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外文翻译--行星齿轮固有频率.doc

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外文翻译--行星齿轮固有频率.doc

附录附录1英文原文NATURALFREQUENCYVEERINGINPLANETARYGEARSABSTRACTToachievenoiseandvibrationreductioninplanetarygearapplications,keydesignparametersareoftenvariedtoavoidresonances,optimizeloaddistribution,andreduceweight.Intheplotsofnaturalfrequenciesversusplanetarygearparameters,veeringphenomenaoccurwhentwoeigenvaluelociapproacheachother,butthenabruptlyveeraway.Theimportanceofveeringismanifestedinthedramaticchangesinthevibrationmodesoftheveeringnaturalfrequenciesandtheconsequentimpactonresponse.Thisworkanalyticallycharacterizestherulesofeigenvalueveeringinplanetarygears.Thecouplingfactorsbetweentwocloseeigenvaluelociareapproximatedbyperturbationanalysis.Specialveeringpatternswereobtainedusingtheuniquepropertiesofplanetarygearvibrationmodes.Theresultsareillustratedbyanexample.Keydesignparameterswereinvestigated,andgeneralizedguidanceisprovidedfortuningplanetarygearnaturalfrequencies.I.INTRODUCTIONNoiseandvibrationreductionarecriticalconcernsinplanetarygearapplications.Duringthedesignprocess,systemparametersarevariedtoevaluatealternativedesignchoices,avoidresonances,optimizeloaddistribution,andreduceweight.Itisimportanttocharacterizetheeffectsofparametervariationsonthenaturalfrequenciesandvibrationmodesforeffectivevibrationtuning.InplanetarygeardynamicmodelsFig.1,thekeydesignparametersincludethemeshstiffnesses,support/bearingstiffnesses,componentmasses,andmomentsofinertia.SomeplotsofnaturalfrequenciesversusplanetarygearparametersarepresentedbyCunliffeetal.1,Botman2,Kahraman3,4,andSaadaandVelex5.Naturalfrequencyplotsinthesestudies,especiallyRef.3,shownaturalfrequencyveeringphenomenawhentwoeigenvaluelociapproacheachotherasaparameterisvaried,butthenabruptlyveerawayliketwosimilarchargesrepellingpointBinFig.2a.Thevibrationmodesoftheveeringeigenvaluesarestronglycoupledandundergodramaticchangesintheveeringneighborhood.Thephenomenonhasbeenstudiedextensively6–9,butithasnotbeenexploredinplanetarygears.Eigenvalueveeringisalsorelatedtomodelocalizationthatcanoccurwhendisorderisintroducedintonominallysymmetricsystemsliketurbineblades,spaceantennae,multispanbeams,andotherstructures6.Inthecaseofespeciallysharpveering,itissometimesdifficulttodistinguishbetweenintersectionandveeringjustbyobservingeigenvalueplots.Curveveering/crossingcomplexityobstructsthetracingofeigenvaluelociunderparameterchanges.Also,whenmultiplecurvesveerorintersectclosetogetherFig.3,strongmodalcouplingandtheassociatedoperatingconditionresponsechangesthatoccurarenotidentifiablefromfrequencylociplots.Theobjectivesofthisworkweretwofold.Thefirstwastoanalyticallyderivesimplerulesthatpredicteigenvalueveeringinplanetarygears.Thesecondwastousetheveeringresults,alongwithpreviouslydevelopedmodalpropertiesandeigensensitivityanalysis,todefinemorefullytheinfluenceofmodelparametersonfreevibrationandtogiveguidancefortuningnaturalfrequencies.LinandParker10,11analyticallycharacterizedtheunique,highlystructuredpropertiesofplanetarygearnaturalfrequencyspectraandvibrationmodes.Theyalsoprovidedsimple,closedformexpressionsforthesensitivitiesofnaturalfrequenciesandvibrationmodestodesignparameters12.Theseanalyticalresultsprovidethenecessaryfoundationforthepresentstudyofveeringrulesinplanetarygears.Theveeringrulesyieldconcreteconclusionsexpressedinsimpleformsforwhentwoapproachingeigenvaluesveerorcross.Theimportanceoftheveeringrulesistoidentifythoserangesinwhichsmallchangesindesignparameterscandramaticallychangethevibrationmodesandconsequentlytheresponse.TheresultsareillustratedonabenchmarkplanetarygearthemodelparametersandnaturalfrequenciesaregiveninTables1and2,respectivelyusedinahelicopterpowertrain.ThelumpedparametermodelderivedinRef.10isusedhere.ThemodelisapplicableforgeneralepicyclicgearswithNplanets.EachcomponenthastwotranslationalandonerotationaldegreeoffreedomDOFinplanarmotion,sothesystemhasL3N3DOF.Numericalresultspresentedareforfixedringconfigurations,andL3N2inthiscase.Theassociatedeigenvalueproblemis

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