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1、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=IH
2、S 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 andopinionsc
3、ontainedherein 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 suppo
4、rtof 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 cont
5、act-_- 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 R
6、esale, 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.INTRODUCTIONproblem
7、s.AndersonandLowenthal4 com- putedoveralllossesduetofrictionand _Thedynamicforcesatthepointoffoundgoodagreementbetweentheoretical toothcontactareofconsiderableinterestpredictionsandexperimentaldata.Krantz tothedesignersofhigh-speed,light-andHandschuh5appliedasimilartech- weightgearing.Accuratepredic
8、tionoftheniquetoanepicyclicgearrig,obtaining dynamicloadscanassistinminimizingthegoodcorrelationatlowoiltemperatures, sizeandweightofatransmission.Inabutpoorercorrelationathigheroiltem- helicopterapplication,wherethetransmis-peratures.However,thistechniquecannot sionisasignificantfractionofvehiclede
9、tectthevariationinfrictionduringthe weight,suchareductionwouldbeanimpor-toothengagementcycle.Thereisalsothe tantfactorinoverallvehicleperformance,problemofseparatingthepowerlossdueto Aprogramtoexperimentallyandtheo-geartoothfrictionfrompowerlossesdue reticallystudyfundamentalmechanismsoftoothersourc
10、essuchasbearings,windage, geardynamicbehaviorisbeingundertakenandsoforth. attheNASALewisResearchCenterinsup-Extensivemeasurementsoflubrication portofajointresearchprogrambetweenconditionsatasliding-rollingcontact NASAandtheU.S.Army.Thispaperpre-havebeencarriedoutondiskmachines6 . sentstheresultsofdy
11、namictooth-filletTheseexperimentsareofconsiderablevalue straingagemeasurementsfromtheNASAinconfirmingtheexistenceofelastohydro- gear-noiserig,anditintroducesatech-dynamiclubricationandinidentifyingthe niqueforusingthesemeasurementstoseparateregimesoflubricationthatpre- separatethenormalandtangential
12、vailunderthevariousslide-to-roll (friction)componentsoftheloadattheratios.However,theusefulnessofthe toothcontact.Resolutionofthecontactmodesofbehaviorandfrictioncoefficients forceisdesirableforseveralreasons,inpredictinglubricationconditionsatan Twoofthesereasonsarethefollowing:actualtoothcontact,w
13、herethedegreeof (I)Aprimaryoutputofanalyticalslidingchangesthroughoutthetooth modelsofgeardynamicbehavioristypi-engagementcycle(typicalduration, callythenormalforceatthepointof250_sec),needstobeverified.Inthis contact(e.g.,Iand2).shortperiodoftime,largechangesoccur (2)Themeasurementofdynamicinthelub
14、ricanttemperature,shear,and frictionofmeshinggearsdoesnotappearviscosityatpressuresupto1.4GPa tohaveyetbeencarriedoutsuccessfully.(200000ibf-in._).Dyson7reported Aninterestingtrialwascarriedouttemperaturesupto400Candoscillatory AbyBenedictandKelly3,butitwasdis-shearratesuptol0 Tsec -IThesecon- conti
15、nuedbecauseofdynamicresponseditionscannotreadilybeproducedoutside ofanactualtoothmesh. VisitingscientistfromAustralian AeronauticalResearchLaboratory. Copyright American Gear Manufacturers Association Provided by IHS under license with AGMA Licensee=IHS Employees/1111111001, User=Wing, Bernie Not fo
16、r 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
17、 standinggear-toothscoringandwear.An(driven)gear(Fig.4).Tomeasuremaximum importantparameterinscoringisthefric-toothbendingstress,thegageswereplaced_ tioncoefficient3.Frictiongreatlyatthe30 tangencylocation9. affectstheheatinputtothelubricantStraingagesignalswereconditioned whenslidingvelocitiesarehi
18、gh.bytwomethods:forstaticcalibrationand Thisreportpresentsdynamic,gear-measurement,astraingage(Wheatstone) toothstrainmeasurementsfromlow-contact-bridgewasused;fordynamicmeasurements, ratiospurgearstestedintheNASAgear-thestraingageswereconnectedviaaslip- noiserlg.Thetechniqueusedtoconvertringassembl
19、ytoasetofconstant-current thesestrainmeasurementsintonormalandstraingageamplifiers. tangential(friction)toothloadsisA4-channel,14-bitdigitaldata described.Plotsofnormalandtangentialacquisitionsystemwasusedtorecordthe forces,forbothstaticanddynamiccondi-dynamicstraindata.Sampleratesof20to tions,arepr
20、esentedforarepresentative50kHzperchannelwereused,dependingon rangeofloadsandspeeds.Thenormaltestgearspeed. forceanddynamicstraindatahavebeenAnopticalencoderwasmountedonthe usedtoverifyageardynamicscodeininputshafttomeasurerollangleandhence anotherrelatedreport8.determineloadlocation;thepositionof th
21、eencoderwasadjustedsoitwouldpro- 2.APPARATUSduce1pulse/revolutionataknownroll angle. 2.1TestFacility 3.TESTPROCEDURE ThesetestswereconductedintheNASA Lewisgear-noiserig(Fig.i).Thisrig3.1Calibration comprisesasimplegearboxpoweredbya 150-kW(200-hp)variablespeedelectricCalibrationofthestraingagesonthe
22、motor,withaneddy-currentdynamometerinstrumented(driven)gearwasconductedto thatloadstheoutputshaft.Thegearboxprovideamatrixofstrainoutputversus canbeoperatedatspeedsupto6000rpm.appliedload.Beforecommencingthestrain Therigwasbuilttocarryoutfundamentalgagecalibration,thegearsweredemagne- studiesofgearn
23、oiseandofdynamictized.Thisdemagnetizationreducedthe behaviorofgearsystems.ItwasdesignedapparentstrainresultingfromthegagesA toallowtestingofvariousconfigurationsmovingthroughthemagneticfieldofthe ofgears,bearings,dampers,andsupports,adjacentgear.Atnormalgearoperating Apoly-Vbeltdriveservedasaspeedsp
24、eeds,magneticeffectscaninducean increaserbetweenthemotorandinputerrorsignalinthegage. shaft.AsoftcouplingwasinstalledonForcalibration,theinstrumentedgear theinputshafttoreduceinputtorquewasmeshedwithaspecialgearwhoseadja- fluctuationscausedbyanonuniformityofcentteethhadbeengroundaway;thisper- thebel
25、tat thesplice,mittedloadingofa singletoothonly.The Testgearparametersareshownincalibrationwascarriedoutforeachofthe TableI,testrigparametersinTable2,twoinstrumentedteethforrollangles andgeartoothprofiletracesinFig.2.rangingfrom12 to30 .Ateachtestpo- Thetoothsurfaceroughnesswasmeasuredbysition(rollan
26、gle)thetorquewasapplied usinganinvolute-gear-checkingmachineatthreelevels-45percent,88.5percent, withadiamondstylusofapproximatelyand132percentofthenominalvalueof 10-_m(0.0003-in.)radius.Thesurface71.8N-m(635in.-ib).Ateachofthese roughnessvariedalongthelengthoftheloadlevelstheslidingdirectionwas too
27、th,withtheregionneartherootreversed(byreversingrolldirection),and appearingtobelightlypolished.Thealinearcurvewasfittothedataforeach maximumsurfaceroughnesswasestimatedtoslidingdirection.Byreversingtheroll be1.3andsecond,toprovideinformation onloadsharingcharacteristicsofthegear assembly.Astraingage
28、bridgecircuitwas usedtorecordstrainsforrollanglesfrom !2 to40 relative_otooth2.Torque levelsof37,88,I00,and!32percentwere app!ied_butunlikethesingle-toothcase, i_nearcurve-fittingofthesedatawasnot appropriatebecauseofthekinematicnon- lineari_iesintroducedbyloadsharingwhen morethanonepairofzeetharein
29、contact. 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-loa
30、dmatrixof28points: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
31、 _-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.
32、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!000or2000samplesperr
33、evolu- 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.im
34、plementationrequirestwodatachannels- 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
35、_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
36、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.Theresponseofthe5.1Calibra
37、tion gagescanthenbeexpressedas Tooth-filletstrainsfor100-percent Sc = anF_ + az2Ff(4.1)torquewereevaluatedbyfittingalinear- curvetothecalibrationdataforthethree St =az_Fn +az2F f(4.2)torquelevels.ThesestrainsatgagesIto 4areplottedinFigs.6and7asafunc- tionofrollangle,forloadingoftoothI. orsimplyasNot
38、ablefrom thesecurvesis the signifi- cantinfluenceofstaticfrictiononstrain S =a_(4.3)output;thetensilegage(seeFig.6(a) showsadifferenceinstrainbetweenthe driving-anddriven-gearcases(whenslid- Iingdirectionreverses)thatis 27percent whereS =Softhemeanstrainreading.Thesignifi- canceofthisistwofold:first
39、,itis tdifficulttoestablisha“no-friction“ curve;andsecond,andpossiblymoreimpor- tant,thesecurves(particularlytheten- Fmilecurve)illustratetheeffectthat _=Fntoothfrictionhasontheresults.Itis apparentfromFig.6thatthecompressive fgageismuchlessinfluencedbyfriction and,thus,wouldbeexpectedtogivethe best
40、indicationofnormalforceifonlyone anda iisthestraininfluencecoeffi-gagewereused.Thisisfurtherconfirmed cient;_thatis,thestrainatiduetoa unitnormalforce(j=I)oraunitfric-bythetoothstraininfluencecoefficients tionforce(j=2).(seeAppendix). Thestraininfluencecoefficientsaj5.2StaticMeshing areevaluatedbyal
41、ternatelysettingF andFfinequations(4.1)and(4.2)toMeasuredstrainisplottedinFig.8 zero.Inpractice,neitherFnorFI canactuallybezerobecauseannormalforceasafunctionofrollangleforstatic meshingofthegears(i.e.,formultiple- betweentheteethisaprerequisiteforatoothcontact)Thisfigureshowsthe slidingforcetodevel
42、op.However,because strainvalueswererecordedforbothdirec-averagestrain(meanofdriving-and tionsofsliding(thatis,fortheinstru-driven-gearvalues)for37-,88-,I00-,and mentedgearactingasbothdrivingand132-percenttorque.Figure9showsin drivengear)ateachrollanglevalue,wegreaterdetailthetooth-filletstrainsfor i
43、nferredthattheaverageofthesetwo_ge2_ge4 strainvaluesisequivalenttothefric-2_0-_ml_m2_r_e_v_. tionlesscase,andthattheeffectoffric-/-_rc_lt et eow uos,coe.-,., ._-_ ficientsaz2anda22(whichrelatetoi_0 friction)areevaluatedfromhalfthe_._y, -_k_,_ differencebetweenthedrivinggearand5oo.“-_-_ Piiq drivenge
44、arcurvesofFig.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 Theanalysisprese
45、ntedaboveignores_ytheinfluenceonstrainsSandStdue-I_0 toloadingonadjacentteeth.Inthecase-2_0k./JIJI_IIIJ ofthin-rimgearsII,thiseffectcanbe3230282624222018161412 ontheorderof12percent.Forthethick-RoUanglefor_oth2.deg rimgearsusedhere,however,theinfluence111111111 fromadjacentteethisatmost3percent2e _2
46、4_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 Associatio
47、n 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 theinstrumentedgearactingasbothd
48、rivenone-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