WI \ \ IIHtI'Il 129 206 THS STRESS ANALYSiS OF A CONNECTING ROD Thesis for the Degree of M. S. MICHEGAN STATE COLLEQE Evin E. Tuffle 1954 Pit-25$ 1.. IHLJHJIILIIMLUWlUlllllHllllUJllHINIIIHIHHHI "” 10385 9595 This is to certify that the thesis entitled STRBS ANALYSIS OF A mNNEO‘l'ING ROD presented by ELVIN E. TUTTLE has been accepted towards fulfillment of the requirements for 12's; degree mm— W Major professor Date ”do! iffy 0,169 )V‘ESI_J RETURNING MATERIALS: P1ace in book drop to LIBRARIES remove this checkout from .—:,1—. your record. FINES wil] be charged if book is returned after the date stamped be10w. Man/92 Y STRESS AflALESES ’F A COfiNECTIHJ ROD By Elvin E. Tuttle ,.i A THESIS Submitted to the School of Graduate Studies of Michigan State College of Agriculture and Applied Science in partial fulfillment of the requirements for the degree of LMSTfliCF SCIENCE Denartment of Mechanical Engineering THESIS EAJBSTIL'l CT A design for a one cylinder engine to be manufactured by the Iichigan State College Mechanical Engineering Department has been developed by Dr. Louis L. Otto, Professor of Automotive Engineering. This thesis is the record of the experimental stress analysis to which the connecting rod for this engine was subjected. The loads to which the connecting rod will be subjected in service were determined theoretically. This analysis involved assumptions of physical and operating characteristics and development of a pressure- volume diagram for the engine. Using the previously developed theoretical loading, a theoretical 'stress analysis was made. To check these results, a sample connecting rod was cut from steel and statically tested using resistance wire strain gages. The sample connecting rod was also checked for stress concentra- tions, using the brittle lacquer coating method. Correlation between the experimental and theoretical stress analysis results was good. The results of the theoretical stress analysis were plotted as-a Soderberg diagram to illustrate the resistance of the connecting rod to repeated stresses. It was shown that a steel connecting rod of this design would be acceptable for use in the proposed engine. The Soderberg diagram also facilitates the checking of the suitability of other materials for use in the connecting rod. ”Whipping stresses and their effect on the connecting rod stresses were also discussed. Assembly torque for the bearing cap holding screws was determined to prevent parting line separation. 331295 ACKNOWLEDGMENTS The author extends his sincere thanks to Dr. Louis L. Otto under whose supervision and guidance this analysis was made. He 18 also indebted to Professor Samuel Mercer, Jr. and the Applied Mechanics Department for tne equipment used in the eXperimental analysis presented. The writer also wisnes to thank Mr. Ray Pearson.for advice and assistance in the manufacture of the sample connecting rod. VITA The author was born November 12, 1928 in the village of Pulaski, Jackson County, Michigan. He attended grade school in Hanover, Morton, and Pulaski, and graduated in May 19h6 from Concord High School, valedictorian of his class. In July l9h6 he joined tne United States Army. During the next thirty—five months he was stationed in Fort Belvoir, Virginia, San Jose Island in the bay of Panama, Fort Clayton, Canal Zone, St. Thomas, Virgin Islands, and Fort Riley, Kansas. During that time he was a stock record's clerk, responsible for maintaining records on both ex- pendable and non-expendable property. For one year he was also manager of the Post Theater on San Jose Island. In June, l9h9 he was discharged from the Army as a Sergeant (Grade III). In September, l9h9 he entered Michigan State College and in June, 1953 received a Bachelor of Science Degree in Mechanical Engineering. He was married in June, 1951. During the summers of 1952 and 1953 and part time during the school year 1952—53 he was employed as a Test Engineer at Reo Motors, Lansing. He is now a candidate for the degree of Master of Science in Mechanical Engineering. He is a member of Tau Beta Pi, Pi Tau Sigma, Phi Kappa Phi, and Green Helmet. II III IV TA R LE OF C ONT ENT 8 Introduction . . . . . . . . Procedure . . . . . . . . . A. Development of Connecting Rod Loading 8. Theoretical Stress Analysis . . . C. Experimental Stress Analysis. . . Data. . . . . . . . . . Discussion of Data. . . . . . . Conclusions . . . . . . . Appendix . . . . . . . A. ‘Whipping Stresses . . . . . B. Parting Line Separation . . . . Bibliography . . . . . . . . 27 3o 33 35 38 39 39 to hi TABLES I Development of Pressure-Volume Diagram . . . . L5 II Crank Angles. . . . . . . . . . . 13 III Reciprocating-Inertia Forces. . . . . . . 20 IV Cosine of Angle Between Connecting Rod and Cylinder Axis. . . . . . . . . . . 20 V Connecting Rod Loading . . . . . . . . 21.2h VI Maximum and Minimum Connecting Rod Loads. . . . 26 VII Experimental Data . . . . . . . . . 33 VIII Results of Experimental and Theoretical Stress Analyses, . . . . . . . . . 3h FIGURES Drawing of Proposed Connecting Rod Design . . . Brake Mean Effective Pressure . . . . . . Mechanical Efficiency . . . . . . . . Engine Horsepower . . . . . . . . Pressure-Volume Diagram hSOO HPM'Wide Open Throttle. Kinematic Sketch of Engine Movement. . . . . Connecting Rod Loading hSOO RPM’Wide Open Throttle . Cross Section of Connecting Rod. . . . . . Sample Connecting Rod . . . . . . . . Development of Soderberg and Goodman Diagrams . . Soderberg Diagram of Connecting Rod Stresses . . Parting Line Portion of Connecting Rod . . . . 10 11 13 l7 19 25 29 32 35 3? ho I INTRODUCTION In September of l9h8 the Mechanical Engineering Department of Michigan State College inaugurated the manufacture of a small air com- pressor as the basis of several courses. The student followed this air compressor from the original casting of parts in the College Foundry through the final manufacture and assembly in the College Machine Shop. Advanced courses such as shop supervision, time study, and foundry re- search also used this air compressor as their base. After assembly the students were allowed to purchase the compressors for the cost of materials. Soon the question arose as to whether a single cylinder engine would not be more popular than the air compreSsor with the students, thus generating more interest in the courses which were'based upon it. An investigation by Dr. Louis L. Otto, Professor of Automotive Engineer- ing at Michigan State College, produced a preliminary design for such an engine. The object of this thesis is to determine, both analytically and experimentally, the stresses which will be encountered in the use of the connecting rod design suggested by Dr. Otto. The connecting rod as tested follows essentially the original design suggested by Dr. Otto, although some minor details were changed from the original design in the interest of easy manufacture. The data pertaining to the engine design developed by Dr. Otto are as follows: Bore - 2.5 inches Stroke — 2.0 inches Compression Ratio - 7.50 to 1 Brake Mean Effective Pressure - 50 psi at hSOO rpm Mechanical Efficiency - alprox. 50% at hSOO rpm Estimated weight of reciprocating parts (Piston, Pin, Rings, Top end of hod, etc.) - 1.05 pounds Weight of rotating end of rod - 0.8 pound Engine type - Four-stroke cycle A drawing of the connecting rod analyzed in this investigation is presented in Figure l. The bearing dimensions of the rod are those developed by Dr. Otto using accepted theoretical procedures and compare favorably with designs now being used in practice. 3'- -28 Jig COP 5c rews 32 /0‘Draff ‘T ‘ ‘ *' ‘IN Fig. 1. Drawing of Proposed Connecting Rod Design TI PM}? 3:131} if: AND Ak-‘Hdul'l‘US A. Development of Connecting Rod Loading The investigation leading to the design of components of this engine required that values of Brake Mean Effective Pressure and Mechanical Efficiency be assumed over the speed range in which the engine will operate. Such assumptions are shown as curves in Figures 2 and 3. These curves have the same general shape as experimentally de- termined curves of actual engines.1 However, the exact determination of these characteristics must await the construction and testing of a sample engine. The horsepower characteristics of the proposed engine were then PLAN .9 determined using the equation2 BHP a ‘wherein: BHP 9 Brake Horsepower P 2 Brake mean effective pressure in psi L = Length of stroke in feet A = Projected area of piston crown in square inches N = Number of power strokes Per minute - in this case half the number of revolutions per minute lFor an example of performance curves for an engine of this type, see Virgil Moring Faires, Applied Thermodynamics, Revised Edition, The MecMillan Company, New York, Seventh Printing, 1950, p. 130 21bid., p. 113 2 Br ‘0 0 fan. . gFig. Effective Pressure I 1 1 . 3 1 + ._ 1|...I .Ill‘l‘. ._-_ . r74.- .0; 1‘ q a . l . s n o I v n ¢ a . . . c . v . . w . s Q O O o 4 . . u a I . - . . . v . ‘ 6 u . . o . . . . . . a . 1 I‘ll... -.| 0 -——¢ .». -. . vb— 7. 4— . v I u o _ . . . : u I; I O 0." » a . u o. 4 v . a O . o i r n 0 T c t. b I . f .o v v o . c . o -l .0‘ 6 I» . n . i s o c . w . . a c o A b ,9 4 . . y o v a s JIL I iiief-$ —.—.—¢ 1 -»'——’——O— -——0--O—--<—"*——9 fir- o a I u 91 a 0 w ‘. . . v e t n a iv]- a 10'+ n - e o L a 4 a 4 e V t . . .- c 4 o o 6.. . . . . . . v .. . . 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The next step in the determination of the connecting rod loading 'was the construction of a pressure volume diagram or indicator card. This was done for wide open throttle operation at hSOO rpm as follows: Let V1 be the volume of the cavity above the piston when the crankshaft is at bottom dead center and V2 be the volume of the cavity above the piston when the crankshaft is at top dead center. Taking volume as the abscissa and absolute pressure as the ordinate of the diagram, let V1 — V2 = one unit of volume._ By definition Vl a V2‘ (Compression Ratio) = 7.5 V2. Substituting we have 7.5V2 - V2 = 6.5V2 = one unit of volume. Thus V2 - 0.15b volume unit and V1 - 1.15b volume units. The displacement of the engine is the area of the top of the piston times the stroke and equals 9.81 cubic inches. The volume unit referred to above is equal to the engine displacement so one volume unit 8 9.81 cubic inches. Then Vl = 11.32 cubic inches and V2 = 1.51 cubic inches. 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H . . 1 . . .. 1. u” . . . 1 1 1 . 1 .. 1 1 I . .1 . 1 1 _ . 1 . . . . . .- .. .. . . A :1 . ..1 - . . A 1. 1- . .1 A... I. .1 1A.. . A......A. . . . . 1 . . . . .1. . . _ 1 — 1 1 1 .11 4 ~ . . 1 _ _ . . . . 1 a o . 1 1 . _ ‘ . ~ .. II .1 ...AIIIIFA A. II .llplll IA. 1 1 . 1 . 1 . . . 1 . . A. >All .A'I..IIIDIIIIAIOI[DILI[I:.IAIILIY(I |r|!l. IAII'I‘IIIA. ...I. I III‘IFAII. .5 .. bIllllIeI'.|IrA.!Aol.tAlI-Os Itilrflb" AL Thus the exhaust line on the diagram lies at 15.78 psi absolute. The compression and expansion strokes were assumed to follow the form PVn = constant, where P is pressure and V is volume. For a realistic result, n was taken as approximately 1.3 for an engine using a mixture of air and gasoline vapor.3 P1 and P2 are the pressures in the cylinder at the beginning and end respectively of the compression - stroke in psi absolute and V1 and V2 have the meanings previously assigned. Then: n n P1V1 ' P2V2 V n V P2 = P (1;) but-«jl a compression ratio 1v v 2 2 so P: 1 i(compression ratio)n The compression stroke was taken as starting at the end of the intake stroke (P1 = 13.56 psia) so P2 = 186.2 psi absolute. Intermediate pressures during the compression stroke were determined by'taking appro— priate values of compression ratio and solving as above. To construct the pressure volume diagram, the brake mean effective pressures assumed earlier were converted to ideal indicated mean effec- tive pressures. Actual Indicated Mean Effective Pressure 1 Brake Mean Effective Pressure x l . For hSOO RPE,'where Mechanical Efficiency Brake Mean Effective Pressure a 50 psia and Mechanical Efficiency 8 50 percent the actual Indicated Mean Effective Pressure 2 100 psi absolute. The ideal Indicated Mean Effective Pressure desired is actual Indicated 3For a.discussion of the choice of values of n, see Ibid., pp. 95-96 15. Mean Effective Pressure x card factor. This card factor compensates for losses at the beginning and end of the strokes due to the time necessary for burning of the airqfuel mixture and valve operation. Past experience has indicated that 1.07 is a reasonable value for card factor. Using this value, the ideal Indicated Mean Effective Pressure is 107 psi absolute. In one cycle this pressure does work by pushing on the piston crown and moving it through a distance equal to the stroke of the engine. Thus the work equivalent of the Indicated Mean Effective Pressure 8 (Ideal Indicated Mean Effective Pressure) x (Piston area) x (Stroke) - 87.5 foot pounds. h w ,_ P2V2 - P1V1 1 2 1 - n . The'work done by the compression stroke, The values previously Obtained were substituted into this equation yielding 1W2 a ~35.6 foot pounds. The negative sign indicates that work is done on the working fluid by the engine. Letting the work done on the ‘ engine by the working fluid after the constant volume energy addition (combustion), during the expansion stroke - 3Wh resulted in 3WL + 1W2 work equivalent of Indicated Mean Effective Pressure. Thus 3WD . work equivalent of Indicated Mean Effective Pressure - 1W2 - 87.5 - (-35.6) - 123.1 foot pounds. Let the ratio of 3Wh/ 1W2 . R. Then R a 3.h7. Since the work done on or by the engine is caused by and proportional to the pressure acting on the piston crown, the ratio of any pressure on the expansion stroke to the corresponding pressure on the compression stroke is also equal to R. Using the above developments, Table I,evaluated for wide open throttle operation at hSOO RPM, is as follows: thid., p. 52 16. TABLE I DEVELOPMENT OF PRESSURE-VOLUME DIAGRAM ======E;i Relative Volume Ratio of Compression EXpansion in Dec1mal of , 1.3 Pressure Pressure Displacement Compre551on (CR) psi Absolute psi Absolute 1 .15).: 1 1 13 .56 86 .9 1.0 1.15h 1.205 16.32 56.5 .9 1.283 1.382 18.73 6h.9 .8 1.882 1 .610 21.80 75 .5 .5 2.31 2.97 h0.2 139.2 .3 3.85 5.76 78.1 270 .25 b.6l 7.30 98.9 3h2 .2 5.77 9.77 132.3 858 .151: 7 .5 13 .75 186 .2 61.5 The complete pressure volume diagram is shown in Figure 5. To more nearly approximate an actual indicator card the corners have been rounded to take into account the time necessary for combustion and valve operation.5 Table II gives angle of crank rotation values from top dead center for corresponding volume values. This Table was used to place the crank angle scale on the pressure volume diagram and was developed as follows: 5For illustrations of actual indicator cards see Ibid., p. 113; Herman Diederichs and William C. Andree, Experimental Mechanical Engineering, Vol. I, John'Wiley and Sons, New York, Seventh Printing, #19D9, p. 306; Lester C. Lichty, Internal-Combustion Engines, Sixth Edition, MCGraw Hill, New York, 1951, p.-Hh8 17. < . > o . . (I. til... ‘YnAl . I II. I‘I.‘ t .IO‘IfiIv‘fYW’lI. 1 la a . . . 1 7 : i 1 1’ 1 I div—H .{Wfi' .-- . .10)....0 I- “1...; --.. 3 I . 4 i l I A 1 1 n v t -h‘hv- - _ -——--.‘ --..”- .‘ \Iyl.01a‘ll 0 $ 2 I .--n--. T I I 1 ...—H-..‘ . o l | v - $ t . .-.. wwwf-..” I ! o . I 0 o t I l 0 - ---Y. -<¢— . u a o I t sov‘w - -.<.'*- 0 . Q I A ? Partial Displacement Volume = percent piston travel x total displacement volume. When total displacement volume = one volume unit, as it does on Figure 5, partial displacement volume = percent piston travel expressed as a decimal. Then total volume = partial displacement volume plus clearance volume. TABLE II CRANK ANGLES Crank Angle % Piston Travel Clearance Total expressed in Degrees as a Decimal Volume Volume 0 0.0 .158 .158 10 .009 .158 .163 20 .037 .158 .191 30 ..081 .158 .235 1‘0 .1110 .158 .29}! f” .211 .158 .365 60 .291 .158 .885 70 .378 .158 .532 80 .867 .158 .621 90 .556 .158 .710 100 - .681 .158 .795 110 .720 .158 .878 120 .791 .158 .985 130 .858 .158 1.008 180 .906 .158 1 .060 150 1987 .158 1.101 160 .976 .158 1.130 170 .998 .158 1.188 180 1.000 .158 1.158 6Lichty, op. cit., p. 882 19. Determination of reciprocating inertia forces was made by evaluation of the equation7 F = 2.88 x 10‘5Mn2r (cos 9 +9£ cos 29)‘Wherein .1 . F a reciprocating inertia force in pounds M a reciprocating weight in pounds n = engine speed in rpm r = crank radius in inches connecting rod length, center to center, in inches N n O 8 crank angle Piston Results of this evaluation are shown in Table III. In this Table it should be noted that forces acting toward the crankshaft are positive and forces acting away from the crankshaft are negative. The total force acting on the piston crown is the effective gas pressure force (absolute pressure minus atmospheric pressure) in psi Crank pin times the area of the piston crown. To this must Shaft e added the reciprocating inertia.force. This Fig. 6. Kinematic Sketch sum must be multiplied by the cosine of of Engine Movement the angle 0 between the connecting rod and the cylinder axis to yield the axial connecting rod force. Evaluation of ¢ for values of crank angle 9 is given in Table IV where the symbols have the meanings shown in Figure 6. _r_-sin sin¢=£sin0 sin 9 ‘1 E - .2222. . . log 8%) - 9.38678 - 10 .1 (For the development of this equation, see Ibid., pp. 882-883 TABLE III RHSIPROCATIN} INERTIA FORCES 8500 RPM w--~»----—O‘--d‘~. —. :- —-‘ 20. Crank Angle . 1 .~ Reciprocating Crank Angle Degrees after “Cg? era 10“ Inertia Force Degrees after Top Center actor Pounds Top Center 0 -l.222 —781 360 10 -1.198 -725 350 20 -l.110 -673 380 30 - .977 -593 330 80 - .805 -889 320 50 - .608 -366 310 60 - .389 -236 300 70 - .172 -108.3 290 80 .035 8.89 280 90 .222 138.3 270 100 .383 232 260 110 .512 310 250 120 .611 372 280 130 .682 815 230 180 .727 881 220 150 .755 859 210 160 .770 867 200 170 .776 871 190 180 .778 872 180 TABLE IV COSINE OF ANGLE BEFNEEN CONNECTING ROD AND CYLINDER AXIS Crank 10 (5 sin 0 Angles . log(sin 9) ' Iog(sin ¢§ log(cos 0) cos 0 O - 180 - - - 1.0000 10 - 170 9.23967 8.58681 9.99967 .9992 20 - 160 9.53805 8.88079 9.99875 .9971 30 - 150 9.69897 9.08571 9.99730 .9938 80 - 180 9.80807 9.15881 9.99552 .9897 50 - 130 9.88825 9.23099 9.99362 .9858 60 - 120 9.93753 9.28827 9.99180 .9813 70 - 110 9.97299 9.31973 9.99032 .9780 8' - 100 9.99335 9.38009 9.98936 .9758 90 1.00000 9.38678 9.98901 .9750 8Ibid., p. 883 21. Table V and Figure 7 show the connecting rod loading for one cycle of wide open throttle operation of the engine at 8500 RPM. TABLE V CONNECTING R00 LOADING 8500 RPM WIDECMmN'NMuHTLE A. EXpansion Stroke Crank Effective Gas Gas:1 Reciprocating RIF + Axial EST: Angle ATC Pressure Pressure Inertia GPF Force 9° PSI Gage Force, # Force, # # # 0 328 1,612 ~781 871 871 10 871 2,320 -725 1,595 1,597 20 858 2,250 -673 1,577 1,581 30 358 1,781 -593 1,188 1,156 80 262 1,289 -889 800 809 50 199 979 -366 613 629 60 189 733 -236 897 506 70 112 550 -108.3 885.7 856 80 89 837 8.89 885.89 856 90 73- 369 138.3 503.3 516 100 62 305 232 537 550 110 53 261 310 571 585 120 87 231 372 603 618 130 82 207 815 622 631 180 38 187 881 628 685 150 38 167 859 626 631 160 28 138 867 605 606 170 17 83.5 871 558.5 555 180 7 38.8 872 506.8 506 22. TABLE V (cont.) 8. Exhaust Stroke ========— tr Crank Effective Gas Gas Reciprocating RIF + Axial Rod Angle ATC Pressure Pressure Inertia GPF Force 9° PSI Gage Force, # Force, # # # 190 2.5 12.3 871 883.3 888 200 1.5 7.37 867 878.37 875 210 1.5 7.37 859 866.37 870 220 1.5 7.37 881 888.37 853 230 1.5 7.37 815 822.37 829 280 1.5 7.37 372 379.37 386 250 1.5 7.37 310 317.37 328 260 1.5 7.37 232 239.37 285 270 1.5 7.37 138.3 181.67 185.1 280 1.5 7.37 8.89 15.86 16.23 290 1.5 7.37 ~108.3. -96.93 -99.0 300 1.5 7.37 -236 -228.63 —233 310 1.5 7.37 ~366 -358.63 -362 320 1.5 7.37 -889 -881.63 —887 330 1.5 7.37 -593 -585.63 -590 380 1.0 8.9 -673 -668.l -670 350 .5 2.86 ~725 -722.58 -723 360 0 0 -781 -781 -781 23. TABLE 7 (cont.) C. Intake Stroke 1 .1 Crank Effective Gas Gas Reciprocating RIF + Axial Rod Angle ATC Pressure Pressure Inertia GPF Force 9° Force # Force, # Force, # # # 370 0 0 -725 -725 -725 380 —.8 -1.97 -673 -678.97 -676 390 -.8 -3.98 -593 -596.98 -601 800 -l ~8.9 -889 -893.9 -899 810 -1 -8.9 -366 -370.9 ~376 820 -1 -8.9 -236 -280.9 -286 830 -1 -8.9 -108.3 -109.2 -111.8 880 -1 -8.9 8.89 3.59 3.68 850 -l -8.9 138.3 129.8 132.8 860 -l -8.9 232 227.1 232 870 -1 -8.9 310 305.1» 312 880 -1 -8.9 372 367.1 378 890 -1 -8.9 815 810.1 816 500 -1 -8.9 881 836.1 881 510 -1 -8.9 859 858.1 857 520 -1 -8.9 867 862.1 868 530 -l -8.9\ 871 866.1 867 580 -1 -8.9 872 867.1 867 TABLE V (cont.) Compression Stroke 28. Crank Effective Gas Gas Reciprocating RIF + Axial Rod Angle ATC Pressure Pressure Inertia GPF Force 9° Force, # Force, ,1} Force, {7‘ ,‘r‘ ,‘f 550 -1 48.9 871 866.1 867 560 -1 -8.9 867 862.1 868 570 0 0 859 859 861 580 1 8.9 881 885.9 851 590 1.5 7.37 815 822.37 829 600 3 18.8 372 386.8 398 610 5 28.6 310 338.6 382 620 8 39.8 232 271.8 278 630 11 58.1 138.3 188.8 193.2 680 15 73.7 8.89 82.19 88.2 650 22 108.2 -108.3 3.9 8.0 660 33 162.2 -236 -73.8 -75.1 670 87 231 -366 -135 ~138.3 680 65 320 -889 . -169 -l70.9 690 91 887 -593 -186 -187 700 133 658 -673 - 19 - 19.06 710 218 1,052 -725 327 327 7‘ 66: I. .III 1-'-t--lPIIIII-Olfili"vvki _ _ . . _- --- -- --....iw- - -... ”..-- 1.5.9. 6 ' C . . I . l 336.5? 5383:. 6.638.. Be 6.6.3.8 .33....)7!!!‘ “8-{‘1 'I.\Ol.6| .l'OI -0106? at- :4-.O|I‘ con _ _ H ,q .. {-8179 31163'!‘\ . _ n A 6 l .1.-- _- ; L--..........+-_.- ...- I8! '1‘. 070.8! ...L 1 O l - . 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K . . . - Q .6 6 Q 6606 a .6 . 6 ..IA .~O’6' . . . .o . o . 66 . 6 6. . . . 6 H .» 6. ~o.l¢ .. . 6 6 . g . ' ... 6 — . . . ..A . . L. * A . 4 .~. “I nu--|(‘(¢llz‘l‘t.’lt "16--01|!| 6 '1’8. 1'» 16a d ..(Jii. . fl ‘7. 4? .1 .J . 8 ”1 . . . j . 1A4 . H . . . u . ... ~ q a . . . . .. ... .. _ . 6 W o~ . . . . . . . .. .. . . . . .. a . 6 ~ 7369-6 .1 V 6.- 6'01! LTv 08L! 60 Volt..kv o 6-164..67 O 6‘ 9. h I- A“. .0 IIN‘. 6106*. AA 06..“ _ . . . . . . . . . a. _. a . . . 6 . . .... . . ..6 . . . . . _ 6 o v ... A. H . L 6 a“ k . . . .. 11:8--le J! . 517.28% 118.1 - ..-IT- ..- -I---...a ..-! i- 17--1 3...»: . H 6 . . . — fi . d. o .. a ” ~ . n I. .I I n 0 1. l .l v I . . . 6 . .6 6 .... a . _ . . . , H ..lv. .u _ . 6 . .o . 6 . ... . . . . ? o A b.---v6 ‘ «- 0‘9‘ ‘51. In A. I ”I w. O.L 60 .v‘ 6 « Q. .6 at 916 0. .0!!! .6L..- will . .6 . . o .. 6 ‘ . . . .. . . . . . . . H 6 . « _ . . 6 L . . o . a. 6. .. . o . fl .6 . v .4 a . a O . 6 .. 6 . . ' cu I, It, 0.- I 6"! I74. 8 4+ fr . i 11 {IL )1} . . ... . _ ml . .. .6 . . . . . . 6 D .... . . 6 ...6 ..n# ‘01. o 0‘136‘80066 . 6 . . n ..h . l L . .. . . . . H ... . in” 6 66.. A) . . .6 7 oc- ‘flortvOl 6|. ... I 8.1“ .6 Oil 0.786.770'40.“V’ 4W) 6 .1 17:: H . [*3 g m .6 O 6 t“”..-# O I” u ‘u ...,6.» H _ . . . .. .66 H a q u H 6 . 1.: -.‘CO 700-..: II' o '6 . e I _ .-O‘Ivo “00.. .-IL ”I. 89-,78- ,0. 09'. A o 6.- O L’o‘“! . 3 A. 6.. ..fi . . . m . .. w. . v .+. . To .4... YO. .f . . 1. ”v 66*. 6.“. .6. d 6. .16....41 “—16.” .. 6| . _ . 6 . N6 .0 6 l... ...? .. .. l .. . . w”. 1: .. 3.137?” ”.... .... 26. The above series of calculations was repeated to determine the maximum and minimum loading for wide open throttle operation at 200 RPM intervals from h30 to hSDO RPM. [1L5 VI MAXImUm AWD MINIMUM CONNECTING HOD LOADS Engine Speed maximum minimum RPM Load Pounds Load Pounds boo 2,220 -8.65 600 2,290 -lh.51 800 2,339 -23.26 1,000 2,381 -36.5 1,200 2,805 ~52.6 1,h00 2,817 ~71.6 1,600 2,h16 -93.6 1,800 2,h16 -118.3 2,000 2,389 -1h6.1 2,200 2,359 ~176.8 2,hoo 2,316 -210 2,600 2,265 -2h8 2,800 2,217 -286 3,000 2,1hS -339 3,200 2,076 -37h 3,800 2,005 -h21 3,600 1,939 -h7h 3,800 1,871 —528 h,000 1,790 —585 h,200 1,716 -685 h,h00 1,635 -708 h,500 1,597 -7h1 h,500* h79 -773.2 * Loading was also calculated for closed throttle operation at hSOO RPM. It was assumed in this case that, on the pressure volume diagram, the compression and ex- pansion lines were identical. 27. B. Theoretical Stress_nnalysis Determination of tension stresses in the connecting rod involved simply dividing the axial tensile load by tne cross sectional area of the rod; 5 = B/A'where s = stress in psi, V = load in pounds and A = cross sectional area of the rod. It must be remembered that, as devel— oped above, negative forces produce tensile, or positive, stresses. In determining compressive stresses the column effect was con- sidered. For a short column hankine's column formula? applies; ss-E[1+K({7)J where I is column length, in inches, F is radius of gyration in inches, and K is a coefficient having a value of O.b x 10‘"h for a fixed end column and 1.6 x lO-h for a pin end column. An enlarged scale drawing was made of the cross section of the con- necting rod and is Shown in Figure 8. To facilitate determination of radius of gyration the area outlined with dotted lines was used in cal- culations. Using the composite area methodlo the moment of inertia about the x axis, Ix’ was determined to be 0.0Jld82 in.h and the moment of h inertia about the y axis, Iy’ was determined to be 0.003h13 in . The area of tne dotted figure is 0.1h2 in.2. It is interesting to note nere that the actual cross sectional area of tne rod is 0.139 in.2 an error 9Lionel 5. Marks, mechanical Engineers: Handboox, Fifth Edition, mcGraw— Hill, New lork, Third Impression, 1951, p. 3567 10Charles 0. Harris, Elementary Engineering Mechanics, Irwin-Farnham, Chicago, 19h7, p. 200 h) of less than two percent. Continuing, ‘p Was evaluated as J.u1327 in“ x IF. 2 -o, . . r and lay was evaluated as 0.b>93 in.2 by use of the relation F3 = . A About the x axis the connecting rod acts as a fixed end column and, 'When appropriate substitutions are made in the hankine formula, it was 0 found that s = (l.Ooll)—. About the y axis the connecting 10d acts as A ' a pin end column and, when apprOpriate substitutions were again made, it was found that s = (1.05h6)§. Thus it may be seen that the higher com- pressive stresses result from column action producing bending in a plane' parallel to the axis of rotation of the crankshaft. Thus hig.est com- pressive stresses may be anticipated on the edge of the flange of the "I" section of the rod. It should be noted again that positive loads as developed above produce compressive, or negative, stresses. 'Whipping stresses are considered separately in a section of the Appendix. 29. com weepoocnoo mo Coapoom mmcao x .m. .mE >~ =H.O n 2H mamom b) x.) I C. Experimental Stress Analysis To check the validity of the theoretical stress analysis, a sample connecting rod was made and tested by the author. This sample rod was machined from a bar of halvan Nb396 steel. A photograph of the completed rod is shown as Figure 9. The sample connecting rod was checked for stress concentrations by coating with "Stresscoat" and applying the static loads previously cal- culated. The loading was done in an Olsen Testing machine located in the Heat Treat Laboratory at Michigan State College. "Stresscoat" is the trade name of a brittle lacquer coating manufactured by the Magna- flux Corporation in Detroit. When the material on which this brittle lacquer is sprayed undergoes strain, the lacquer cracks in a direction perpendicular to the strain. The spacing of these cracks indicates the magnitude of strain and consequently the stress. It was found that, under the maximum compression load, a tension stress of approximately 30,000 psi occurred on the top edges of the crank bearing boss. This stress is due to the ”wrapping" action of the bearing boss around the crank pin. This would indicate that close tolerances must be maintained in the manufacture of the engine parts to prevent "wrapping" action. ‘ A resistance wire strain gage was then mounted on the edge of one flange in the middle of the I-beam section of the connecting rod. The rod was then statically loaded as before. The gage used was an SH-h type A-l9 manufactured by the Ealdwin-Lima—Hamilton Corporation of Philadelphia. This gave had a resistance of 61 ohms and a gage factor 00 of 1.61. The resistance wire strain gage measures the strain of the 31. material on which it is cemented by measuring the change in resistance of a tiny wire grid due to the dimensional change of the stretching wire. In this case the resistance change of the gage was measured by use of a Wheatstone bridge contained in an Anderson Strain meter. This instrument reads directly in micro-inches per inch strain and is cal— ibrated for use with a 12C)ohm gage with a gage factor of 2.05. Thus, to convert to actual strain the readings were multiplied by a resistance and a gage factor correction of 1'61 . 61 2 .05 correction factor of The true stresses were then calculated by multiplying the strains ll determined above by the modulus of elasticity of steel, 29,000,000 psi. llMarks, op. cit., p. 398 Pa a [I /~o T‘1 . . 1 1:” . .-‘ “V ’3 r‘ “ f. .‘.:._ I _ l, .0 ‘, v L . .4 :, UL~‘;‘.. "v.21. .LL .1 33. III DATA Data obtained from the experimental stress analysis is given in Table VII. From this data empirical equations for tension stresses and TABLE VII EXPERIMENTAL DATA Load in Strain Reading Actual strain Stress in Pounds in '4 in ./in . in ’4 in ./in p51 77h 11h 176 5100 h22 63 97 2820 O O O O ..1790 —285 -th 42,780 ~2hl7 ~395 ~610 «lZVOO compression stresses in terms of load were evolved. For tension, 3 = 6.62P. For compression 3 = 7.25?. In both equations 5 is stress in psi and P is load in pounds. These equations are only approximate but match the observed values with a maximum error of 1.56 percent. Table VIII is a tabulation of the maximum tension and compression stresses in the connecting rod over the operating speed range of the engine. The experimental results are computed using the empirical equations developed above. 3h. TABLE VIII RESULTS OF THEORETICAL AND EXPERIMEKTAL STRESS ANALYSES Engine Max. Tension Stress, psilMax. Compression Stress, psi Speed * RPM l Theoretical [Experimental] TheoreticalflJgEkperimental too 62.0 57.3 16,910 16,100 600 10h.1 96.1 17,h60 16,600 800 167 15h 17,810 16,930 1,000 25h.5 2t2 18,170 17,280 1,200 378 3&8 18,350 17,hh0 1,h00 51h h7h 18,h00 17,500 1,600 671 620 18,395 17,h90 1,800 8&9 78h 18,390 17,t90 2,000 1,0h9 968 18,210 17,320 2,200 1,268 1,170 17,980 17,100 2,h00 1,507 1,390 17,630 16,780 2,600 1,780 1,6u2 17,300 16,h20 2,800 2,050 1,892 16,890 16,070 3,000 2,h30 2,2h0 16,370 15,580 3,200 2,680 2,h80 15,800 15,020 3,hoo 3,030 2,790 15,300 1h,550 3,600 3,h00 3,1ho lb,780 lh,0h0 3,800 3,785 3,500 1h,280 13,580 h,000 h,200 3,870 13,6h0 12,990 'L,200 u,625 h,270 13,080 12,h20 h,h00 5,080 h,690 12,h70 12,850 h,500 5,310 8,910 12,180 11,580 u,500* 5,550 5,110 3,650 3,u70 * Closed throttle It should be noted that correlation between theoretical and eXperi- mental results was good, thus confirming the theoretical stress analysis. 35. IV DISCUSSION OF DATA The treatment of stresses of the nature developed in this con- necting rod must include some means of taking into account the reaction of the material to repeated load. Such treatments are the use of the Goodman or the Soderberg theories.12 Assume a loading which produces a stress pattern similar to that shown in Figure 10(a). Let 58 be the endurance limit, su be the ultimate strength, and Sp be the elastic strength of the material. Then, according to the Goodman theory s1. sa 5 s = 1 - - , and according to the Soderberg theory ,_3 e 1 _ _§ . Se Su Se 'U These relationships are best shown on a diagram such as Figure 10(b). According to theory, if the point resulting from plotting the stress con- Stress £4 8 m“ U) o .5 Soderberg a) '8 .p m m 0.. .Q A SP 7 Su Time Steady Stress, 3a (a) (b) Fig. 10. Development of Soderberg and Goodman Diagrams 12The Goodman and Soderberg theories and Figure 8 are taken from Glenn Murphy, Advanced Mechanics 3f Materials, McGraw—Hill, New York, l9h6, pp. 9-10 36. ditions on such a diagram lies outside the line, failure will occur. It may be seen that the Soderberg theory is the more conservative of the two. In applying these theories to engineering problems it is common to assume that the reversed loading applied to the member is approximated by a sine function having the same maximum and minimum values. This was done for the theoretical data and the results are shown as a Soderberg diagram as Figure 11. The theoretical stresses were used in this case since, as shown in Table VIII, they are at all speeds slightly more severe than the experimental stresses. Also included on the diagram is the failure line for a steel with a yield point of h0,000 psi and an endurance limit of 30,000 psi. 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If other materials are used, the Soderberg diagram in Figure 11 provides a convenient means to judge their suitability. 39. APPENDIX A. ‘Whipping Stresses In addition to the stresses imposed on the connecting rod by the direct axial forces, whipping stresses were investigated. The maximum whipping stress is developed at the time when the connecting rod is at right angles with the crank throw and may be found by the Bach13 formula: Sb = 2 x 10"6n2rAd12/Z Sb 3 whipping stress in psi where n engine speed in rpm r = crank radius in inches A a cross sectional area of the rod in square inches d - specific weight of rod material in pounds per cubic inch .2 - length of connecting rod in inches 2 3 - section modulus in inches The above equation indicates that Sb varies as n2 so it was only necessary to consider high speed operation. Assuming a material of specifiC'weight 0.28 pounds per cubic inch and an engine speed of b,SOO RPM, the whipping Sbfififi was evaluated to be 1,318 psi. Since the maximum stresses con- sidered in this paper occur when the connecting rod is vertical and since the magnitude of the whipping stress is relatively small, the whipping stress is neglected in the stress analysis. 13Lichty, P. 553 ho. B. Parting Line Separation As the cap screw holding the bearing capcnfix>the connecting rod is tightened the surface of the bearing cap is forced against the mating surface on the connecting rod. See Figure 12. This causes compression stresses to be set up in both the cap and the rod. If the tensile force T is great enough to cause the cap and rod to separate, we have parting line separation, a very undesirable situation. Separation will occur first at B since, in addition to axial tension, bending will tend to take place tending to cause compression at A. Fig. 12. Parting x.) To check for parting line separation, a Line Portion of Connecting Rod strain gage was cemented to the inner surface of the connecting rod bearing boss at G with the bearing cap removed. The gage was then connected to the Anderson Strain Meter and the bridge ‘was balanced. Next the bearing cap was put in place and the screws were tightened. Experience has indicated that a torque of from six to nine pound feet is satisfactory for a l/h - 28 cap screw so in this case a torque of eight pound feet was used. This caused the Anderson Strain meter to indicate a compressive strain in the gage at G. Next the maximum anticipated tensile load was applied to the connecting rod as- sembly. This caused a reduction in the amount of the indicated com- pressive strain but did not reduce this strain to zero. It was therefore concluded that parting line separation did not occur and an assembly torque of eight pound feet was used for the rest of the testing. bl. BIBLIOERAPHY Diederichs, Herman and Andras, Hilliam 0., Experimental Mechanical E-"uneerinr Volune I, John Niley and Sons, New York, Sevent1 xrlntin" 1949,103309. Faires, Virgil Moring, pplied T1ernodynm 1393: evised Udition, The lacfillan ~191npany,Mew 31r:, Seventh trintingh 1950, hRQ pp. Harris, Charles 0., Elementary Encineerinw Mechanics, Irwin-Farnhan, Chicago, l9n7, ha S’pn Lichty, Lester 6., Internal—Combustion Enrines, Sixth Edition, M Sraw-Hill, New lork, 1991, 59tp . Marks, Lionel 8., Mechanical 'ngineers' Hand0)ok, Fifth Edition, McGraw-Hill, New Iork, Third Impression, 1951, 2236 pp. Murphy, Glenn, Advanced Mec:1anics of Materials, McGraw-Hill, New York A, l9h6, 337 pp. Jed? 2a ‘75 I111111111111111“