1、92 FTM 8The Role of Reliability forBearings and Gearsby: Charles A. MoyerThe Timken CompanyAmerican Gear Manufacturers AssociationTECHNICAL PAPERThe Role of Reliability for Bearings and GearsCharles A. Moyer (retired)The Timken Company, Canton, OhioThe statements and opinions contained herein are th
2、ose of the author and should not be construed as an official action oropinion of the American Gear Manufacturers Association.ABSTRACT:Life prediction or performance assessment is primarily done for bearings or gears with recognition of the significant roleof stress level to such assessments. Reliabi
3、lity or probability of performance is known to relate to the stress-liferelationship but the details as to how these interact are not often clearly defined.This paper details the experimental basis for the relationship between stress (load), life and reliability for bearings andgears considering the
4、 similarity and differences of their respective systems. The role of stress level and life scatter interms of the Weibull distribution will be addressed. The background and equations to calculate the reliability factors, asincluded in both bearing and gear standards, are then developed.Copyright 199
5、2American Gear Manufacturers Association1500 King Street, Suite 201Alexandria, Virginia, 22314October, 1992ISBN: 1-55589-588-3The Role of Reliability for Bearings andGearsby Charles A. MoyerWithin any vital operating equipment, the S_reliability of the components that make _ _up the unit must be kno
6、wn if any sound 2predictions of life or stress capability_re to be made. Reliabilty of course is k_. t _not an independent quality or factor of _any component, whether it be bearing or _._gear. The interdependenceof these three _ _ :_-_ _kfactors,life,stress(orloadleveland “reliability was demonstra
7、ted years ago _.interlinking plots in what Weibull Ncalled the complete fatigue diagram.p _ .EoSection 1 on the figure is the typical -I 0 0._s (;0 0.2sS/N curve with S representing stress on a ._/./_J_/y _D2 _4 _0blinear scale and N representing life instress cycles on a log scale. The curves o - ,
8、0zlabeled P are the full range of /_/,7 ._._/jprobabilty that can theoretically occur /from PrO (100% reliability) to P=I (zero / ,_. _-_ /./_04reliability). All testing or real life _“ ,_ _,_component operations fall within theseextremes. For a given stress and expected ,n_or determined life, a pro
9、bability or i _Nreliability value must exist. Forbearings and gears one tends to consider Fig. 1 The Complete Fatigue Diagram (i).only a few specific curves represented bysection i of the diagram.In sections 2 and 3 of Fig. i, other eventually used in gear and bearingrepresentations of the stress-li
10、fe- standards, they have been developed fromreliability relationship are illustrated, tests. The S/N curves are based onFor this figure the spacing of the curves fatigue tests and the reliability-life orand the log or linear scales are reliability-stress relationships dependarbitary. In actuality th
11、e underlying on related or additional testing, usuallydistributions or scales are determined by with multiple tests at each of severalexperiment. And when curves are drawn and stress levels.Reliability-Life for Bearings 70 )leof 229 85mm boreThe reliability-life relationship forbearings has been gen
12、erated from multipletests run on all types of rolling elementbearings. Bearing life has been expressedas B-IO or L-IO for years and is L-IO inthe latest bearing standards (2)(3)(4).L-IO is defined as basic rating life inmillions of revolutions so that for a (-_group of apparently identical rolling Z
13、bearings, operating under the same _conditions, 90 percent are expected to meet or exceed rating life and ten cr 99percent are expected to fail earlier.Thus, reliability in the broader sense is O0the percentage of an identical group that E-will reach or exceed a specified life. Z ILJJFor an individu
14、al bearing its reliability 0is the probability that it will reach or rrexceed the specified life. LUO_ 99._It has been determined that lives ofidentical bearing groups could be Irepresented by the Weibull distributionas shown in Fig. 2. In 1972 the bearingload ratings and fatigue life standards(5)(6
15、) incorporated the concept of lifeadjustment factors so that applicationlife (L-na) could be more closelyassessed rather than rating life (L-IO) 0.01.02 .04.06 .I .2 .4 .6 1.0 2.0that assumed operating conditions thatwould only lead to classical subsurfacerolling contact fatigue. The reliability REL
16、ATIVE LIFEfactor a(1) as given in the referenceswas based on a Weibull dispersion Fig. 2 Typical Weibull Distribution Plot.parameter or slope of 1.5. It can bedetermined with the equation: extensive Weibull analysis presented by4.483,in(lOO/R)i/l.5 Tallian(7) in 1962. Tallians data was ona(1) = i 93
17、 test groups of 2520 bearings coveringwhere, about 30 years of testing,of which 91a(1) = a life ratio giving values percent were ball bearings. In theother than 1.0 for other reliabilities; surival range of 40 to 90 percent, thea(1)=l.O for L-IO life. fatigue failures fit the WeibullR = reliability
18、as expressed in distribution very well with a Weibullterms of percent survival, slope (m) of 1.0, very close to the 1.125m = Wsibull slope = 1.5 for (9/8) value of m that is used in theequation i. standard ball bearing rating equations.However, in the survival range of 95 toA generalized equation fo
19、r any value of 99.9 percent a deviant line, showingWeibull slope may also be useful and is: excess life held for the early failures,was put through the lowest life bearingsa(1) = 9.4912*in(lOO/R) I/m 2 giving a Weibull slope here of 1.5. Fig.3 from reference (7) shows a Weibull plotWith a Weibull sl
20、ope of 1.5 a(1) valuesfrom 90 to 99.97 percent survival. Thus,are normally presented in tabular form asfor at least ball bearings, a Weibulltaken from references (2)(3) for ball andslope of 1.5 seemed suitable for equationroller bearings: 2 or would justify equation i above.Table i: Reliability a(1)
21、 ValuesReliability % L-ha a_l) A sizeable group of tapered roller90 L-IO 1.00 bearings, representing standard95 L-5 0.62 production lots over a five year period,have been fatigue tested with SAE 2096 L-4 0.5397 L-3 0.44 mineral oil of closely controlled98 L-2 0.33 viscosity and inlet oil temperature
22、controlled at 38C(I00 F). The test99 L-I 0.21 bearings ranged in size from 12.0 to 85.0mm bore Considering the similiarity ofAs Table 1 indicates, reliability wasonly considered for values greater than the test conditions, it was possible to90 percent This was partly from the express the bearings“ l
23、ives as a ratio of“ experimentallife to expected life or as90 ._a / 70Compositesampleof 346595 “ 80_TaperedRollerBearings2095 bearings spalledJj 90m= 1“6r=O99(crrcef)99 -o _ 95. -/-/ .d Z 98-, / _ _rr99.9 “ _JO 99.5-/ 1 :“ 99 97 “,././ !. 0 oX_l _1 QOl _1 LO _r“WFig. 3 Life Distribution: Early Failu
24、res 95 _ J * ITallian, Reference (7) / 1 lzrelative life. The expected life for each 198/ / i i : I ,! rsize bearing was determined using that 99.99 . I _ I , Ibearings specific rating and its test 0.01 .02 ,04.06 .I .2 .4 .6 1.0 2.0loads. The resulting Weibull distributionis given in Fig. 4 (8). Th
25、is is a portion RELATIVE LIFEof a Weibull plot from 70 to 99.99percent survival.Fig. 4 Composite Weibull Distribution ofThe composite sample consisted of 3465 3465 Tapered Roller Bearings.bearings, of which 2095 spelled to thelaboratory criteria of fatigue limit of6.5 square mm. The Weibull slope is
26、 1.6with little indication of deviation fromthe calculated population line. Thus, m (or load level) is known to cause aequal to 1.5 may be considered acceptable reduction of life scatter for generalfor use in equation 2 for roller forms of high-cycle fatigue (9).bearings and is perhaps slightlyconse
27、rvative. For roller bearings and for An example of this from fatigue tests ofline contact, for reliabilities less than a large sample of 19 mm bore tapered90 percent, m equal to 1.5 may be roller bearings, tested as seven sub-considered. For 50 percent reliability (L- groups is given in Fig. 5. Thes
28、e tests50), a(1) would have a value of 3.51. For were run with the same inlet oilpoint contact (as ball bearings) with m temperature and oil flow rate for allequal to 1.0, reliability of 50 percent seven stress levels. The test Hertzianwould give a(1) equal to 6.56. contact stresses ranged from 1420
29、 HPa(206KSI) to 2365 HPa (343K6I) and as canAlthough the bearing standards accept the be seen, the Weibull slope showed areliability values as given in Table i, general increase (decrease in lifeit is possible that other Weibull slopes scatter) with increase in stress. Themay occur, especially with
30、smaller line through the points is based on asamples. Values of m from 1.39 to 3.34 regression that has a correlationwere given in reference (8) for tapered coefficient of 0.83. The correlationroller bearings. The average value of m indicates a significant trend to thecalculated for all the test gro
31、ups in data, but is low enough that otherreference (7) was 1.3 with plus and minus factors not clearly identified also haveone sigma limits of 1.6 to 0.95 given in an influence. Therefore, at presentTallians closure to discussions of his reliability for bearings is primarilypaper. Differing operatin
32、g conditions, computed from equation I and influencesespecially those, such as changes in the that could change this in actuallambda ratio, that cause changes in applications, including stress level, arefailure mode are recognized to contribute not usually considered.to changes of m. Increase of str
33、ess level1381 1725 2070 2415 (MPA) Table 3: Expressions of Probability3,0 , , Requirements of Failure Survival_95 percent confidence band Application Probability Probab.on Weibullslope i/i0000 0.0001 99.99 I/I000 0.0010 99.90LU 2.5- / i/i00 0.0100 99.00O. / i/I0 0.i000 90.00q I T i/2 050o0 5000O0 On
34、e can assumethat the two parameter-,J 2.( Weibull distribution should represent the-J original reliability factor values inTable2. UsingWeibullprobabilitypaper_- the reliabilityfactorvalues C(R),K(R)h_ canbe plottedversussurvivalI._ probabilityas illustratedon Fig. 6. Theline can be represented by a
35、 simpleequation in the genre of equation i asfollows:1.0 _ f I C(R),K(R) = 0.68/in(I/S) I/II4 3200 250 300 350 (KSI)HERTZIAN CONTACT STRESSThe equation is not exact but determinesFig. 5 Relation of Hertzian Contact reliability factors within 2 percent asStress to Weibull Slope “m“. shown on Table 2,
36、 the second column fromthe right. It may also be possible toconsider the reliability factors as lifefactors rather than stress since lifeReliability-Life for Gears scatter may be easier to determine fromtesting than the variability of stressReliability for gears, as given in the level. If one assume
37、s, for pittingANSI/AGMA 2001-B88 Standard (I0), is fatigue, that the relationship of lifereally in terms of reliability-stress, factor C(L) versus number of load cyclesTable 17-1 from the standard gives the N can be used from Standard 2001-B88C(R) times 10/3 or 6.667. However, for higherG(I)=I.0 for
38、 L-I life. reliability values the “lines,“ forR =reliability in terms of percent example, of 95 percent or 99 percent,survival, would have smaller stress-life exponents.This fact may need to be takenintoRecognizing the link between life and account if the life scatter actuallystress the C(R),K(R) fa
39、ctor values for decreases with higher stress andreliability can be determined by the increases with lower stress.following version of equation 7:For gears, the same assumption is takenC(R),K(R) =i/99.50,1n(100/R) I/II4 8 for 99 percent reliability that thisvalue holds for the stress-life exponentof
40、1/0.058 or 17.86 for pitting fatigue Referencesas illustrated in the AGHA Standard inFig. 16-1. However, if life scatter I. Weibull,W.,“A Statisticaldecreases with increased stress as Fig. 7 Representation of Fatigue Failures inindicates then the stress-life exponent Solids,“ Trans. Royal Institute
41、ofwould decrease for reliabilities greater Technology, Nr 27, Stockholm, Sweden,than 99 percent (for example, 99.9 or 1949.99.99 percent reliabilities). Thisinterrelation of stress-life and 2. _,“Load Ratings and Fatigue Lifereliability will need to be taken into for Ball Bearings,“ American Nationa
42、laccount for improvement to both gear and Standard, AFBMA Std. ANSI/AFBMA Standardbearing life prediction and this concept 9-1990, July 17,1990.impacts the understanding of endurancelimit or infinite life at lower stresses 3. _,“Load Ratings and Fatigue Lifewhere life scatter would be greatest, for
43、Roller Bearings,“ American NationalInfinite life with reliability of perhaps Standard, AFBMA Std., ANSI/AFBMA Standard50 percent confidence would not be very 11-1990, July 17, 1990.helpful in .fatigue life prediction.4. _,“Rolling Bearings-Dynamic loadThis discussion has centered primarily on rating
44、s and rating life,“ Internationalpitting fatigue for both bearings and Std. ISO 281, First Ed., 1990-12-01.gears. That K(R) was in some of thetables implies that the life factors 5. _,“Load Ratings and Fatigue Lifewould be the same. However, the exponents for Ball Bearings,“ AFBMA Standard 9,on the
45、stress-life curves on Fig. 16-2 June 1972.(AGMA Standard 2001-B88), for the bendingstrength life factor, K(L) are different 6. _,“Load Ratings and Fatigue Lifethan for pitting fatigue. For case for Roller Bearings,“ AFBMA Standard ii,carburized steel the exponent is 0.1192. June 1972.Thus if the Wei
46、bull slope from Fig. 6 israised by this exponent, that is 7. Tallian, T.,“Weibull Distribution of(ll.4)exp 0.1192, it will equal 1.34. The Rolling Contact Fatigue Life andimplication of this is that the fatigue Deviations Therefrom,“ ASLE Trans. 5,life Weibull slope of 1.34, being higher pp183-196,
47、1962.than the 1.15 Weibull slope for pittingfatigue, that life scatter for bending 8. Moyer, C.A.,“The Status and Future offatigue is less than for pitting or Roller Bearing Life Prediction,surface fatigue. If this is true then the Proceedings Int. Ind. Tribologyinclusion of K(R) in some of the Symp
48、osium, Northwestern Un., Aug. 1990,equations considered in this paper may STLE SP-31, Advances in Engineeringnot be valid. Additional bending fatigue Tribology, Ed. Y. Chung & H.S. Cheng,scatter data is needed to explain this pp89-99, April 1991.life scatter difference.9. Rice,R.C.,“Fatigue Data Ana
49、lysis,“Summary Statisticsand Data Analyses. MetalsHandbook, Vol 8 Mechanical Testing, pp695-The experimental basis of the reliability 713, Ninth Xdition 1989.life factors used for bearings has beengiyen_ The equivalent factors have been i0. _“Fundamental Rating Factors anddeveloped for gears and have been Calculation Methods for Involute Spur andcompared to pitting fatigue life scatter Helical Gear Teeth,“AGMA Standarddata run on two groups of spur gears ANSI/AGMA 2001-B88, Sept. 1988.r
