Design of a Fatigue Testing Machine Citation Farmer, Verdine Ellsworth (1916) Design of a Fatigue Testing Machine. Bachelor's thesis, California Institute of Technology. doi:10.7907/5f1r-pc84. https://resolver.caltech.edu/CaltechTHESIS:07172024-164229145 Abstract No abstract. Item Type: Thesis (Bachelor's thesis) Subject Keywords: (Mechanical Engineering) Degree Grantor: California Institute of Technology Division: Engineering and Applied Science Major Option: Mechanical Engineering Thesis Availability: Public (worldwide access) Research Advisor(s): Unknown, Unknown Thesis Committee: Unknown, Unknown Defense Date: 1 January 1916 Record Number: CaltechTHESIS:07172024-164229145 Persistent URL: https://resolver.caltech.edu/CaltechTHESIS:07172024-164229145 DOI: 10.7907/5f1r-pc84 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 16561 Collection: CaltechTHESIS Deposited By: Benjamin Perez Deposited On: 17 Jul 2024 22:23 Last Modified: 17 Jul 2024 22:30 Thesis Files PDF - Final Version See Usage Policy. 8MB Repository Staff Only: item control page

THESIS Design of a Fatigue Testing Machine by V • E • ]'armer . Class of Nineteen Hundred and Sixteen Department of Mechanical Engineering. THROOP COLLEGE OF TECHNOLOGY Pasadena, California. 1916 . CONTENTS. I. Introduction. II. Formulae and Data of Design. III. Blue Prints. 1 I. Introduction. The Testing of Materials Labor-atory at Throop Colle ge of Technolo gy is equipped with a '?'hi te-Souther fatigue testing machine, The machine is of the revolvin g arm type and the specirren is loaded as a cantilever. The specimen can be loaded up to its elastic limit or even higher but the ra.ngE: for test is from seventy to one hundred percent. The time of a test is between two and three weeks as a maximum; thereiore the mac'hine is of importance in the College or research labora tory only. The objections to the TThite-Souther machine are as follows. 1- The time required to run a series of tests is very long , because of the fact that only two specimens are tested at the same time. 2- The specimen is costly and must be me de up by a machinist. 3- An empirical formula is used to determine the stresses in the material. 4- The specimen is loaded as a cantilever and therefore the maximum stress occurs at a fixed point and it will always break at this fixed point, independently of any local weakness that exists, 5- The specimen is lon g and the r efore a series of tests rnay not (because of changes tbat may occur in a bar} give comparative results. 2 6- Because of the shape of the specimen the piece cannot be tested in tension after it has been partiaJ.ly fatigued .. The present type of design is of the revolving beam. The specimen is subject to a uniform bending moment over the entire 1ength of the part una..er test. The range of loading is from fifty percent. to one r.undred percent. of the elastic limit. The time of test is cut down in as much as ten specimens can be tested at once. The machine is adapted to Coll€ge or nesearch Laboratories. Commer- cial tests are made in a very short time and give very good comparative results for the acceptance of new materials. If one is stud;i,ing the effects of repetition of stress in a specimen loa0 ed inside of the elastic limit of the material, this mactine is adapted to his work. The machine as designed is an attempt to use the good points of' the old_ machine Hnd combine vd th these the correction of tbe worst of its faults. The followinr paragraphs show how the faults of the ~bite-Souther mac~ine were ccrrectea and used in the new design. The time of a single test will take two or three weeks as a maximum. This depends on the relation of the load impressea to teat required to stress the piece to its elastic limit. A piece stressed to its elastic limit 3 will not run for as many alternations of stress as one loaded beneath the elastic limit. lf a series of tests are conducte~ several pieces are cut from the same rod T (A_,,,. and tested -aEf various proportions of the elastic limit. In case six tests were made from fifty percent. to one hundred percent. of the elastic limit, by variation of ten percent. each there would be six specimens to be tested. Two specimens can be tested at the same time in the White-Souther macr: ine. In ordeY to make such a series of tests the time required would be nearly six weeks. In case check runs were made another six weeks would be required. If the new design, which has ten spindles, were used the time wou)d be cut d ovvn to the length of tirre reouired to nm the longest test ( name)y. two weeks). If a check run were required, four of the second set could be tested at the same time as the first. Although the time per speci- m€n is not reduced the total time is cut down by testing ten specimens at a time. The cost of the White-Souther specimen is between three dollars and four dollars. This i~ due to the ex- treme care required in getting the dimensions absolutly exact. Any machine or file marks near the dang6rous sec- tion decrease the life of the piece. This is overcome in the new design by the use of a sirnp1e specimen reduced in area for part of its length in order not to have any bending in the chucks. The reduced section is circular in 4 shape and may be any length, one inch being suggested for a suitable length. The radius oi the fillet between the reduced snd large sections need not be an accurate circular arc. It can be made up with any tools that are on band and a diameter of an eighth of an inch is suggested. This simplicity makes it possible for anyone with an ordinary knowledge of a lathe to make up the specimens. The use of an empirical formula to determine the stresses in the material is not objectional in itself. It is due to the fact that it any slight change is made in the ahape of the specimen a change would be made in the stress caused by given loadine. Thus any slight change in the dimensions as specified by the maker, would render the stresses, as det ermtned b~i the :formula, somewhat in error. '11his is due to the fact that the formula was derived from results obtained cy testing pieces made in exact accordance with the working drawings of the piece. In the present design this is overccr:ie by subjecting the specimen to a uniform bending moment over thE. entire length of its reduced section. the formula The stress can be easily calculated from M = pl/e. M: bending moment impressed on the piece expressed in inch-pounds. p = stresses in the material expressed in pounds per square inch. l - moment of inertia of the section. 5 e = this distance of the outside fiber to the neutral exis. With a certain moment the value of "p" depends on the values of "I" and "e". These in turn depend on the cross-section of the piece alone. Thus the influence of the length and the care of getting the dimensions exact have been eliminated. A cantilever specimen is subject to the maximum stress in one section only. This means that, if there is any irtegularity in the metal in any other section, the break would not be affected by this. This is due to the fact that the piece is not under maximum stress at this point. obtained. In this way high values would often be By taking a piece subject to a uniform bend- ing moment over its entire length this can be overcome. It is thus overcome in the new specimen. The values thus obtained would be unif'ormily lowE:r than those obtained with the old machine. This is an a~vantage in as much as it showE values at the weakest point in the specimen. In case there were any irregularities the weakest section would necessarily give way first. This lower value obtained will therefore give more uniform result£> of the tests. A bar of any material may vary greatly from one end to the other. The use of a long specimen which bas a 6 maximum stress at one point only increases the danger of missing the weak pleces in the bar. If several tests are made on pieces from the same bar and each piece is loaded to stress the material to different values the results may not show results t~at should compare with th€ loadings, i.e. the results may not be in accordance with the loadines or proportional to the loadings. In a long specimen this discrepancy is due to the change in composition of the bar itse1f. B~T using short pieces this chance for a chanre in composition is reduced to a minimum. Two complete specimens in the old machine have a length of between fifteen and sixteen inches. The new specimens may be made as short as three and one-half inches thereby getting nearly five instead of two from the same length of bar and by this lessening the danger of a difference in composition in the various specimens. Another test that can be made with the !3pecimens of the new design is as follows;- a piece that has been partially fatigued may be tested in tension and comparative values of tension obtained for different degrees of iatigue. This is valuable to determine how a piece should be loaded after it had been subjected to a given number of reversals of stress. This will be of interest in determining the factor of safety for various wcrk. Nothing like this could be done with the old specimen because of its shape. 1 II. Formulae and Data of Design. Lever arm - the maximum weight - 25 lbs. The length of the lever arm is to be such that a one pound weight will put a stress of two tr.cusand (2000 ) pounds per square inch into the specimen. M 1r = l = p I 64 e p = p 1 X 64 d • h. e = d = 4i inc 2 ~ a4 X 2 " p ... 1 = 2000 XII X (ll d4 3 32 - one pound p = 2000 lb/in~ 1 = 24. 54 inches - length of' lever arm. hlake the arm of steel seamless tubing. Use a one inch tube one-sixteenth inch thick. I e = 'ii" Gd 1 ) 4 - { d 2 ) 4] e = d 2 = 21 inch. 64 X d 2 I = { 4 -(-g) 7 4] 1T_ll e I e 32 dl = one inch. d2 = 7/8 inch. = 0.0411 Se ction Modulus required M = Ll e I € X 25 -- 2515000 = 0.0391 Jl = p 1 . - 24.54" 25 lbs. f, = 16000 lb/in2 X 2 This tube is sufficiently strong. Because it must be threaded at its weakest section a sleeve is inserted into the tube at this point with a slight press fit. The thickness of the straightening sleeve must be at least one-sixteenth inch. A piece of three-quarter inch extra strong pipe turned down tc 0.8755 inch outside diameter gives the required thickness. The bearings. spindle. Ball bearings to be used. Four per Thrust load to be carried by the bearings. M = 625 inch-pounds. Assume bearings as three inches apart. Radial thrust on bearing 625 3 = 208.3 pounds Axial thrust - Weight of head and weights assume to be equal to thirty (30) pounds. Equivalent radial load= 300 pounds. Total radial load= 510 pounds. Use Norma - Light Series - No. 206. (Bore= 1.1811 inches ( ( Outside Diameter= 2.4410 inches. ( (Width= 0.6299 inches Chuck for holding specimen. Reamed with No. 7 Brown and Sharpe taper reamer; taper linch to one foot. - Diameter at large end= 13/16". 3 Required thickness of sleeve. Assume force used when inserting specimen into chuck= 60 pounds. tan-l e = 1 24 - 0.0417 .•.. e - 20- 21.9' e = 1 0 - 10.~5' 2 48.9. N = 60 x 48.9 · = 2840 lbs. Area - ( 1 ~) 16 'ft x 2 = 5.10 square inches. p = 2 84 0 = 567 lbs. per square incb. 5.10 Assume 600 pounds because the hole is not l Z./16 inches in diameter throughout the entire length. Hoop Tension in hollow cylinder. p = -dW 2h p = 14 000 lbs/in? w= 600 lbs/in? , h = .8125 X 600 2 :x 14000 d = 0.8125 inch h = 0.0174 inch h = thickness . •. The chuck need only be sli gh tly over 1/ 64 inch thick to withstand the driving to place. Driving gears. 4 )riving gears. (Continued) Using one to one ratio - 45° Helical gears - Both left handed (to get desired direction of rotation). Maximum outside diameter= 2,4410 incr.es Ni.imimum inside II - 1.5000 " Assume : Diametral pitch= 12 18 teeth. True normal helix = 18 n-= 1.50 ~itch Diameter= 1 - 5 = 2.120 inches .7071 Outside diameter (.:_g__!_~) = 2.287 inches a ia .P Drive shaft - 1500 r.p.m. No calculations could be made as t o the power required to drive the machine, because it is not known lfiow much power is consumed in deforming the specimen. It bas been estimated that the tot a l power would be between three and five horse po~er. A one inch shaft will carry this load at 1500 r.p.m. The counting mechanism. Ey mounting a five figure coutjter on the bead of each spindle the need of a reducing gear is eliminated. Veeda counters, which register once every complete turn are used. These must be equipped with a five point star wheel, and tr.E:r eforc the r eadings on the counter mu s t be multiplied by five to give correct results. One end 5 of each specimen will have to be drilled and tapped for a one-fourth inch bolt. The depth of thread reouired is one-half inch. The ~pace left for the counter may b€ used for the switch for the d r j ving motor. i\ilount the switch on a one-half inch piece of fiber eight inches square. One- half inch holes are dr11led in each corner one inch from the sic1es. The machine is to lie mounted on one of the tables in the 'Testing Labon:tory. The motor is to be direct connected to the shaft by some form of flexible coupling. BRONZE BRONZE Steel . 3f" y -~ I I 1::::, · I t ;..· I . t ~OJ .....+---+-....._--+-.+-'---. ~ 1 If , 7 B-1-S ToperReamer t-< I 1. i i ··- 2.1-1-.5 /6 ' A ~ l<)l-..i-- : I±. 00 I ,, I I ,, u ,.. ~ 1" 8 l J. J. I ~ ~ -~ e._ ___ t •ZO thd 2'' ->- • ··> - · 8 ;.J..." 8 .Y -< I . -< X y ~v ~ ~ - \ -</f I ; • ~,~+ • y ''"' I y Y. ~~~)~ 1 f in. to the foot. I ~ I l z935" . 3" I \ ► : /./8/8 I" I/ .00OJ II -c •• gR #-10 ddll-[11 thd.top >-i I I ZO th'd.per in. 1j" 2'' 3" .Y I /" I ~f thd per in. I iLA/1. top ==-==/8==.:I Felt f] drill ====-►=,=1 ~+ Make /0 of each Steel I" Z ! I >- _j_ 3" -< ~I• ~ 1- >- ► y yy ,,.t-)1~ A'" A. /R ◄ BI · 3" 4- Ji It I" . 40 drill- s top 44 thd. I·+ - ~:•.1i.;'1i I - 0 ~ >-ti~} l 44 All j "taps-,.. dies are A.SM£ Standard '/ FAT/Gil£ TESTING MACHINE THROOP COLLEGE r TECHNOLOGY 1 i___J" II Thesis Pasadena, Calif thd. per,n. Feb.26,/9/6 Scale-Full Size VEFarmer. Steel Seamless Tube Specimen I" Steel 8 Bronze 7'' 8 -< >- A "-.; -r I L_ i~ . I A k ~ 14 -< /" 4-R. I" -< l"E I" ,:~ , lo1~ A :: t--.lOJ >- ' 1 ., X A C\t "' /1' 4R -< /" >- -15flelical gear. LH I~ Pitch -/8 teeth Pitch dia. = 2./212/n. :: f\, lw} fi ~ l\\r ~ ~ ~ Taper l' to/ I ~ >- ::: "' ~ .Ai y J. "I~ -<//8/8 .0003 >- y A =..... 11 1 A ~ I R.i!88" < J.. i't)j~ I'<) ~,~ It) l 'l'l--- ' -< X ,, i.' 1fi >- 13" /6 8 >- II' X 3" -1 Etra Strong Pipe II 7BtS Toper reamer jln. to the foot ~ "l0v y I ::elf) ~ ::: y X ::: \ ~l~ y ~ If thd per in. -< I I /'' >- ½10:, ). :8 75.. >-, OCKJ! 1 -< I U .S.Standard y I,, :::~ I I I I I y I I y I I I I I I f1 ake 10 of each. A I I I l/8/8 /0003 ,. ,_ I,, -< l:I" >- Thesis I I I I I I I y FATIGUE TEST/IVG MAC/I/NE TflR00P COLLEGE TECl/lr'OLOCY 0, Pasadena, Caltf March /8,/916 Scale - Full Size V.E.Fcrrmer Casr Iron 2 8.L.. . . -< Bronze Fiher >- ► ...L" ,{ A - tt40 drill /tap 44thd ..l ..... ,~ y 16 I __ ~" 8 " ► .L ... 1" >-4 4 ti X 40drtll ). 8-rap 44 thd "'lt¥- I y lg/"I --< Brass - 41 30 drill Maire /0 1 '' gR ... --r ► Fiber 1'' ~"' ::: --q~ - i ";f I J.. I - 1-- 1- - y 1R ~ 'r -( ~I~ ---,- I'' ~ ,. 'J.. " J.. "'y ...._l't- - !:::J~ .. ,l y 0)1~ A ' ;:1-t)J(b + Steel ~ I r y ~I~ ~,co 1 -< 11 thd. A ;'' I" I II ..,_8-< 8 Make 10 ,.... Make ZO .::, A ''"' y 5'' '8 ). # . 7" 'It\( ~16 .t .. . ..........._ _.....,_ ~lt"r-f~ ----..--- ::: y ,1 A >- 4"R J. Make 10 X \ y -11-thd /Jthd ~,'} y y US.Jtonoard y y Thesis ••. I'' ~ I" lz Maire 10 ► :8 Make ZO rATIO/lE TESTING MACHINE THROOP COLLEOE t TECHNOLOGY 0 Pasadena,Ca/Jf • March i>7, /9/6 Scale - Full Size V.EFormer Casr Iron Secfton AB Make I A i ,, f l---..:{=; L- _ dr//~2__ '~ ~ - - i - - - - - - 4 - •- - - - - - - - --- __ L ___ , - - - 1- ·-·- ·-- - - - -·-- -·· ·-- - -- - ------ --- - - - - -- -- ~~ ; ~ I - ' \,Q -- _--1 ------ - - - - - - - ----~I'!-- .' y 3'' :,ff > /' .... 1,1''-< -< 1- l I I I 25" I I 3.l.'' ~ 3.L" ;? I I //' J + + + i I l" l ! -< 2,4 ~~-< I I 3.L" ~ 23" ►°Ji-< I t 1f"i ! L" 3R jJ';J,.111- j'tap /3 (hd i //'' l /1' t .L" ! I y . I 1 I 3~I " I I I y I I I : 3~ Two Required Scale - Fuf/Size -3.L" ~ II ►~-< -t---$- -~+-+!--,- - r - - - -'..-i--t,1I I : 11 II 36'' Cast Iron /'1ake One >- 3.L'' z ► s>" 76~ -< ). Thesis -------- -----I I I I I I I 1,f' I'' R ► Scale-Full Size I I I ~II - -< 8 I I ! y > A FAT/GILE TEST/;VOMAC/1/IVE Tl/ROOP COLL£OE r T£Clllv'OLOCY 0 Pasadena, Calif March R9,/9!6 V.£Farmer. ,.... Scale-.,- =/ Casi Iron Moire One ·~ A ....... I , - - t - - - - - - + - - - ~ . . - { - - + - - - 11---- ~ -x --- - - i I_ {f)---+- . -<- -I . f I,,, --- ---- ---- I I -.. A I" -► -< ------+ -- -- - ~ /4 -< -< -< ;;'' 'O ~ '\c ::. ~ y _y --- )'- y I J fl >- :A t"IO -:: y 4R r-- 1- ~ ~-------~--l---------1---"-;l ----.:1 ___ I 3" --- -~ Br nze 36'' I I I I I I I Ste-el I 1." 4~ I >-- MakeR Scale Full Si-7e Thesis /0 thd per in. 8 Re9wrect Scale Full Size US. standard IAT/OLtE TEST/NO MACIIINE THROOP COLLEGE 1 TECIIIVOLOCY 0 PC1sadena, Calif Morch /!9,19/6 Scale - ;/1" V.EFarmer. i I Cold rolled Sha /ting f~, • Scale #: 38 .. 1/2dr//l-:/-tap l'Othd y 3-j 3f Jj 3j 3-{" + +2g·.,, A 3[ Bronze Holes dn/led for PratN Whitney taiper pm"4 Make I Scale Full Siz.e I Steel Scale Full Size Make II Steel Scale. Full Size !/- -< -< >- ► _j_"-< -< . 4 7 A /. I ► /? >- A ~,~ y -<16 A 15 °1/elical gear L.H. ).. Ii pitch - /8 teeth ' y co oO C\c "' : ~ I _J_" 3;! ECZZd y ~77ZZ21 :I I f V A Make I y Thesis §_ -< 8 Make /0 Ma e I Pitch dia. • 2./?l?in. >-< d. + >- FAT/OU,£ TEST/NO MACHINE THROOP COLLECE 1 TECHNOLOGY 0 Paso den a, Caf.: April 8~ 19/ 6 J'ca/e - shown V.E. Farmer. Cast Iron A -x- '-0 y l /re- g'' 9 · II I I >'( ).. I 5" 5" 3" Holes dnJ/ed- 8 dri/1- 8 deep-;;r-top -/0 thd /3" . II ff dr,/1-j tap- /3 thd. Make I Casi Iron Cast Iron • Make 40 Make ZO Noke /0 Wt , 5/b. Wt. =Rlb. Wt · !lb. Wt. with rod = 5 lh. j'~ou.nd rod _ Steel Thesis 7 FATIOLLE TESTING MACHINE THROOP COLLEDE rTECHN0LOGY 0 Pasadena, Call( · April 10, 19/6 ;Scale - 4I"= I " VE.Farmer. ' Section AB C enter bearmg hobbitmd in post!ion A 0 0 0 Qo 0 0 0 h - - - ~ - - - ~. -~ ;; b □ LJLJD Assembly Thesis FAT/CUL TEST/NC MACHINE THROOP COLLECE rTff!INOLOC Y 0 Pasadena, Colt/ Scale - j-''. I" Hay ,?3, /9/6 VE.Farmer :