THE UNIVERSITY OF MICHIGAN INDUSTRY PROGRAM OF THE COLLEGE OF ENGINEERING DESIGN RELIABIDI-TY OF AUTOMOTIVE fCOMPONENTS Charles Lipson Allen H. Krafve May, 1962 IP-566

TABLE OF CONTENTS Page LIST OF FIGURES. o..... oo... oo os o e oe @e ene o LISTRODCTIGURES................................................ 1 THE PROBLEM OF SCATTER........................................ 1 TE LOG-NORMAL DISTRIBUTION........eo..............0......... 2 RELIABILITY OF AUTOMOTIVE COMPONENTS........................o. 5 THE DESIGN LIFE FACTORSS................................. 5 APPENDIXe o o o o................................... oo... o.. o........ 9 TREFERENCESIG S FooACToRSo eo......... o o..... oo...... oi 10 ii

LIST OF FIGURES Figure Page 1 Life Expectancy of Ball Bearings.............................. 12 2 Scatter in Life of Engine Exhaust Valves - Fleet Test2...... 13 3 Scatter in Life of Engine Exhaust Valves - Dynamometer Test.................................................. 14 4 Scatter in Life of Gears-Bevel: Solid Circles; Hypoid: Open Circles3...........000 000 000.........0.ooQ................................. 15 5 Distribution of Fatigue Life - 0o.o06% carbon steel, 50-57.5 KSI Tensile................................................. 16 6 Experimental and Calculated Distributions of Bevel Gear Fatigue Life.............. e............................. 17 7 Design Life Factors at Different Reliabilities - Some Automotive Components................. eoo..oo............ 18 8 Design Life Factors at Different Reliabilities - Bevel and Hypoid Gears.............................O O 19 9 Design Life Factors at Different Reliabilities - Radial Ball Bearings..............O................................. 20 10 Design Life Factors at Different Reliabilities - Rear Axle ShaftS eo Fators a Diffe.r.....................e R..eliabiliti..e 21 11 Design Life Factors at Different Reliabilities - Roller Chains..............0e G o o oeoe e o oe e o o eo...........................e 22 12 Design Life Factors at Different Reliabilities - Some Steels............................................... 23 13 Design Life Factors at Different Reliabilities - Annealed Steel and Nickel Magnetically Presorted........................ 24 14 Design Life Factors at Different Reliabilities - Comparison Between Laboratory Specimens and Manufactured Components...... 25 15 Design Life Factors at Different Reliabilities - Comparison Between Parts Subjected to Flexural Loading and Contact Loading.......................................................o. 26 16 Scatter Band of Monel Metal8..............,..... 000. 000. 00027 iii

Figure Page 17 Scatter Band of 1050 Steel.........28 18 Scatter Band of Aluminum Alloys - A: Sand Cast; B: Permanent Mold; C: Wrought0 eo........o o o o......... 29 19 Stress-Life Relationship at Various Reliabilities - 1050 Steel, 81Rob *.. e......i................... o30 20 Stress-Life Relationship at Various Reliabilities - 4340 Steel. 363 BHN........ o..o.................................... 31 21 Design Stress Factors at Various Lives - Some Materials...... 32 22 Stress-Life Relationship at Various Reliabilities - Radial Ball Bearings oe.. o.. o.. o...o 33 23 Design Stress Factors at Various Lives - Radial Ball Bearings~ 34 iv

Introduction In the design of automotive components to resist fatigue a number of factors are used to account for surface finish, type of loading, mode of loading, size, etc. These factors have been experimentally determined for various materials and operating conditionso However, because of the inherent scatter in the engineering properties, each of these factors represents a mean value computed from the scatter of the observed data. The performance of an automotive part in service is judged by the number of failures or time to failure of a small number of components rather than by the mean life. This, in turn depends on the degree of scatter, Thus in a meaningful design it is essential to incorporate a reliability factor which would provide for this scatter. Reliability can be defined as the probability of a product performing a specified function, under given conditions, for a specified period of time, without failure~ Thus, the function of the part, the operating conditions, and the time of operation are all important aspects of reliability0 In statistical terms reliability is the converse of the probability of failure. If the probability of failure is 1 the part will fail and, therefore, the reliability is zero, Similarly, if the probability of failure is zero the part will not fail and reliability is 1 or 100, if expressed in percent. Thus, 80% reliability means 20% failure, 95% reliability means 5% failure, etc0 Thus, reliability implies an avoidance of failure0 In the case of automotive components this means principally fatigue failures as most automotive parts are subjected in service to repetitive loading, The Problem of Scatter It is the fundamental characteristic of manufactured parts that they exhibit variation in life when subjected to identical loading conditions. Aside from the variations resulting from the human error in testing, or from the limitations of the test equipment, the principal variation lies in the parts themselves0 No two pieces produced are exactly the same, no matter how refined is the process0 Although the differences may be small, they nevertheless exist, This is illustratedlb, the anti-friction bearing in truck front wheel spindles (Fig0 l)o Although the rated life is 100,000 miles, 10% of the bearings may fail under 20,000 miles and another 10% will last over 200,000 mileso

-2All automotive parts show scatter, some to a greater degree than others. Engine exhaust valves, for example, exhibit considerable variation in life.2 In Fig. 2 each group comprises a number of engines, all of the same design, which were tested in fleet operation. The life of a valve shown is an average between the first and the second valve that failed in a given engine. Similar tests conducted on the dynamometer (Fig. 3) under controlled conditions show about the same degree of scatter as in fleet operation. This suggests that scatter is an inherent characteristic of a fabricated part. Faced with this problem of scatter it has been intuitively recognized that it will not suffice to evaluate an automotive part from a single sample and a recourse must be taken to an average (mean) of a number of samples. This has been a widely accepted method of evaluating data. The use of the average alone has a serious drawback. Half of the specimens have a life lower than the average and, therefore, a design based on the mean value implies a 50% reliability, that is, half of the parts will fail. This would be an intolerable condition and the reason that 50% failures do not occur in actual practice is because in. design calculations based on mean values generous factors of safety are provided. This has been recognized for some time and efforts have been made, mostly on empirical basis, to focus attention on the low end of the scatter band. Figure 4 refers to considerable data accumulated on bevel and hypoid gears.3 The recommended design line for maximum of 5% failures is obviously much more meaningful than the commonly used mean line which implies 50% failures. The only shortcoming of the method shown in Fig. 4 is that it necessitates collection of considerable amount of data, generally beyond the capacity of an average industrial laboratory. This study was undertaken to provide a useful basis for design of automotive components which would provide for the inherent scatter in their lives. The Log-Normal Distribution Meaningful analysis of scatter data necessitates the use of statistical methods.ll1l12l3 The dispersion, or scatter, is described by a numerical factor. The usual measure of standard deviation can be used in connection with a normal distribution of occurrences, or the log-standard deviation can be used with the log-normal distribution. More refined methods, such as the extreme value distribution, the probit method, or the staircase method of fitting a regression line to the distribution did not offer any higher accuracy in the present case.

-3For this study the log-normal distribution was used.5'6. The reason for using this distribution is that fatigue data plotted on a linear scale show a skewed distribution4'5 (Fig. 5). The explanations for this are numerous. One of the most logical ones is that a limit of values exists at the lower end of the scale, as a part cannot have negative life or strength, while no limit exists at the upper end of the scale. Further, one very large value will have greater effect on the mean than will several small values. Thus, the mean tends to be above the peak value of occurrences. Through the use of logarithms, a skewed distribution of values can be transformed into a close approximation of a normal distribution. The statistical methods applicable to a normal distribution are much simpler, are readily applied and are as meaningful as other statistical methods. For this reason, all statistical operations have been performed with the logarithms of life. Several checks performed with the present data confirmed that the resulting distributions were nearly normal. Figure 6 shows one such check. Line A is a plot of bevel gear data based on a log-normal distribution of fatigue life of bevel gears. This method, discussed later in the report in greater detail involves the conversion of life N to log N and then finding log N (which is meand l og N (standard deviation of log N) and plotting the ratio of N/N (right hand ordinate in Fig. 6) for different levels of reliability (upper abscissa). Line C is a plot of the life test data on a logarithmic probability paper. This method is based on the fact that the cumulative distribution function of any log-normal distribution will plot out as a straight line on the logarithmic probability paper. Hence we can tabulate our data in the order of failure and assign them rank R m/n+l, where m is the ranked order of a given specimen from a total of n specimens in a sample. That is, if we have specimens whose lives are Nl, N2, Nm **.. Nn we assign them ranks l/n+l, 2/n+l 4... m/n+l,.... n/n+l respectively. These ranks are then plotted on the Percent Failures (lower abscissa) and the lives on the life-cycles (left hand ordinate) and we plot these on the logarithmic probability paper. Next we fit the best straight line to this plot (by least square method). If the distribution of the data were lognormal we would get a straight line on this paper. This is the case as evidenced by Line C. Now if we wish to plot the ratio of N/N for different reliabilities, all that is necessary is to draw a line through 50% probability, parallel to line C. This produces line-B which is quite compatible with the calculated line A.

-4The statistical analysis of fatigue data can be handled in two ways, A distribution of stresses at a fixed life can be found, or a distribution of life at a particular stress. In the first phase of this study the distribution of life values at a given stress was considered. Most of the test data obtained on automotive parts was available in this form. Generally, the load or stress was set and the parts were run to failure. The number of cycles was then recorded for each part and the scatter observed. This may have been repeated at a different stress level or at several levels. The most common measure of dispersion of occurrences is the standard deviation. The most important property of this parameter is that 68o23% of the occurrences in the normal distribution are contained within the range of one standard deviation above and below the mean value; 95o45% within + 2 standard deviations; and 99.73% within + 3 standard deviations0 This property is especially useful for the purpose of finding a scatter factor, as the maximum percentage of failure can be readily expressed as a certain number of standard deviations from the mean0 Furthermore, because the number of occurrences outside of a particular standard deviation range includes, both parts of very long life and parts with short life, a range of three standard deviations is equivalent to a failure level of o135%, or a reliability level of 99o865%; two standard deviations 2,28% failures, or 97-72% reliability level; 1.645 C gives 5% failures or 95% reliability; 1o282 a gives 10% failures or 90% reliability; 1 a 16% failures and 84% probability; and,675 C gives 25% failures and 75% reliability level~ Standard deviation in the log-normal distribution can be calculated from the following expression~ Cs ( N (l og )2 where standard deviation (actually the "best estimate" of the population variance) log N mean value of the logarithms of the life values to the base 10 Z (log N)2 = summation of the squares of the logarithms of the life values n number of specimens in sample

Knowing log N and K a (where K is the desired multiple of a) by subtracting K a from log N. the log of life corresponding to a given reliability is obtained. By taking the anti-log of this life and dividing it by the mean life (50% reliability) the Design Life Factor is derived. This factor is thus life at a given probability divided by life at 50% probability and it is plotted against percent reliability on a log-probability paper. Figures 7-15 constitute these plots for various cases. Reliability of Automotive Components In this manner, considerable data obtained over a period of years, and also some found in literature was analyzed in the manner indicated above and plotted as shown in Figures 7-15o In these graphs the upper and lower abscissas represent percent reliability and percent failures respectively, The ordinate gives Design Life Factors, The original data, from which these calculations were made were expressed as life in cycles, hours, miles, etco A low design factor means high scatter and a high factor considerable uniformity in the life of the. parts tested. The stress or load levels corresponding to the above lives were the design stresses under which these parts were tested. In most cases these were located somewhat below the midpoint between the ultimate tensile strength and the endurance limit of the material In those cases were lives were available at several stress levels the information was so noted and further analyzed, The Design Life Factors The analysis of Figs0 7-13 suggests the following. Because of manufacturing variations one would expect more scatter in actual automotive parts than in laboratory specimens. This was found to be approximately the case, as shown in Fig. 14. Within the manufactured parts themselves (Figs0 7-11), those parts which are subjected in service to contact loading (ball bearings, hypoid and bevel gears, engine valves) were found to have lower life factor than parts under flexural loading (crankshafts, springs, fans, etc,) Figs 15, Note that the transmission helical gears had a relatively high life factor (Fig0 7), In this case the critical load was flexural as all the failures occurred at the root of the tooth, The wide scatter of members under contact loading has been generally recognized.7 In the case of ball bearings life is inversely proportional to the ninth power of the unit pressure, so that even a sligth variation in the bearing geometry or in the applied load may produce considerable variation in life,

-6Finally, no particular interrelationship can be expected within the various automotive components (Fig. 7-11). The scatter in life and thus the value of the design life factor at any reliability level depends on many things: the complexity of design at the critical section, uniformity of material properties, method of manufacture, quality of the inspection methods, etc. and these will differ among the various automotive parts. Thus a shaft whose critical section is a keyway would be expected to show higher variability in life than a shaft whose critical section is a large fillet. The size and the method of grinding the fillet can be carefully controlled and therefore, the shaft should show a relatively good uniformity in life. On the other hand it is more difficult to control the manufacture of a keyway and more scatter can be expected. Thus, in Fig. 7 higher design life factor was obtained for a cast wheel, where in the region of maximum stress there was no abrupt changes in section than in wheel spindles which had an 1/8" fillet radius. For design purposes 95% reliability may be used in design calculations of parts whose failure can be regarded principally as an economic loss but not a loss of life of vehicle occupants. Into the first category belong body, engine, transmission, and some drive line components. For the latter (steering and suspension parts) a 99.9% reliability should be used -instead. The information in Figs. 7-11 is tabulated under the two headings in Table 1. The Design Stress Factors For design purposes some problems are best solved in terms of the life at a given stress, while others in terms of stress at a given life. Figures 7-13 and Table 1 provide the information for the former. That is, at any required level of reliability the design life as a fraction of the mean life can be determined, In this manner, the average life of automotive components, conventionally obtained from laboratory tests, can be translated into a more meaningful design life where reliability and thus the maximum percentof failure can be stated, The other category of design problems calls for the solution of stresses at a given life. To do this it is first necessary to establish the variation in the life scatter with the stress level. A casual review of literature8,9,10 indicates that in some cases scatter is independent of stress, while in other cases it may either slightly or pronouncedly increase or decrease with the stress level (Figs. 16-18). The same was found to be true in the present case.

It is significant to note (Figs. 12 and 13) that in the case of materials magnetically sorted for permeability and tested in torsion the design life factor: 1) is largely independent of stress: 2) it is much higher for any level of reliability than materials not sorted. This reflects the uniformity of samples obtained. The benefit of this uniformity to the service life of automotive components is worth notingo In Figs. 19 and 20, by dividing at a given life, the stress at 99o86% reliability (3 standard deviations) by the stress at 50% reliability (mean stress) a Design Stress Factor S99 g86/S50 was obtained. This was repeated for various materials, with results as shown in Fig0 21l It will be noted that for the softer materials studied, in order to assure ourselves of 99o86% reliability, that is less than 15 failures in 10,000 pieces, it is necessary to design the part to approximately 80% of the average value of the fatigue strength0 For the 4340 steel the percent reduction in the fatigue strength will be considerably greater. Thus, for a life of 500,000cycles the design should be based on approximately 50% of the mean fatigue strength found in handbooks for this particular life. Similar study was made for ball bearings, with the results shown in Fig0 23 which was derived from Figo 22~ The design stress here should be 80% of the mean fatigue strength0 The above analysis was concerned with the finite life regions (sloping lines) of the stress-life relationships0 Calculations were also made for the endurance limit regions of several automotive components0 Here, however, the data were less well defined0 In some cases the distribution was found to be normal, in other cases log-normal, and in a few cases not at all defined

Design Life Factors Automotive Parts Reliability 99.9 Wheel.66.45 Leaf Spring.60. 38 Fan.57.35 Transmission Gear ~49.26 Crankshaft - Design A.46.22 Crankshaft - Design B.40.18 Front Wheel Spindle.33 *13 Engine Exhaust Valve.20.05 Hypoid Gear, 93 KSI.33.13,Hypoid Gear, 105 KSI.37.16 Bevel Gear, 75 KSI.32.11 Bevel Gear, 93 KSI.27.084 Ball Bearing, 388 KSI.34.13 Ball Bearing, 430 KSI.26.08 Ball Bearing, 475 KSI.30.ll Ball Bearing, 510 KSI.34.14 Ball Bearing, 540 KSI.24.07 Axle Shaft, Automobile, 27 KSI 3.5.14 Axle Shaft, Automobile, 38 KSI.46 o24 Axle Shaft, Automobile, Shot Peened.37.16 Axle Shaft, Farm Tractor, 30 KSI.57.34 Axle Shaft, Farm Tractor, 54 KSI.52.29 Roller Chain, 650 lb.35.14 Roller Chain, 800 lb.32.12 Table 1

Appendix Some additional information on the characteristics of the automotive components studied: Ball Bearings: 1/2?' radial, SAE 52100. Also see reference 15 Bevel and Hypoid Gears: See reference 3 Wheels: Truck, malleable iron Leaf Springs: Truck, SAE 4068, 444-477 BHN Gears: Truck, Transmission Helical, SAE 8620, carburized, 58-63Rc.Crankshaft: Automobile, SAE 1046, 228-269 BHN Front Wheel Spindles: Automobile, SAE 1046, 248-293 BHN Engine Valves: Truck, Exhaust Valves Axle Shafts: Farm Tractor, SAE 8635, 269-321 BHN Axle Shafts: Automobile, SAE 8650, 388-444 BHN, Also see reference 14 Roller Chains: American Standard No. 40 Fan: Automobile, 6 blade spider type, SAE 1020

-10References 1. J. M. Stokely, R. C. Gray, and S. R. Calish, "Automotive Gear Lubricants and Greases," Paper presented at Southern California Section Meeting, Los Angeles, March 15, 1951. 2. K. L. Pfundstein and J. D. Bailie, "Factors Affecting Tractor Valve Performance," SAE Journal, July, 1952. 3. W. Coleman, "An Improved Method for Estimating the Fatigue Life of Bevel Gears and Hypoid Gears, " SAE Preprint No. 627, June, 1951. 4. Battelle Memorial Institute, "Prevention of the Failure of Metals Under Repeated Stress," John Wiley & Sons, Inc, p 202. 5. E. Epremian and R. G. Mehl, "Investigation of Statistical Nature of Fatigue Properties," NACA Technical Note 2719, June, 1952. 6. G. E. Dieter and R. F. Mehl, "Investigation of the Statistical Nature of the Fatigue of Metals," NACA Technical Note 3019, September, 1953. 7. H. Styri, "Fatigue Strength of Ball Bearing Races and Heat-Treated 52100 Steel Specimens," ASTM, Preprint No. 23, 1951.. 8. H. W. Russell and W. A. Welcker, Jr., "Endurance and other Properties at Low Temperatures of Some Alloys for Aircraft Use," NACA Technical Note No. 381, 1931. 9. H. W. Russell and W. A. Welcker, Jr., "Damage and Overstress in the Fatigue of Ferrous Metals," ASTM Proceedings, Vol. 36, Part II, 1936. 10. H. J. Grover, S. A. Gordon, L. R. Jackson, "Fatigue of Metals and Structures," Department of the Navy, 1954. llo. A. M. Freudenthal and E. J. Gumbel, "Distribution Functions for the Prediction of Fatigue Life and Fatigue Strength, " The Institution of Mechanical. Engineers, International Conference on Fatigue of Metals, September, 1956. 12. M. N. Torrey and G. R. Gohn, "A Study of Statistical Treatment of Fatigue Data'," ASTM Preprint No. 70, 1956.

-11References (conti'd) 13. W. Weibull, "Statistical Design of Fatigue Experiments," Journal of Applied Mechanics, Vol. 19, No. 1, March, 1952. 14. 0. Jo Horger and C. H. Lipson, "Automotive Rear Axles and Means of Improving Their Fatigue Resistance," ASTM Symposium on Testing of Parts and Assemblies, 1946. 15. J. Leiblein and M. Zelen, "Statistical Investigation of the Fatigue Life of Deep-Groove Ball Bearings," National Bureau of Standards, Vol. 57, No. 5, November, 1956, Research Paper No. 2719.

350 300 250 "0o w 200 w 00 I 4 150 Figure 1. Life Expectancy of Ball Bearings..

70 ENGINE EXHAUST VALVE LIFE FLEET TEST He 60 ro 50 CD 8 o 40 () w~~~~~~~~~~~~~~~~~~~~~ -'J 4 > 30 w "43 ~. CD~~~7 w CD ~ (D $~ 20 0310 CD I0O U) ct~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~m GROUP I GROUP 2 GROUP 3 GROUP 4 GROUP 5 ENGINE Y ENGINE Y ENGINE Y ENGINE G ENGINE G

ENGINE EXHAUST VALVE LIFE DYNAMOMETER TEST 1000 900 800 700 0 600 w 500 400 300 200 100 0 G - GROUP I GROUP 2 GROUP 3 GROUP 4 GROUP 5 ENGINE A ENGINE B ENGINE B ENGINE B ENGINE B Figure 3. Scatter in Life of Engine Exhaust Valves - Dynamometer Test2.

0zj 200 c+ 0 ( 0 0 ( 0 O0' 100 C) H'~~~~~~~~~;V'o 70 - ~ ~..~ 50 _ _ _ _ _ _ _ _ _ _ __0 0 0 03 90 cn 50 PROPOSED DESIGN LIMIT -G em eo e W (NOT OVER 5 PER CENT FAILURES) (D 0CD o 03 0 to F-' 0'2 to 03 4 6o 7o LIFE -CYCLES

hd %J'l I H o O Z 40 (D I~ 0 020 0Ii 0 10 20 30 40 50 60 70 80 90 100 0 bd 60... cI~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 3~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ CL Z 40 0 20 0~~~~~,,~ ~~~0 I0 20 30 40 50 60 70 80 90I0 LIFE- CYCLES /I0

PERCENT RELIABILITY O9999R 999 99.8 995 99 98 95 90 80 70 60 50 —'~~~~~~ -~~0.9 ___a__f~ - ~0.8 or'/'~C 0.7 0.6 ___ -~~~0.5 H0.4 P~ SCALES _0.3 __ - w <o~ QLi / a2,o, o o A- CALCULATIONS C) U) (Log - NORMAL) 10~~~~~~~~J~~~~~~~~~ 4 b- -- J __ —-_ B-PARALLEL TO C _ 0._ HI — ___________ __ ___ -0.09 N - H.o (e o ~ ~ ~ ~ ~~ ~ ~ ~~~~. o8 i-l,0.08 0.07 5: __ — ~~O04 > r 0.03:____ __ _ 4 h... 0,01 0.1 0.2 0.5 I 2 5 I0 20 30 40 50 60 70 80 9019 9 P0 L'F PLUSo5 ILEE FIR SCALES ~ C -TEST DATA - -0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~.02L 10P 0.01 QOI OJO.2 0.51 2 5 10 20 30 40 5060 70 80 90 95 98 99 PERCENJT FAILURES

PERCENT RELIABILITY 99.99 99 998 99.5 99 96 95 90 80 70 60 50,,O1 0.9 ~ 0.8 0.7 0.6 0.5 WHEELS ___-4~t —Fjc7 —t —-"' 0.4 LEAF SPRINGS 0. 0 j FANS 01k/ 00 eo I I * c..J 4 GEARS _0.2 C'SHAFT A / 0 I') C'SHAFT B w 0.1 WHEEL o. 9 SPINDLES o.oe 0.07 0.06 co OX4 0.05 - LLd -.04 z w ENGINE >_ VALVES 003. w UJ 0.02 J 0.01 0.01 0.1 02 0.5 I 2 5 I0 20 30 40 50 PERCENT FAILURES Figure 7. Design Life Factors at Different Reliabilities - Some Automotive Components.

PERCENT RELIABILITY 99.99 999 998 995 99 96 95 90 80 70 60 50 O.9 0.9 0.7 0.6 I. J In co 0.34 w LLJ 0~ HYPOID GEAR /~~~~~~~~~~~~~~~~~~~~~~~~ 105 KSI - J 0.1 %*% HYPOID GEAR 0.09 > 93 KSI // /.... oo. BEVEL GEAR 0.08 75 KSI 007 0.06 BEVEL GEAR w 93 KSI M. Z w id) 0.04 (. 0.03 w I., 0.02 0.01 001 0.1 0.2 0.5 I 2 5 I 20 30 40 50 PERCENT FAILURES Figure 8. Design Life Factors at Different Reliabilities - Bevel and Hypoid Gears.

-20PERCENT RELIABILITY 99.99 999998 99.5 99 98 95 90 80 70 60 50 _Q9 5~10 KSF 4 -J 0.01 0.I0.2 I0 0.4 T,;, IMKEN B-I 0 LIFE w PERCENT FA LURESU 0. 510 KSI o.1 388 KSI. / _/. ao _ad 0.04 rn 475 KSI 07, o~o 430 KSI z.0 540 KS 2. I 2 2 050 LL 0.01 PERCENT FAILURES Figure 9- Design Life Factors at Different Reliabilities - Radial Ball Bearings.

PERCENT RELIABILITY 99.99 928998 99 5 99 96 95 90 80 70 60 50 Q8 0.7 0.6,0 oo, —~ 01001- 0.5 FARM TRACTOR 0 30 KSI w FARM TRACTOR 54 KSI _ o <_ AUTOMOTIVE 0 0. 38 KSI AUTOMOTIVE w (SHOT PEENED) U. 43 KSI 0.1 - AUTOMOTIVE!09 27 KSI l. 0.07: 0.06 0.05 z 0.04 > CD. LU. oo002 00 0.1 02 0.5 I 2 5 I0 20 30 40 5000 PERCENT FAILURES Figure 10. Design Life Factors at Different Reliabilities - Rear Axle Shafts.

-22PERCENT RELIABILITY 99.99 999 998 995 99 98 95 90 80 70 60 50 1.0 0.8 Gs _;__" - 0.7 0.6 0.5 __J w 0.2 0 0 I LL. 650# o.009 8O0 # 0.08 _1 0.07 006 005 zi w 0.04 > 0.03 w LU. LiL Iz. 0.02 -'~~~ -'~~~ - 0.01 o.o0 0.1 0.2 0.5 I 2 5 10 20 30 40 50 PERCENT FAILURES Figure 11. Design Life Factors at Different Reliabilities - Roller Chains.

-23PERCENT RELIABILITY 99.99 9Gt9 998 99.5 99 98 95 90 80 70 60 50 -------, —.. —--- ~-. —-, —— ~ ~ ~ ~ ~ ~~ ~~ ~~~~~~- 1.0 Q9 ANNEALED Q8 STEEL 0.7 MAGNETICALLY _ _ SORTED 0.6 0.5 J~~~~~~~~~~~~~0.4 - w 4340 ___ 70.6 KSI 0.2 0 1050 81.4345 KSI 0.I ~,~~~~~~~~~~~~~~~~0 0.08 0.074 cr LLL 4340 ~ ~~~~70.6 KSI ~L~f —-~t —~-+-t —~-"- 0.06 0o.04:,,,"'.1 Q2 G5 2 5 20 30 40 0.03 w Q02 - -. ______ - - - 0.01 o,, 0.01 0.1 02 0.5 I 2 5 0 20 30 40 50 PERCENT FAILURES Fig~ure 12. Design ILfe Factors at Different Reliabilities - Some Steels.

-pa7V~o'0;r'd XTT ~~r~arrGUelG TGTO11 pUP TaG4S peU'[uYtr - ST4-l. qI9T'!:Te %u~a:.TJJT-CI %- )~Yq -oz, J a:TJ u'SGC'' oT a'n'T, S3WnlIV-I LN33N3d 09 O OL Oa 01 9 I 9'0 ZO Io C0O I00 -,, ____ -10 -I G) *oo,, m Z o 0 ITI 900 r Z Ga 90ro 600 0' rri ~~~~~~~~~~" no Ul r0 -I ~(1 0'0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~00 9'o m ~ ~ Y..~1331S.L'. 9,0 60 0OG 09 OL 0 06 96 06 66 G96 966 686 6666 A.11I8VI3I.N3D8I3d

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?' H t-i bd U -7 / 0~~~~~~~~~~~~~~0 0, (Dm M (D tj 0 0 z~~~~~~~~~~~~_/.~ ~~ - m'S'100~ ~~~~~~~~~~~7 1- r WC+ (DU S~~~Y _ I - 11 H0 as ci - PiH I-I.~~~~~~~~~~~~~~~~~~~~~~. hd (D P10 o LIFE AT GIVEN RELIABILITY /LIFE AT 50~/ RELIABILITY Hi. I~i

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45 44 H1 *- 0 -J 0 43 m U) 40 1 t42 U) v V) r U,) H 41 0 0 H 40 39 10 10~ 10~ 101 0 LIFE - CYCLES

ot F. STRESS- psi/ STRESS-psi/ STRESS psi/ * C.0 cm pt p PI Cl),o. I 0. I 00,0. D,, O3O O ~0

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r _ tl" T- q.l:':TTGU snOF'eTA a dTqsuOT.:q..eoE,.TI-:go q.S OZ.0':.,TZ STRESS - KSI C a e e O OD(D0 0 0 0 0 0 00 00 PERCENT RELIABILITY-o — o A CA 0o r0-C /' ~. I1

CD c —1.0 to 0.9 ~' | | 6D___ ___-.C/) ~ ~. 1l. 0.8 a _ (D: 06 _0 0.2 51 I I 4 - 1050 STEEL RE11 * ~ J 5 - 1045 STEEL BHN191.30. 8 - 4340 STEEL Rc38 LIFE - CYCLES (cD i-.. o3 56 m~ ~ ~~K01 051

0CD H'__ d LIF- 3 0 U U 100 02 CD 100 —— 500 c' 9 so.00o - - 00LIFE - CYCLES ()~ rH p.,

'TT'1 TS'TP:e - Sa-TI snoWte'- Vs seXO Oz ssaxS UST[sa ZJ aomird STRESS AT 99.86 %O/o RELIABILITY STRESS AT 50 % RELIABILITY.o. 0 P OPo I0'r- I" C~.