外文翻译--行星齿轮固有频率-精品_精品文档Word格式文档下载.doc

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附录@#@附录1@#@英文原文@#@NATURALFREQUENCYVEERINGINPLANETARYGEARS@#@ABSTRACT@#@Toachievenoiseandvibrationreductioninplanetarygearapplications,keydesignparametersareoftenvariedtoavoidresonances,optimizeloaddistribution,andreduceweight.Intheplotsofnaturalfrequenciesversusplanetarygearparameters,veeringphenomenaoccurwhentwoeigenvaluelociapproacheachother,butthenabruptlyveeraway.Theimportanceofveeringismanifestedinthedramaticchangesinthevibrationmodesoftheveeringnaturalfrequenciesandtheconsequentimpactonresponse.Thisworkanalyticallycharacterizestherulesofeigenvalueveeringinplanetarygears.Thecouplingfactorsbetweentwocloseeigenvaluelociareapproximatedbyperturbationanalysis.Specialveeringpatternswereobtainedusingtheuniquepropertiesofplanetarygearvibrationmodes.Theresultsareillustratedbyanexample.Keydesignparameterswereinvestigated,andgeneralizedguidanceisprovidedfortuningplanetarygearnaturalfrequencies.@#@I.INTRODUCTION@#@Noiseandvibrationreductionarecriticalconcernsinplanetarygearapplications.Duringthedesignprocess,systemparametersarevariedtoevaluatealternativedesignchoices,avoidresonances,optimizeloaddistribution,andreduceweight.Itisimportanttocharacterizetheeffectsofparametervariationsonthenaturalfrequenciesandvibrationmodesforeffectivevibrationtuning.Inplanetarygeardynamicmodels（Fig.1）,thekeydesignparametersincludethemeshstiffnesses,support/bearingstiffnesses,componentmasses,andmomentsofinertia.SomeplotsofnaturalfrequenciesversusplanetarygearparametersarepresentedbyCunliffeetal.[1],Botman[2],Kahraman[3,4],andSaadaandVelex[5].@#@Naturalfrequencyplotsinthesestudies,especiallyRef.3,shownatural@#@@#@frequencyveeringphenomenawhentwoeigenvaluelociapproacheachotherasaparameterisvaried,butthenabruptlyveerawayliketwosimilarchargesrepelling（pointBinFig.2a）.Thevibrationmodesoftheveeringeigenvaluesarestronglycoupledandundergodramaticchangesintheveeringneighborhood.Thephenomenonhasbeenstudiedextensively[6–9],butithasnotbeenexploredinplanetarygears.Eigenvalueveeringisalsorelatedtomodelocalizationthatcanoccurwhendisorderisintroducedintonominallysymmetricsystemsliketurbineblades,spaceantennae,multispanbeams,andotherstructures[6].Inthecaseofespeciallysharpveering,itissometimesdifficulttodistinguishbetweenintersectionandveeringjustbyobservingeigenvalueplots.Curveveering/crossingcomplexityobstructsthetracingofeigenvaluelociunderparameterchanges.Also,whenmultiplecurvesveerorintersectclosetogether（Fig.3）,strongmodalcouplingandtheassociatedoperatingconditionresponsechangesthatoccurarenotidentifiablefromfrequencylociplots.@#@Theobjectivesofthisworkweretwofold.Thefirstwastoanalyticallyderivesimplerulesthatpredicteigenvalueveeringinplanetarygears.Thesecondwastousetheveeringresults,alongwithpreviouslydevelopedmodalpropertiesandeigensensitivityanalysis,todefinemorefullytheinfluenceofmodelparametersonfreevibrationandtogiveguidancefortuningnaturalfrequencies.LinandParker[10,11]analyticallycharacterizedtheunique,highlystructuredpropertiesofplanetarygearnaturalfrequencyspectraandvibrationmodes.Theyalsoprovidedsimple,closed-formexpressionsforthesensitivitiesofnaturalfrequenciesandvibrationmodestodesignparameters[12].Theseanalyticalresultsprovidethenecessaryfoundationforthepresentstudyofveeringrulesinplanetarygears.Theveeringrulesyieldconcreteconclusionsexpressedinsimpleformsforwhentwoapproachingeigenvaluesveerorcross.Theimportanceoftheveeringrulesistoidentifythoserangesinwhichsmallchangesindesignparameterscandramaticallychangethevibrationmodesandconsequentlytheresponse.Theresultsareillustratedonabenchmarkplanetarygear（themodelparametersandnaturalfrequenciesaregiveninTables1and2,respectively）usedinahelicopterpowertrain.@#@ThelumpedparametermodelderivedinRef.10isusedhere.ThemodelisapplicableforgeneralepicyclicgearswithNplanets.Eachcomponenthastwotranslationalandonerotationaldegreeoffreedom（DOF）inplanarmotion,sothesystemhasL=3（N-3）DOF.Numericalresultspresentedareforfixedringconfigurations,andL=3（N-2）inthiscase.Theassociatedeigenvalueproblemis@#@II.VEERING/CROSSINGCRITERION@#@Amethodfordetectingeigenvalueveering/crossingingeneraldynamicsystemsisintroducedhere.PointBinFig.2aisanexampleofveering.Whentwoeigenvaluelociveeraway,theirlocicurvaturesindicatetheabruptnessofcurvedirectionchanges.PerkinsandMote[7]proposedavee