AGMA-91FTM10-1991.pdf

91 FTM 10 v DynamicMeasurementsof Gear Tooth Frictionand Load by: B. Rebbechi,F. B. Oswald and D. P. Townsend NASA,Lewis ResearchCenter _A V , AmericanGear ManufacturersAssociation :_TECHNICAL PAPER Copyright American Gear Manufacturers Association Provided by IHS under license with AGMA Licensee=IHS Employees/1111111001, User=Wing, Bernie Not for Resale, 04/18/2007 11:53:51 MDTNo reproduction or networking permitted without license from IHS -,-,- Dynamic Measurementsof Gear Tooth Friction and Load B. Rebbechi, F. B. Oswald and D. Townsend NASA, Lewis Research Center TheStatements andopinionscontainedherein arethoseoftheauthorandshouldnotbeconstruedasan officialactionor opinion ofthe American GearManufacturers Association. ABSTRACT: A program to experimentallyand theoretically study fundamentalmechanisms of gear dynamic behavior is being conductedat the NASA Lewis Research Centerin supportof ajoint research program between NASA and the U. S. Army. Thispaperpresentstheresults ofdynamictooth-fillet straingage measurementsfromtheNASA gear-noiserig, andit inlroduces atechniqueforusingthese measurementsto separate thenormalandtangential(friction) components of the load at the tooth contact-_- Copyright © 1991 American Gear ManufacturersAssociation 1500 King Slreet, Suite 201 Alexandria,Virginia, 22314 October,1991 ISBN:1-55589-607-3 Copyright American Gear Manufacturers Association Provided by IHS under license with AGMA Licensee=IHS Employees/1111111001, User=Wing, Bernie Not for Resale, 04/18/2007 11:53:51 MDTNo reproduction or networking permitted without license from IHS -,-,- DynamicMeasurementsofGearToothFriction andLoad BrianRebbechl,FredB.Oswald,and DennisP.Townsend NationalAeronauticsandSpace Administration LewisResearchCenter Cleveland,Ohio44135 i.INTRODUCTIONproblems.AndersonandLowenthal4 com- putedoveralllossesduetofrictionand _Thedynamicforcesatthepointoffoundgoodagreementbetweentheoretical toothcontactareofconsiderableinterestpredictionsandexperimentaldata.Krantz tothedesignersofhigh-speed,light-andHandschuh5appliedasimilartech- weightgearing.Accuratepredictionoftheniquetoanepicyclicgearrig,obtaining dynamicloadscanassistinminimizingthegoodcorrelationatlowoiltemperatures, sizeandweightofatransmission.Inabutpoorercorrelationathigheroiltem- helicopterapplication,wherethetransmis-peratures.However,thistechniquecannot sionisasignificantfractionofvehicledetectthevariationinfrictionduringthe weight,suchareductionwouldbeanimpor-toothengagementcycle.Thereisalsothe tantfactorinoverallvehicleperformance,problemofseparatingthepowerlossdueto Aprogramtoexperimentallyandtheo-geartoothfrictionfrompowerlossesdue reticallystudyfundamentalmechanismsoftoothersourcessuchasbearings,windage, geardynamicbehaviorisbeingundertakenandsoforth. attheNASALewisResearchCenterinsup-Extensivemeasurementsoflubrication portofajointresearchprogrambetweenconditionsatasliding-rollingcontact NASAandtheU.S.Army.Thispaperpre-havebeencarriedoutondiskmachines6 . sentstheresultsofdynamictooth-filletTheseexperimentsareofconsiderablevalue straingagemeasurementsfromtheNASAinconfirmingtheexistenceofelastohydro- gear-noiserig,anditintroducesatech-dynamiclubricationandinidentifyingthe niqueforusingthesemeasurementstoseparateregimesoflubricationthatpre- separatethenormalandtangentialvailunderthevariousslide-to-roll (friction)componentsoftheloadattheratios.However,theusefulnessofthe toothcontact.Resolutionofthecontactmodesofbehaviorandfrictioncoefficients forceisdesirableforseveralreasons,inpredictinglubricationconditionsatan Twoofthesereasonsarethefollowing:actualtoothcontact,wherethedegreeof (I)Aprimaryoutputofanalyticalslidingchangesthroughoutthetooth modelsofgeardynamicbehavioristypi-engagementcycle(typicalduration, callythenormalforceatthepointof250_sec),needstobeverified.Inthis contact(e.g.,Iand2).shortperiodoftime,largechangesoccur (2)Themeasurementofdynamicinthelubricanttemperature,shear,and frictionofmeshinggearsdoesnotappearviscosityatpressuresupto1.4GPa tohaveyetbeencarriedoutsuccessfully.(200000ibf-in._).Dyson7reported Aninterestingtrialwascarriedouttemperaturesupto400°Candoscillatory AbyBenedictandKelly3,butitwasdis-shearratesuptol0 Tsec -IThesecon- continuedbecauseofdynamicresponseditionscannotreadilybeproducedoutside ofanactualtoothmesh. VisitingscientistfromAustralian AeronauticalResearchLaboratory. Copyright American Gear Manufacturers Association Provided by IHS under license with AGMA Licensee=IHS Employees/1111111001, User=Wing, Bernie Not for Resale, 04/18/2007 11:53:51 MDTNo reproduction or networking permitted without license from IHS -,-,- Frictionatthetoothcontactistooth-rootfilletsonboththeloaded importantfordeterminingnotonlypower(tensile)andunloaded(compression)side lossandefficiency,butalsoforunder-oftwoadjacentteethontheoutput standinggear-toothscoringandwear.An(driven)gear(Fig.4).Tomeasuremaximum importantparameterinscoringisthefric-toothbendingstress,thegageswereplaced_ tioncoefficient3.Frictiongreatlyatthe30 °tangencylocation9. affectstheheatinputtothelubricantStraingagesignalswereconditioned whenslidingvelocitiesarehigh.bytwomethods:forstaticcalibrationand Thisreportpresentsdynamic,gear-measurement,astraingage(Wheatstone) toothstrainmeasurementsfromlow-contact-bridgewasused;fordynamicmeasurements, ratiospurgearstestedintheNASAgear-thestraingageswereconnectedviaaslip- noiserlg.Thetechniqueusedtoconvertringassemblytoasetofconstant-current thesestrainmeasurementsintonormalandstraingageamplifiers. tangential(friction)toothloadsisA4-channel,14-bitdigitaldata described.Plotsofnormalandtangentialacquisitionsystemwasusedtorecordthe forces,forbothstaticanddynamiccondi-dynamicstraindata.Sampleratesof20to tions,arepresentedforarepresentative50kHzperchannelwereused,dependingon rangeofloadsandspeeds.Thenormaltestgearspeed. forceanddynamicstraindatahavebeenAnopticalencoderwasmountedonthe usedtoverifyageardynamicscodeininputshafttomeasurerollangleandhence anotherrelatedreport8.determineloadlocation;thepositionof theencoderwasadjustedsoitwouldpro- 2.APPARATUSduce1pulse/revolutionataknownroll angle. 2.1TestFacility 3.TESTPROCEDURE ThesetestswereconductedintheNASA Lewisgear-noiserig(Fig.i).Thisrig3.1Calibration comprisesasimplegearboxpoweredbya 150-kW(200-hp)variablespeedelectricCalibrationofthestraingagesonthe motor,withaneddy-currentdynamometerinstrumented(driven)gearwasconductedto thatloadstheoutputshaft.Thegearboxprovideamatrixofstrainoutputversus canbeoperatedatspeedsupto6000rpm.appliedload.Beforecommencingthestrain Therigwasbuilttocarryoutfundamentalgagecalibration,thegearsweredemagne- studiesofgearnoiseandofdynamictized.Thisdemagnetizationreducedthe behaviorofgearsystems.ItwasdesignedapparentstrainresultingfromthegagesA toallowtestingofvariousconfigurationsmovingthroughthemagneticfieldofthe ofgears,bearings,dampers,andsupports,adjacentgear.Atnormalgearoperating Apoly-Vbeltdriveservedasaspeedspeeds,magneticeffectscaninducean increaserbetweenthemotorandinputerrorsignalinthegage. shaft.AsoftcouplingwasinstalledonForcalibration,theinstrumentedgear theinputshafttoreduceinputtorquewasmeshedwithaspecialgearwhoseadja- fluctuationscausedbyanonuniformityofcentteethhadbeengroundaway;thisper- thebeltat thesplice,mittedloadingofa singletoothonly.The Testgearparametersareshownincalibrationwascarriedoutforeachofthe TableI,testrigparametersinTable2,twoinstrumentedteethforrollangles andgeartoothprofiletracesinFig.2.rangingfrom12 °to30 ° .Ateachtestpo- Thetoothsurfaceroughnesswasmeasuredbysition(rollangle)thetorquewasapplied usinganinvolute-gear-checkingmachineatthreelevels-45percent,88.5percent, withadiamondstylusofapproximatelyand132percentofthenominalvalueof 10-_m(0.0003-in.)radius.Thesurface71.8N-m(635in.-ib).Ateachofthese roughnessvariedalongthelengthoftheloadlevelstheslidingdirectionwas tooth,withtheregionneartherootreversed(byreversingrolldirection),and appearingtobelightlypolished.Thealinearcurvewasfittothedataforeach maximumsurfaceroughnesswasestimatedtoslidingdirection.Byreversingtheroll be1.3andsecond,toprovideinformation onloadsharingcharacteristicsofthegear assembly.Astraingagebridgecircuitwas usedtorecordstrainsforrollanglesfrom !2 °to40 °relative_otooth2.Torque levelsof37,88,I00,and!32percentwere app!ied_butunlikethesingle-toothcase, i_nearcurve-fittingofthesedatawasnot appropriatebecauseofthekinematicnon- lineari_iesintroducedbyloadsharingwhen morethanonepairofzeethareincontact. 8_-I_7c_Asforthesingie-too_hcase,thesemeas- urementswerecarriedouzfortheinstru- _qu_S.-S_n_a_r_m_.mendedgearactingasbo_hthedrivenand drivinggear,thusreversingthesliding 2000_,_D_vingge_direction. I_D_v_g_r3.2.2Dynamics_raindata.-Dynamic I_0 b_strainswererecordedforthe4gages,for -_aspeed-loadmatrixof28points:4speeds _orquelevels(16_31,47,63,79,94, _0and !0 percent of the nominal value of 71.8 N-m(635 in.-ib).The data were 0recordedby14-bitdatarecordersviaa (a)Gage2,_iles_in. _slip-ring assembly.S_Dlerates used were _50000Hzperchannelforthe2000-,4000-, _F_and6000-rDmspeeds,and20000Hzper _-1_o_-_channelforzhe800-rpmspeed.Acontinu- ._ousrecordtconsistingof!0000data _-1500scans,wasmadeateachspeedsoastogive arecordlengthof0.2sacat50000Hz, -_ooand 0.5 sac at 20 000 Hz.Because of the interestincomparingtensileandcom- _IIII_IIIDressivestrainsoneachtooth,datafrom 28_24_1816i_12 Roll_gle. d_thesetwogagesweresimultaneously recordedalongwith_heencodersignal. (b)Gage1,_mpr_si_s_in.Thisprocedurewasrepeatedforthesecond _gu_6.-S_¢s_-_n gage_m,sin_le_o_0aoinginstrumentedtooth. on_om 1(am_ws_owmil_on).Theda_awerethendigitally resa_pled,byusinglinearinterpolation, ateither!000or2000samplesperrevolu- D_vinggeart_OTM.(depend_nc_onspeed)andsynchronously 40| _“-:-. -Ddvenge_.averaged.Timedomainsynchronousaverag- _atechnicuenow_ideusein 20_._-“_- gear _diagnostics!0_,wasusedheretoreduce 01IIIIIIIIInoiseeffects(especiallyfromthetorque fluctuationcausedbythebeltdrive).Its (a)_age4._nsiles_in.implementationrequirestwodatachannels- C ionefortimingsignaldataandonefor o_-_._._straindata.Thetimingsignaldatapro- _videdresampleintervalsforexactlyone -15_ revolution. -,30282624_181614124.ANALYSI S Roll _gle,deg b)Gage3, compmssives_in.Forasingletooth,measurementofthe _gu_7.-Sm_cs_ingage_mme_u_d_o_2strainoutputsSandSofgages -_rsingl_o_loa_ngon _o_1 (_sshowrollmountedonthecompresslveandtensile direc_on),sidesofthetoothrespectively(Fig.4) -will,inprinciple,enableresolutionof thetoothforcesFn(normal)andFz Copyright American Gear Manufacturers Association Provided by IHS under license with AGMA Licensee=IHS Employees/1111111001, User=Wing, Bernie Not for Resale, 04/18/2007 11:53:51 MDTNo reproduction or networking permitted without license from IHS -,-,- (tangential),provldedthattheresponseof5.RESULTSANDDISCUSSION thesetwogagestothetwoforcesis linearlyindependent.Theresponseofthe5.1Calibration gagescanthenbeexpressedas Tooth-filletstrainsfor100-percent Sc = anF_ + az2Ff(4.1)torquewereevaluatedbyfittingalinear- curvetothecalibrationdataforthethree St =az_Fn +az2F f(4.2)torquelevels.ThesestrainsatgagesIto 4areplottedinFigs.6and7asafunc- tionofrollangle,forloadingoftoothI. orsimplyasNotablefrom thesecurvesis the signifi- cantinfluenceofstaticfrictiononstrain S =a_(4.3)output;thetensilegage(seeFig.6(a) showsadifferenceinstrainbetweenthe driving-anddriven-gearcases(whenslid- Iingdirectionreverses)thatis 27percent whereS =S¢ofthemeanstrainreading.Thesignifi- canceofthisistwofold:first,itis tdifficulttoestablisha“no-friction“ curve;andsecond,andpossiblymoreimpor- tant,thesecurves(particularlytheten- Fmilecurve)illustratetheeffectthat _=Fntoothfrictionhasontheresults.Itis apparentfromFig.6thatthecompressive fgageismuchlessinfluencedbyfriction and,thus,wouldbeexpectedtogivethe bestindicationofnormalforceifonlyone anda iisthestraininfluencecoeffi-gagewereused.Thisisfurtherconfirmed cient;_thatis,thestrainatiduetoa unitnormalforce(j=I)oraunitfric-bythetoothstraininfluencecoefficients tionforce(j=2).(seeAppendix). Thestraininfluencecoefficientsa±j5.2StaticMeshing areevaluatedbyalternatelysettingF andFfinequations(4.1)and(4.2)toMeasuredstrainisplottedinFig.8 zero.Inpractice,neitherFnorFI canactuallybezerobecauseannormalforceasafunctionofrollangleforstatic meshingofthegears(i.e.,formultiple- betweentheteethisaprerequisiteforatoothcontact)Thisfigureshowsthe slidingforcetodevelop.However,because strainvalueswererecordedforbothdirec-averagestrain(meanofdriving-and tionsofsliding(thatis,fortheinstru-driven-gearvalues)for37-,88-,I00-,and mentedgearactingasbothdrivingand132-percenttorque.Figure9showsin drivengear)ateachrollanglevalue,wegreaterdetailthetooth-filletstrainsfor inferredthattheaverageofthesetwo_ge2_ge4 strainvaluesisequivalenttothefric-2_0-_ml_m2_r_e_v_. tionlesscase,andthattheeffectoffric-/-_rc_lt et eo°w uos,coe.-,., ._-_ ficientsaz2anda22(whichrelatetoi_0 friction)areevaluatedfromhalfthe_._y, -_k_,_ differencebetweenthedrivinggearand5oo.“-_-_ Piiq drivengearcurvesofFig.6.Likewise,0 thestraincoefficientsa nanda2zIIJJJIJI (whichrelatetonormalforce)areeval-_(a)_a_d_nsiles_msi_of_om. uatedfromtheaverageofthesetwocurves. ThesolutionforFandF_isfound by premultiplyingbothnsidesofequation(4.3)m5_-_0m_ge11_mG_e32 bya-1;hence0 =E al-'(s(4.4)-=o Theanalysispresentedaboveignores_ytheinfluenceonstrainsSandStdue-I_0 toloadingonadjacentteeth.Inthecase-2_0k./JIJI_IIIJ ofthin-rimgearsII,thiseffectcanbe3230282624222018161412 ontheorderof12percent.Forthethick-RoUanglefor_oth2.deg rimgearsusedhere,however,theinfluence111111111 fromadjacentteethisatmost3percent2e _24_2018161412 (compareFigs.6and7).Inthedatapre-Rollang_f_oml.deg sentedinthispaper,theinfluenceof(b)Unl_dcompmssi_s_insi_oft_m. adjoiningteethhasbeenincluded.The computationalprocedureisoutlinedintheRgure 8.-Av_g_ sm_cs_indamon _0 _ccessive Appendix._“ Copyright American Gear Manufacturers Association Provided by IHS under license with AGMA Licensee=IHS Employees/1111111001, User=Wing, Bernie Not for Resale, 04/18/2007 11:53:51 MDTNo reproduction or networking permitted without license from IHS -,-,- gages1to4at100-percenttorque,withThetotalnormalforcebetweenthe theinstrumentedgearactingasbothdrivenone-ortwo-toothpairsinmeshshouldbe anddrivinggear.ThecurvesofFig.9areequalto1718N(386ibf).Thisvalueis theaveragedresultofthreetrials.Fromthetorquedividedbythebasecircle theresultsofFig.9,andtheinfluenceradius.Thenormal-forcecomponentofthe -coefficientmatrixpreviouslydescribed,plotsshowsagreementwithin1.5percentof plotsofnormalandfrictionforcestheexpectedvalue. (Fig.I0)havebeenderivedfromthestaticAnabsolutevalueforthefriction dataforthe100-percent-torquecase.forcecannotbedeterminedduringcalibra- tionsincethecoefficientoffrictionat 2_-D_vingge_thetoothcontactpoint