1、09FTM10AGMA Technical PaperTheEffectofFlexibleComponents on theDurability, Whine,Rattle, and Efficiency ofan AutomotiveTransaxle GeartrainSystemby A. Korde and B.K. Wilson,Romax Technology, Inc.The Effect of Flexible Components on the Durability, Whine,Rattle, and Efficiency of an Automotive Transax
2、le GeartrainSystemAmol Korde and Brian K. Wilson, Romax Technology, Inc.The 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.AbstractGearengineershavelongrecognizedtheimportance
3、ofconsideringsystemfactorswhenanalyzingasinglepair of gears in mesh. These factors include important considerations such as load sharing in multi-meshgeartrains and bearing clearances, in addition to the effects of flexible components, such as housings, gearblanks, shafts, and carriers for planetary
4、 geartrains. However, in recent years transmission systems havebecomeincreasinglycomplex,withhighernumbersofgearsandcomponents,whilethequalityrequirementsand expectations in terms of durability, gear whine, rattle and efficiency have increased accordingly. Withincreased complexity and quality requir
5、ements, a gear engineer must use advanced system design tools toensure a robust geartrain is delivered on time, meeting all attribute, cost and weight requirements. As astandard practice, finite element models have traditionally been used for analyzing transmission systemdeflections,butthismodelinge
6、nvironmentdoesnotalwaysincludeprovisionsforanalysisofrattle,efficiency,norconsiderationsforattributevariation,whichoftenrequiremanyrunstobecompletedinashorttimeframe.An advanced software tool is available for the analysis of transmission system durability, whine, rattle andefficiency, all within a s
7、ingle programming environment, including the effects of flexible components such ashousings,gearblanks,andshafting,whilealsoallowingmanufacturingvariationstudiestobeperformed. Anexample transaxle case study is examined in detail.Copyright 2009American Gear Manufacturers Association500 Montgomery Str
8、eet, Suite 350Alexandria, Virginia, 22314September 2009ISBN: 978-1-55589-963-93The Effect of Flexible Components on the Durability, Whine, Rattle, andEfficiency of an Automotive Transaxle Geartrain SystemAmol Korde, Brian K. Wilson, Romax Technology, Inc.IntroductionThroughout the gearing industry,
9、the naturalprogression of higher consumer expectationsrequires that gear design engineers be tasked withcreating quieter, more durable and efficientdesignswhile at the same time reducing costs anddevelopment time. Previous accepted practices ofoptimizingagearpairindependentlyoftheintendedapplication
10、, or “system”, performing expensive andtime consuming durability and noise/vibration test-ing of system prototypes, then adjusting the geardesigns accordingly before repeating the testingcycle, is quickly becoming not only impractical, butunaffordable. Companies simply do not have theresources, espe
11、cially during an economic down-turn, to rely on prototype testing to drive the gear-traindesign;testingshouldonlybeutilizedasafinalverification of a design optimized using various sta-tistical methodologies in conjunction with state-of-the-art geartrain system CAE analysis tools 1, 2,.These advanced
12、 CAE tools have been previouslyshown to allow the prediction of the system gearwhine performance of a complex automatic trans-mission used in an automotive application 3, 4.Thepredictionsincludedstatictransmissionerrorofa planetary gearset factoring in the effects of time-varying factors such as loa
13、d sharing and carrierdeflections, mode shapes and natural frequencies,absolute levels of vibration due to the gear meshforces, and manufacturing variation due tomicrogeometry variation.Additional studies using the advanced geartrainsystem CAE tools included analysis of the high-mileage gear whine pe
14、rformance of an automatictransmission, as well as microgeometry inspectionmethods used to accurately represent the actualplanetary gearset hardware 5. Predictions of highmileage performance is important to severalindustries for varying reasons: for automotive ap-plications, the residual value of pre
15、viously-ownedvehiclescanbenegativelyaffectedbythepresenceof passenger compartment gear whine, even if thenoise itself is not indicative of an impending gearfailure; for aerospace applications, the rate of gearwear due to geartrain system effects can be criticalto designing a robust gearset beyond ju
16、st followingbasic gear standards.Further studies using the same geartrain systemCAE tools have shown the importance of includingrepresentative boundary conditions, such as thedriveline downstream inertia and gearbox housingloads, and the resulting effect on noise, vibrationand durability predictions
17、 6. Clearly, the flexiblehousing containing the geartrain was a criticalcomponent enabling the correct mesh misalign-ment to be predicted as part of the total system,therefore allowing a more robust non-linear gearcontactstudytobeperformed. Additionalinvestiga-tions also showed that the downstream e
18、ffects ofthe durability rig (inertia, dynamics) can inadver-tently effect the outcome of the durability testing it-self, compared to how the geartrain would performin the actual vehicle. The study demonstrated thatdurability rig testing, without proper analysis, mayprovide an incorrect indication of
19、 actual durabilityperformance, possibly leading to unexpectedfailures in the field.An issue not clearly demonstrated for geartrainsystems such as transmissions and transaxlesusedinvariousindustrialapplicationsistheneedforincluding flexible components as part of thesystemanalysis,specificallyforanaly
20、sisofperformanceat-tributes such as gear durability, whine, rattle, andtotalsystemefficiencywithpredictionsforindividualcomponent efficiency contributions. For transmis-sions with rigid housings, explicitly designed to notdeflect significantly even under high geartrainloads, perhaps the flexibility
21、of the housing is notsocriticalforthemakingaccurategearmeshmisalign-ment predictions for instance. However, forapplications where the gearbox housing is opti-mizedforweight,usingmaterialssuchasaluminumand magnesium with thin-walled designs, housingflexibility becomes exceedingly important whenanalyz
22、ing geartrain deflections not only for high4loads, but across a wide range of loadingconditions.This paper will investigate the housing flexibilityissue using a generic manual transaxle used in anautomotive as an example. The transaxle wasmodeled using the advanced CAE tool previouslyreferenced 1-6,
23、 both with and without the housingas shownin Figure1. All gear,bearing andshaftingdetailswerethesame,exceptthattheouterbearingrace connections to the condensed finite elementmodel of the housing were set to ground for theconfiguration without the housing. Therefore, thedifferences between the perfor
24、mance attributesanalyzed and presented below represent the effectof the housing. Additional capabilities inherent tothe inclusion of the housing as part of the geartrainsystem analysis will also be demonstrated.Mesh misalignmentFor the purposes of the mesh misalignmentinvestigation, the aforemention
25、ed transaxle wasanalyzed with the powerflow of the system setthrough first gear only, predicting the alignment ef-fects at the first gear and final drive meshlocations,as indicated in Figure 2.Figure 1. Advanced CAE transaxle system model, with and without the housingFigure 2. First gear powerflow (
26、green) and mesh locations (red) for transaxle system modelThe geartrain was subjected to loading conditionscovering light to heavy throttle in an automotiveapplication, both with and without the housing. The5resultingmeshmisalignmentswere predictedusingcalculations encompassing the fully-coupled, si
27、xdegree-of-freedom system model for each config-uration. The mesh misalignment predictions areshown in Figure 3.A more detailed analysis of each configurationshows the contribution to the mesh misalignmentfrom individual components and the associatedclearances and deflections is shown in Table 1.The
28、 importance of including the flexible housing aspartofafully-coupledtransaxlesysteminthemeshmisalignmentpredictionscanthereforebesubstan-tiated analytically, providing opportunities tomanage undesirable misalignment as a system,rather than immediately assuming options areeithermicrogeometrymodificat
29、ions,suchascrown-ing, or housing stiffness actions, such as addingribs. Perhaps changing the shaft materialproperties or dimensions would be a more feasibleand effective solution; or, a combination of allapproaches. Figure 4 shows the lay-shaft deflec-tions, for example, with and without the housing
30、influence at 1200 Nm, demonstrating a substantial-lyhigherdeflectionoftheshaftwiththebearingssetto ground. Using statistical methods such asDesign of Experiments 1,2, the mesh misalign-ment can be managed objectively.Transmission error and contact patternsThe foundation of a successful non-linear ge
31、armesh contact analysis is to fully understand andquantify the relative positions of the two meshinggears7. Determiningthe housinginfluence onthemisalignment predictions istherefore aprerequisitefor accurately predicting static transmission errorand the load distribution throughout a tooth meshcycle
32、. For the theoretical gears used in this inves-tigation, five microns of lead crowning and involutebarreling were added to both the first gear and finaldrive gear pairs inorder toavoid somelevel ofedgeloadingoverthewiderangeofgeartrain torquesap-plied. Noothersignificant microgeometrymodifica-tions
33、were used in the analysis.Table 1. Misalignment contribution analysis,with and without the housing1st speed Hsg No hsgPinion 1 Wheel 1gear mesh-58.56 -78.34Wheel 1GearGear bearing outerGear bearing innerSupport shaftBearing innerBearing outer (hsg)-38.71-1.0700-42.860.506774.72-55.6- 1.300-54.13-0.1
34、67950Pinion 1GearGear bearing outerGear bearing innerSupport shaftBearing innerBearing outer (hsg)-19.860.1689800-20.091.23-1.17-22.74-0.7199700-22.980.962110Final drive mesh misalignment 1st gear mesh misalignmentFigure 3. First gear and final drive mesh misalignment predictions, with and without t
35、he housing6Figure 4. Lay shaft deflections, 1200 Nm, with (top) and without (bottom) the housingTable 2 lists the peak-peak static transmission pre-dictions as well as the first three harmonics for the400 Nm load case of the previous misalignmentstudy, with and without the housing influence.From a s
36、ystem dynamics stand point, clearly thehousingisneededinordertofollowanyqualityfunc-tiondeployment (QFD)process forgear whine,fac-toring in the customer requirements cascaded tovibration targets at a system housing location theQFD process for gear whine is clearly outlined inReference 1, then procee
37、ding to cascade to thesubsystem, and finally to the component level. AQFD example for gear whine is given in Figure 5.Table 2. Static transmission error: peak-peak, harmonics, and percentage difference, finaldrive/1st gear, with and without the housingFinal drive,hsgFinal drive,no hsgFinal drive,%di
38、ff1st gear, hsg 1st gear, nohsg1st gear, %diffTE (pk-pk) 1.29 3.48 270 1.35 3.92 290TE (1st harmonic) 0.62 1.5 242 0.65 1.64 252TE (2nd harmonic) 0.08 0.31 388 0.13 0.51 392TE (3rd harmonic) 0.02 0.21 1050 0.03 0.11 3677Figure 5. Quality function deployment (QFD) plot for management of system gear w
39、hineAn example of predicted housing vibration due tothe first gear mesh order, the “system” part of theQFD process, exerted to 400 Nm of output load, isshown in Figure 6.Without the housing, a gear designer will typicallyattempt to minimize the transmission error withoutfactoring in details of the s
40、ystem influence under alldesignloads,whichincludesthe“path”betweenthemesh excitation creating forces and relatedvibration along the shafting, through the bearings,forcing the housing to vibrate at the mesh frequen-cy. However, without the appropriate boundaryconditions, including the housing influen
41、ce, thesource optimization process (e.g. static transmis-sion error) cannot be properly implemented withoutsome level of risk. Even the geartrain “subsystem”dynamics cannot be confidently evaluated, both interms of amplitude and frequency content, withoutthe effects of the gearbox housing influence
42、asevidenced by the dynamic transmission errorpredictions, shown in Figure 7.Furthermore, including the housing effects into thetransaxle system analysis allows examination ofvarious mode shapes that could potentially nega-tively affect the housing vibration. Presenting interms of displacement, strai
43、n and kinetic energies,allows the entire transaxle design team to worktogetherinorderto finda solutionto desensitizethetransaxle to the inherent static transmission errorexcitations (the transfer functions in the lower QFDquadrants). An example of such a CAE analysis isshown in Figure 8.In order to
44、optimize the load distribution, reviewingstatic transmission error values are of course notsufficient. Standard practice is to review load dis-tribution plots for a complete tooth mesh cycle.Again, the effect of the housing influence is evidentby comparison of the plots in Figure 9, showing theload
45、distribution for the final drive gear mesh forboth configurations, exerted to 400 Nm half-shafttorque. Without the housing, the final drive gearsetis demonstrating more edge loading and a higherload per unit length than when considering theflexibilities of the housing using fully-coupled six-degree-
46、of-freedomcalculationsforbothinstances.8Figure 6. Predicted housing vibration due to gear mesh vibration, 400 NmFigure 7. Dynamic transmission error, 1st harmonic, first gear, 400 Nm, with and without thehousingFigure 8. CAE model of transaxle, 573 Hz mode: displacement, strain energy, and kinetic e
47、nergy;includes housing influence9Figure 9. Contact patterns, final drive gear mesh, 400 Nm, with (top) and without (bottom)housingThe implications of an incorrect contact patternanalysis may result in the specification ofunnecessary or overaggressive microgeometrymodifications, especially for higher
48、 loads as the dif-ference in mesh misalignment between housing/no-housing configurations increases as previouslyshown in Figure 3. As the gears are modified toaccommodate higher loads, often the contact atlighter loads is compromised, resulting inincreasedstatic transmission error and subsequently h
49、igherlevels of passenger compartment gear whine.DurabilityTraditionally, durability performance is the geardesigners first priority, and since this irrefutable,self-evident requirement has been in place for somany years, with an abundant of effort put forth bythousands of engineers and researchersworldwidefor more than one hundred years, it can be perplex-ing that gear failures are still all too common of anoccurrence. The practical issue facing gearboxdesign engineers is that the gearbox performance10requirements seem to consta
