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1、外文原文:NATURALFREQUENCYVEERINGINPLANETARYGEARSABSTRACTToachievenoiseandvibrationreductioninplanetarygearapplications,keydesignparametersareoftenvariedtoavoidresonances,optimizeloaddistribution,andreduceweight.Intheplotsofnaturalfrequenciesversusplanetarygearparameters,veeringphenomenaoccur
2、whentwoeigenvaluelociapproacheachother,butthenabruptlyveeraway.Theimportanceofveeringismanifestedinthedramaticchangesinthevibrationmodesoftheveeringnaturalfrequenciesandtheconsequentimpactonresponse.Thisworkanalyticallycharacterizestherulesofeigenvalueveeringinplanetarygears.Thecouplingf
3、actorsbetweentwocloseeigenvaluelociareapproximatedbyperturbationanalysis・Specialveeringpatternswereobtainedusingtheuniquepropertiesofplanetarygearvibrationmodes.Theresultsareillustratedbyanexample.Keydesignparameterswereinvestigated,andgeneralizedguidanceisprovidedfortuningplanetarygearn
4、aturalfrequencies.I.INTRODUCTIONNoiseandvibrationreductionarecriticalconcernsinplanetarygearapplications.Duringthedesignprocess,systemparametersarevariedtoevaluatealternativedesignchoices,avoidresonances,optimizeloaddistribution,andreduceweight.Itisimportanttocharacterizetheeffectsofpara
5、metervariationsonthenaturalfrequenciesandvibrationmodesforeffectivevibrationtuning.Inplanetarygeardynamicmodels(Fig.1),thekeydesignparametersincludethemeshstiffnesses,support/bearingstiffnesses,componentmasses,andmomentsofinertia.Someplotsofnaturalfrequenciesversusplanetarygearparameters
6、arepresentedbyCunlifleetal.[1],Botman[2]?Kahraman[3,4],andSaadaandVelex[5].Naturalfrequencyplotsinthesestudies,especiallyRef.3,shownaturalfrequencyveeringphenomenawhentwoeigenvaluelociapproacheachotherasaparameterisvaried,butthenabruptlyveerawayliketwosimilarchargesrepelling(pointBinFig.
7、2a)・Thevibrationmodesoftheveeringeigenvaluesarcstronglycoupledandundergodramaticchangesintheveeringneighborhood.Thephenomenonhasbeenstudiedextensively[6—9],butithasnotbeenexploredinplanetarygears.Eigenvalueveeringisalsorelatedtomodelocalizationthatcanoccurwhendisorderisin
