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1、附录附录1英文原文NATURALFREQUENCYVEERINGINPLANETARYGEARSABSTRACTToachievenoiseandvibrationreductioninplanetarygearapplications,keydesignparametersareoftenvariedtoavoidresonances,optimizeloaddistribution,andreduceweight.Intheplotsofnaturalfrequenciesversusplanetarygearparamete
2、rs,veeringphenomenaoccurwhentwoeigenvaluelociapproacheachother,butthenabruptlyveeraway.Theimportanceofveeringismanifestedinthedramaticchangesinthevibrationmodesoftheveeringnaturalfrequenciesandtheconsequentimpactonresponse.Thisworkanalyticallycharacterizestherulesofei
3、genvalueveeringinplanetarygears.Thecouplingfactorsbetweentwocloseeigenvaluelociareapproximatedbyperturbationanalysis.Specialveeringpatternswereobtainedusingtheuniquepropertiesofplanetarygearvibrationmodes.Theresultsareillustratedbyanexample.Keydesignparameterswereinve
4、stigated,andgeneralizedguidanceisprovidedfortuningplanetarygearnaturalfrequencies.I.INTRODUCTIONNoiseandvibrationreductionarecriticalconcernsinplanetarygearapplications.Duringthedesignprocess,systemparametersarevariedtoevaluatealternativedesignchoices,avoidresonances,
5、optimizeloaddistribution,andreduceweight.Itisimportanttocharacterizetheeffectsofparametervariationsonthenaturalfrequenciesandvibrationmodesforeffectivevibrationtuning.Inplanetarygeardynamicmodels(Fig.1),thekeydesignparametersincludethemeshstiffnesses,support/bearingst
6、iffnesses,componentmasses,andmomentsofinertia.SomeplotsofnaturalfrequenciesversusplanetarygearparametersarepresentedbyCunliffeetal.[1],Botman[2],Kahraman[3,4],andSaadaandVelex[5].Naturalfrequencyplotsinthesestudies,especiallyRef.3,shownaturalfrequencyveeringphenomenaw
7、hentwoeigenvaluelociapproacheachotherasaparameterisvaried,butthenabruptlyveerawayliketwosimilarchargesrepelling(pointBinFig.2a).Thevibrationmodesoftheveeringeigenvaluesarestronglycoupledandundergodramaticchangesintheveeringneighborhood.Thephenomenonhasbeenstudiedexten
8、sively[6–9],butithasnotbeenexploredinplanetarygears.Eigenvalueveeringisalsorelatedtomodelocalizationthatcanoccurwhendisorder
