i-.y-#" EMPHMCAL DESIGN" HAYES iiiiiiimniinfliinwiinnrf iir • "i " A n^on P \/y 'rifhl- .OiUME'UL UNIVERSIT'; ^BRARIES ITHACA. N. Y. 14833 -4 . : { I 4^ Engineering Library Carpenter Hal! TJ 230.H4 r"'" ""'"•"'•l' Library ..^'"{''■'■{cal design; Cornell University Library The original of tiiis book is in tine Cornell University Library. There are no known copyright restrictions in the United States on the use of the text. http://www.archive.org/details/cu31924004245720 EMPIRICAL DESIGN BY LESLIE D. HAYES, M.E. Assistant Professor of Machine Design, Sibley College Cornell University. 1915 CARPENTER & CO. Ithaca, N. Y. CONTENTS. CHAPTER I. Empirical Design 5 Definition; Empirical Methods in Modern Design; Method of Application; Empirical Equations. CHAPTER II. Screw Fastenings 11 General Forms; Forms of Threads; Bolts; Nut Locks; Washers; Screws for Metal; Screws for Wood. CHAPTER III. Keys and Taper Pins 25 Use of Keys; Forms and Proportions for Keys; Woodruff System of Keys; Key ways or Key Seats; Taper Pins. CHAPTER IV. Shafting and Shaft Fittings 33 Shafting; Key ways; Couplings; Permanent Couplings; Clutch Couplings; Collars. CHAPTER v. Shaft Fixtures 46 General Nature; Purpose and Qualities of Bearings ; Forms of Bearings; Adjustments of Bearings; Proportions for Babbitted Bearings; Quarter-box Bearings; Bearing Sup- ports; Stands and Base Plates; Wall Brackets; Wall Box Frames; Hangers. CHAPTER VI. Transmission Members 62 General Statement; Pulleys; Belts; Handwheels; General Nature and Properties of Gears; Proportions and Proper- ties of Gear Teeth; Materials used in Gears; Proportions for Spur Gears; Proportions for Bevel Gears; Proportions for Worm Gears; Commercial Gears; Cams. 2 Contents CHAPTER VII. Pipe and Pipe Fittings 79 Varieties of Pipe; Wrought Iron and Steel Pipe; Pipe Threads; Pipe Joints; CoupHngs; Pipe Flanges; Pipe Bends; Pipe Fittings; Valves. Decimal Equivalents 95 Trigonometric Functions 96 Index 101 \ \ PREFACE. This book has been planned especially to meet the needs of the second year students in the Department of ^Machine Design of Cornell University. It is hoped, however, that the material is of a nature and the arrangement such as to meet, in a fair degree, the needs of other technical schools and colleges for a course in design to follow the elementary' Mechanical Drawing and Descriptive Geometry before the student has had the necessary preparation in Mechanics for a course in theoretical design. It is intended to give in a convenient form such tables, formulas and curves for the empirical proportioning of machine parts as are necessary in a brief course in Empirical Design, and such instruc- tion as to the methods of their derivation and use that the student, upon the completion of the course, may be able to use material of this nature understandingly and to derive new material if he so desires. The data have been collected at different times and have been in use in teaching this course in Cornell University for a considerable period. The purpose and manner of using the various machine parts is explained in detail for the benefit of those students whose previous training has left them wholly unfamiliar with machinery. In the descriptions and explanations a fair knowledge of the principles of Mechanical Dra'u-ing, Descriptive Geometry and Analytical Geometry has been assumed. No attempt has been made to intrude upon the field of the engineer's handbook but the proportions have been carefully com- piled with the intent that any here given shall be reliable within the limits of good design, and some of the more commonly used mathematical tables have been added with a view to making it a desirable book for reference in the more advanced classes in Machine Design. Acknowledgment is due to Professors E. H. Wood and C. D. Albert and to Mr. L. J. Bradford for suggestions and criticisms. The author is indebted to Professor Wood for the use of the pro- portions derived by him for many of the machine parts described, and several manufacturers have responded freely to requests for information. June, 1915. L. D. H. CORRECTIONS FOR EMPIRICAL DESIGN BY L. D. HAYES Page 13, line 7, for "lyV D" read "ifV D." 20, " 8, for "countersunk" read "flat." 37. " 20, to the equation for dimension F add "but not less than 2/ — G." 47, Fig. 36 (e), invert. " SI, line 6, for "V" read "Y." 58, " 18, add "F is the diameter of the bolts which sustain the bracket." 70, Fig-. 54, add "(a)" and "(b)" beneath the left-hand and right-hand portions re- spectively. 87, line 10, for "page 91" read "page 92." 87, " 19, in the parentheses add "in tees and crosses and one-half in laterals." 99, top right-hand corner, for "Cotangents" read "Tangents." 104, line 25, for "24" read "22."' CHAPTER I. EMPIRICAL DESIGN. 1. Definition. — When a machine part has been proportioned from experience obtained in making other similar machine parts and without any direct application of the theory and principles of rational machine design it is said to have been designed empirically. Before the principles and laws which make modern design a fairly exact science had been discovered all design was of an empirical nature, differing little from guess work at first but becoming more and more exact as the result of increasing experience, and the elimination of such designs as were found to be too weak or too expensive in either material or labor. 2. Empirical Methods in Modem Design.— With the discovery of the laws governing the design of a machine part empirical methods of design were usually superseded. Sometimes this involved con- siderable change in the earlier designs but more often there was little change. It would seem, then, that continued study of these principles and laws must entirely displace empirical methods of design. There are, however, two classes of parts in the design of which empirical methods are likely to continue, e. g., those parts of such complex form that it is very difficult, if not impossible, to discover and apply the principles involved, and that large class of parts in use in so many sizes of similar proportions that, although rational methods may have been used in the design of the extreme sizes, the intermediate sizes are much more cheaply designed by empirical means based upon the proportions for the extreme sizes. The discussion of the first of these two classes is beyond the scope of this book but an attempt will be made to discuss some of the parts falling within this second class and to study the empirical methods used. 3 . Method of Application. — The machine parts to which empiri- cal methods will be applied belong to a large class of parts in such general use under such similar conditions that they are now made in a number of standard sizes having the same general form and 5 6 Empirical Design proportions and purchasable in the open market at a cost much less than that at which they could be designed and built especially for each case. Empirical methods are also often applied by manu- facturers in the design of parts which they have occasion to make in a number of sizes even though those parts are never placed upon the market except in conjunction with some complete machine. Any of these machine parts of modern origin have usually had their dimensions for a large and a small size determined by the principles of rational machine design, while the dimensions for parts of older origin may have been determined empirically. In either case the corresponding dimensions for the intermediate sizes, and sometimes for a small range beyond the selected extreme sizes, are determined according to some chosen law of variation. This may usually be done most conveniently by graphical methods. To make a graphical determination of this kind the nominal sizes (by nominal size is meant that dimension which gives name to the size, as the outside diameter in the case of a handwheel), for the range through which it is desired to construct the part, are laid off to any convenient scale of abscissas and ordinates erected at these points. On the ordinates corresponding to the two sizes, usually near the limits of the desired range, for which all the dimensions are known (having been previously determined either by rational or by empirical methods) the values of these dimensions are laid off to scale. This scale should be so chosen that the dimensions may be read easily to as small a fraction of an inch as it is desirable to work in manufacturing the part. What the value of this fraction shall be is a matter for the judgment of the draftsman. His decision must be largely influenced by the size of the part, whether it is to be left in the rough or to be machined to size and, if it is to fit some other part, the nature of the fit required. Its value is rarely smaller than a sixteenth of an inch in unfinished castings, unless they are very small, and may often be as great as a fourth inch or a half inch in large castings. Having assumed the law of variations for one of these dimensions a curve following that law is drawn through the two points already determined for that dimension. The intersections of this curve with each of the remaining ordinates gives the value of this dimension for the corresponding sizes of the part to the same scale as that to which the known values were laid off. Empirical Design 7 As an example, in the handwheel, Fig. 1, let it be required to find the sizes of shafts (dimension B) suitable to yse with a series of Fig. 1 nominal sizes (dimension A) when these dimensions are known to be f" and 1|" for the 6" and 16" wheels respectively, and the variation assumed to be by direct proportion. On the base line, Fig. 2, lay off the nominal sizes and on the ordinates corresponding to the 6" and 16" sizes lay off to scale |" and IJ" locating points ^ ■^ < ^ ^ \ ^ ^^ t^ 'l f u rTiS r X 'l ^ — =1 ^ n tN — f- rr* te '0 f^ i^ ^ ^ 9 -J H 7!S ■^ y _ J> -- " _ 8 12 16 A'Phmeter of Handwheel Fig. 2 20 a and 6 respectively. The straight line through these points represents the law of variation and by its intersection with the 8 Empirical Design several ordinates determines the required shaft diameters, as 1" for the 12" wheel. Jn the same way the line through points c and d determines the corresponding values for the diameters of hubs for these handwheels. These curves may be left in their present form for the values to be read off when needed, the equations of the curves may be written and the values for the dimensions ascertained by substitutions in these equations, or the values for the dimensions for all sizes that it is desirable to manufacture may be read off from the curve at once and tabulated for use. Of these three methods the latter is the most convenient for general drafting room use while the first two have the advantage of showing clearly the relation between the several dimensions of the machine part. 4. Empirical Equations. — The equations have an advantage when compactness is a desirable quality and they may also be readily combined to show the relation between any two dimensions, whereas the cur\'es refer all dimensions to the nominal size. For these reasons the equation method will be used quite largely in this book. Applying the slope form, y = mx + b, of the equation for a stmight line, to the curves of Fig. 2, and using the symbols of Fig. 1, gives B = AA + i" (1) and C = |A+ i" (2). As the diameter of the hub is more naturally a function of the diameter of the shaft than of the outside diameter of the hand- wheel, equations (1) and (2) may be combined to eliminate A giving C = 2B (3). When the variation desired for the dimensions of intermediate sizes does not conform to the straight line construction given above the careful design of one or two additional sizes will readily locate a suitable curve on the graphical construction, but it may be neces- sary to resort to some of the less simple methods of mathematics or to the use of logarithmic cross-section paper to obtain an equa- tion for that curve. As these methods of determination permit considerable variation in the values taken for the dimensions it is often sufficiently accurate and much easier to approximate the Empirical Design 9 curve by two straight lines as illustrated in Fig. 3, where the curve B represents the selected law of variation for the thickness of babbitt in a certain type of bearing, in proportion to the diameter, 1 1 fl) 2) _^ -B t^ ^ == " ^ ) Fig. 14. Hanger Screws. — Hanger screws differ from lag screws in that the heads have been replaced by nuts the forms and threads of which are the same as shown for bolts in Fig. 6(a) and (c) on page 13. They are used in wood when the conditions are similar to those under which a stud would be used in metal. The stock sizes are the same as for lag screws, but the length is measured from point to the outer end of thread for the nut. The stock forms have one square or hexagonal nut and gimlet or cone point. Specify diameter, length, nut and point. Wood Screws. — Wood screws are used for light work correspond- ing to that for which machine screws are used in metal. Their diameters and lengths are measured in the same manner as for machine screws. They are carried in stock with round, flat and French heads and gimlet point only. These forms of heads are the same as those shown for machine screws in Fig. 11(c), (d) and (e) on page 22. The stock diameters and lengths are given in Table V on page 21. Specify number, length and head. CHAPTER III. KEYS AND TAPER PINS. 12. Use of Keys. — Keys are used primarily to prevent rotation of gears, pulleys, etc., relative to the shafts upon which they are mounted. This is accomplished by fitting the key so that it stands parallel to the axis of the shaft, partly within the shaft and partly within the hub of the gear or pulley as shown in end view in Fig. 15. The grooves or recesses cut in the hub and shaft to receive the key are called keyways or key seats. Well fitted keys may also prevent in some degree the tendency of the keyed mem- bers to slide along the shaft. In heavy machinery subject to shock Fig. 15. two keys placed 90° apart are often used. When so placed they insure the advantage of contact at three places even though the hub and shaft are not accurately fitted. 13. Fonns and Proportions for Keys. — Special conditions may justify the use of a great variety of forms of keys. Only those forms, however, which have become standardized and are found in general practice will be discussed in this book. All of these standard forms are of uniform width throughout their lengths. They should fit the sides of the key seats accurately. Straight keys are also of uniform thickness while taper keys vary uniformly in thickness from end to end. Each of these forms may be either square or rectangular in cross section and are called square keys and fiat keys respectively. The length of the key de- pends on the length of hub of the keyed-on member and is usually about §" longer. When the point of a driven key is not accessible, a gib or head, as shown in Fig. 16, is formed on the other end for the purpose of withdrawing the key, the proportions of the key 25 26 Keys and Taper Pins remaining otherwise unchanged. The gib is seldom required on a straight key. The measurements of keys and key seats, illustrated in Figs. 15 and 16, are made as follows: A = width of key = length of gib, B = thickness of key = height of gib, C = depth of key seat in shaft, C' = depth of key seat in hub, L = length of key. Straight Keys. — Keys without taper are used in machine tools and where accurate centering is required. Theoretically, they 5 A-f- m FiG. 16. should bear on the sides only. Such keys are usually square in cross section. Since the shafts of machine tools are designed for extra stiffness these keys are smaller in proportion to the size of the shaft than are the keys on line shafts which are usually of this same form. This is best shown by a comparison of the sizes given in Tables \T and VII. TABLE VI. Square Keys for Machine Tools. Diameter of Shaft. Size of Key. Diameter of Shaft. Size of Key. - a 1 -lA U-i^ lf-2A 2i-2ii ix 1 i^xA ix i AxA 2i- 3M 4-5^ 5i- 6^ 7-8^ 9 -10-i n -12-1 iix a ^x M ^x H l^xl^e lAxlA li^xiA The keyed piece may be prevented from sliding by means of set screws through the hub, bearing on the top of the key, but this method tends to throw the keyed member off center. Flat keys without taper (except at the point, which may be relieved slightly to assist in starting the key) are fitted to drive, bearing on all four sides. They are used on work subject to shock Keys and Taper Pins TABLE VII. Keys for Shafting. 27 Diameter of Shaft. Size of Key. Diameter of Shaft. Size of Key. lA-lf llf-2i 2A-2J 2H-3i 3A-3i 3i*-41 4T^-4i 4M-5i -X i ^x f IFX h -X 1 -X 1 |x f 1 xl Hxll Uxli 5A- 51 5H- 6i 6A- 7i 7A- 8i 8,%- 9i 9A-10- lOA-iu llA-12'- 12A-13i Ifxl^ lixli 1JX1<: 2 xli 2ixi; 2ixli 2fxli 3 x2 Six 2 and heavy loads, such as in keying cranks and flywheels to engine shafts where the tendency to push the shaft out of center is resisted by the close fitting of the hub. The thickness is usually about five- eighths of the width. Standard proportions are given in Table VIII. TABLE VIII. Flat Keys. Diameter of Shaft. Size of Key. Diameter of Shaft. Size of Key. -1 ixA 3A-3J |x - i>^-ii AxA 3A-4 1 X - lA-U fxi 4it-5 1 X a li^-lf AxA 5A-6 1 X -i lM-2 ix.A 6,^-7 1 X 2,^-21 fxf 7,^-8 lixl 2A-3 |xA 1 Straight keys, either square or flat, are usually purchased in long bars which have been cold drawn to the exact section desired and from which keys may be cut to any desired length. Specify width, thickness and length in the order named. Taper Keys. — Taper keys are used to prevent sliding as well as turning of the keyed-on member. They are also used in work subject to shock and heavy loads, such as in keying cranks and flywheels to engine shafts, and for fastening pulleys and gears to shafts, etc. The standard taper for the thickness is |" per foot of length. As these keys bear on all sides one of the key seats must also be tapered. This taper is made in the key seat in the hub. Members to be fastened with taper keys should fit the shafts very 28 Keys and Taper Pins closely; otherwise driving the key will throw them off center. The thickness of taper keys is measured at the large end. The form of the cross section at that end may be either square or flat. The proportions given in Tables VII and VIII apply equally well to taper keys. Tapered square keys, with or without gib, are listed by manu- facturers, with cross sections from |" to 3" square varying by j^" and with lengths from IJ" to 24" varying by J". Flat tapered keys are not listed except as made to order. Specify width, thick- ness and length in the order named. For the purpose of comparison, the proportions adopted for use by a few of the larger users of keys are given in Table IX in which D denotes the diameter of the shaft. TABLE IX. Proportions of Keys. U. S. Navy Sf d. Jones & Laughlin. Porter-Allen Co. Width. Thickness. AD + i" AD + i" JD AD + ^" i D -H i " tVD-Fo.i6" Feather Keys or Splines. — Where the keyed piece is to slide along the shaft the key is either made long enough to provide for this motion, or it is fastened to the sliding piece and the key way in the shaft is made long enough to permit the desired amount of sliding. Such keys, called feather keys or splines, are frequently made thicker than their width as shown by the dimensions given in Table X. This additional thickness is to provide sufficient TABLE X. Dimensions of Feather Keys. Diameter of Shaft. Size of Feather. Diameter of Shaft. Size of Feather. -1 i X f 3A- 4 1 xli lA-li Ax A 4A- 5 14x11 lA-ii 1 X i 5A- 6 Ifxlf lA-if Ax A 6A- 7 lixlf 1^-2 i X f 7A- 8 l|x2 2,^-21 f X J 8A- 9 2 x2i 2A-3 ix i 9A-10 2ix2i 3A-3^ ixl Keys and Taper Pins surface to withstand the wear due to the sliding contact and to resist the more severe load conditions due to the looser fitting of the feather key. Two keys, placed on opposite sides of the shaft, are sometimes used to improve the conditions for sliding. They are fastened in the shaft by sunk round head cap screws, the diame- t.er of the heads being about three-fourths the width of the feather. The screws should enter the shaft a distance equal to the diameter of the screw. Where a feather key is placed at the end of a shaft it is sometimes dovetailed into the shaft. Another form of feather key is designed to fit accurately into a keyway of the form shown in Fig. 19(b) on page 34. They are set into the shaft a depth equal to the width of the key and are fitted to drive. No additional fastening is necessary to secure them in place. These feather keys may be purchased in standard sizes designated by numbers. These numbers are the same as those given in Table XI for Woodruff Standard Keys and the widths and lengths agree with the values there given for the widths and diame- ters for the corresponding numbers. Specify the number of the key. 14. Woodruff System of Keys.— The Woodruff keys consist of circular segments, as shown in Fig. 17, which are set in keyways cut Fig. 17. in the shafts by means of milling cutters of the same radius as the segment. They have the advantage of adjusting themselves perfectly to any taper of the keyM'^ay in the hub, but there is also the disadvantage that the keyed-on member must always be forced on over the key after the key is in position. These keys are made in a large number of standard sizes designated by numbers and letters. Fig. 17 shows the form of the shorter keys, the proportions 30 Keys and Taper Pins for which are given in Table XI. The sizes suitable for use in the various diameters of shafts are given in Table XII. TABLE XL Proportions for Woodruff Standard Keys. G l" s& 2; -3 ID >, si ■ot4 BO>, ■saw •2 « Em P'S raw ■st A B C D A B c D 1 1 2 tV i 1^ B A A tV 2 i ^ A A 16 H Tk A ^ 3 1 2 1 ^ A 17 li TiV A ^ 4 i yv ^ 1^ 18 U 1 i A 5 5 8 1 8 ^ ife C li A A 1^ 6 1 ^ rff T^ 19 11 ■•■4 T^ A ^ 7 3 4 1 H tV T^ 20 u 8V 6V ^ 8 i ^ ^ Vs 21 11 ■•■4 1 4, * ^ 9 3 1 fk ^ tV D u tk A ^ 10 i tV ^ i^ E 11 ■•■4 3 8 A A 11 1 A ^ T^ 22 1* 1 4 1 8 A 12 * A 1^ T^ 23 J-8 fk A A A * i i tV F 1^ 3 8 Vk A 13 1 t\ A T^ 24 ■•-2 i i «V 14 1 3^ _7_ 64 ^6 25 H A A _7_ 64 15 1 1 4 i A G li i A A TABLE XII. Diameter of Shaft. Number of Key. Diameter o£ Shaft. Number of Key. A- f 1 ii^-ii 1 2, 4 3, 5 3, 5, 7 6, 8 6, 8,10 9,11,13 9,11,13,16 lA li-lA if-iA ii-i| i-i-l-| I1I-2 2A-2 4 11, 13, 16 12, 14, 17, 20 14, 17, 20 15, 18, 21, 24 18, 21, 24 23,25 25 In the longer keys the distance, D, is considerably increased, otherwise the form of the key differs only in the squaring of the ends that project above the shaft. Sometimes, where longer keys Keys and Taper Pins 31 are desirable, two or more keys of the shorter form are set in the shaft end to end. Specify the number of key in the bill of material. 15. Keyways or Key Seats. — Practice is not wholly uniform as to the relative depths of the keyways in the shaft and in the hub. In the United States the ordinary practice is to make the depth of each equal to one-half the thickness of the key. This depth is measured at the side of the keyways as shown in Fig. 15 on page 25. For a taper key the keyway in the hub is tapered and its depth is measured at the deeper end. 16. Taper Pins. — Taper pins are used to prevent rotational or axial sliding between bodies through which they pass. The holes for tapered pins are reamed to the same taper as the pin and the pin is driven tight. They may also be used in the place of keys in light work. Standard taper pins (usually called "Pratt & Whitney Standard Taper Pins") have a uniform taper of J" in diameter per i Pig. 18. foot of length. The length is measured from end to end of the uniform taper as shown in Fig. 18, the ends being convex. They are made in standard diameters designated by numbers and with TABLE XIII. Proportions for Taper Pins. 00 1 .2 3 4 Length, L. Diameter, D. W 0.136 0.156 0.172 0.193 0.219 0.250 p. 5 6 7 8 9 10 Length, L. 1 u n 1* Diameter, D. W 0.289 0.341 0.409 0.492 0.591 0.706 32 Keys and Taper Pins lengths varying by |"- The exact and approximate diameters of the large end and the stock lengths for the different sizes are given in Table XIII. The limits of the stock lengths and diameters listed by differ- ent makers vary slightly. The range included in Table XIII may be considered representative of ordinary practice. Specify number and length of pin. CHAPTER IV. SHAFTING AND SHAFT FITTINGS. 17. Shafting. — A shaft consists of a long, cylindrical bar of wrought iron or steel so mounted in bearings that it may rotate about its own longitudinal axis, transmitting this rotation to other machine parts which are attached to it. That portion of the shaft which lies within the bearing is designated as the journal. The bearings are sometimes called journal boxes or simply boxes. Shafting is the term applied to the stock material of cylindrical form from which shafts are made. Formerly wrought iron was the material chiefly used. It was rolled when hot into cylindrical bars and when cold turned in lathes to exact size and polished. The stock sizes of the hot rolled bars varied by J" and they were reduced xj" in finishing thus establishing a set of stock sizes for shafting varying by J" but always ys" less than each even J" in diameter. In later years the wrought iron shafting has been largely supplanted by steel which has been rolled to exact size when cold, and is known as "cold rolled shafting." Increased facilities of manufacture and more exact methods of design have led to more stock sizes. These vary by smaller inter- vals and start from the even inches as a base. In all cases, how- ever, where the interval in these stock sizes is greater than ys" the • old standard sizes are maintained in addition. The lists of some of the representative dealers give diameters varying by j^" from Ys" up to 4" and by |" up to 5". Shafts above 5" in diameter are usually forged to order. The commercial lengths vary greatly but approximate 24 feet for full length pieces, with 30 feet as a maxi- mum. Dealers furnish shafting to specified lengths. A small extra charge is made for pieces under 12' or over 24 feet in length. These limits vary somewhat with the different dealers. 18. Keyways. — Machine parts which are attached to a shaft may depend wholly upon the tightness of their grip and friction for the driving power received but, except for hght loads, it is customary to make the connection positive by inserting keys as 33 34 Shafting and Shaft Fittings described in article 15 on page 31. Owing to the improved facili- ties possessed by the makers and the larger dealers for cutting the keyways in shafting, it is usually advisable to purchase shafting with the keyways cut to order. These keyways may be cut with an ordinary milling cutter having a width equal to the width of the key, which leaves the ends curved to the radius of the cutter as shown in Fig. 19(a), or they may be cut with an "end mill" having a diameter equal to the width of the key. In keyways cut with an end mill the ends may be left semi-circular as shown in Fig. 19(b), or, after cutting with the "end mill," the ends of the keyway may be cut out square as shown in Fig. 19(c), by chipping with a cape (a) (b) Fig. 19. ic) chisel. These forms are increasingly expensive in the order given on account of the additional labor and equipment required. Key- ways of the second form of limited size may be cheaply made in small shafts for machine tools. 19. Couplings.^ — ^As stated in article 17, shafting is made in relatively short pieces which must be fastened together end to end when in place so that their centers shall at all times be truly aligned. Many of these fastenings may be of a permanent nature while others must be of a nature to permit disconnection at frequent intervals. Those of the latter class are commonly called clutches or clutch couplings. 20. Permanent Couplings. — ^There are several types of per- manent couplings. For very light work a sleeve coupling may be used. This consists of a simple sleeve, as shown in Fig. 20, into Shafting and Shaft Fittings 35 which the ends of the shafts may be inserted and secured by set. screws. It is necessary that the heads of these set screws shall be sunk into the sleeve or that headless set screws be used to avoid Fig 20. Fig. 21. danger to workmen. Sometimes, where keyways in the shaft are objectionable or have not been provided, keyless couplings are used in which the grip on the shaft is frictional only. The neces- sary pressure is obtained by forcing the halves of a sleeve together by means of rings driven over the tapered ends of the sleeve as shown in Fig. 21, or by forcing a sleeve on over a tapered bushing by means of bolts as illustrated in Fig. 22. Fig. 22. Where a more positive connection is desired keys may be used with a sleeve in which case it is made in halves, as shown in Fig. 23, to bolt together over the keys when they are in place. It would Shafting and Shaft Fittings otherwise be necessary to make the keyways in the shafts extend beyond the sleeve an amount equal to the length of the key, to Fig. 23. allow the key to be inserted. Any of these couplings which tighten up on the shafts are known as compression couplings. Fig 24. A positive connection may also be obtained by the use of flanged couplings, illustrated in Fig. 24 and shown in section in Fig. 25. These couplings are generally finished all over and the overhanging Fig. 25. Shafting and Shaft Fitting 37 rim prevents danger from the clothing of workmen catching on the bolt heads or nuts. The bolt holes are reamed for coupling bolts as described in article 7 on page 14. These bolts are made to fit the holes accurately in order that each bolt shall take its share of the load. The accurate centering of the shafts is secured by extending one of them entirely through its coupling until it enters the mating coupling on the other shaft or, at an added expense, the face of one of the flanges may be recessed to receive a corresponding projection on the face of the other as shown in section in Fig. 26. The following empirical equations were derived from the com- mercial cast iron couplings of one of the leading makers. The Fig. 26. dimensions determined from these equations are to be taken to the next larger or the nearest tb " or |" according to the judgment of the draftsman. A = diameter of shaft. B = If A + l" C = l|A + 2d + IJ". D = l|A + 4d + li". E = 2j^A-|-lf". F= l + d. ■12"). G = iA + U" (sizes li" = |A + f"(sizes3|"- H = AA + I". J = yjA + Y2" but not less than |". K = ^A + Te " but not less than |". L = xfA + 4 "• 38 Shafting and Shaft Fittings n = number of bolts = f A + 3. d = diameter of bolts = |A + ys"- I = length of bolts = G + d + |". 21. Clutch Couplings. — There are two general classes of clutch couplings; jaw clutches, in which there is a positive connection made by the interlocking of projecting parts, called jaws; and friction clutches, in which the connection is wholly frictional and produced by forcing blocks of wood or other material firmly against a disk of metal. Jaw Clutches are made either with square jaws. Fig. 27(a), or with spiral jaws. Fig. 27(b) . One set of jaws is keyed firmly to the end of one of the shafts while the matmg set slides on a feather key in the other shaft to mesh or release as desired. The number of . I (a) Fig. 27. ib) jaws is usually two or three, varying with the size of the clutch. The angles between the successive jaws must be accurately con- structed in order that the load may be properly divided between the jaws. Those with spiral jaws are more easily thrown in but will drive in one direction only, and hence must be made in right- hand and left-hand shapes. Square jawed clutches will operate in either direction but require a small amount of backlash (rota- tional play between the jaws when in mesh) to facilitate throwing in. It is necessary that the end of the driven shaft shall be con- tinuously sustained in alignment with the driving shaft. For this purpose there is inserted into the jaw which is fixed to its shaft a finished ring into which the end of the other shaft projects, as shown in Fig. 27(a) . This ring is made separately and afterward fastened in place, in order to facilitate the machining of the jaws. Since the ring turns on the end of the shaft when the clutch is thrown out. Shafting and Shaft Fittings 39 oil holes must be provided for lubrication. It is usual to provide an oil hole in each space between the jaws so that one may always be available when oiling without turning over a heavy shaft. The sectional drawing, Fig. 28, shows a clutch with three square jaws and with the finished ring removed. The proportions given in the following empirical equations were derived from the dimen- FiG. 28. sions of commercial cast iron clutches sold by one of the leading makers and are suitable for either square or spiral jawed clutches. A backlash of 2° is allowed in the square jawed clutches. A = diameter of shaft. B = If A + f". C =2|A + 1|". D = IIA + A"- E = fA + f". 40 Shafting and Shaft Fittings F = A + 1". G = IIA + U". H = lfA + i". M=iA + |". The finished ring is also of east iron and is held in position by means of headless set screws placed one at each jaw, with half its diameter in the ring and half in the jaw. The points of these screws should Fig. 29. bear in order that the screws may be tightened. The following table gives the sizes of set screws used in the different sizes of clutches'. Shaft. Set Screw. Diameter. Diameter. Length. i i i i i i The sliding jaw is given an overtravel of J" for shafts up to l^e" diameter, f " from 1|" to 4||-", and |" above 5". Jaw clutches are thrown in or out by means of a lever or shifter of the general form illustrated in Fig. 29. This is connected to a collar. Fig. 27(b), that runs in a groove in the hub of the part of the clutch which slides on the feather key. This collar is of cast iron made in t'wo pieces to bolt together in the groove as is shown in the liey drawing, Fig. 80, to which the following empirical proportions apply. Shafting and Shaft Fittings — rS-H 41 Fig. 30. A = diameter of shaft. H = (see Fig. 28). J = (see Fig. 28). M= If A + 2i". N = B + Jf"toB + i« O P - 8 UP. 2d + i". Ij A but not less than I5" d + ^". 2A + IJ"- 8 -^ T^ 8 • Q R S T d I diameter of bolts = 1^ A + 3%' length of bolts = S + d + |". The hub turns continually in the collar when the feather key is in the driving shaft, or in any case, when the clutch is in. An oil hole must, therefore, be provided in one-half of the collar in such a position that it may be up at whatever angle the lever may be given in setting up. The lever may be vertical, horizontal, or at any intermediate angle as desired but, in the middle of its throw, it should stand approximately at right angles to the shaft. It is made of wrought iron and tapers to a handle at the end, as in Fig. 29. The fork is forged in parts so that they may be placed over the projections on 42 Shafting and Shaft Fittings the collar and then be bolted to the lever as shown in the key draw- ing, Fig. 31, to which the following proportions apply. A = diameter of shaft. P= (see Fig. 30). a = 2j^A + l|". b = liA+lf". c = 2P. e = P + A". f = If P. h = |g. k = |c + |". ni= diameter of boks = g. n = 3g. Fig. 31. Friction Clutches are made in too many forms and of construc- tion too complex for discussion here but their general characteris- tics are illustrated in Fig. 32. A collar sliding on the shaft controls the levers which operate the friction grip. Sliding of this collar may be effected by a hand lever like that illustrated in Fig. 29, if the clutch is small. For large clutches, a hand wheel and gears as illustrated in Fig. 33 are used to operate the lever. These clutches Shafting and Shaft Fittings 43 are largely used where the connection has to be made when the driving shaft is in motion at a considerable speed, since they avoid Fig. 32. the sudden shock of a positive connection, but they have the disad- vantage of requiring good adjustment to prevent slipping under load. 22. Collars. — A shaft is prevented from endwise motion through the supporting bearings by means of collars, Fig. 34, which are clamped to the shaft by means of set screws. The finished sides Fig. 33. of these collars bear against the finished ends of the bparings. Formerly plain collars of rectangular section with standard set screws were used. These were dangerous because of the projecting set screw heads which caught the clothes of workmen, winding 44 Shafting and Shaft Fittings them about the shaft. Many states now have laws prohibiting their use. The common headless set screws which are slotted so as to be tightened with a screw-driver were too weak to be satis- factory when used with the plain collars but the introduction of Fig. 34. safety set screws. Fig. 13, page 23, has removed this difficulty. Such screws used with the plain collar should be short enough to be entirety beneath the surface of the collar when tightened. In the safety collars, Fig. 34, the set screw head is surrounded by a ring and the projecting flanges at the sides protect the work- men from contact with this ring as it revolves. Safety collars of Fig. 35. the general form shown are made in halves that may be bolted together around the shaft and thus avoid taking down a shaft to put on an additional collar. The following empirical proportions for safety collars were derived from dimensions taken from com- mercial collars of the form drawn in section in Fig. 35 and sold by one of the leading makers. One low head set screw is used for shafts under 3" in diameter and two for larger sizes. Shafting and Shaft Fittings 45 d = diameter of set screw. L = length of set screw. A = diameter of shaft. B = A + 2L + d. '-' = s^A + g". D = AA + 1". E = ^VA + i", but not to exceed D + i". One Set Screw. Two Set Screws. d L M N d + I". 2 d + f ". 2d + i tsA + f '', but not to exceed ^ A. 2d- i". 3i d + i". 2 d, but not to exceed d + f ". CHAPTER V. SHAFT FIXTURES. 23. General Nature. — Under the head of shaft fixtures are included all of those fixed parts by means of which a shaft is sus- tained in its proper position with regard to the building in which it is located. These fixtures may be conveniently divided into the bearings, which are actually in contact with the shaft, and the bearing supports intermediate between the bearing and the posts, walls, or floor timbers, which furnish the ultimate support for the shaft. 24. Purpose and Qualities of Bearings. — The purpose of a bear- ing is to support a shaft and to constrain it to revolve about its own axis while the bearing remains attached to some stationary body. For this reason it must present a polished, well lubricated inner surface for contact with the surface of the shaft. This sur- face must be of such material as to cause the least possible damage to the shaft in case of failure of the lubrication and, at the same time, to resist wear when properly lubricated. Cast iron furnishes a fairly good surface as long as it is well lubricated but, in case the lubricant fails, it does great damage to the shaft because of its superior hardness. To save the shaft the bearing metal should, be the softer. Materials, such as brass, bronze, or babbitt metal, which combine this softness with the requisite wearing qualities are too expensive to use for the construction of the whole of the bear- ing and are used simply as a lining for the inner surface, the frame or remainder of the bearing being of cast iron. In case of damage these linings are easily replaced. When the lining is of brass or bronze it is usually machined to fit a correspondingly machined surface of the cast iron frame. Linings of babbitt metal, owing to its low melting point, are cast in the frame which is already completed in other ways. There are grooves or holes, called anchorages, in the inner surface of the frame, into which the metal sets and is prevented from rotating or sliding axially. In the cheaper bearings a short piece of shafting 46 Shaft Fixtures 47 of the proper diameter is carefully centered in the frame with close fitting collars at the ends and the babbitt metal poured around the shafting. The shrinkage of the metal as it cools tends to draw such linings away from the frame. The better bearings are poured with a surplus of metal which is afterward hammered into the anchorages and the surface machined to size. 25. Forms of Bearings.^ — The varying positions of the shaft, methods of supporting the bearings, and methods of supplying the (a) (b) (d) (c) Fig. 36. (e) 48 Shaft Fixtures lubricant to the bearing surfaces have resulted in so many forms of bearings that but the briefest mention may be made of them in this book. Usually the shaft is horizontal and the bearing is of some such form as shown in part section in Fig. 36(a). If it be vertical the general form, changes to that of Fig. 36 (b). Since the set screws of the collars described in article 22 cannot be depended upon to support the weight of the shaft, there must also be pro- vided for a vertical shaft a special form of bearing, known as a step bearing, Fig. 36(c), in which the lower end of the shaft rests. Bearings may be solid, as in Fig. 36(b), requiring to be slipped on over the end of the shaft. In most cases, however, they are split along the center line of the shaft. Fig. 36(a), so that it may easily be removed. This also provides opportunity to take up looseness due to wear. These parts are designated as the cap and the base and they are held together by two or more bolts, known as the cap bolts. A bearing may be supported from beneath, requiring a flat bottom for the base. Fig. 36(a) ; from the side, requiring a vertical side on the base. Fig. 36(d); or it may be suspended on pivots at the center. Fig. 36(e). The lubricant may be supplied through an oil hole. Fig. 36(d) ; it may be carried from an oil reservoir by a wick, which is pressed against the shaft. Fig. 36(a); or it may be carried up to the top of the shaft from a reservoir beneath by means of rings or chains, Fig. 36(e), which rest upon and revolve with the shaft, while dipping into the oil in the reservoir. 26. Adjustments of Bearings. — In order that a shaft may run properly its axis must be as near to a straight line as it is practicable to obtain. To accomplish this straightening or alignment of the shaft provision must be made so that the supporting bearings may be adjusted either vertically or horizontally or in both directions in a plane perpendicular to the axis of the shaft. One of these adjustments, the horizontal, in the case of Fig. 36(a) and the vertical in Fig. 36(b) and Fig. 36(d), is usually provided for by elongation of the holes in the base through which it is bolted to a support. These bolts may be designated as the holding bolts to distinguish them from the cap bolts. The remaining adjustment, or, in the case of Fig. 36(e), both adjustments, should be provided in the support for the bearing. The making of these adjustments is called aligning the shaft. Shaft Fixtures 49 In split bearings provision is made to prevent the shaft from becoming loose as the lining of the bearing wears away. When the lining is new thin strips of metal or hard pressed paper, called liners or shims, are placed on each side of the shaft between the cap and base so that the cap bolts may be tightened firmly without pinching the shaft. These liners are then removed one at a time Fig. 37. as the wear progresses until all have been removed, when a new lining is put in and the process repeated. In split bearings the edges of the linings along the division should be chamfered so that the lubricanlj may not be scraped off and forced out at the joint but may be drawn around with the shaft. This chamfering should not extend to the ends of the bearing lest it furnish a means of escape for the lubricant. Endwise adjustpent of horizontal shafts is provided by means of setting the coUai-s (see article 22 on page 43) which bear against 50 Shaft Fixtures the finished ends of the bearings. In vertical shafts this adjust- ment is made by raising or lowering the step bearing. 27. Proportions for Babbitted Bearings. — ^The following empiri- cal equations were derived from measurements taken from a simple form of commercial babbitted shaft bearing, designed to be sup- ported from beneath and having oil hole lubrication as shown in the key drawing, Fig. 37. In small beariags, for shafts less than 2f " in diameter, two cap bolts are used and holes drilled for babbitt anchorages. In larger sizes four cap bolts are used and dovetail grooves cored for the anchorages. To prevent endwise displace- ment of the babbitt these anchorages should not extend to the ends of the bearing. The cap bolts and holding bolts are provided with hexagon nuts. A = diameter of shaft. d = diameter of holding bolts = |A -|- 3^ "but not to exceed JA. di = diameter of cap bolts = f d. t = ^A + ^", but not to exceed ^A + j^", or i"- B = length of bore = 3A. C = lj^A + 2t + i". D = C - iA. E = If A -I- 4" (4 cap bolts), = G -f J -f 3d -f JA -f V' (2 cap bolts). F = E + 3d + i". G = l|A + 2t + di-hi". H = f A + IJ", but not to exceed A. J = 2 di + I"- K = H + J + jijA + I" (4 cap bolts), = l|A-fi"(2capbolts). L = I A, but not less than |C + |". M = |C - AA + I", but not to exceed A. N = xVA + A"(approx.). P = I A, but not less than J A + |". R = P-- 8 S = lA - 1" Shaft Fixtures 51 T = 2(1 + i". U = 2d + |". V = iA + i". W=l|di + i". X = not less than di + yS ". Y = fA + i". Z = ^jA. In order that the oil hole in the top of the cap may be made without machining or coring it is made large enough to mold in x-IKu-l xH.k^^j^H HGI- FiG. 38. green sand. The oil is preyented from flowing out around the shaft too freely by filling the oil well with cotton waste or other absorbent material. The general proportions given below, which apply to the key drawing, Fig. 38, are for the type of babbitted bearing suitable for machine frames. The grease cup shown may be replaced by any suitable form of oiling device without other changes in the bearing. Through bolts should be used whenever possible. If the bearing 52 Shaft Fixtures is so placed that this is not possible, studs or tap-bolts may be substituted. The offset in the division between the cap and the base is machined to an accurate fit and prevents sidewise displace- ment of the cap. The cover to the oil well being a separate casting may be relatively thin. A = diameter of bore. B = length of bore = A to 4 A to suit conditions. t = thickness of babbitt = y6 A + 5 ", but not to exceed yj A + i " . C = A + 2t. D = l|A + i". d = diameter of bolts = 1^ A + i" (use 4 except for short bearings, then use 2) . E =D + lid. F =iB. G = d -t- 1". H = 2 d -f i". J ^ IfA + i". K = |A + i". L =it. M=^A + i". N = M-hK. P = |A or to suit. Q = I A or to suit. R = ft. S = 3t-i". T =2t-|". U = j^A + A". V = iB. W= |U. Y_ _3_ A J 3_// — 64 -^ T^ 16 - 28. Quarter-box Bearings. — These bearings get their name from the fact that the bearing surface or box is divided into four Shaft Fixtures 53 parts or "quarters," Fig. 39, each of which may be moved up against the journal by means of independent adjusting wedges or screws. By this means any wear that may have occurred can be taken up in a more nearly correct manner than could be done with Pig. 39. bearings divided into but two adjustable parts. When the wear in a bearing is due to a resultant pressure in a single direction, such as the weight of the supported shaft alone, a two-part bearing will provide the only needed adjustment. When, however, the direc- tion of this resultant pressure changes during the rotation of the shaft it becomes necessary to provide a more complete adjustment to take up the wear, and aJ^o to keep the shaft in true alignment. 54 Shaft Fixtures Bearings of this type are much used for steam engines and are usually of quite large dimensions . They are not purchasable alone . Either the base is a part of the engine frame or it is a pedestal designed especially to be attached to the engine frame or to its foundation. The base is recessed to receive the parts of the box and the adjusting wedges. A strip in the center of the bottom of this recess is machined to receive the bottom section df the box, which may or may not be provided with a vertical adjustment by liners or a wedge. A portion of each side of the recess is machined to support the adjusting wedges which move the box and shaft horizontally. This adjustment is necessary to keep the correct distance between the center line of the shaft and the center of the cylinder. Each of these wedges is drawn up by means of two studs passing through the cap which, since they cannot be drawn tight without binding the shaft, are kept in position by tneans of jam nuts. The motion of these wedges should be sufficient to take up wear equal to one-half the thickness of the babbitt on each of the side sections of the box. The cap and base are machined to an accurate fit at the sides and a strip in the center of the under side of the cap is machined to bear on the top section of the box. The cap is drawn down by means of studs set in the top of the base until the top section of the box bears firmly on liners placed between it and the side sections . Each of the sections of the box is machined for contact with the adjacent sections. These boxes when worn or in case of accidental over-heating have to be removed to be relined with babbitt. It is, therefore, desirable that it should be possible, by loosening the cap and blocking up the shaft, to slide them out and replace them without removing the shaft from position. Where this sliding is endwise it is necessary to attach a circular plate to the frame or pedestal and around the shaft or to provide some other means to keep them from working out from the vibration of the engine while run- ning. Under normal conditions the lubricant is oil fed either from large oil cups or piped to the bearing from a tank. In addition there is usually a provision for an emergency lubrication by packing a recess in the cap with some solid grease that will melt and flow into the bearing should the temperature rise above the normal. Shaft Fixtures 55 There are many designs of quarter-box bearings, that of which the description has been given and to which the following empirical proportions apply, being one of the simplest. Some of the varia- tions from this design are, use of a single adjusting wedge; substitution of set screws for the adjusting wedges ; adjustment of the lower box by means of a wedge; adjustment of the upper box by means of set screws ; and making the bearing self -oiling by pro- viding an oil reservoir and oiling chains running in suitable chan- nels in the boxes. A = diameter of bore. B = length of bore = lJAto2jA. C = 0.225 A -I- i". D = |A. E = diameter of wedge bolts = J■^^. + j". (Core holes in cap J" to ^" larger.) F = minimum thickness of wedge = 2 E. (Taper = li" in 12".) G = diameter of cap bolts = j-^A + I". (Core holes in cap J" to J" larger.) H = 2 G -f i". T — J-A -I- 1" J =AA-FJ". K = 0.45 A -I- i". L =iA + i". M.= ^\A + i". N = f M. O = f M. P = |M. Q = f M. R = f M. S =iB. T = iA -+- f "- U = f T. V = ^VA + i". 56 ■ Shaft Fixtures 29. Bearing Supports. — Bearings may be attached directly to the top or to the under side of floor timbers, to posts, or to walls- It rarely occurs, however, that the shaft is brought into the desired position when so fastened. Interposing an intermediate member Fig. 40. not only removes the shaft farther from the wall, floor, or ceiling but may also provide a convenient adjustment for aligning the shaft. These intermediate members vary in size and proportion according to the diameter of the shaft with which they are used, and with the distance of the shaft from the floor, wall, or ceiling from which it is supported. Fig. 41. 30. Stands and Base Plates. — When the shaft is to be supported from beneath, the intermediate member may have the general form of the floor stand, Fig. 40. The stock sizes vary by 6" in nominal height up to 42". This height may, in each size, be varied a small amount (usually less than an inch) by means of the adjusting wedges. These are operated by meaiis of the set screws and secured by the jam nuts shown at the sides. When it is desirable that the elevation of the shaft from the floor shall be small a base plate, Fig. 41, may be used in the place of the stand. This may or may not have the provision for vertical adjustment. Shaft Fixtures 57 31. Wall Brackets. — When the bearing is to be supported from a wall or post it may be placed upon a wall bracket as illustrated Fig. 42. in Fig. 42. These brackets are fastened to a wall by means of through bolts, or to wooden posts by means of hanger screws, or HSk 58 Shaft Fixtures lag screws. The holes in the bracket for these fiastenings are elongated vertically to provide an adjustment for aligning the shaft. In order to reduce the number of stock sizes of these brackets, the manufacturers proportion them so that the distance of the shaft from the wall, called the extension of the bracket, may be varied a sufficient number of inches either way from the nominal value so as to meet the extensions of the adjacent sizes. For the same reason the proportions for each nominal extension of bracket, which vary with the diameter of the shaft to be supported, are taken suitable for a certain maximum diameter of shaft and that bracket used for the several diameters of shaft next smaller. These considerations determine the values of C, D and E in the following proportions which were taken from the catalogue of a prominent maker and which apply to the key drawing, Fig. 43. In these pro- portions, A is the diameter of the shaft to be supported; B is the nominal extension of the bracket ; E is the diameter of the holding bolts for the bearing, the square heads of which are placed in, and held from turning by the sides of, the grooves in top of the bracket. A B c D E F G A B c D E F G n 12 8 4J a f 3 3f 12 11 6f 1 1 1 18 8 4i ^ i 18 11 64 1 1 14 to 24 8 H i 1 to 24 11 6f 1 14 14 30 8 4J i 7 14 30 11 61 1 14 If 24 36 8 4i i 1 U 44 36 11 61 1 li 14 2f 12 10 5f 7 8 7 8 7 8 41 18 10 5* J * 1 18 12 7* 1- 14 1- to 24 10 5f 7 8 1 14 to 24 12 7* llf 14 1^ — '30 10 5f i 1 H 30 12 74 1- 14 1- 34 36 10 5i 7 8 H i| 54 H = E + 4". N = B + C. T =F + I = 14 E + 4". = 2F. U = JD. J =fE. P =2F + M. V =2F. K =I + 2J. Q =K + 3F. W = 4F. L =E + Jj". R = Q + 3F. X = 4G. M = E - 4"- S =P + 2F. 32. Wall Box Frames. — When it is necessary to have a bearing where a shaft passes through a wall, a wall box frame. Fig. 44, is set in the wall to support the bearing, which is fastened to it by means of bolts or studs. This frame may be provided with wedges for Shaft Fixtubes 59 vertical alignment of the shaft as shown in Fig. 44, or the bearing may be bolted directly to the bottom of the frame as indicated in Fig. 44. the key drawing, Fig. 45, to which the following description and empirical proportions apply. The raised strips on the inside of the bottom of the frame are to provide the necessary finished surface for contact with the finished portion of the bottom surface of the base of the bearing without machining the entire surface. Since each size of frame takes several sizes of bearings the width of these finished strips must be suflBcient to permit the finished portions extending across the ends and center of any size of bearing, within the range used with this frame, to rest wholly on the strips when at E- -JD ■T^L- 1hH -E Fig. 45. the extreme points of sidewise adjustment in either direction. Should there be a considerable space between the outer and center strips in any frame additional intermediate strips may be placed there to furnish a support to the bearing along the edge of the base. The sizes of these frames are designated by numbers, each num- ber serving for sizes of bearings as follows: 60 Shaft Fixtures Frame Number. 1 2 3 4 5 If 2| 31 4i 6 to to to to to 2i 3i • ;3^4j 5i 6i Diameter of Shaft. 7 to 7i • 2 In general they must be designed with reference to the particu- lar form of bearing they are to support. The proportions here given were determined for use with the babbitted bearing described in article 27 on page 50. A = maximum diameter of shaft to be used in frame. B = 2iA + 2i". C = 2t A + 7"- D=f A. E = i^A + W. F = E + i". G-IB. H = iA. K = jC = width of frame. L = distance between holding bolts for bearing (see article 27) . 33. Hangers. — When the bearing is to be supported from above, the intermediate member takes the form of a drop hanger, Fig. 46, which receives a bearing of the type shown in Fig. 36(e) on page Fig. 46. Shaft Fixtures 61 47. Horizontal adjustment is provided by the elongated holes for the bolts at the top of the hanger and vertical adjustment is secured from the pivot screws shown above and below the bearing. The drop hangers are carried in stock with different amounts of drop increasing by 2" intervals from 8" up to 24" and by 6" Fig. 47. intervals from that to 36" except that shafts above 3" in diameter require more than the minimum drop of 8". An adaptation of these hangers for attaching to a post is shown in Fig. 47. These post hangers provide no variation of the distance of the shaft from the post. At the left of each figure may be seen the brace links which may be removed so that the shaft may be dismounted without removing the hanger from its fastenings. CHAPTER VI. TRANSMISSION MEMBERS. 34. General Statement. — In this chapter are considered some of those machine parts which are usually attached to revolving shafts. These include such members as pulleys, gears, cams, etc. Their adjacent members such as belts and cam followers are briefly mentioned. No attempt has been made to carry the discussion beyond the information needed for the drawings of a brief course in Empirical Design. 35. Pulleys. — The use of pulleys either keyed to shafts for the purpose of transmitting power or running loose on shafts for the purpose of guiding or supporting belts is too common to require any description. Pulleys are usually made of cast iron, of wood, of stamped steel or of combinations of these materials. They are made both solid and split. Split pulleys consist of two equal halves bolted together at hub and rim. Otherwise the proportions are the same as for solid pulleys. Driving pulleys and those under heavy loads should be keyed to the shaft. Those under light loads may be secured to the shaft by means of set screws or the compres- sion of bushings. There is a wide variation in the diameters of shafts upon which a pulley of any nominal size (outside diameter) may be used. The hubs are made large enough for, the largest probable diameter of shaft. In solid pulleys, and in split pulleys which are to be keyed to the shaft, the hubs are bored and the keyways cut to order before shipping from the factory. Split pulleys which are to' be secured by the compression of bushings have their hubs already bored to receive the largest diameter of shaft. For shafts of smaller diameters split bushings are supplied to make the necessary reduc- tion. Such pulleys and a supply of bushings are usually carried in stock by dealers. The stock sizes vary to some small extent with different makers. In general they vary by 1" from 6" to 36" in diameter and by 2" from S6" up to 144"- The widths of face vary by 1" from S" up to 62 Transmission Members 63 12" and by 2" from 12" up to 60". The minimum stock width increases from 3" for pulleys 36" and less in diameter, up to 12" for 112" and over in diameter. The maximum width of face increases from 12" for pulleys 6" and 7" in diameter, up to 60" for pulleys 96" and over in diameter. When the hubs are bored and the keyways cut to order the width of face may be reduced from the nearest stock size to any desired width at a slight added expense. Ob- viously any change from a stock diameter will require building entirely to order at a correspondingly increased cost. The arms of pulleys are usually elliptical in cross section. The arms of very large cast iron pulleys are tapered both in width and \-E~i Fig. 48. thickness, those of smaller pulleys in width only. The amount of taper in width varies fromj" to |" per foot per side, and in thick- ness from I" to j^" per foot per side. The thickness of pulley arms is made from 0.4 to 0.5 the width. The wider pulleys are made with a double set of arms to sustain the rim. Some pulleys not so wide in proportion to their diameters are made with either single or double sets of arms. In addition to the bore of the hub and the face of the rim the ends of the hub and the edges of the rim are finishied. The following proportions for cast iron pulleys having six arms apply to the key drawing, Fig. 48, when all dimensions are in inches. A = diameter of shaft. B = diameter of pulley. 64 Transmission Members C = width of face = 1 J width of belt. D = f -V B X C for single belts, = j^ V B X C for double belts. E = D-^BtoD-JjB. F = JE (taken to next larger yj" for values less than §")• G = j" per foot width of face. (This is an average value. The crown is made greater on narrow pulleys and less on wide ones.) H = f C, (This is an average value. H should be greater for loose than for tight pulleys.) = I C + ]^B + 1 "- (This gives good values for tight pulleys.) J = A + f D but not to exceed If A + i"- K = diameter of set screw = ^ (J — A) + 1^" when bearing on shaft, = width of key when bearing on key. L = 2K. M= iK. N = H K. The following equations give satisfactory radii for drawing the several curved surfaces but should not be given as dimensions. Fig. 49. For the crown of the pulley R = C'^-^SG. For the ellipse of the arms, Fig. 49, ri = f the major axis, n is found by trial to pass through the extremities of the major axis and tangent to the arcs of radius n. 36. Belts. — ^The discussibn in this article will be confined to belts of flat cross section^uch as would be used op. pulleys having rims of the general form snown in Fig. 48. Belts may be made of leather, of cotton, of rubber, or of combinations of these materials. Transmission Members 65 The ends of the belt are fastened together as smoothly as practic- able, forming a closed loop Avhich is passed tightly over the faces of two or more pulleys. Its ability to transmit power is dependent upon the tightness of the belt on the driving and driven pulleys, upon the friction between the belt and the pulleys, and upon the area of cross section of the belt. In commercial belting the stock sizes of cross sections vary both in width and in thickness. Leather Belting. — The different thicknesses of leather belting are obtained by cementing together two or more thicknesses of leather. Such belting is known as single, double, triple and quadruple leather belting according to the number of thicknesses (W Fig. 50. used. Single belting, ys" to i" thick, and double belting, ■^" to ys" thick, are the thicknesses commonly used. The standard widths of leather belting are, i" to 1" varying by |"; 7" to 28" varying by 1"; 1" to 4" varying by J"; 28" to 40 '^ varying by 2"; 4" to 7" varying by §"; 40" to 72" varying by 4". •The following empirical equations give good values for the power ^hich may be transmitted by leather belts having effective tensions of 38 pounds and 60 pounds per inch of width for single and double belts respectively, at speeds not exceeding 1,000 feet- per minute. D = diameter of pulley in inches. N = revolutions per minute of pulley. W = width of belt in inches. H. P. = horse power transmitted ■ tor single belts, \ 3,300 WDN for double belts. 2.100 ^ 37. Handwheels. — ^A handwheel is used in the place of a crank or wrench in places where it is desirable to be able to grasp with the 66 Transmission Members same ease and force in all phases of a rotation. The handwHeel consists of a hub and spokes of the form usual to pulleys, and a rim of such form as to readily fit the hand. The rim is most frequently Fig. 51. circular in section or modified as in Fig. 50(a) to afford an easier grip for the larger sizes. The U. S. Navy uses a rectangular form with the comers slightly rounded in its smaller sizes and modified to the form of Fig. 50(b) in its larger sizes. Small sizes may be finished all over but in the larger sizes the rim and ends of the hub alone are finished. The spokes or arms are usually straight but may be curved as in Fig. 51 to relieve stresses due to shrinkage in rK,H Fig. 52. Transmission Members 67 casting. The most common cross section is in the form of an ellipse. Handwheels are not carried in stock and no standard propor- tions can be given. The nominal size is the outside diameter of the rim. Table XIV gives good values for the dimensions shown in the key drawing, Fig. 52, for the 6" and 16" sizes. Values for these dimensions for other sizes from 4" to 24" may be obtained by the graphical method described in article 3 on page 5, using a straight line for the curve, in each case. TABLE XIV. Proportions for Cast Iron Handwheels. A B c D E F G H K 6 16 f li 2.i a ■ f li 1 3 1 5 8 i i 1 8 li 38. General Nature and Properties of Gears. — ^A gear consists primarily .of a hub and arms, similar to those for pulleys, which ^^^ftT»».^ w support a rim upon the surface of which teeth are formed. These teeth interlock with the teeth of a mating gear. Fig. 53, to transmit the power. Where one of these gears has a small number of teeth it is known as a pinion. There is an imaginary smooth surface passing through the teeth of each gear at approximately their mid-height which rolls upon the corresponding surface of the mat- 68 Transmission Members ' ing gear. These imaginary surfaces are called the pitch surfaces of the gears. Gears may be classified in a general way according to the forms of their pitch surfaces. Spur gears, Fig. 53(a), have cylinders for pitch surfaces; bevel gears, Fig. 53(b), have conical frustums for pitch surfaces; and worm gears, Fig. 53(c), have pitch surfaces of double curvature. A pair of equal bevel gears with shafts perpendicular are called mitre gears. A cross section taken through a cylindrical or a conical pitch surface is a circle, called the pitch circle or pitch line. Its diameter is called the pitch diameter. For bevel gears the pitch circle is taken at the larger end of the frustum. The linear distance in inches from center to center of adjacent teeth, measured along the arc of the pitch circle, is known as circular pitch. The ratio of the number of teeth to the diameter of the pitch circle in inches is called diametral pitch. The following relations are obvious from the above definitions: D = pitch diameter in inches, N = number of teeth, N Pd = diametral pitch = _ , Pc = circular pitch = ^r^ = — . , N Pd 39. Proportions for and Properties of Gear Teeth.— The force which may be exerted by a gear tooth upon its mating tooth is dependent upon its thickness, width, and height, and upon its linear velocity. By the width of the tooth is meant the distance, f, across the face of the gear in Fig. 54. The thickness of a standard gear tooth at the pitch line is one-half the circular pitch (approximate in the case of gears having cast teeth). The height 2" of a standard gear tooth has been empirically fixed at ■— plus 0.157" . . • 1" an allowance of ~ — for clearance. Of this height -~ extends outside the pitch line and is called the addendum. Experiments by Mr. Wilfred- J. Lewis have shown that owing to increasing shock, the allowable working fibre stress in gear teeth decreases as the velocity increases. Table XV gives values of allowable fibre Transmission Members 69 stresses for cast iron gear teeth for various linear velocities in feet per minute at the pitch line. These values may be increased ZJ times for steel. TABLE XV. Allowable Fibre Stresses in Cast Iron Gear Teeth. Velocity. Stress. 0-100 8000 200 6000 300 4800 600 4000 900 3000 1200 2400 1800 2000 2400 1700 His experiments showed further that increasing the width of the tooth beyond three times the circular pitch was not effective in increasing the strength of the tooth although widths from 2§ po to 3§ Po give good results, in the following equations : . a = addendum = — ; Pd > h = total height of tooth = f = width of face = 3 pc = These proportions may be summarized 2.157" Pd 9.42" Pd ' = 0.687 Pc v = linear velocity in feet per miaute at the pitch line t: X D X R.P.M. 12 s = allowable fibre stress in pounds per square inch at velocity, v ; n = number of teeth on weaker gear; W = safe load on tooth in pounds = spef r 0.124-^:^ " for 15° involute teeth, and for cycldidal teeth when the diameter of the describing circle equals the radius of the 12 tooth pinion. (Lewis.) The teeth of gears are usually machined to exact size and form, in blanks prepared for the purpose. These are called cut teeth. If the teeth are large the amount of machining is reduced by casting to approximate form with proper allowance for finishing. It is customary in making drawings for cut gears to draw the blanks without teeth. In cross section views the height of the tooth is indicated on the section of the rim without cross hatching, as 70 Transmission Members shown in Fig. 54. The number and form of the teeth and their diametral pitch is specified in a note. Some large gears for rough work may have their teeth cast to form as closely as possible and be used without machining. Such gears are said to have cast teeth, and drawings for them should show the teeth in detail fully dimensioned. The number of teeth and circular pitch is given in a note. 40. Materials used in Gears. — The material most commonly used for gears is cast iron. Because of the greater amount of wear upon their teeth, pinions to work with cast iron gears are frequently Fig. 54. made of steel. The same relative equalization of wear may also be obtained by making the teeth of the gear of hard wood mortised into the cast iron rim. Such gears are known as mortise gears. When gears are run at high speeds the noise may be greatly decreased by making the pinion of rawhide, fibre, or cloth tightly compressed between cast iron or steel plates at the sides. 41. Proportions for Spur Gears. — ^Very small spur gears or pinions are made solid without distinction between hub and rim. Gears of suflBcient size so that the normal hub and rim would be separated but having less than 36 teeth are made with a continuous web in the place of arms. Gears having from 36 to 60 teeth have four arms. Those having more than 60 teeth should have six arms except in the case of very large gears which may have from eight Transmission Members 71 to twelve arms. The usual cross sections for the arms of spur gears are elliptical, Fig. 54(a), or in the shape of a cross. Fig. 54(b). These arms are tapered |" per foot per side in width and the thickness of elliptical arms is usually made one-half of the width. In small gears the thickness of elliptical arms may be made uniform at an average value. The following proportions are for cast iron spur gears having six arms and apply to the key drawings, Fig. 54, when all dimensions are in inches. In dimensioning drawings for these gears the out- side diameters and pitch diameters should be given as decimals, unless the exact value can be otherwise expressed. A = diameter of bore. D = pitch diameter. Pd= diametral pitch. Pc = circular pitch. f = width of face. n = number of teeth. 15 A^i« ^-D .,5.D ., n + 250 B=A + 1.6pe + - = A + - + ^-^=A + ^^^. C = f +^ ^ * + 40- 6.67" E = 2i pc = ' = width of arm at pitch line. Pd F = f E = thickness of arm at pitch line. 5 45" G = D - 1.735 Pc = D '■ — (taken to next smaller |" or i")- Pd H = iF. J =H. 7.22" K = 2.3 Pc = = width of arm at pitch line. Pd L = f - 2 R. ^r 1 1-57" M=ipe=— . N = 0.3pc=«-^^" Pd O =iK. 72 Transmission Members P = O. R = M. Taper of arms = |" per foot per side in width. 42. Proportions for Bevel Gears. — Bevel gears may be designed for use on shafts intersecting at any desired angle but that angle is usually 90°. Very small beVel gears or pinions may have the hub and rim solid. Gears somewhat larger have a continuous web Fig. 55. joining the rim to the hub with broad stiffening ribs, Fig. 55, to resist the side pressure. In large bevel gears these stiffening ribs are placed opposite the middle of each arm giving it a T section. Bevel gears should be so laid out that as few of the dimensions as possible shall need to be in decimals and at the same time to avoid decimal dimensions on adjacent members. This may be best accomplished by making the distance from the finished surface at the back of the hub to the apex of the conical pitch surface an amount which will not involve a decimal. The distance from this surface to the outer points of the teeth, the outside diameter and the pitch diameter are then the only dimensions which need to be expressed in decimals for cut teeth. If the teeth are to be cast the radii used in laying out the approximate tooth profiles should Transmission Membees 73 also be given as decimals. The angles which the faces of the teeth and the edges of the rim make with a plane perpendicular to the shaft should be given. These angles are called the face angle and edge angle respectively. The angles and the decimal dimensions should be computed. The following equations which apply to the key drawing, Fig. 55, give good proportions for cast iron bevel gears when all dimensions are in inches. d = pitch diameter. Po = circular pitch. Pd = diametral pitch. 9.4" A = width of face = 3 pc — J" = "^ - i", but not to exceed I d one-third the length of element of pitch cone. B = length of hub = A -f — (for gears), Pc .78" = A + . = A + ■ (for pinions) . - 4 Pd C = bore of hub. D = diameter of hub = IfC + (i"to4"). 1.53" E = thickness of metal in arms or web = .48 Pc = - — Pd ■ F = distance from bottom of tooth to face of web or arm = .45 Pc = -^ — Pd (Used only in laying out and not given on drawing.) G = outside diameter = d + Fig. 56. 43. Worm Gears. — ^The worm, shown at the top in Fig. 53(c), is the driving member. A cross section through the screw thread of a standard worm is shown in Fig. 56. The following equations 74 Transmission Members apply to the key drawings, Figs. 56 and 57, and give the usual proportions for steel worms working with cast iron gears. All dimensions are in inches. Pig. 57. d = pitch diameter of worm. p = linear pitch. a = addendum = 0.3183 p. h = depth of thread = 0.6866 p. n = number of threads in worm. L = lead of worm = n X p. T = number of teeth in worm wheel. T R = velocity ratio of worm to wheel = — n' A = bore of wheel. B = diameter of hub = If A + (i"_toi"). C = length of hub = H + -jVD or to suit. Transmission Members 75 D = pitch diameter of wheel. E = throat diameter of wheel = D + 2a. F = outside diameter of wheel (untrimmed) = E + 2G (1 -cos^). G = throat radius of wheel = |P — 2a. H = width of face of wheel = Psin^+ (i"to J"). J = thickness of web = 0.48 p. K = thickness of rim = 0.48 p. M = bore of worm in inches. N = root diameter of worm = P — 2h. P = outside diameter of worm. Q = minimum length of thread on worm = \ E" - (E -4a)°. « = face angle of wheel. ^ = gashing angle = helix angle of worm. Tan ^ = ^. X d 44. Commercial Gears. — The demand for gears is so varied that it is not feasible for the manufacturers to attempt to carry in stock gears to meet all conditions. .This is especially true for other than cast iron spur gears with cut teeth. Such gears, completely finished, are carried in stock by some makers in several of the more commonly used pitches and with enough different numbers of teeth to meet most needs. The pitches most commonly carried are 8, 12, 16, 20 and 24. The numbers of teeth vary by somewhat irregular intervals from 12 up to 150 or more. Considerably fewer sizes of cast iron bevel gears with cut teeth, in pairs, for shafts at 90°, are also carried in stock. These include mitre gears in numer- ous pitches from 4 to 32 and gears with velocity ratios from 3 : 2 to 4 :1 in three or four different pitches. Finished spur and bevel gears with cast teeth are carried in somewhat larger pitches and less variety of numbers of teeth. Very small spur and bevel gears and worm wheels of brass are also carried. While this statement gives a general idea of what may be obtained exact information must be secured from the catalogs of the individual makers. Wherever it is feasible to use these finished stock gears a consider- 76 Transmission Members able saving in expense is effected. No changes from stock dimen- sions may be made, however, except as to bore of hub and that at an added cost. Patterns for spur gears of any desired pitch and number of teeth, and for pairs of bevel gears of any pitch and velocity ratio, are usually carried iji stock. Gears from these patterns may be quickly cast to order. Finished patterns for spur and bevel mortise gears are carried in stock by some manufacturers in some- what fewer sizes. 45. Cams. — Cams are not carried in stock commercially. The sizes in Table XVI are given by Guldner for gas engine cams having ±. j' o- .__. UJ A \ 1 \\ k V)^ -c- - . Fig. 58. hardened steel rolls, carrying a load not to exceed 3000 pounds per inch of length. In the absence of other proportions these may be used for disk cams in general within the range of sizes given. When the diameter of cam shaft is 1 " or less the diameter of roU may be made \\ times the diameter of shaft. The other dimensions shown in the key drawing. Fig. 58, may be taken as given by the equations below. All dimensions , are in inches. B = diameter of hub or boss = If A + |". C = length of hub = A to 2 A. D = least radius of cam or radius of base circle = ^B + (i^"to|*')- This may be made larger if conditions require a larger cam. Transmission Members 77 H may be made to suit or may be omitted entirely. The face of the cam is usually made a little wider than the length of the roll. The roll is preferably carried in a forked end, but it may be offset if necessary to save space. TABLE XVI. Gas Engine Cams and Rolls. ^ ■ Length of RoU. o u OJ g .1 % Im 'S IS 1 p ° s s Q A E F F G li 1* . i a A If u f \ 1 u 2i a H f If 2s 1 4 1 H li 2^ H 1t^ J 2 3 H li 1 2i 31 lA 1t^ lA 2i 4 U If li (o) Fig. 59. cw The following equations give good proportions for the stamp mill cam and its tappet shown in Fig. 59(a) and (b). 7i 78 Transmission Members A = diameter of cam shaft. B = 2|A. C = 1|A. D = iA. E = JD. F = IJE. G = A. H = iA. J =fA. K = diameter of stamp stem. L = 3K. M= SiK. N = fK. O = 2K. P = If K. CHAPTER VII. PIPE AND PIPE FITTINGS. 46. Varieties of Pipe. — Pipe, made from various materials such as wood, tile, cast iron, wrought iron, steel, lead, brass, etc., is kept in stock by manufacturers. The processes by which each of these is formed vary widely. They include casting in a mold; squirt- ing through a hole partially closed by a mandrel; forcing a mandrel through a solid billet of metal; bending and welding the edges of a strip of metal; and bending and riveting the edges of a sheet of metal. The discussion in this book will be confined to wrought iron and steel pipe formed by bending and welding. 47. Wrought Iron and Steel Pipe. — Pipe made from steel has very largely replaced wrought iron pipe for the conveying of water, gas and steam. Wrought iron remains in use chiefly in those places where resistance to corrosion is a determining factor. The terms "wrought iron" and "steel" are used so indiscriminately in this connection that a positive statement is necessary wherever either would not be acceptable. Steel is usually supplied when not otherwise specified. The methods of manufacturing these two are very similar. The metal is rolled into strips of the correct thickness for the pipe and of a width which will bend into a tube with sufficient allowance for welding. The smaller diameters of pipe are butt welded while larger diameters are lap welded. The ends are trimmed back as far as necessary to remove all imperfectly welded portions and, on standard pipe 12" and less in diameter, threaded . An additional charge is made for threading extra weight or large diameter pipe. Four thicknesses or weights of pipe 12" and less in diameter are made. These are commercially known as merchant, card or full weight, extra strong and double extra strong pipe. The term "standard" is applied by some to full weight pipe and by others to merchant pipe. Merchant pipe is generally understood unless otherwise specified but great care must be taken when using the term. The inside diameter of the card or full weight pipe roughly 79 80 Pipe and Pipe Fittings approximates the nominal size. The outside diameter for any nominal size is made the same for each weight so that the same fittings and threading machinery may be used. The proportions for the commercial sizes of wrought iron and steel pipe and the standard threading for each are given in Table XVII. The pro- portions for merchant pipe differ so little from those for full weight pipe that no different values are listed by the manufacturers. The TABLE XVII. Wrought Iron and Steel Pipe and Pipe Threads. Diameters. Areas. Threads. Actual Inside. Inside. E^E II P II II a 1 8 111 .s 1 o 1 1 1 to 1 2 1" a 4J 1 1 II Q t-i s Ih 1 Pit; ij ■SOg 1 0.405 0.270 0.205 0.067 0.033 27 0.334 0.19 1 0.540 0.364 0.294 0.104 0.068 18 0.433 0.29 3 8 0.675 0.494 0.421 0.191 0.139 18 0.568 0.30 4 0,840 1.050 0.623 0.542 0.244 0.304 0.231 0.047 14 0.701 0.39 i 0.824 0.736 0.422 0.533 0.425 0.140 14 0.911 0.40 1 1.315 1.048 0.951 0.587 0.861 0.710 0.271 Hi 1.144 0.51 li 1.660 1.380 1.272 0.886 1.496 1.271 0.615 Hi 1.488 0.64 li 1.900 1.610 1.494 1.088 2.038 1.763 0.930 Hi 1.728 0.56 2 2.375 2.067 1.933 1.491 3.366 2.935 1.744 Hi 2.201 0.58 2i 2.875 2.468 2.315 1.755 4.780 4.209 2.419 8 2.619 0.89 3 3.500 3.067 2.892 2.284 7.388 6.669 4.097 8 3.241 0.95 3i 4.000 3.548 3.358 2.716 9.887 8.856 5.794 8 3.738 1.00 4 4.500 4.026 3.818 3.136 12.730 11.449 7.724 8 4.234 1.06 4i 5.000 4.508 4.280 3.564 16.961 14.387 9.976 8 4.731 1.10 5 5.562 6.045 4.813 4.063 19.990 18.193 12.965 8 5.290 1.16 6 6.625 6.065 6.751 4.875 28.886 26.976 18.665 8 6.346 1.26 7 ,7.625 7.023 6.625 5.875 38.743 34.472 27.109 8 7.340 1.36 8 8.625 7.982 7.625 6.876 50.021 46.664 37.122 8 8.334 1.46 9 9.625 8.937 8.625 62.722 58.426 8 9.327 1.67 10 10.750 10.019 9.750 78.822 74.662 8 10.446 1.68 11 11.750 11.000 10.750 95.034 90.764 8 11.439 1.78 12 12.750 12.000 11.750 113.098 108.430 8 12.433 1.88 14 14.000 13.250 137.887 8 13.676 2.00 Pipe and Pipe Fittings 81 mill lengths usually approximate to 24 feet but may include pieces as short as 12 feet. A small extra charge is made for pipe cut to specified lengths. This, however, may be more economical when the desired lengths are known, than to cut the pipe on the job. Specify nominal size, weight and length. In pipe 14" and more in diameter the nominal size is the outside diameter. This is commonly known as outside diameter or O. D. pipe. The stock sizes vary by 1" up to 22" and by 2" from 22" to 30". Such pipe is made in thicknesses varying by ys" from J" to f " for sizes up to 20", from ^" to f " up to 22", from f " to f " up to 28" and from ^" to f " for 30", except that a thickness of H" is not made in any of the diameters . f " and f " are the more generally used thicknesses. Outside diameter pipe is generally furnished with plain ends and random lengths. Mill lengths run about 24 feet. Specify nominal size, thickness and length. 48. Pipe Threads. — Upon the recommendation of a committee of the American Society of Mechanical Engineers the Briggs standard of pipe threads was adopted on October 27, 1886, by the manufacturers in the United States of wrought iron pipe for gas. Fig. 60. steam and water. The change to steel pipe has caused no change in the standard used. A cross section through the Briggs threads appears in the longitudinal section of pipe shown in Fig. 60. The sides of the thread section make an angle of 60° with each other and with the axis of the pipe. The top of the thread and the bottom of the space in the theoretical form are rounded slightly making the depth 0.8 of the pitch. In general this rounding of the corners of the thrfcad is not obtained in practice owing to difficulty in grinding the cutting tools. A sharp V form at the root, and the point cut off flat, leaving the depth 0.833 of the pitch, is the usual section found. The thread is cut on a taper of f" per foot. In 82 Pipe and Pipe Fittings addition to the threads perfect at both top and bottom there are two effective threads imperfect at the top only. Normally the pipe should enter the fitting a distance equal to the length of perfect thread. The two additional turns provide a margin in case of imperfect fitting. The remainder of the thread is not of full depth and does not enter the fitting. The following equations give the complete proportions for the thread : D = outside diameter of pipe ; N = number of threads per inch ; L = length of perfect thread = - ' Li = length of effective thread = N 6.8" + 0.8 D N Tzr T = total threaded length = — '- ^;^^:-^ The values of D, N and L for the commercial sizes of pipe are given in Table XVII on page 80. 49. Pipe Joints. — There are two general types of pipe joints. The adjacent ends of two sections of pipe may be screwed into a simple threaded sleeve, called a coupling, or flanges may be attached to the ends of the sections of pipe and the adjacent flanges bolted together. The former of these types is very much used for pipe of small diameters under low pressures. 50. Couplings.^ — ^These couplings are made of wrought iron with right-hand threads for all standard sizes of pipe up to 12" and are furnished with the pipe unless it is ordered flanged. For 2" pipe and smaller, couplings of malleable iron with right-hand threads are carried in stock. For 8" pipe and smaller, couplings of malleable iron threaded one end right-hand and the other end left- hand are carried in stock. For all couplings the nominal size is the same as the nominal size of the pipe which it fits. They are carried in stock either black or galvanized. Black is usually supplied unless otherwise specified. 51. Pipe Flanges. — The most common type of pipe flange is that shown (with a section cut away) in, Fig. 61. These flanges screw on the ends of the pipe. Thin rings of rubber, asbestos, or Pipe and Pipe Fittings 83 some soft metal like copper or lead, are placed between the flanges before bolting together, in order to make the joint tight. These rings are called gaskets. The pipe should extend sufficiently through the flange to be faced off even with the face of the flange Fig. 61. and should bear on the gasket. The bolts are used in multiples of four and are equally spaced to straddle the center lines. The bolt holes are drilled |" larger than the nominal diameter of the bolts. Formerly there were two recognized systems of pipe flanges for different pressures. These were the A. S. M. E. Standard Pipe Flanges for pressures up to 125 pounds per square inch and the Fig. 62. Manufacturers' Standard Pipe Flanges for pressures up to 250 pounds per square inch. Both of these systems are being super- seded by the American or United States Standard Pipe Flanges for each of the above pressures. These two weights of flanges are known respectively as standard and extra heavy. Values for the dimensions indicated in Fig. 62 have been determined for nominal diameters of pipe up to 100" for standard flanges, and up to 84 Pipe and Pipe Fittings 48" for extra heavy flanges. The values of these dimensions and the numbers and sizes of bolts for each weight for sizes up to 48" are given in Table XVIII. When the diameter of the bolt is If" or over stud bolts are recommended. Bolts with square heads and hexagon nuts are recommended for smaller sizes. Standard flanges 32" and over and all extra heavy flanges are spot bored for nuts. On all extra heavy flanges the finished face extends out to within yj" from the inside edge of the bolt holes. The thickness of the flanges outside this point is reduced xS" in order that the full pull of the bolts may be exerted in compressing the gasket between the finished faces. Devices to keep the gasket from being blown out, such as a circular depression in one flange in which the gasket is placed and compressed by means of a cor- FiG. 63. responding projection on the mating flange, are not mentioned in the specifications of the American Standard. They are, however, much used in high pressure work. The screwed joint between the pipe and flange, while the most common, is not satisfactorily effective under high pressures. Numerous* methods have been devised to improve it. The one which, for cast flanges, seems to have proved most generally satisfactory is shown in Fig. 63. The pipe is passed entirely through the flange and the end afterward, expanded to form a flange of its own. It is this latter flange which is faced true to form the seat for the gasket. The cast iron flanges serve as bolting rings to draw the sections of pipe together. Flanges made of steel may be welded to the ends of the pipe, but this method is propor- tionately more expensive. Any of these methods are open to the objection that the faces must be machined after the flange is on. They cannot, therefore, be used in many places where machinery is not available. This objection is not very serious since, for the Pipe and Pipe Fittings 85 TABLE XVIII. American Standard Pipe Flanges. Standard- -125 Lbs Pressure. Extra Heavy — 250 Lbs. Pressure. Flange. Bolts. Flange. Bolts. Diameter. i Diameter. Si s. lU V s u 0. +a •8 tH* 1 U u i -3 I O g a; 2' u Q I pq g 1 ■s tS B c D B C D S 1 4 3 A 4 1% 4i 3} }} 4 } u 41 3? * 4 7 16 5 3i 3 4 4 } li 5 3- A 4 1 6 4} }f 4 5 8 2 6 4i f 4 6i 5 7 s 4 f 2i 7 5i ^ 4 1 7i 51 1 4 I 3 7i 6 4 f 8i 6f 1} 8 3 4 3i 8i 7 H 4 f 9 7} lA 8 i 4 9 ^\ -i 8 f 10 7f li 8 3 4 4i 9J 71 -^ 8 3 4 lOi 8} lA 8 f 5 10 8i -1 8 i 11 9i If 8 3 4 6 11 9i 1 , 8 . 12i lOf lA 12 3 4 7 12i lOi li^ 8 ■ 14 111 1} 12 I 8 131 Hi n 8 ■ 15 13 If 12 7 9 15 13i li 12 ■ 16i 14 If 12 10 16 14i lA 12 ■ m 15} H 16 12 19 17 li 12 1 8 20* 17i 2 16 u 14 21 18f If 12 23 20} 2} 20 11 ■*■ 8 15 22i 20 If 16 24- 21} 2A 20 1 1 At 16 23i 21i ii% 16 255 22} 2} 20 1} 18 25 22f lA 16 li 28 24| 2f 24 1 1 20 27i 25 IH 20 1 30i 27 2- 24 1 22 29i 27i IH 20 1 33 29} 2- 24 1 24 32 29J 11 20 1- 36 32 2 24 1 26 34i 31f 2 • 24 1 38J 34} 2i| 28 1 28 36i 34 2ff 28 ll 401 37 2-4 28 1 30 381 36 2i ^28 \~- 43 39} 3 28 If 32 411 38i 2i 28 1- 45i 41} 3s 28 1 '■ ■*-8 34 43f 401 2-^ 32 1^ 471 43} 3- 28 If 36 46 42i 2f 32 li 50 46 35 32 12^ -^8 38 481 45i 2f 32 If 52} 48 3,^ 32 1 7 40 60J 47J 2i 36 If 54i 50} ^-h 36 If 42 53 49J 2f 36 If 57 52f 3}} 36 If 44 55i 511 2f 40 59} 65 31 36 .•2 46 57i 531 2ii 40 If 61} 57} 3f 40 2 48 59J 56 2i 44 If 65 601 4 40 2 86 Pipe and Pipe Fittings best results, the screwed flange should also be trued up after it is on. Except on large contracts, where it would pay to set up the necessary machinery on the job, it is advisable to have the pipe cut to lengths and all flanges put on and faced true at the mill. 52. Pipe Bends. — Besides the straight sections, pipe in sizes up to* 24" may be obtained curved to various forms such as those shown in Fig. 64. The curved portions are bent to the arc of a circle but short straight portions at the ends are necessary in mak- Expansion U Bend. Fig. 64. Double Offset U Bend, (e) ing the bends. The recommended values for the radii of the curved portions and the necessary lengths for the straight ends are given in Table XIX. By using extra strong pipe these radii may be reduced to the minimum values given in the table but the makers do not guarantee such bends against buckling. Pipe bends are usually made to order. The distance between the flange faces and the amount of the offset in the offset bend, Fig. 64(c), and the amount of the offset in the double offset U bend, Fig. 64(e), are optional within certain limits. Straight portions of limited length may usually be added where desired in any of the forms. In all cases pipe bends are furnished with the flanges on and faced true to the desired angle. Pipe and Pipe Fittings TABLE XIX. Proportions for Pipe Bends. 87 Radius of Bend. Radius of Bend. M 1 s i 'a, 1 i 1 .1 c s •2 1 s M 2 m R R s R R S 2i 12i 7 4 10 50 40 12 3 15 8 4 12 60 50 14 3i 17i 10 5 14 70 65 16 4 20 12 5 15 75 70 16 4i 22i 14 6 16 80 78 18 5 25 15 6 18 108 88 18 6 30 20 7 20 120 104 18 7 35 24 8 22 132 132 18 -fv8 40 28 9 24 144 144 18 9 45 35 11 - 53. Pipe Fittings. — ^The forms of pipe fittings are too numerous for complete description or illustration in this book. They are usually of cast iron but steel or bronze castings may be required for special work. Their flanges conform to the specifications given for pipe flanges in article 51. The finished center to face or face to face distances and the minimum thicknesses of body metal in standard fittings for sizes of pipe up to 48" are given in Tables XX and XXI and corresponding values for extra heavy fittings are given in Tables XXII and XXIII. The symbols apply to the key drawings, Fig. 65 on page 91, which illustrate some of the more common forms. The nominal size of pipe is that corresponding to the largest opening in the fitting. The direct passage through a fitting is known as the run. The side openings are called branches. When these openings are of different sizes those of the run are given first and followed by those of the branches. Tees, crosses and laterals are made in two lengths of run, known respectively as short body and long body patterns. The short body is used only when the diameter of the largest branch is considerably less than (approximately two-thirds) that of the run, in sizes of pipe 18" or larger. The maximum diameter of branch for the short body pattern and the minimum outlets for these fittings are given in the tables. 88 Pipe and Pipe Fittings TABLE XX. AMERirAN Standard Flanged Fittings. Tees, Crosses and Elbows. Standard Weight —1 25 Lbs. Pressure. s| Distance Center to Face. U-, Tees and Crosses. Elbows. i 2>, 1 Short Body. 1 U 'SS P. s .S o o .9 o G .3 2 1 ►J .11 OS to s. s A B c A D E is 1 34 34 If 5 A u 3f 3f 2 54 n 4 4 2i 6 TS 2 4i 44 24 64 A 2i 5 5 3 7 A 3 5i 54 3 7i A 3i 6 6 34 84 A 4 64 64 4 9 4 44 7 7 4 94 4 5 74 74 44 lOi 4 6 2 8 8 6 114 A 7 2 84 84 64 12i i^ ^8 2 9 9 54 14 ■i"^ 9 2 10 10 6 15i 44 10 2 11 11 64 164 a 4 12 2 12 12 74 '19 H"- 14 3 14 14 74 214 V 1 15 3 144 144 8 22| ;■ 16 3 15 15 8 24 1 18 12 3 164 13 154 164 84 264 lA 20 14 3 18 14 17 18 94 29 14 22 15 3 20 14 18 20 10 314 lA 24 16 3 22 15 19 22 11 34 14 26 18 3 23 16 20 23 13 364 lA 28 18 3 24 16 21 24 14 39 If 30 20 3 25 18 23 25 15 414 lA 32 20 3 26 18 24 26 16 44 14 34 22 3 27 19 25 27 17 464 lA 36 24 3 28 20 26 28 18 49 It 38 24 3 29 20 28 29 19 514 I4i 40 26 3 30 22 29 30 20 54 If 42 28 3 31 23 30 31 21 564 l4i 44 28 3 32 23 31 32 22 59 11 46 30 3 33 24 33 33 23 614 IM 48 32 3i 34 26 34 34 24 64 2 Pipe and Pipe Fittings 89 TABLE XXI. American Standard Flanged Fittings. Laterals and Reducers Standard Weight— i 25 Lbs. Pressure. 4 Distance Center to Face. Face to Face. Laterals. Laterals. 13 >, pq-g 4^ 3 Long Body, Short Body. i^ < 13 O m o ►J Short Body. i 1^ 3 d bo g .1 N 1 1 1 CO s S A B c A D E Ss 1 4 4 2 5 1 n 4| 4i 24 54 ■V i n 4i 44 2i 6 4 2 5 5 3 64 1 21 54 54 34 7 A 3 6 6 34 71 ^ 3i 64 64 4 84 A 4 7 7 44 9 f 4i 74 74 44 94 5 8 5 8 8 5 lOi a 6 2 84 84 54 114 7 2 9 9 6 12| i 8 2 10 10 6 14 i 9 2 104 104 64 154 ' 10 2 114 • 114 7 164 ^ 12 2 13 13 8 19 14 . 2 15 15 84 214 14 15 2 154 154 9 22| lA 16 2 164 164 94 24 ■li 18 12 3 18 14 17 18 10 264 If 20 14 3 194 154 184 194 104 29 14 22 15 3 204 164 20 204 11 314 ^P 24 16 3 224 17 214 224 12 34 26 18 3 24 19 23 24 13 364 i-i 28 18 3 26 19 24 26 14 39 30 20 3 274 204 254 274 15 414 2 32 20 3 29 204 264 29 16 44 24 34 22 3 304 22 28 304 17 464 24 38 24 3 324 234 294 324 18 49 2| 38 24 3 34 234 304 34 19 514 2,^ 40 26 3 354 25 31- 354 20 54 2^ 42 28 3 37 264 33- 37 21 564 2H 44 28 3 39 264 344 39 22 59 241 46 30 3 404 274 355 404 23 614 2| 48 32 3i 42 29 374 42 24 64 3 Pipe and Pipe Fittings 91 TABLE XXIII. American Standard Flanged Fittings. Laterals and Reducers . Extra Heavy — 250 Jbs. Pressure •si 1 El Distance Center to Face. Face to Face. Laterals. Laterals. vi Long Body. Short Body. -a i s •o a O I 3 1 o J3 1 1 a" .IS m F G F J H K M N P s 1 61 2 6i 8* i li 7- 2i 7i 9* i li 8^ 2| 81 11 i 2 Y 9 2i 9 114 i 91 lOi 2i lOi 13 A 3 11 3 11 14 6 A 3i 12^ 3 121 154 6i A 4 131 3 13i 16i 7 1 4i 141 3i 144 18 7* 5 5 15 Si 15 m 8 a 6 2 17i 4 17i 214 9 3 4 7 2 19 H 19 23i 10 H 8 2 20i 5 20J 25i 11 -i 9 2 221 5 22i 27i Hi - 10 2 24 6i 24 29* 12 if 12 2 27i 6 274 33i 14 1 14 2 31 6i 31 37i 16 li 15 2 33 6^ 33 39i 17 lA 16 2 34i 7i 34i 42 18 u 18 9 3 37i 8 37* 32i 3 31 45i 34 19 If 20 10 3 40i 8i 40i 36 3 34 49 37 20 li 22 10 3 43§ 9i 43* 39 3 37 53 40 22 lA 24 12 3 47i 10 47i 43 3 41 57i 44 24 If 26 26 IH 28 28 U 30 30 2 32 32 2J 34 34 2i 36 36 2f 38 38 2A 40 40 2A 42 42 2^ 44 44 2-1 46 46 2- 48 48 3 92 Pipe and Pipe Fittings Th A-- M Tee. i m:- Reducing Tee. ib) q=l= -C^ ?- ^■ Reducing Cross. (Short Body) Long Radius Elbow. Reducing Lateral. Reducer. (Short Body) (« (0 Fig. 65. 54, Valves. — ^Valves for the purpose of shutting off the flow of fluid through a pipe are made in two general types, namely, globe valves and gate valves. These two tjpes are shown in sec- tion in Figs. 66(a) and 66(b) respectively. The gate valve is for some purposes preferred to the globe valve because of the more Pipe and Pipe Fittings 93 direct passage of the fluid when the valve is open. Many other forms of valves are made for special purposes. The openings of SgWh (.a) (b) Fig. 66. the valve may be threaded and the pipe screwed in or they may be flanged. The flanges on valves are made to conform to the specifications given in article 51 on page 82. Decimal Equivalents of Fractions of One Inch. 16 32 11 13 15 1 3 .015625 .03125 .046875 .0625 5 7 .078125 .09375 .109375 .125 9 11 .140625 .15625 .171875 .1875 13 15 .203125 .21875 .234375 .25 17 19 .265625 .28125 .296875 .3125 21 23 .328125 .34375 .359375 .375 25 27 .390625 .40625 .421875 .4375 29 31 .453125 .46875 .484375 .5 10 11 12 13 14 15 32 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59' 61 63 ■ .515625 .53125 .546875 .5625 .578125 .59375 .609375 .625 .640625 .65625 .671875 .6875 .703125 .71875 .734375 .75 .765625 .78125 .796875 .8125 .828125 .84375 .859375 .875 .890625 .90625 .921875 .9375 .953125 .96875 .984375 .95 96 Natural Trigonometric Functions 1 SINES i 0' 10' 20' 30' 40' 50' 60' 1 0.00000 0.00291 0.00582 0.00873 0.01164 0.01454 0.01745 89 1 0.01745 0.02036 0.02327 0.02618, 0.02908 0.03199 0.03490 88 2 0.03490 0.03781 0.04071 0.04362 0.04653 0.04943 0.05234 87 3 0.05234 0.05524 0.05814 0.06105 0.06395 0.06685 0.06976 86 i 0.00976 0.07266 0.07556 0.07846 0.08136 0.08426 0.08716 85 5 0.08716 0.09005 0.09295 0.09585 0.09874 0.10164 0.10453 84 6 0.10453 0.10742 0.11031 0.11320 0.11609 0.11898 0.12187 83 7 0.12187 0.12476 0.12764 0.13053 0.13341 0.13629 0.13917 82 8 0.13917 0.14205 0.14493 0.14781 0.15069 0.15356 0.15643 81 9 0.15643 0.15931 0.16218 0.16505 0.16792 0.17078 0.17365 80 10 0.17.305 0.17651 0.17937 0.18224 0.18509 0.18795 0.19081 79 11 0.19081 0.19366 0.19652 0.19937 0.20222 0.20507 0.20791 78 12 0.20791 0.21076 0.21360 0.21644 0.21928 0.22212 0.22495 77 13 0.22495 0.22778 0.23062 0.23345 0.23627 0.23910 0.24192 76 14 0.24192 0.24474 0.24756 0.25038 0.25320 0.25601 0.25882 75 15 0.25882 0.26163 0.26443 0.26724 0.27004 0.27284 0.27564 74 16 0.27564 0.27843 0.28123 0.28402 0.28680 0.28959 0.29237 73 17 0.29237 0.29515 0.29793 0.30071 0.30348 0.30625 0.30902 72 18 0.30902 0.31178 0.31454 0.31730 0.32006 0.32282 0.32557 71 19 0.32557 0.32832 0.33106 0.33381 0.33655 0.33929 0.34202 70 20 0.34202 0.34475 0.34748 0.35021 0.35293 0.35565 0.35837 69 21 0.35837 0.30108 0.36379 0.36650 0.36921 0.37191 0.37461 68 22 0.37461 0.37730 0.37999 0.38268 0.38537 0.38805 0.39073 67 23 0.39073 0.39341 0.39608 0.39875 0.40142 0.40408 0.40674 66 24 0.40074 0.40939 0.41204 0.41469 0.41734 0.41998 0.42262 65 25 0.42262 0.42525 0.42788 0.43051 0.43313 0.43575 0.43837 64 26 0.43837 0.44098 0.44359 0.44620 0.44880 0.45140 0.45399 63 27 0.45399 0.45658 0.45917 0.46175 0.46433 0.46690 0.46947 62 28 0.46947 0.47204 0.47460 0.47716 0.47971 0.48226 0.48481 61 29 0.48481 0.48735 0.48989 0.49242 0.49495 0.49748 0.50000 60 30 0.50000 0.50252 0.50503 0.50754 0.51004 0.51254 0.51504 59 31 0.51504 0.51753 0.52002 0.52250 0.52498 0.52745 0.52992 58 32 0.52992 0.53238 0.53484 0.53730 0.53975 0.54220 0.54464 57 33 0.541G4 0.. 54708 0.54951 0.55194 0.55436 0.55678 0.55919 56 34 0.55919 0.56160 0.56401 0.56641 0.56880 0.57119 0.57358 55 35 0.57358 0.57596 0.57833 0.58070 0.58307 0.58543 0.58779 54 36 0.58779 0.59014 0.59248 0.59482 0.59716 0.59949 0.60182 53 37 0.00182 0.60414 0.60645 0.60876 0.61107 0.61337 0.61566 52 38 0.61566 0.61795 0.62024 0.62251 0.62479 0.62706 0.62932 51 39 0.62932 0.63158 0.63383 0.63608 0.63832 0.64056 0.64279 50 40 0.64279 0.64501 0.64723 0.64945 0.65166 0.65386 0.65606 49 41 0.65606 0.65825 0.66044 0.66262 0.66480 0.66697 0.66913 48 42 0.66913 0.67129 0.67344 0.67559 0.67773 0.67987 0.68200 47 43 0.68200 0.68412 0.68624 0.68835 0.69046 0.69256 0.69466 46 44 0.69466 0.69675 0.69883 0.70091 0.70298 0.70505 0.70711 45 60' 50' 40' 30' 20' 10' 0' 1 COSINES 1 Natural Trigonometric Functions 97 1 COSINES 1 1 0' 10' 20' 30' 40' 50' 60' CO 1.00000 1.00000 0.99998 0.99996 0.99993 0.99989 0.99985 89 1 0.99985 0.99979 0.99973 0.99966 0.99958 0.99949 0.99939 88 2 0.99939 0.99929 0.99917 0.99905 0.99892 0.99878 0.99863 87 3 0.99863 0.99847 0.99831 0.99813 0.99795 0.99776 0.99756 86 i 0.99756 0.99736 0.99714 0.99692 0.99668 0.99644 0.99619 85 5 0.99619 0.99594 0.99567 0.99540 0.99511 0.99482 0.99452 84 6 0.99452 0.99421 0.99390 0.99357 0.99324 0.99290 0.99255 83 7 0.99255 0.99219 0.99182 0.99144 0.99106 0.99067 0.99027 82 8 0.99027 0.98986 0.98944 0.98902 0.98858 0.98814 0.98769 81 9 0.98769 0.98723 0.98676 0.98629 0.98580 0.98531 0.98481 80 10 0.98481 0.98430 0.98378 0.98325 0.98272 0.98218 0.98163 79 11 0.98163 0.98107 0.98050 0.97992 0.97934 0.97875 0.97815 78 12 0.97815 0.97754 0.97692 0.97630 0.97566 0.97502 0.97437 77 13 0.97437 0.97371 0.97304 0.97237 0.97169 0.97100 0.97030 76 14 0.97030 0.96959 0.96887 0.96815 0.96742 0.96667 0.96593 75 15 0.96593 0.96517 0.96440 0.96363 0.96285 0.96206 0.96126 74 16 0.96126 0.96046 0.95964 0.95882 0.95799 0.95715 0.95630 73 17 0.95630 0.95545 0.95459 0.95372 0.95284 0.95195 0.95106 72 18 0.95106 0.95015 0.94924 0.94832 0.94740 0.94646 0.94552 71 19 0.94552 0.94457 0.94361 0.94264 0.94167 0.94068 0.93969 70 20 0.93969 0.93869 0.93769 0.93667 0.93565 0.93462 0.93358 69 21 0.93358 0.93253 0.93148 0.93042 0.92935 0.92827 0.92718 68 22 0.92718 0.92609 0.92499 0.92388 0.92276 0.92164 0.92050 67 23 0.92050 0.91936 0.91822 0.91706 0.91590 0.91472 0.91355 66 24 0.91355 0.91236 0.91116 0.90996 0.90875 0.90753 0.90631- .65 25 0.90631 0.90507 0.90383 0.90259 0.90133 0.90007 0.89879 64 26 0.89879 0.89752 0.89623 0.89493 0.89363 0.89232 0.89101 63 27 0.89101 0.88968 0.88835 0.88701 0.88566 0.88431 0,88295' 62 28 0.88295 0.88158 0.88020 0.87882 0.87743 0.87603 0.87462 61 29 0.87462 0.87321 0.87178 0.87036 0.86892 0.86748 0.86603 60 30 0.86603 0.86457 0.86310 0.86163 0.86015 0.85866 0.85717 59 31 0.85717 0.85567 0.85416 0.85264 0.85112 0.84959 0.84805 58 32 0.84805 0.84650 0.84495 0.84339 0.84182 0.84025 0.83867 . 57 33 0.83867 0.83708 0.83549 0.83389 0.83228 0.83066 0.82904 56 34 0.82904 0.82741 0.82577 0.82413 0.82248 0.82082 0.81915 55 35 0.81915 0.81748 0.81580 0.81412 0.81242 0.81072 0.80902 64 36 0.80902 0.80730 0.80558 0.80386 0.80212 0.80038 0.79864 53 37 0.79864 0.79688 0.79512 0.79335 0.79158 0.78980 0.78801 52 38 0.78801 0.78622 0.78442 0.78261 0.78079 0.77897 0.77715 51 39 0.77715 0.77531 0.77347 0.77162 0.76977 0.76791 0.76604 50 40 0.76604 0.76417 0.76229 0.76041 0.75851 0.75661 0.75471 49 41 0.75471 0.75280 0.75088 0.74896 0.74703 0.74509 0.74314 48 42 0.74314 0.74120 0.73924 0.73728 0.73531 0.73333 0.73135 47 43 0.73135 0.72937 0.72737 0.72537 0.72337 0.72136 0.71934 46 44 0.71934 0.71732 0.71529 0.71325 0.71121 0.70916 0.70711 45 1 60' 50' 40' 30' 20' 10' 0' 1 o u SINES 98 Natural Trigonometric Functions I TANGENTS w 1 0' 10' 20' 30' 40' 50' 60' 6 0.00000 0.00291 0.00582 0.00873 0.01164 0.01455 0.01746 89 1 0.01746 0.02036 0.02328 0.02619 0.02910 0.03201 0.03492 88 2 0.03492 0.03783 0.04075 0.04366 0.04658 0.04949 0.05241 87 3 0.05241 0.05533 0.05824 0.06116 0.06408 0.06700 0.06993 86 4 0.06993 0.07285 0.07578 0.07870 0.08163 0.08456 0.08749 85 5 0.08749 0.09042 0.09335 0J)9629 0.09923 0.10216 0.10510 84 6 0.10510 ,0.10805 0.11099 0.11394 0.11688 0.11983 0.12278 83 7 0.12278 0.12574 0.12869 0.13165 0.13461 0.13758 0.14054 82 8 0.14054 0.14351 0.14648 0.14945 0.15243 0.15540 0.15838 SI 9 0.15838 0.16137 0.16435 0.16734 0.17033 0.17333 0.17633 80 10 0.17633 0.17933 0.18233 0.18534 0.18835 0.19136 0.19438 79 11 0.19438 0.19740 0.20042 0.20345 0.20648 0.20952 0.21256 78 12 0.21256 0.21560 0.21864 0.22169 0.22475 0.22781 0.23087 77 13 0.23087 0.23393 0.23700 0.24008 0.24316 0.24624 0.24933 76 14 0.24933 0.25242 0.25552 0.25862 0.26172 0.26483 0.26795 75 15 0.26795 0.27107 0.27419 0.27732 0.28046 0.28360 0.28675 74 16 0.28675 0.28990 0.29305 0.29621 0.29938 0.30255 0.30573 73 17 0.30573 0.30891 0.31210 0.31530 0.31850 0.32171 0.32492 72 18 0.32492 0.32814 0.33136 0.33460 0.33783 0.34108 0.34433 71 19 0.34433 0.34758 0.35085 0.35412 0.35740 0.36068 0.36397 70 20 0.36397 0.36727 0.37057 0.37388 0.37720 0.38053 0.38386 69 21 0.38386 0.38721 0.39055 0.39391 0.39727 0.40065 0.40403 68 22 0.40403 0.40741 0.41081 0.41421 0.41763 0.42105 0.42447 67 23 0.42447 0.42791 0.43136 0.43481 0.43828 0.44175 0.44523 66 24 0.44523 0.44872 0.45222 0.45573 0.45924 0.46277 0.46631 65 25 0.46631 0.46985 0.47341 0.47698 0.48055 0.48414 0.48773 64 26 0.48773 0.49134 0.49495 0.49858 0.50222 0.50587 0.50953 63 27 0.50953 0.51320 0.51688 0.52057 0.52427 0.52798 0.53171 62 28 0.53171 0.53.545 0.53920 0.54296 0.54674 0.55051 0.55431 61 29 0.55431 0.55812 0.56194 0.56577 0.56962 0.57348 0.57735 60 30 0.57735 0.58124 0.58513 0.58905 0.59297 0.59691 0.60086 59 31 0.60086 0.60483 0.60881 0.61280 0.61681 0.62083 0.62487 58 32 0.62487 0.62892 0.63299 0.63707 0.64117 0.64528 0.64941 67 33 0.64941 0.65355 0.65771 0.66189 0.66608 0.67028 0.67451 56 34 0.67451 0.67875 0.68301 0.68728 0.69157 0.69588 0.70021 55 35 0.70021 0.70455 0.70891 0.71329 0.71769 0.72211 0.72654 54 36 0.72654 0.73100 0.73547 0.73996 0.74447 0.74900 0.75355 53 37 0.75355 0.75812 0.76272 0.76733 0.77196 0.77661 0.78129 52 38 0.78129 0.78598 0.79070 0.79544 0.80020 0.80498 0.80978 51 39 0.80978 0.81461 0.81946 0.82434 0.82923 0.83415 0.83910 50 40 0.83910 0.84407 0.84906 0.85408 0.85912 0.86419 0.86929 49 41 0.86929 0.87441 0.87955 0.88473 0.88992 0.89515 0.90040. 48 42 0.90040 0.90569 0.91099 0.91633 0.92170 0.92709 0.93252 47 43 0.93252 0.93797 0.94345 0.94896 0.95451 0.96008 0.96569 46 44 0.96569 0.97133 0.97700 0.08270 0.98843 0.99420 1.00000 45 01 1 60' 50' 40' 30' 20' 10' 0' 1 1 CO TANGEN rs 1 Natural Trigonometric Functions 99 a COTANGENTS 1 0' 10' 20' 30' 40' 50' 60' o 00 343.77371 171.88540 114.58865 85.93979 68.75009 57.28996 89 1 57.28996 49.10388 42.96408 38.18846 34.36777 31.24158 28.63625 88 2 28.63625 26.43160 24.54176 22.90377 21.47040 20.20555 19.08114 87 3 19.08114 18.07498 17.16934 16.34986 15.60478 14.92442 14.30067 86 4 14.30067 13.72674 13.19688 12.70621 12.25051 11.82617 11.43005 85 5 11.43005 11.05943 10.71191 10.38540 10.07803 9.78817 9.51436 84 6 9.51436 9.25530 9.00983 8.77689 8.55555 8.34496 8.14435 83 7 8.14435 7.95302 7.77035 7.59575 7.42871 7.26873 7.11537 82 8 7.11537 6.96823 6.82694 6.69116 6.56055 6.43484 6.31375 81 9 6.31375 6.19703 6.08444 5.97576 5.87080 5.76937 5.67128 80 10 5.67128 5.57638 5.48451 5.39552 5.30928 5.22566 5.14455 79 11 5.14455 5.06584 4.98940 4.91516 4.84300 4.77286 4.70463 78 12 4.70463 4.63825 4.57363 4.51071 4.44942 4.38969 4.33148 77 13 4.33148 4.27471 4.21933 4.16530 4.11256 4.06107 4.01078 76 14 4.01078 3.96165 3.91364 3.86671 3.82083 3.77595 3.73205 75 15 3.73205 3.68909 3.64705 3.60588 3.56557 3.52609 3.48741 74 18 3.48741 3.44951 3.41236 3.37594 3.34023 3.30521 3.27085 73 17 3.27085 3.23714 3.20406 3.17159 3.13972 3.10842 3.07768 72 18 3.07768 3.04749 3.01783 2.98869 2.96004 2.93189 2.90421 71 19 2.90421 2.87700 2.85023 2.82391 2.79802 2.77254 2.74748 70 20 2.74748 2.72281 2.69853 2.67462 2.65109 2.62791 2.60509 69 21 2.60509 2.58261 , 2.56046 2.53865 2.51715 2.49597 2.47509 68 22 2.47509 2.45451 2.43422 2.41421 2.39449 2.37504 2.35585 67 23 2.35585 2.33693 2.31826 2.29984 2.28167 2.26374 2.24604 66 24 2.24604 2.22857 2.21132 2.19430 2.17749 2.16090 2.14451 65 25 2.14451 2.12832 2.11233 2.09654 2.08094 2.06553 2.05030 64 26 2.05030 2.03526 2.02039 2.00569 ,1.99116 1.97680 1.96261 63 27 1.96261 1.94858 1.93470 1.92098 1.90741 1.89400 1.88073 62 28 1.88073 1.86760 1.85462 1.84177 1.82907 1.81649 1.80405 61 29 1.80405 1.79174 1.77955 1.76749 1.75556 1.74375 1.73205 60 30 1.73205 1.72047 1.70901 1.69766 1.68643 1.67530 1.66428 59 31 1.66428 1.65337 1.64256 1.63185 1.62125 1.61074 1.60033 58 32 1.60033 1.59002 1.57981 1.56969 1.55966 1.54972 1.53987 57 33 1.53987 1.53010 1.52043 1.51084 1.50133 1.49190 1.48256 56 34 1.48256 1.47330 1.46411 1.45501 1.44598 1.43703 1.42815 55 35 1.42815 1.41934 1.41061 1.40195 1.39336 1.38484 1.37638 54 36 1.37638 1.36800 1.35968 1.35142 1.34323 1.33511 1.32704 53 37 1 .32704 1.31904 1.31110 1.30,323 1.29541" 1.28764 1.27«94 52 38 1.27994 1.27230 1.26471 1.25717 1.24969 1.24227 1.23490 51 39 1.23490 1.22758 1.22031 1.21310 1.20593 1.19882 1.19175 50 40 1.19175 1.18474 1.17777 1.17085 1.16398 1.15715 1.15037 49 41 1.15037 1.14363 1.13694 1.13029 1.12369 1.11713 1.11061 48 42 1.11061 1.10414 1.09770 1.09131 1.08496 1.07864 1.07237 47 43 1.07237 1.06613 1.05994 1.05378 1.04766 1.04158 1.03653 46 44 1.03553 1.02952 1.02355 1.01761 1.01170 1.00583 1.00000 45 S 60' 50' 40' 30' 20' 10' 0' 1 1 Tj VNGENTS INDEX. Addendum, definition of, 68. Adjustments of bearings, 48. Anchorages for babbitt, 46. Automobile bolts, special characteristics of, 14. table of proportions for, 16. Babbitted bearings, proportions for, 49. methods of lining, 46. Base plates, use of, 56. Bearings, adjustments of, 48. babbitted, proportions for, 49. methods of lining, 46. commercial forms of, 47. general description of, 46. materials used for, 46. methods of supporting, 48, 55. quarter-box, description and use of, 52. proportions for, 55. step, use of, 47. Belting, leather, commercial sizes of, 65. Belts, use of and materials for, 64. Bevel gears, pitch surfaces of, 68. proportions for, 72. stock sizes of, 75. Bolts, automobile, special characteristics of, 15. table of proportions for, 16. coupling, description and stock sizes of, 14. hexagonal heads and nuts for, use of, 13. machine, description and stock sizes of, 1.3. proportions for heads, nuts and threads for, 12, 14. stud, description and stock sizes of, 15. table of dimensions for, 14. tap, description and stock sizes of, 15. use of, 12. Boxes, definition of, 33. quarter, description and use of, 53. frames, wall, description and use of, 58. proportions for, 59. Brackets, wall, description and use of, 56. proportions for, 58. Cams, disk, proportions for, 76. for gas engines, proportions for, 76. stamp mill, proportions for, 77. Cap screws, description and stock sizes of, 20. Castellated nuts, description and use of, 17. table of proportions for, 16. Cast iron washers, table of, 19. use of, 18. Circular pitch, definition of, 68. Clutch couplings, description of, 38. Clutches, friction, use of, 42. jaw, description and use of, 38. proportions for, 39. shifting collar for, 41. shifting lever for, 42. 102 Index Collars for shafting, proportions for, 44. use of, 43. shifting for jaw clutches, description and use of, 40. proportions for, 41. Compression couplings, definition of, 35. CoupUng bolts, description and stock sizes of, 14. Couplings, clutch, description of , 38. compression, definition of, 35. flanged, description of, 36. proportions for, 37. for shafting, requirements for, 34. keyless, description of, 35. pipe, description and stock sizes of, 82. sleeve, description of, 34. Cut washers, table of proportions for, 19. use of, 18. Decimal equivalents of fractions of one inch, 95. Diametral pitch, definition of, 68. Disk cams, proportions for, 76. Edge angle, definition of, 73. Empirical design, definition of, 5. Empirical equations, determination and advantages of, 8. Empirical methods, application to standardized machine parts, 5. use of in modem design, 5. Face angle, definition of, 73. Feather keys, description and use of, 28. i tables of proportions for, 28, 30. Flanged couplings, description of, 36. proportions for, 37. Flanges, pipe, desci-iption and forms of, 82. table of dimensions for, 85. Floor stands, use of, 56. Fractions of an inch, decimal equivalents of, 95. used in dimensions, 6. Friction clutches, use of, 42. Gas engine cams, proportions for, 76. Gaskets, definition and use of, 82. Gears, bevel, proportions for, 72. pitch surfaces of, 68,^ stock sizes of, 75. commercial stock sizes of, 75. dimensioning on drawings of, 69, 71. materials used for, 70. mitre, definition of, 68. stock sizes of, 75. mortise, definition of, 70. purpose and forms of , 67. spur, pitch surfaces for, 68. proportions for, 70. stock sizes of, 75. worm, pitch surfaces of, 68. proportions for, 73. stock sizes of, 75. Gear teeth, proportions and properties of, 68. Gib keys, description and use of, 25. stock sizes of, 28. Index 103 Graphical determinations in empirical design, 6. Handwheels, empirical design of bore and hub for, 6. use and forms of, 65. Hanger screws, description and stock sizes of, 24. Hangers, shaft, use of, 60. Jam nuts, use of and proportions for, 17. Jaw clutches, description and use of, 38. proportions for, 39. shifting collar for, 41. shifting lever for, 42. Journal boxes, definition of, 33. Journals, definition of, 33. Keys, feather, description and use of, 28. tables of proportions for, 28, 30. gib, description and use of, 25. stock sizes of, 28. special proportions for, 28. standard forms and proportions for, 25. straight, use of, 26. taper, stock sizes of, 28. use of, 27. use of, 25. Woodruff system of, 29. Key ways or key seats, definition of, 25. in shafting, 33. proportions for in the United States, 31. Lag screws, description and stock sizes of, 24. Leather belting, commercial sizes of, 65. Machine bolts, description and stock sizes of, 13. Machine screws, A. S. M. E. standard for, 21. description and stock sizes of, 21. Marine nut locks, description of and proportions for, 18. Mitre gears, definition of, 68. stock sizes of, 75. Mortise gears, definition of, 70. Nut locks, use of, 17. marine, description of and proportions for, 18. Nuts, castellated, description and use of , 17. table of proportions for, 16. jam, use of and proportions for, 17. Pinion, definition of, 67. Pins, taper, description and stock sizes of, 31. Pipe, varieties of, 79. wrought iron and steel, commercial sizes and weights of, 79. table of dimensions of, 80 Pipe bends, description of, 86. table of dimensions for, 87. couplings, description and stock sizes of, 82. fittings, flanged, description of, 87. tables of dimensions for, 88, 89, 90, 91. flanges, standards for, 83. table of dimensions for, 85. joints, general types of, 82. threads, Briggs standard, proportions of, 81. table, of, 80. 104 Index Pitch, diametral, definition of, 68. circular, definition of, 68. circle or pitch line, definition of, 68. diameter, definition of, 68. surfaces, definition and comjnon forms of, 67. Pulleys, commercial sizes of, 62. proportions for, 63. Quarter-box bearings, description and use of, 52. proportions for, 55. Safety collars, proportions for, 44. Screw fastenings, general classes of , 11. specifications on drawings, 11. standardization of, 11. use of, 11, 19. Screws, cap, description and stock sizes of, 20. for metal use of, 19. for wood, use and forms of, 23. hanger, description and stock sizes of, 24. lag, description and stock sizes of, 24. machine, A. S. M. E. standard for, 21. description and stock sizes of, 21. set, description and stock sizes of, 22. use of, 11,19. wood, description and stock sizes of, 24. Set screws, description and stock sizes of, 24. Shaft, definition of, 33. couplings, requirements for, 34. fixtures, classification of, 46. Shafting, commercial sizes of, 33. Sleeve couplings, description of, 34. Splines, description and use of, 28. tables of proportions for, 28, 30. Spur gears, pitch surfaces for, 68. proportions for, 70. stock sizes of, 75. Stamp mill cams, proportions for, 77. Standardized machine parts, design of by empirical methods, 5. Step bearings, use of, 47. Straight keys, use of, 26. Stud bolts, description and stock sizes of, 15. Studs, description and stock sizes of, 15. Tap bolts, description and stock sizes of, 15. Taper keys, stock sizes of, 28. use of, 27. Taper pins, description and stock sizes of, 31. Threads, screw, common forms of, 12. pipe, Briggs standard, proportions of, 81. table of, 80. Trigonometric functions, natural, 96. United States standard thread, description of, 12. Valves, globe and gate, description of, 92. Wall box frames, description and use of, 58. proportions for, 59. Index 105 Washers, cast iron, table of dimensions for, 19. use of, 18. wrought iron and steel, table of dimensions for, 19. use of, 18. Woodruff system of keys, description of, 28. table of proportions for, 29. Wall brackets, description and use of, 56. proportions for, 58. Wood screws, description and stock sizes of, 24. Worm gears, pitch surfaces of, 68. proportions for, 73. stock sizes of, 75. m -