 00 0.147 Wi 1 7 0.409 M 3f 0 0.156 A 1 8 0.492 1 4* 1 0.172 ti n 9 0.591 1! 51 2 0.193 10 0.706 M 6 TABLE CXIII. DIMENSIONS OF TAPER-PIN REAMERS. No. of Taper- pin Reamer Total Length of Reamer Length of Cutting Edges. Length of Shank. Diam. at Small End of Reamer No. of Taper- pin Reamer Total Length of Reamer Length of Cutting Edges. Length of Shank. Diam. at Small End of Reamer 000000 If 1 1 0.057 3 3# 21 11 0.182 00000 n 1 1 0.078 4 31 2# 11 0.205 0000 if n I 0.091 5 4f 3 If 0.239 000 if n * 0.108 6 51 4 11 0.270 00 21 1 TjB ** 0.125 7 61 41 If 0.328 0 2f H 0.134 8 71 51 2 0.395 1 2f If 1 0.145 9 8§ 61 21 0.479 2 3 • 2 1 0.161 10 91 7 21 0.578 REAMERS 443 The number of flutes in taper-pin reamers should be chosen as follows: Number of Taper-pin Reamer. Number of Flutes. 000000-00 4 0-7 6 8-10 8 Taper Reamers for Morse Standard Taper Sockets. — For reaming Morse standard taper sockets two reamers are used, one roughing and one finishing. The construction of the former has already been described. The finishing reamer is made like the taper-pin reamer, with the excep¬ tion, of course, that the taper is according to the Morse standard taper gauges. This taper is different for the different sizes or numbers of Morse tapers, but is approx¬ imately five-eighths inch per foot. The exact figures for the taper are given in Table CXIV. These reamers are provided with a square, the length of which should be about equal to the diameter of the shank. The size of the square should be three-quarters the diameter of the shank. This leaves a small round on the corners of the square which is desirable for the appear¬ ance of the tool as well as for the convenience of handling a tool without sharp corners. In Table CXIV are given all essential dimensions for these reamers, and in Table CXV the dimensions for Morse standard taper shanks. These taper shanks are the ones most extensively used of all standard taper shanks. It is practically the only taper shank ever used on drills and reamers. 444 SMALL TOOLS The number of flutes in roughing as well as finishing reamers should be as follows: Reamer for Morse Taper Sockets No. Number of Flutes. 0-1 6 2-4 8 5 10 6 14 7 16 TABLE CXIV. DIMENSIONS OF REAMERS FOR MORSE STANDARD TAPERS. No. of Morse Standard Taper. Total Length of Reamer. Length of Cutting Edges. Length of Shank. Diameter at Small End, Finishing Reamer. Diameter at Small End, Roughing Reamer. Taper per Foot. 0 4 21 11 0.252 0.242 0.625 1 4f 2f 11 0.369 0.359 0.600 2 51 31 21 0.572 0.562 0.602 3 6f 4 2f 0.778 0.768 0.602 4 8 5 3 1.020 1.010 0.623 5 91 61 3f 1.475 1.465 0.630 6 12 81 31 2.116 2.106 0.626 7 15 11 4 2.750 2.740 0.625 REAMERS 445 TABLE CXV. DIMENSIONS OF MORSE STANDARD TAPERS. Fig. 242 Number of Taper. Diameter of Plug at Small End. Diameter at End of Socket. Standard Plug Depth. Whole Length of Shank. Depth of Hole. End of Socket to Key-way. Length of Key-way. Length of Tongue. Thickness of Tongue. Width of Key-way. Shank Depth. Taper per Foot. D A P B H K L T t S 0 0.252 0.356 2 2ff 2A m TS 1 A 0.160 2A 0.625 1 0.369 0.475 2* 2A 2A 2ts 1 A a 0.213 21 0.600 2 0.572 0.700 3 A 2$ 21 1 * i 0.260 21 0.602 3 0.778 0.938 3f 31 3 ts Irk A A 0.322 3 A 0.602 4 1.020 1.231 4tV 4f 41 31 11 1 ft* 0.478 41 0.623 5 1.475 1.748 5A 6 51 4R 11 ft f 0.635 5f 0.630 6 2.116 2.494 n 8 A 7* 7 If 1 I 0.760 8 0.626 7 2.750 3.270 10 Hf 101 91 2f If H 1.135 HI 0.625 Taper Reamers for Brown and Sharpe Standard Taper Sockets. — Roughing and finishing reamers are used the same as for the Morse taper sockets. The taper is one- 446 SMALL TOOLS half inch per foot, except taper No. 10, which is 0.5161 inch per foot. In Table CXVI are given all the essential dimensions for the reamers, and in Table CXVII the dimensions for the taper shanks. It will be noticed that in certain cases there are a number of different lengths corresponding to the same number of taper, all being of the same diameter at the small end. While the lengths of the shanks are different, the reamers can all be made the same for the same number of taper, inas¬ much as the diameter at the small end is the same, and the only thing to consider is to make the length of the cutting edges of the reamers long enough for the longest or deepest taper socket of a particular size, in which case they, of course, will be sufficient for the shorter lengths. TABLE CXVI. DIMENSIONS OF REAMERS FOR BROWN AND SHARPE STANDARD TAPERS. No. of Taper. Total Length of Reamer. Length of Cutting Edges. Length of Shank. Diameter at Small End, Finishing Reamer. Diameter at Small End, Roughing Reamer. Taper per Foot. 1 2 11 2 . 0.197 0.187 0.500 2 2f If H 0.247 0.237 0.500 3 4 21 il 0.309 0.299 0.500 4 4 21 il 0.347 0.337 0.500 5 41 2 1 il 0.447 0.437 0.500 6 61 4 21 0.497 0.487 0.500 7 71 4f 21 0.597 0.587 0.500 8 71 4f 21 0.747 0.737 0.500 9 n 5 21 0.897 0.887 0.500 10 101 n 31 1.042 1.032 0.516 11 ii 7f 31 1.247 1.237 0.500 12 Hi 3f 1.497 1.487 0.500 13 121 8f 31 1.747 1.737 0.500 14 13 91 31 1.997 1.987 0.500 15 13* 9f 31 2.247 2.237 0.500 16 14 101 31 2.497 2.487 0.500 17 15 11 4 2.747 2.737 0.500 18 151 HI 4 2.997 2.987 0.500 TABLE CXVII. DIMENSIONS OF BROWN AND SHARPE TAPER SHANKS. Fig. 243 Taper. Diameter at End of Socket. Whole Length of Shank. Shank Depth. Diameter of Plug at Small End. Standard Plug Depth. Depth of Hole. End of Socket to Key-way. 1 Length of ■ Key-way. Width of Key-way. A B C D E F G H K 1 0.239 1A lie 0.200 A Irk A 1 0.135 2 0.299 iff 11 0.250 i A 1A iH 1 0.166 3 0.375 1^ 11 0.312 il If iM ! 0.197 3 0.385 2-b 21 0.312 if 11 1 23 f 0.197 3 . 0.395 2f§ 21 0.312 2 21 iy f 0.197 4 0.402 U 1M 0.350 H U A 0.228 4 0.420 2A 2A 0.350 itt m ill IS 0.228 5 0.523 2A 2A 0.450 if ii 1A f 0.260 5 0.533 2A 0.450 2 21 ill I 0.260 5 0.539 o21 2A 0.450 21 21 2A i 0.260 6 0.599 2M 21 0.500 2f 21 2H 1 0.291 6 0.635 3H 3f 0.500 31 31 3H 1 0.291 7 0.704 3fr 3A 0.600 21 2f 2f§ If 0.322 7 0.720 3i 3M 0.600 21 3 2M If 0.322 7 0.725 3f 3fl 0.600 3 31 0 2 9 If 0.322 7 0.767 4f 4y 0.600 4 41 02 9 6 T2 If 0.322 8 0.898 41 41 0.750 3A 311 m l 0.353 8 0.917 4A 4A 0.750 4 41 ■JST l 0.353 9 1.067 4f 4f 0.900 4 41 31 if 0.385 9 1.077 5 41 0.900 41 4f 41 il 0.385 10 1.260 K27 K 28 1.0446 5 51 4 U i A 0.447 10 1.289 6H m 1.0446 5 A 5H sy i A 0.447 10 1.312 7* 6A 1.0446 6A 6H 6A i A 0.447 11 1.498 6p 1.250 5M 6A K25 i A 0.447 11 1.531 711 7M 1.250 61 61 611 i A 0.447 12 1.797 4 7H 1.500 71 71 6A il 0.510 13 2.073 8A 8i% 1.750 71 71 7 A il 0.510 14 2.344 9A 9^ 2.000 81 81 8A 1A 0.572 15 2.615 9M 9§1 2.250 81 81 8A i A 0.572 16 2.885 lot 101 2.500 91 91 9 A 0.635 3 156 2 76n 94 91 18 3.427 3.000 101 101 C o % 2 fE-kD>l- k-- -c- -B- 1 Figs. 244 and 245. Locomotive Taper Reamers and with taper shanks, as shown in Figs. 244 and 245. While there are a great many various standards in use in dif¬ ferent railroad shops, the commonly accepted standard taper for locomotive taper reamers is one-sixteenth inch per foot. In Table CXIX are given the principal dimensions for locomotive taper reamers with squared shanks as com¬ monly made. The dimensions for the fluted part of those with taper shank, generally Morse taper, are exactly the same, the only difference being the over-all length, which, REAMERS 451 of course, is dependent upon the number of Morse taper shank used. The common practice is to use the following numbers of Morse taper shanks for the sizes given below: Sizes of Reamers. Number of Morse Taper Shank. From 1 to A inch. 1 From | to | inch. 2 From if to 1A inches. 3 From 11 to Iff inches. 4 From If to 2 inches. 5 TABLE CXIX. DIMENSIONS OF LOCOMOTIVE TAPER REAMERS WITH SQUARED SHANK. (See Fig. 245.) Diam. at Small End of Reamer Total Length Length of Flutes. Length of Neck. Length of Collar. Length of Square. Diam. of Collar. Size of Square. A B C D E F G H i 5 4 f 1 f A 1 A 5f 41 A IS 1 f A f 61 5 A I A 16 A 71 51 I 1 t f f 1 8 6 A A f A A A 8f 61 f if if if 1 f 9f 7 f f i f A if 10 71 f if- it if t f 10f 8 If if l i if l Hf 9 if i i A l f l 12f 10 f i if if if if 14 11 ft i i A if it H 15$ 12 1 i if if 1 if 16$ 13 Ifs 1 i A i| if 11 17f 14 If i if if iA if 18f 15 If i H if 1A if 19f 16 If i if if if if 20f 17 If i if 2 if 2 21f 18 If f if 2f iA 452 SMALL TOOLS The length of the neck between the taper shank and the cutting portion of the reamer should be from three-eighths inch on the quarter-inch size to one inch on a two-inch reamer. The size of these reamers is measured at the ex¬ treme small end of the fluted portion. The number of flutes should be as follows: Sizes of Reamers. Number of Flutes. From i to § inch. 6 From yq to It inches. 8 From 1]^ to If inches. 10 From Iff to 2 inches. 12 Pipe Reamers. — Pipe reamers, Fig. 246, are used to precede pipe taps. They are made of the same sizes as pipe taps, excepting that the dimensions of the pipe reamer correspond to the root diameters of the thread of pipe taps. The taper of pipe reamers is three-quarters inch per foot. They are fluted with the same kind of cutters as hand reamers of sizes corresponding to the diameter at the small end of the pipe reamers. Finishing reamers only are used. The number of flutes for different pipe sizes is as follows: Pipe Size. Number of Flutes in Reamer. F rom | to f. 6 From | to |. 8 From 1 to If. 10 From 1^ to 2. 12 From 2| to 3. 14 3t_'. 16 4. . 18 The small end of pipe reamers is slightly chamfered, as shown in Fig. 246, in order to facilitate the entering of the reamer in holes which are of about the same size as the REAMERS 453 small diameter of the reamer. Dimensions for pipe reamers are given in Table CXX. Pipe reamers are gauged in the same way as pipe taps, previously described, and the same limits of error are permissible. TABLE CXX. DIMENSIONS OF PIPE REAMERS. Pipe Size. i f 1 H 2 2* 3 3* 4 Diameter at Size Line. 0.343 0.447 0.582 0.721 0.931 1.170 1.515 1.755 2.230 2.667 3.292 3.792 4.292 Dis¬ tance from Size Line to Small End. A if a i i H 1A If lit Diam. of Shank H A A f If if H 2* 2f 2fi 3 Length of Fluted Part. 1 If U H if if if 2 2f 2f 31 3# 3f Length of Shank. If If If 2 2i 2* 2f 3 3f 4 4f 4A 4f Total Length. 2f 2f 3f 3f 3f 4i 4f 5 5f 6f 7f Length of Square. if f if 1 If If lii lit 2f 2f Size of Square. 1 A A A if if l if if itt lit 2f 21 454 SMALL TOOLS Taper Reamers for Bridge Builders. — Taper reamers for bridge builders, commonly called bridge reamers, are made with Morse taper shank or straight squared shank, as shown in Figs. 247 and 248. The fluted portion is tapered for a distance D, Fig. 248, and the remaining part of the flutes, E, is straight. These reamers are used for rough structural construction work and are not required to be finished with the same degree of care as reamers for machine construction. After hardening, the flutes are usually left unpolished. These reamers are Figs. 247 and 248. Taper Reamers for Bridge Builders made in sizes from one-half to 1| inches. The taper per foot of the tapered portion at the end of the reamer, as usually made, is given in Table CXXI, together with the essential dimensions of the straight-shank type of reamer. The dimensions for the fluted portion of those with Morse taper shank are exactly the same, the only differ¬ ence being the total length, which, of course, is dependent upon the size of Morse taper shank used. The common practice is to provide the one-half up to five-eighths inch sizes with No. 2, and all sizes eleven-sixteenths inch and larger in diameter with No. 3 Morse taper shank. The size of the reamer is measured on the straight part of the flutes. In the case where an odd number of flutes is REAMERS 455 employed, the size must be determined by a ring gauge. The number of flutes is made five in all sizes below and including seven-eights inch diameter, and six for larger sizes. TABLE CXXI. DIMENSIONS OF REAMERS FOR BRIDGE BUILDERS. ■e Diameter of Straight Pari of Reamer. Diameter at Point of Reamer. Taper per Foe of Tapered Portion. Total Lengtl of Reamer. Length of Tapered Part. Total Lengtl of Flute. Length of Shank. Diameter ol Shank. Length of Square. Size of Square. A B C D F G H I K i I 1 81 3 51 21 A 1 A A A 1 8f 3 51 21 1 A t t A 8f 3 5i 21 A t A A i t li 81 3 6 21 f A A A H 91 3 61 21 A i 1 A 1 11 9f 3 61 21 I A A 1 A 11 9f 3 6f 21 It 1 t ' It t H 91 3 6 It 0 15 " H> 1 A A I TC U 101 3 71 3 1 l A 1 TC 23 T2 if 101 3 71 3 It i A A u I li 10f 3 7f 3 l il i 1A It 101 3 71 3 LA i A A H 1 l* lOf 3 7f 3 il il 1 Table of Amount of Taper in Certain Lengths. — Table CXXII is given in order to facilitate the figuring of the diameter at a certain place of a tapered tool when the diameter at another place and the taper per foot are given. Suppose, for instance, that the diameter at the small end of a reamer is three-quarters inch, the taper is three-thirty-seconds inch per foot (the common taper for locomotive reamers in many railroad shops), and the diam¬ eter at the large end of the flutes is desired. The length of the flutes is 9| inches. By the use of Table CXXII we find: 456 SMALL TOOLS ^ taper per foot in 9 inches. 0.0703 ^ taper per foot in f inch. 0.0059 This added to diameter at small end. 0.7500 Equals diameter at large end. 0.8262 Grooved Chucking Reamers. This tool, shown in Fig. 249, is partly a reamer and partly a twist drill. The cutting is performed by the beveled edges A, which form an angle of 60 degrees with the axis of the tool. The reamer is provided with three larger semi¬ circular flutes, which are cut on a right-hand spiral, and with three smaller grooves between these. The larger grooves form passages through which the chips pass away; the smaller grooves convey the lubricant to the cutting edges. This form of reamer is extensively used in screw machines for enlarging cored holes, and also in drill presses for enlarging drilled holes, it being easier to enlarge a drilled hole to size by a grooved chucking reamer than to try to drill the hole to size by an ordinary twist drill. This reamer is commonly provided with both straight and Morse taper shank. When provided with Morse taper shank the following numbers of taper shanks should be used for the various sizes of grooved reamers: Diameter of Reamer. No. of Morse Taper Shank. From \ to § inch. 1 From to \ inch. 2 From to li inches. 3 From 1^ to If inches. 4 From 1|| to 3 inches. 5 W / y Fig. 249. Grooved Chucking Reamer TABLE GIVING THE AMOUNT OF TAPER IN A CERTAIN LENGTH WHEN THE TAPER PER FOOT IS GIVEN. REAMERS 457 2083 I .250 I .3333 I .4167 TABLE CXXII Continued. REAMERS 459 The length of the fluted part is given in Table CXXIII. The total length of the reamer is dependent upon the length of the Morse taper shank used. When made with straight shank, this latter may be selected of such length that the total length of the tool is the same as when a Morse taper shank is used. The diameter at the point of this reamer is larger than at the shank end of the flutes, the amount of back taper being 0.003 inch per foot. This prevents the tool from binding in the hole chucked. The spiral of the flutes should be so selected that the edges of the flutes make an angle of between 25 and 20 degrees with a plane through the axis of the reamer. This corresponds to a lead of the spiral equal to from about 7 to 8.5 times the diameter of the reamer. This is practically the same amount of spiral as is used on twist drills. TABLE CXXIII. LENGTH OF FLUTED PORTION OF GROOVED CHUCKING REAMERS. Diameter of Reamer. Length of Fluted Portion. Diameter of Reamer. Length of Fluted Portion. Diameter of Reamer. Length of Fluted. Portion. 4 4 4 84 2 9f A 4* H 8f 24 94 1 5 l 84 24 10 51 H 8f 2f 104 4 6 14 9 24 104 64 if 94 2f 10f f 7 14 94 2f 104 44 74 if 9f 24 10f f 8 if 94 3 10| 84 H 9f Center Reamers. Center reamers are used for forming the centers on which work is to revolve in lathes or grinding machines. They 460 SMALL TOOLS are made in two different styles. The older one, Fig. 250, has only one cutting edge, formed by cutting away the metal down to the center of the tool and relieving the beveled portion of the remaining half so that a cutting edge is produced. The second and later style is that shown in Fig. 251, which has four flutes or cuts. These cuts are straight, and the lands between the cuts are relieved on the beveled part. The inclusive angle of the point of the tool must, of course, be that used for lathe centers, or 60 degrees. Fig. 250. Old Style Center Fig. 261. New Style Center Reamer Reamer These reamers are made with a straight shank. The dimensions of both styles are the same and are given in Table CXXIV. TABLE CXXIV. DIMENSIONS OF CENTER REAMERS. (See Figs. 250 and 251.) Full Di¬ ameter of Reamer. Total Length. Length of Beveled Portion, Approx. Length of Straight Portion. Length of Shank. Diameter of Shank. A B C D E F i n ih 1 A t if IS : i s 1 i i 2 t h T5 n i I 2f u M H A i 2f M 2 3 3? H 1 1 2 f f 7 t 2 4 if A l 2 4 f REAMERS 461 Flat-sided Reamers. Very small reamers are sometimes provided with flats instead of actual flutes, the sharp intersection or corner between two flats acting as a cutting edge. These reamers are used for small dowel and taper-pin holes, etc. The diameter of the reamer is, of course, measured over the sharp corners. If the reamer tapers, the taper of the flats will evidently not be the same as the taper of the reamer itself, and the milling-machine head used when milling the flats must be set to a different angle from that which the Fig. 252. Determining the Angle to which to set the Index Head for Milling Flat-sided Reamers cutting edge makes with the center line. A simple formula can be given expressing the relation between the taper per foot, the number of flat sides in the reamer, and the angle to which to set the milling-machine head. Referring to Fig. 252, if a = one-half included angle of cone,