1、08FTM14AGMA Technical PaperEffects of AxleDeflection and ToothFlank Modification onHypoid Gear StressDistribution andContact Fatigue LifeBy H. Xu, J. Chakraborty,J.C. Wang, Dana HoldingCorporationEffects of Axle Deflection and Tooth Flank Modification onHypoid Gear Stress Distribution and Contact Fa
2、tigue LifeHai Xu, Jay Chakraborty and Jyh-Chiang Wang, Dana Holding CorporationThe statements and opinions contained herein are those of the author and should not be construed as anofficial action or opinion of the American Gear Manufacturers Association.AbstractAs well known in involute gearing, pe
3、rfect involute gears never work perfectly in real world. Flankmodificationsareoftenmadetoovercometheinfluencesoferrorscomingfrommanufacturingandassemblyprocessesaswellasdeflectionsofthesystem. Thesamedisciplineappliestohypoidgears. Thispaper,firstof all, presents an approach on validating FEA predic
4、ted axle system deflections. Next, influences of axledeflectionsandtypicalflankmodifications(lengthwisecrowning,profilecrowningandtwist)oncontactpatternand stress distribution of the hypoid gear set are simulated by using an example face-hobbed hypoid geardesign. Finally, two groups of experimental
5、hypoid gear sets are made with two different designed flankmodifications. Actual tooth surface topographies are examined by using a Coordinate Measuring Machine(CMM) to assure the desired flank modifications are achieved. These experimental gear sets are tested toinvestigate the impact of flank modi
6、fications on actual gear life cycles. Test results of the sample gears arereported to illustrate the effect of tooth flank modifications on contact fatigue life cycles.Copyright 2008American Gear Manufacturers Association500 Montgomery Street, Suite 350Alexandria, Virginia, 22314October, 2008ISBN: 9
7、78-1-55589-944-83Effects of Axle Deflection and Tooth Flank Modification on Hypoid Gear StressDistribution and Contact Fatigue LifeHai Xu, Jay Chakraborty, Jyh-Chiang Wang, Dana Holding CorporationIntroductionHypoidgears arewidely usedinmany applications,such as axles and All/Four-Wheel-Drivetransmi
8、ssions for on and off highway vehicles.Recent studies on hypoid gearing are found in thesubject of tooth surface generation and contactanalysis of hypoid gears manufactured by facehobbing process 1-4, noise 5 and dynamics 6,frictionandefficiency7-8,wear 9-10,lubrication11,aswellaslappingandsuper-fin
9、ishing12. Fora hypoid gear drive applied in heavy vehicle axles,the durability has been the primary concern. Axledeflections have a significant impact on gear toothstrength 13 while axle deflectiondata aretypicallyobtained through experimental measurements of aloaded axle under certain controlled co
10、ndition 14.Unexpected deflections can cause severe edgeloadingthatisdetrimentaltogearsurfacelifeaswellas noise performance. As well known in involutegearing, perfectinvolutegearsnever workperfectlyinrealworld. Flankmodifications areoftenmadetoovercome the negative impacts of errors comingfrom manufa
11、cturing and assembly processes aswell as deflections of the system. The same disci-pline applies to hypoid gears. For heavily loadedhypoid gears, flank modifications are particularlycritical to achieve required durability performanceunderrelativelylargeaxledeflections4. Therearebasically three types
12、 of flank modifications, namelyprofile crowning, lengthwise crowning and twist15. For hypoid gears, in addition to tool geometryand basic machine settings, higher order machinesettings are also very important to achieve desiredflank modifications 15-16.The objective of this paper is to study the imp
13、act ofaxledeflectionandtoothflankmodificationonhypo-id gear stress distribution and contact fatigue life.Firstly an approach to validate axle systemdeflections will be proposed. Secondly, by usingcomputer programs and an example face-hobbedhypoid gear design, influences of axle deflectionsand typica
14、l flank modifications on contact patternand stress distribution of thehypoid gear set willbesimulated. Finally, several experimental hypoidgearsetsaremadewithtwodifferentdesignedflankmodifications. These samples are tested underhighcyclefatiguedrivesideonlyconditioninanaxleassembly to investigate th
15、e impact of flankmodifications on actual gear life cycles.MethodologyAxle deflectionAxledeflectionisoneofthemostcriticalinformationfor design and analysis of hypoid and spiral bevelgear drives. Axle deflection is commonly defined,as shown in Figure 1, in terms of E, P, G and ,which are normally deri
16、ved from experimentalmeasurements. Positive E, P, G and representdeflections under certain load condition that wouldenlarge pinion offset, pinion mounting distance,gear mounting distance and shaft angle, respec-tively. Many gear design and analysis softwarehave been developed and are commerciallyava
17、ilabletoday that takea predefinedset of E, P, Gand to describe the rigid body motions and incor-porate them into gear contact analysis to simulatethe loaded contact characteristics of the geardrives.Figure 1. Definition of E, P, G and 4Without knowing the deflections of the axle forwhich the gears a
18、re designed, an ideal gear designon paper or a perfect development showing onloose gear set may possibly lead to poor perform-ances in axle assembly, such as excessive geartooth wear, low fatigue or impact life cycles,unacceptablenoiseanddynamicbehaviors. Beforea physical axle is built, numerical or
19、 analyticalmethod is the only way to estimate the deflections.Inthisstudy,anFEAmodeliscreatedusingANSYSasshowninFigure2. Thepredicteddeflectiondataneed to be validated or corrected.Figure 2. FEA model of an axle deflectionanalysisExperimentalmeasurementof theaxledeflectionisthe conventional approach
20、 to validate the FEA pre-dictions. With the availability of a physical axle,actual measurement can be conducted. In thisstudy, measurements are taken based on theprocedure that is similar to Gleasons procedure14. Figure3illustrates thesetupusedinthismea-surement. However, this type of measurement is
21、very costly and time consuming. Furthermore,measuredresultsforaparticularaxledonotapplytootheraxlemodelsorthesamemodelbut withdiffer-entconfigurations. It isnot practical,if notpossible,to repeat the measurement across different axlemodels or different configurations. To overcomethese disadvantages,
22、 in this study, an indirectapproachis proposedtovalidatetheFEApredicteddeflections.Figure 3. Experimental measurement of anaxle deflectionIt is known that axle deflections will alter gear con-tact patterns in terms of contact area size, contactpath,positionsandshapesontoothsurfacesaswellas transmiss
23、ion errors. In other words, under cer-tain controlled conditions, variations of contact pat-terns for a gear set are the direct responses fromaxledeflections. Thisledtotheideatousecomput-er simulations with FEA predicted deflections tocompare simulated contact patterns to the onesfromactualloadedcon
24、tacttests. If,underthesameloadcondition,thesimulatedcontactpatternsagreewith the actual patterns obtained from loaded con-tact tests, then onecan consider that thedeflectiondata predicted from FEA are valid. If not, the FEAmodel needs to be refined. This is also a develop-ment process toachieveavali
25、dFEA modelfor axledeflection analysis. In this study, the validation iscarried out following the procedures describedbelow:1) Conductloadedcontacttestper DanaCommer-cial Vehicle System procedure. In this study,performloadedcontacttests atfiveloadingcon-ditions, i.e. No Load, 25% of Full Load, 50% of
26、Full Load, 75% of Full Load and 100% of FullLoad. Pictures of the contact patterns underthese loads are recorded as shown in Figure4(a-e);2) Use a computer program (LTCA, Loaded ToothContact Analysis) to simulate the contact pat-terns under the same five levels of loads.5Deflections predicted by the
27、 FEA analysis atthese five loading conditions are used;3) Compare respective patterns betweensimulated and actual ones;4) If the comparisons show good agreement be-tween calculated patterns and actual patterns,then the FEA predicted deflections arevalidated. Otherwise,refinetheFEA modelandrepeat Ste
28、p (2)-(3).In this study, the resulting contact patterns fromcomputersimulationwithFEApredicteddeflectionsareshowninFigure4(a-e). At allthesefiveloadingconditions, the LTCA simulated patterns agreewellwith the actual patterns. Thus the deflectionspredictedbytheFEAprogramareconsideredvalid.The validat
29、ed deflections can then be used forfurthergearanalysisanddesignimprovement. Thisapproach can be used for other axle modelsprovided the loaded contact patterns are available.With the development of this process, the FEAmodelcanbefurtherrefinedandtrainedsothatonecanrely ontheFEA predicteddeflections w
30、ithgoodconfidence for future axle/gear design anddevelopment.Figure 4. Comparison between simulated contact pattern (a-e) and actual painted pattern (a-e):(a-a) No load; (b-b) 25% of full load; (c-c) 50% of full load; (d-d) 75% of full load; (e-e) 100%of full load6Flank modificationsFlank modificati
31、ons to a conjugate gear pair arenormallydesignedtoavoidedgecontact andstressconcentration which could result from deflectionsunder load, manufacturingerrors andmisalignmentetc. Flankmodificationsarealsodesiredforeaseofmanufacturability. There are basically three typesofgeartoothflankmodifications,na
32、melylengthwisecrowning, profile crowning, and longitudinal twist.For hypoid and spiral bevel gears, lengthwisecrowning is mainly a result of cutter radius change.Lengthwise crowning can also be achieved bycutter head tilt in conjunction with blade anglemodification 15. Figure 5(a) illustrates a typi
33、calease-off (also called mismatch, a term used todescribe the deviations of the actual toothsurfacesto theoretical conjugate surfaces) and TCA (ToothContactAnalysis)asaresultoflengthwisecrowningtothepinionmember. Profilecrowningnormallyre-sults from blade profile curvature. It can be alsoachieved by
34、 a mechanism called modified roll 15.Figure5(b) showstheease-offandTCAas aresultof profile crowning with added blade profilecurvature. Shown in Figure 5(c) are an exampleease-off and TCA as a result of tooth twist. Toothtwist,alsoknownasbias,canbeachievedbycuttertilt or using higher order machine mo
35、tions, such ashigher orders of helical motion and modified roll.These three types of flank modifications are oftencombinedtoachievedesiredcontactpattern,ease-off and transmissionerror. Flank modifications canbemadetobothpinionandgear surfaces,althoughin practice they are often designed for pinionsur
36、face only for hypoid and spiral bevel gears.In the following section, impact of flankmodifications on hypoid gear contact pattern andstress distribution will be simulated by a computerprogram. Inthisprogram,ease-offischaracterizedby using a two dimensional quadratic model as afunction of spiral angl
37、e difference, pressure angledifference, lengthwise crowning, profile crowningand twist 17. The resulting coefficients from aleast square approximation for lengthwise crown-ing, profile crowning and twist of the quadraticmodelaredefinedastheamountofrespectiveflankmodifications that will be referred i
38、n the nextsection.Computer simulation of the impacts ofdeflections and flank modifications on hypoidgear contact pattern and stress distributionGiventhevalidatedaxledeflections,E,P,Gand,acomputerprogram(LTCA)isusedtoinvestigatetheimpacts of axle deflections and flank modificationson gear contact pat
39、tern and stress distribution. Inthis paper, a hypoid gear designed with face hob-bing process is used as an example. Figure 6(a)shows a loaded contact pattern and contact stressdistribution simulated by the computer programwithout considering any deflections. From thisfigure one may be concerned abo
40、ut the edgecontact at toe while has no concern at heel.However,performingthesameanalysisbutwiththeconsideration of the axle deflections. Figure 6(b)clearlyindicates thisdesignmayhaveedgecontactat heel while have no concern at toe. Based onFigure6(a),onemayconsidermakingareasonableadjustment to shift
41、 the pattern toward heel, whichwill in fact, as evident in Figure 6(b), adverselyworsen the contact by having severe edge contactat heelthat couldleadtoearly contactfailure. Thusgear contact pattern must be designed and devel-oped appropriately based on the axle deflectioncharacteristics to avoid un
42、favorable contact that isvery important to achieve a satisfactory contactfatigue life.Figure 5. Illustration of flank modification and resulting contact patterns7Figure 6. Contact patterns and stressdistribution analyzed (a) without deflections;and (b) with deflectionsFigure 7 to 9 show the results
43、from LTCA with axledeflectionsandwithdifferentamountofflankmodifi-cations. Inthis paper, flank modifications aremadeto pinion only and the ring gear is kept unchanged.In this study, profile crowning variations arecontrolledbyusingdifferentpinionbladecurvatureswhile all other parameters remain unchan
44、ged.Figure 7(a) and 7(b) show the contact pattern andstress distribution with 20 and 100 inch radii ofcurvatureonpinionbladecutting side, respectively.It is observedthat whiletheoverallcontactpatternsdo not differ significantly under load; the computedmaximum contact stress does vary from 2117 to201
45、2 MPa, an over 5% reduction with 100 inchradius of curvature on pinion blade.Figure 7. Contact patterns and stressdistribution analyzed with pinion blade profileradii of curvature (a) 20 inches; and (b) 100inchesFigure 8. Contact patterns and stressdistribution analyzed with pinion lengthwisecrownin
46、g (a) 0.007 inches; and (b) 0.005inchesIn this study, lengthwise crowning is achieved bychanging pinion machine settings including basicand higher order motions while no blade geometrychange. Figure 8(a) and 8(b) show the results with0.007 inch and 0.005 inch lengthwise crowning de-signed on pinion
47、tooth surface, respectively. It isevident that with 0.005 inch lengthwise crowning,the contact pattern is much longer and themaximum contact stress is about 6% lower.Figure 9. Contact patterns and stressdistribution analyzed with pinion longitudinaltwist (a) 0 degree; and (b) 1.5 degreesFigure 9(a)
48、and 9(b) showthe results with 0degreeand 1.5 degree longitudinal tooth twist designed onpinion tooth surface, respectively. It is obvious thatwith1.5deglongitudinaltwist, thecontact patternis8longerindiagonaldirectionwithlessthan2%reduc-tion on the maximum contact stress. In this study,longitudinalt
49、wist is obtained by changing basic andhigher order machine settings while locking theblade geometry.It should be mentioned that in the comparisonsabove, for example in Figure 9, as a result oflongitudinal twist, there are also some amount oflengthwise and profile crowning change ascalculated by the computer program. For thecomparisons inthis section, cares havebeentakento keep the differences other than the targetedmodification as small as possible. Meanwhile, forhypoid and spiral bevel gears, the flank modifica-
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