Engineering Ex Perv 00000 i 00042

7/29/2019 Engineering Ex Perv 00000 i 00042

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HI LLINO SUNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN

PRODUCTION NOTEUniversity of Illinois at

Urbana-Champaign LibraryLarge-scale Digitization Project, 2007.


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EEgineering Experiment Station was established byactibn of the Board, of.Trustees D.ember 8, 1903.9,Italong vious lines of egineering, and to stdy prob.lems of importaneo to professional engineers bnd to the manufac-turing, rail-way, iinbig,..congtr. tional and industrial interests ofthe state.e,

in the heads of the several departments of the College of Engi- .neering, These constitute' the' Station Staff, and with theDirector, determine the character of the investigations to be under-sometimes by a rseach fellow as gradate ork, sometimes bya inember of the instructiol force of the College of Engineering,

more frequently by aninvestigator belonging to the StationThe results of these investigations aie published in the *'form of bulletins,, which record mostly the ekperimentsof the

Station's'8ow0 staIF of investigators. - There will also be issuedfrom time to time ini the' form of 3irculars, compilations giving^.*;'^^S^Bt^ul^^CI

~e~F.'j "'''^i '^^ 'y :^l^N^l^'^'


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UNIVERSITY OF ILLINOISENGINEERING EXPERIMENT STATION

BULLETIN NO. 42 DECEMBER 1909

THE EFFECT OF KEYWAYS ON THESTRENGTH OF SHAFTS

BY HERBERT F. MOORE, ASSISTANT PROFESSOR OF THEORETICAL ANDAPPLIED MECHANICS, ENGINEERING EXPERIMENT STATION

CONTENTSI. INTRODUCTION

PAGE1. Preliminary...................................... 32. Acknow ledgm en t................................... 43. Notation and Formulas ................ ........... 4

II. TEST PIECES, TESTS, AND METHOD OF TESTING4. Test Pieces ................. ..................... 55. Description of Apparatus ......................... 76. Procedure of Tests................... ......... . .. 10

III. DATA AND RESULTS7. Ultimate Strength of Shafts with and without Keyways 108. Effect of Length of Keyway ......................... 119. Effect of Two Keyways 900 Apart .................... 11

10. Effect of Keyways on Turned Shafting............... 1211. Strengthening Effect of Key in Place ............... 1212. Effect of Keyway on Stiffness of Shaft. .......... 1313. Efficiency of Shafts with Keyways .................... 1314. Torsional Strength of Shafts with Keyways.......... 16


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THE EFFECT OF KEYWAYS ON THE STRENGTHOF SHAFTS.

I. INTRODUCTION.1. Preliminary.-In the transmission of power by means of

shafting and pulleys or gears, the common method of fasteningthe pulley or gear to the shaft, so that the two will rotatetogether, is by means of a key inserted in a keyway cut in theshaft, and extending into a corresponding keyway cut in the'hubof the pulley or gear. The strength and the proper proportion-ing of keys have been subjects of considerable study and of someexperimentation, but the effect of the keyway on the torsionalstrength of the shaft has apparently been studied but little.Evidently, the keyway must weaken the shaft in which it is cut.It would seem that the sharp corners of the keyway and its loca-tion at one side of the shaft might weaken the shaft more thanthe relatively small size of the keyway would lead us to expect.In view of the very extensive use of shafts with keyways and thesmall amount of information available on the subject, the effectof keyways on the torsional strength of shafts has seemed to thewriter a problem worthy of some experimental study. This bul-letin is an account of a brief investigation carried on in theLaboratory of Applied Mechanics by the Engineering ExperimentStation of the University of Illinois.

The mathematical analysis of the strength of a shaft with akeyway cut in it is a problem of great complexity. The commontheory of stresses in shafts applies only to shafts of circular cross-section. Mathematical researches by Saint Venant and othershave developed the theory of square, rectangular, triangular, andelliptical shafts, but, so far as the writer knows, there has beenno successful attempt to develop the mathematical theory of thestress in a shaft with a keyway cut in it. However, as the rangeof sizes of shafts and keys in common use is not very great, itwas thought that an experimental study of the effect of keywayson the strength of shafts might lead to formulas which may besafely used in nearly all the cases met by the designer of shaftsand keys.


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4 ILLINOIS ENGINEERING EXPERIMENT STATION

It was found possible to investigate by direct experiment theeffect of keyways on the strength of shafts of various sizes, andto study the effect of keyways on the strength of shafts subjectedto combined bending and twisting.

For this use in calculation and design, it was thought best tocoin a term to permit comparison between a shaft with keywayand an uncut shaft. Adopting a nomenclature similar to thatused by many writers on the strength of riveted joints, the ratioof the strength of a shaft with a keyway to the strength of a sim-ilar shaft without a keyway is hereafter spoken of as the efficiencyof the shaft with keyway.

If a shaft with a pulley keyed to it is given a permanenttwist, the removal of the pulley is frequently a matter of greatdifficulty; while if a shaft carries a sleeve or gear with a key slid-ing in a keyway, any permanent twist practically ruins the shaft.For these reasons the elastic limit of a shaft under torsion is takenas the measure of its strength.

2. Acknowledgment.-A considerable part of the experimen-tal work herein described was performed by the following seniorstudents of the College of Engineering of the University of Illi-nois in the preparation of their graduating theses in MechanicalEngineering:

Mr. F. E. Leidendeker, Class of 1908.Mr. O. Craig and Mr. J. C. Lund, Class of 1909.

The writer wishes to express his appreciation of the faithfuland careful work of the above students. Acknowledgment is alsomade to the Whitney Manufacturing Company of Hartford, Con-necticut, for cutters for keyways of the Woodruff system of keys.

The work was undertaken with the approval of ProfessorArthur N. Talbot, head of the department of Theoretical andApplied Mechanics, to whom the writer is indebted for many help-ful suggestions, both as to methods of experimentation and tointerpretation and arrangement of results.

3. Notation and Formulas.-The following notation is used:d = actual diameter of shaft in inches.w = width of keyway - diameter of shaft.h = depth of keyway - diameter of shaft.T = torsional (twisting) moment on shaft in inch pounds.M = bending moment on shaft in inch-pounds.


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MOORE-EFFECT OF KEYWAYS ON STRENGTH OF SHAFTS 5

J = polar moment of inertia of cross-section of shaft(for circular shaft, J ).10.2

f = greatest fiber stress in shaft due to torsion.o = angle of twist of shaft in degrees.I = length of shaft in inches.Es = modulus of elasticity of material of shaft in shear

(torsion).e = efficiency of shaft with keyway.k = ratio of angle of twist of shaft with keyway to angle

of twist of similar uncut shaft.H. P. = horse-power.

r. p. m. = number of revolutions per minute.The following formulas are used:

T 2fJT-0= x57.3Es d

H.P.T = 63 020 H. Pr.p.m.The first two formulas are based on the following assump-

tions; (1) that a plane section of the shaft remains plane duringtorsion; and (2) that the fiber stress varies uniformly from zero atthe axis of the shaft to a maximum at the outer fiber, i. e., the mod-ulus of elasticity for shear remains constant. The first assump-tion is not true for shafts which are not circular in cross-section.

II. TEST PIECES, TESTS, AND METHOD OF TESTING.

4. Test Pieces.-The principal object of this investigationwas to obtain values of the efficiency of shafts with keyways, andas nearly all shafting in common use is cold-rolled, the principalseries of tests was made on specimens of cold-rolled steel shaft-ing. The diameters of the test shafts of these series were 11, 1TA,li-, and 21 in. Shafts were tested under simple torsion and undertorsion combined with bending. The bending moment appliedto the shaft was in one case equal to the torsional moment, and inanother equal to three-fifths the torsional moment. Table 1 showsthe sizes of shafts and the sizes of the keyways cut in them.


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TABLE 1.DIMENSIONS OF SHAFTS AND KEYWAYS.SERIES OF 1909.

RelativeDia. Shaft Dimensionsinches of Keyway

dw A

0.1250.1250.18750.1250.1250.18750.1250.1250.18750.1250. 1250.1875

Actual Dimensionsof Keywayincheswidth depth

For transmitting power, it is common American practice touse a square key whose width and depth are each equal to aboutone-fourth the diameter of the shaft (Kent's Pocket-Book, pp.975 - 976). This means a keyway in the shaft in which w = 0.25and h = 0.125. The depth of keyway is measured as shown inFig. 1.

FIa. 1.Shafts were also tested with keyways for the Woodruff sys-

tem of keying. The outline of the Woodruff key and its keyway

~~~~__ ___

--------


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are shown in Fig. 2. In choosing the sizes of Woodruff keywaysto be cut in the test shafts, the shearing strengths of variousstandard sizes of keys were figured, and a standard size was

FIG. 2.chosen such that the shearing strength of two keys equaled, asnearly as possible, the torsional strength of the solid test shaftin question. The sizes of the Woodruff keys chosen are shownin Tables 2 and 4.

In addition to the above tests for effect of single keyways onthe strength of cold-rolled shafting, tests were made (principallyin the 1908 series) which yielded data on the following subjects:ultimate strength of shafts with keyways; effect of two keywaysat right angles; effect of length of keyway; effect of keyways onturned steel shafting.

All keyways, except in the tests for studying the effect oflength of keyways, were cut to a length equal to about four timesthe diameter of the shaft, no keyway being longer than eightinches.

All material for the test shafts was bought in the openmarket. Both the cold-rolled and the turned shafting were ofordinary soft steel. All tests were planned in duplicate, and witha very few exceptions, all tests were made in duplicate.

5. Descriptionof Apparatus.--All shafts tested under simpletwisting were tested in the 230000 in.-lb. Olsen torsion testingmachine in the Laboratory of Applied Mechanics of the Univer-


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sity of Illinois. To the test shaft were attached long arms inpairs, one arm of a pair carrying a pointer, and the other a scale.The angle of twist between these two arms was measured by themotion of the pointer over the scale. Fig. 3 shows a test shaft

FIG. 3.

of the 1909 series in position with the pointers and scales attached.In this shaft were cut four keyways, each keyway being 900round the shaft from the adjacent keyways. The angle of twistof the shaft was measured over five portions of its length, fourportions of length being occupied by the keyways and one beingwithout keyway. The latter portion was generally at the middleof the shaft.

The apparatus used for studying the effect of combined twist-ing and bending on shafts with keyways is shown in Fig. 4. Tothe ends of the test shaft S were keyed arms AA extending atright angles to the shaft. Equal forces FF were applied in avertical direction at points on these arms at a distance p from theaxis of the shaft. The test shaft was supported on bearings GGby means of steel balls B, bearing on hardened steel bushings.


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FIG(. 4.

The distance a from the arm A to the center of the nearer bear-ing was the same at the two ends. The test shaft then was sub-jected to a bending moment Fa over that portion between bear-ings, and to a twisting moment Fp over its entire length (the verysmall friction of the ball bearings being neglected). The ratio ofthe twisting moment to the bending moment equals-.a

The forces FF were applied by the moving crosshead of atesting machine. The entire apparatus shown in Fig. 4 rested onthe upper weighing head of the testing machine. The load reg-istered on the weighing table of the machine was equal to 2F. Theforce F was transmitted to each of the arms AA through a smallspherical pointed knob resting in one of the holes HHHH, thetwisting arm being varied by using different holes. The bear-ings GG could be moved axially along the shaft, thus allowingthe bending moment to be varied. In the tests under combinedtwisting and bending, the keyway cut in the test shaft was locatedat one side of the center of the shaft, and the angle of twist wasmeasured over the portion of the shaft containing the keyway,


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10 ILLINOIS ENGINEERING EXPERIMENT STATIONand also over the solid portion. The apparatus for measuringangle of twist was the same as in the tests under simple torsion,and is shown in the diagram in Fig. 4, in which K represents thekeyway, PP the pointers, and Sc the scale.

6. Procedure of Tests.-In the 1908 tests, which were all onshafts under twisting only, the method of conducting the test wasto apply torsion continuously until the yield point was passed,frequent readings of twisting moment and of corresponding angleof twist being taken. After the yield point was passed, the twist-measuring apparatus was removed, and the torsion applied untilthe shaft broke, the maximum twisting moment carried beingnoted.

In the 1909 tests, both under simple torsion and under com-bined twisting and bending, the method of procedure was as fol-lows: A small initial load was applied to the shaft, and an initialreading taken on the twist-measuring apparatus; more load wasthen applied and the angle of twist read; the load was thenreleased to its initial value, and the angle of twist again read, anypermanent set being thus detected; a load slightly greater thanthe previously applied load was then put on the shaft, and thisload in turn released to the initial value. This process wasrepeated with applications of increasing loads until the yield pointof the shaft was passed.

III. DATA AND RESULTS.7. Ultimate Strength of Shafts with and without Keyways.-

Table 2 (tests of 1908) shows the results of tests to breaking ofshafts with and without keyways. It seems that a shaft with asingle keyway of common dimensions has about the same ultimatestrength as a shaft without keyway. In the torsional tests todestruction, after the elastic limit of the shaft had been passed,the keyways gradually closed up and at rupture they wereentirely closed. The larger keyways and the two keyways 900apart lowered the ultimate strength somewhat. The variation instrength due to difference in material of the shafting seems tocause more variation in ultimate strength than is caused by dif-ferent keyways. As previously pointed out, the elastic limit of ashaft is more significant than its ultimate strength.


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TABLE 2.ULTIMATE STRENGTH OF SHAFTS WITH KEYWAYS AND WITHOUT KEYWAYS.

Values are the average results of two tests.Keyway Maximum axiuwiting Computed H.Moment Fiber Stress 100 rp.mWidth Depth in.-b. (solid s h aft)inches inches Ib. persq. in.

Diameterof Shaftinches

1% in.cold-rolled

1/ in.turned

1S%n. cold-rolled

2 in.cold-rolled

2 in.turned

0Y4

%No. 10No. 15

0No. 10No. 15

00

No. 16No. 210 7

No. 16No. 21

274002760030 3002440027 60027 2002550026 20025 300253002580025500237002410054 70056400

103 700102 100101 50094200104 500105 300100 500100 50094200

94 20089 80085 000

70 55071 00078 00063 00071000700006580067 60065 20065 200664006570061 000621006500067 000660006500064 600600006650067 00064 00064 00060006000057 20054 100

43.443.848.038.743.843.140.441.640.140.140.940.437.638.286.889.6

164.5162.0161.1149.1165.7167.0158.7158.7149.1149.1142.5134.8

Remarks

Shaft without keyway

Keyway for No. 10 WoodruffKeyway for No. 15 Woodruff2 keyways 900 apartShaft without keyway

Keyway for No. 10 WoodruffKeyway for No. 15 WoodruffShaft without keywayShaft without keyway

Keyway for No. 16 WoodruffKeyway for No. 21 WoodruffShaft without keywayKeyway for No. 16 WoodruffKeyway for No. 21 Woodruff

8. Effect of Length of Keyway.-Several special tests weremade on the effect of keyways on the strength of shafts. In gen-eral, these tests, while too few in number to justify final con-clusions, gave suggestive or tentative results.

The keyways in nearly all the shafts tested were cut to atotal length of about four times the diameter of the shaft, no key-way being longer than 8 inches; but in several special shafts, key-ways were cut 18 inches long. No difference between strength ofshafts with long keyways and of similar shafts with the usualshorter keyways was observed.

9. Effect of Two Keyways 900 Apart.-One test was made ofa shaft having cut in it two keyways 90' apart, the two keyways

0%4

%No. 10No. 15

0M14M

No. 10No. 150

0TaAfa

No. 16No. 210T'Ia

No. 16No. 21

~~


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being located in the same cross-section of the shaft. While theresult of this single test is by no means conclusive, it is of interestto note that the reduction in strength at elastic limit of the shaftby these two keyways was nearly three times as great as thereduction in strength at elastic limit of a similar shaft by onesuch keyway.

10. Effect of Keyways on Turned Shafting.-The tests madewere mainly on cold-rolled shafting, but in the 1908 series a fewtests were made on test specimens of turned shafting. Owing tothe imperfect method used in the 1908 tests for locating the elasticlimit, these results must be regarded as tentative. In these teststhe:effect of keyways on the strength of turned shafting at theelastic limit seemed to be about the same as the effect of keywayson the strength of cold-rolled shafting.

11. Strengthening Effect of Key in Place.-During the tests,the question arose as to the difference in strength of a shaft withempty keyway and a shaft on which a pulley was keyed in place,the key nearly filling the keyway. It was judged best, however,to test shafts with empty keyways, as there is usually a part ofthe keyway at either end not filled by the key, and a perfect fitof the key in the keyway is by no means certain, especially afterlong service and, therefore, for purposes of design the emptykeyway determines the strength of the shaft.

TABLE 3.RATIO OF ANGLE OF TWIST OF SHAFT WITH KEYWAY

TO ANGLE OF TWIST OF SIMILAR SHAFTWITHOUT KEYWAY.

Dimensions of KeywayDiameterof Shaftinches w = 0.25 v = 0.25 w = 0.50 Woodruffh =0.125 =0.1875 = 0.125 System*

1M 1.24 1.25 1.27 1.11S1.14 1.24 1.19 1.111" 1.18 1.21 1.36 1.18S1.16 1.21 1.41 1.1111l 1.29 1.48 1.54 1.12

S1.10 1.25 1.18 1.05% 1.10 1.28 1.37 1.10Average 1.17 1.27 1.33 1.11

*See Table 4 fo r sizes of Woodruff Keyways.


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12. Effect of Keyway on Stiffness of Shaft.-The amount oftwist in a shaft transmitting power is frequently of importance.Table 3 gives the ratio of angle of twist of shafts with keywaysto angle of twist of shafts without keyways as computed from thedata of the torsional tests for stresses within the elastic limit.The results are fairly well represented by the equation

k = 1.0 + 0.4 w + 0.7 h,in which k = ratio of angle of twist of shaft with keyway to angleof twist of similar shaft without keyway, w = width of keyway- diameter of shaft, and h = depth of keyway - diameter ofshaft.

Keyways for two Woodruff keys of shearing strength suffi-cient to develop the full twisting strength of shaft seemed toreduce the stiffness of the shaft somewhat less than did a keywayfor a square key whose side measures one-fourth the diameter ofthe shaft.

In considering the torsional stiffness of a shaft, it must beremembered that the keyways reduce the stiffness only over thatportion of length which they actually occupy.

13. Efficiency of Shafts with Keyways.-The efficiency of ashaft with keyway has already been defined as the ratio of strengthat elastic limit of a shaft with keyway to the strength at elasticlimit of a similar shaft without keyway.

The determination of the elastic limit of a shaft under torsionis somewhat difficult; when the outer fibers are stressed to theelastic limit, the stress is taken more largely by the inner fibers,and the change of angle of twist is not so sudden as is the changeof stretch at the elastic limit in a piece under tension, where thefibers are stressed nearly uniformly, and all begin to yield atnearly the same time. In the 1908 tests, each test shaft carriedonly a single keyway, and comparison between the strength ofshafts with keyways and the strength of similar shalts withoutkeyways was made by testing different specimens. This alloweda comparison of the ultimate strengths, which are very clearlydefined; but in comparing elastic limits, the variation betweenthe material of different specimens was sufficiently great to throwsome doubt on the accuracy of the efficiency of shafts with key-ways, as determined by this method. In the 1909 tests, the elas-tic limit of a section of shaft with keyway was compared with


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14 ILLINOIS ENGINEERING EXPERIMENT STATIONthat of an adjacent section without keyway in the same shaft.Thus the error due to difference in material was greatly reduced,but by this method the ultimate strength of only the weakestsection of the shaft could be obtained. So while all the resultson ultimate strength have been obtained from the 1908 tests, theefficiencies of the shafts with keyways have been obtained entirelyfrom the 1909 tests.

In computing results, J. B. Johnson's method of locating theelastic limit was found most satisfactory*. Fig. 5 to 12 give thedeformation and set curves for the 1909 series of tests. Thesolid lines show the deformation (angle of twist) under load, whilethe broken lines show the set. The elastic limit as determinedby Johnson's method is shown on each curve by a short line drawnacross the deformation curve, and it will be noted that the stressat which noticeable permanent set begins is in all cases nearlythe same as the stress at the elastic limit as determined by John-son's method.

Table 4 shows the efficiency of the various test shafts of the1909 series of tests, using the term efficiency as previouslydefined. From this table it would appear that for a set of shaftsof different sizes having the dimensions of the keyway kept pro-portional to the diameter of shaft, the efficiency does not depend,in any noticeable degree, on the size of shaft. The efficiencydoes not seem to be affected by the addition of a bending momentas great as the twisting moment. The efficiency of a shaft withtwo keyways cut in the same plane for two Woodruff keys, ofsuch size that the strength of solid shaft was equal to the shear-ing strength of the two Woodruff keys, is about the same as theefficiency of a shaft with a keyway whose width equals one-fourththe diameter of the shaft and whose depth equals one-eighth thediameter of the shaft.

The results of the foregoing tests are fairly well representedby the equation

e = 1.0 - 0.2 w - 1.1 hin whiche = efficiency of shaft with keyway,w = width of keyway - diameter of shaft,h = depth of keyway - diameter of shaft.

*J.B. Johnson's method of locating the elastic limit consists in finding the point on thestress-deformation curve at which the deformation is increasing fifty per cent more rapidly thanits initial rate of increase. See Johnson's "Materials of Construction", pp. 18-20.


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MOORE-EFFECT OF KEYWAYS ON STRENGTH OF SHAFTS 15TABLE 4.

EFFICIENCY OF SHAFTS WITH KEYWAYS.Eifficiency - elastic strength of shaft with keywayelastic strength of shaft without keyway

Dimensions of KeywayUnder simple torsion:Cold-rolled shaft, dia. 1/ in.Cold-rolled shaft, dia. lI in.

Cold-rolled shaft, dia. 1 in.Cold-rolled shaft, dia. 2Y in.

Under combined torsion and bending:1. Twisting moment = Bending momentCold-rolled shaft, dia. 1% in.Cold-rolled shaft, dia. l1t in.2. Twisting moment = I Bending momentCold-rolled shaft, dia. 1M in.Cold-rolled shaft, dia. 11i in.

General Average

w = 0.50A = 0.125

0.7620.8030.7580.7480.7640.8480.7050.6300.6800.5840.671

0.8950.8700.7400.8150.752

w 0.25 = 0.25h= 0.1875 A 0.125

0.7600.8460.8170.7100.7500.7750.6890.6360.698

0.6970.775

0.6700.735

0.735

0.8800.9000.8890.8600.8240.8390.8250.7910.8030.854

0.9400.8880.8320.8400.850

WoodruffSystem*

0.8400.8600.8150.8260.8350.9430.8610.7160.7500.8580.8400.9300.8800.8560.8100.845

*In lM-in, shafts keyways were cu t for No. 15 Woodruff keyslUI-in. shafts keyways were cu t for No. 25 Woodruff keysl' -in. shafts keyways were cu t for No. S Woodruff keys2i-in. shafts keyways were cu t for No. U Woodruff keys

This equation gives efficiencies slightly lower than those observedfor keyways of small width or depth, and efficiencies about thesame as those observed for keyways in which w = 0.50 and h =0.125; or w = 0.25 and h = 0.1875. As this equation is entirelydependent on the results of experiments, it should not be usedfor points much outside the limits of the experiments. The limitsof the above series of tests were keyways having w = 0.50 andh = 0.1875.

Fig. 13 affords a convenient graphical method of applyingthe above formula, and is used as follows: To determine the effi-ciency of a shaft with a given (or proposed) keyway, locate onthe diagram a point whose vertical distance from 0 equals thevalue of h, and whose horizontal distance from 0 equals the valueof w. This point will, in general, fall between two lines repre-senting values of efficiency, and the efficiency of the shaft in ques-tion may then be estimated with sufficient accuracy. The spacewithin the triangle OAB represents the range covered by the


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O 0 0 00.Widfh of keywvay-Dioame ter o f shoaf =/.0

FIG. 13.tests actually performed, and covers the proportions of keywayscommonly used in practice.

14. TorsionalStrength of Shafts with Keyways.-The object ofthese tests was to determine ratios of strength and stiffnessbetween shafts with keyways and shafts without keyways. Thenumber of tests was not sufficient to give very much informationas to the properties of cold-rolled steel shafting. However, as amatter of general interest, the values found in these tests for themodulus of elasticity in shear (torsion), and of the fiber stress atthe elastic limit of the cold-rolled test shafts at sections withoutkeyway, have been tabulated in Tables 5 and 6.Taking the fiber stress at the elastic limit of cold-rolled steelshafting at 37 500 lb. per sq. in. (a value slightly less than theaverage found in the tests), and the efficiency of shafts with key-ways from the equation e = 1.0 - 0.2 w - 1.1 h, values for the

I


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MOORE-EFFECT OF KEYWAYS ON STRENGTH OF SHAFTS 17TABLE 5.

MODULUS OF ELASTICITY INSHEAR (TORSION) OF COLD-ROLLED STEEL SHAFTING.

Diameter of Modulus ofTest No. Shaft inches Elasticity

46474849505152

1IY1&1A42V42Y4

Average

129000001200000012490000108000001266000011 340 0001171000011985 000

TABLE 6.ELASTIC LIMIT IN TORSION

OF COLD-ROLLED STEELSHAFTING.

Tt Diameter of Fiber Stresses t NShaft inches b. per sq. in.

46 1 4330047 1il 3680048 1 , 3850049 11 3680050 l1t 4050051 2Y 3620052 2V 40500

A verage 38 940

twisting moments and the horse-power at 100 r.p.m., transmittedby cold-rolled shafts stress to the elastic limit, have been computedfor various sizes and tabulated in Table 7. These values are forshafts with keyways for square keys whose side measures aboutone-fourth the diameter of the shaft. In the use of this table, asuitable factor of safety should be allowed.


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TABLE 7.STRENGTH OF SHAFTS WITH KEYWAY.

The table gives the calculated twisting moment and horse-power at 100r.p.m., transmitted in torsion by cold-rolled shafting with keyway whenstressed to the elastic limit. Fiber stress is assumed at 37 500 lb. per sq. in.The keyway is cut for a square key whose side measures approximately one-fourth the diameter of the shaft. No allowance is made for bending action.In applying this table, a suitable factor of safety should be used.

Diameter Sie o Key ting Horse-poernches inches inlb. at 100 r .p.m.

1 M 5980 9.51 A, 7080 11.21% A 8510 13.5113 A 9 980 15.71 A4 11680 18.51A 41 13390 21.31% Ai 15550 24.716 % 17590 27.91% % 20 190 32.01A ii 22600 35.91% ii 25660 40.71I1 A 28500 45.2S1 A 32060 50.91 35350 56.11% -S 39420 62.611 Y4 43180 68.52 % 47860 75.92A A1 52140 82.72% i 57900 91.12A 62 210 98.72M 68160 108.22A 73 490 116.62% 9 80 120 127.12A % 86 080 136.62 % 93 470 148.3


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NV)

I

(I)

LA


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g

O

V)

k

,J,

LJ J

(f)

Is

t4.

O O O 0 O o o

/IY6LEOF T 5/ST //I DE6REE5 PER /NCH-OF LE/G6THIFIG. 6. DIAGRAMS OF TESTS UNDER COMBINED BENDING AND TWISTING.

S/Yo. I 0


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'I

Cr)O

(J)

Ki-)

A/1GLE OF TW/ST //V DEGREES PER/ CH OF LE/Y67THFIG. 7. DIAGRAMS OF TESTS UNDER COMBINED BENDING AND TWISTING.


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.1(f)

KI~i

I)

Vf)

0i-K.K(IKKZZ

e7/YGLE OF 7I/S T //Y DEGREES PER INCH OF LENGTHFIG. 8 DIAGRAMS OF TESTS UNDER COMBINED BENDING AND TWISTING

Igopooouu h n. *I ~n


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Mt)ORE-EFFECT OF KEYWAYS ON STRENGTH OF SHAFTS 23

CM > >

R/VGLE OF TVW/5 T //I DE6REES PER I//CHOF LE/YGTHFIG. 9 DIAGRAMS OF TESTS UNDER COMBINED BENDING AND TWISTING.

%


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2

U)

QI

0,V4' \-0 N.1 1 'f471YGLEOF T7N/ST /I-DE6REES PER / ICHOF LEZNGTH

FIG. 10 DIAGRAMS OF TESTS UNDER TWISTING ONLY.


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4 0 201

/0

7/YG6 E OF TiW/5T /1/ DEGREES PER /IYCH OFLEIYGTHFIa. 11 DIAGRAMS OF TESTS UNDER TWISTING ONLY.


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Ai)

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PUBLICATIONS OF THE ENGINEERING EXPERIMENT STATION*Bulletin No . 1. Tests of Reinforced Concrete Beams, by Arthur N. Talbot. 1904.*Circular No. 1. High-SpeedTool Steels, by L. P. Breckenridge. 1905.*Bulletin No. 2. Tests of High-Speed Tool Steels on Cast Iron, by L. P. Breckenridgeand Henry B. Dirks. 1905.*Circular No. 2. Drainage of Earth Roads, by Ira 0. Baker. 1906.Circular No. 3. Fuel Tests with Illinois Coal. (Compiled from tests made by the Tech-

nologic Branch of the U. S. G. S.. at the St. Louis, Mo., Fuel Testing Plant, 1904-1907, by L. P.Breckenridge and Paul Diserens. 1909.*Bulletin No. 3. The Engineering Experiment Station of the University of Illinois, by

L. P. Breckenridge. 1906.*Bulletin No . 4. Tests of Reinforced Concrete Beams, Series of 1905, by Arthur N.Talbot. 1906.*Bulletin No. 5. Resistance of Tubes to Collapse, by Albert P. Carman. 1906.*Bulletin No. 6. Holding Power of Railroad Spikes, by Roy I. Webber. 1906.*Bulletin No. 7. Fuel Tests with Illinois Coals, by L. P. Breckenridge, S. W. Parr and

Henry B. Dirks. 1906.*Bulletin No. 8. Tests of Concrete: I. Shear: II. Bond, by Arthur N. Talbot. 1906.*Bulletin No. 9. An Extension of the Dewey Decimal System of Classification Ap-

plied to the Engineering Industries, by L. P. Breckenridge and G. A. Goodenough. 1906.*Bulletin No. 10. Tests of Concrete and Reinforced Concrete Columns, Series of 1906, by

Arthur N. Talbot. 1907.*Bulletin No. 11. The Effect of Scale on the Transmission of Heat through Locomotive

Boiler Tubes, by Edward C. Schmidt and John M. Snodgrass. 1907.*Bulletin No. 12. Tests of Reinforced Concrete T-beams, Series of 1906, by Arthur N.Talbot. 1907.*Bulletin No . 13. An Extension of the Dewey Decimal System of Classification Applied

to Architecture and Building, by N. Clifford Ricker. 1907.*Bulletin No. 14. Tests of Reinforced Concrete Beams, Series of 1906, by Arthur N.

Talbot. 1907.Bulletin No. 15. How to Burn Illinois Coal without Smoke, by L. P. Breckenridge. 1908.Bulletin No. 16. A Study of Roof Trusses, by N. Clifford Ricker. 1908.*Bulletin No. 17 . The Weathering of Coal, by S. W. Parr, N. D. Hamilton, and W. F.

*heeler. 1908.Bulletin No. 18. The Strength of ChainLinks, by G. A. Goodenough and L. E. Moore.

1908.*Bulletin No. 19. Comparative Tests of Carbon, Metallized Carbon and Tantalum Fila-

ment Lamps, by T. H. Amrine. 1908.*Bulletin No. 20. Tests of Concrete and Reinforced Concrete Columns, Series of 1907, byArthur N. Talbot. 1908.Bulletin No. 21. Tests of a Liquid Air Plant, by C. S. Hudson and C. M. Garland. 1908.*Bulletin No. 22. Tests of Cast-Iron and Reinforced Concrete Culvert Pipe, by Arthur N.

Talbot. 1908.Bulletin No. 23. Voids, Settlement and Weight of Crushed Stone, by Ira O. Baker. 1908.Bulletin No. 24. The Modification of Illinois Coal by Low Temperature Distillation, by

S. W. Parr and C. K. Francis. 1908.Bulletin No. 25. Lighting Country Homes by Private Electric Plants, by T. H.

Amrine. 1908.Bulletin No. 26. High Steam-Pressures in Locomotive Service. A Review of a Report tothe Carnegie Institution of Washington. By W. F. M. Goss. 1908.Bulletin No. 27. Tests of Brick Columns and Terra Cotta Block Columns, by Arthur N.

Talbot and Duff A. Abrams. 1909.Bulletin No. 28, A Test of Three Large Reinforced Concrete Beams, by Arthur N.

Talbot. 1909.Bulletin No. 29. Tests of Reinforced Concrete Beams: Resistance to Web Stresses.Series of 1907 and 1908, by Arthur N. Talbot. 1909.Bulletin No. 30. On the Rate of Formation of Carbon Monoxide in Gas Producers, by J.

K. Clement, L. H. Adams, and C. N. Haskins. 1909.*Out of Print.


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PUBLCATIONS OF THE ENGINEBRING BXPERIPIBNT STATION-ContinuedBulletin No, 31. Fuel Tests with House-heating Boilers, by J. M. Snodgrass. 1909.Bulletin So. 32. The Occluded Gases in Coal, by S. W. Parr and Perry Barker. 1909.Bulletin No. 33. Tests of Tungsten Lamps, by T. H Amrine and A. Guell. 1909.Bulletin No. 34. Tests of Two Types of Tile Roof Furnaces under a Water-tube Boiler,

by J. M. Snodgrass. 1909.Bulletin No. 35. A Study of Base and Bearing Plates for Columns and Beams, by N.Clifford Ricker. 1909.Bulletin No. 36. The Thermal Conductivity of Fire-Clay at High Temperatures, by JK. Clement and W. L. Egy. 1909.Bulletin No. 37. Unit Coal and the Composition of Coal Ash, by S, W. Parr and W. F.Wheeler. 1909.Bulletin No. 38. The Weathering of Coal, by S. W. Parr and W. F. Wheeler. 1909.Bulletin No. 39. Tests of Washed Grades of Illinois Coal, by C. S. McGovney. 1909.Bulletin No. 40. A Study in Heat Transmission, by J. K. Clement and C. M. Garland.

1910.Bulletin No. 41. Tests of Timber Beams, by Arthur N. Talbot. 1910.Bulletin No. 42. The Effect of Keyways on the Strength of Shafts, by Herbert F. Moore

1910.


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TNILVEIRSITY OFTTX' m NOI

THIE STATE TYNIVERSITY

Languages and Literatures, Philosophical and Political Set-

buildings; well-equipped laboratories and shops. Graduate

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Aand undergradu'Iate courses in Archiectue ArchitecturalOLLEW: 4sN3Rq n eeibiy 1

Engineering; Archqitectural ecoration; Civil Engineeriig;I[uniipal and Sanitary Engineering; Electrical Engineering;Mechanical Engipeerihg, Mining Engineering, RailwayEngineering).

COLLE OF SCIENCE (Astronomy, Botany, Cliemistry Ge-ology, Mathenatics, Physics, Physiology, Zoolog-).COLLEGE OF AGRICULTURE (Animal,Husbandry, Agronomy,Dairy Husbandry, Eorticulture, Veterinary Science, House-COLLEGE OF LAW X(Theyears' course).COLLEGE OF MEDICINE (College of Physiloias and Surgeons,Chicago). (Four ears' course).


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