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外文翻译--应用参数动力学研究蜗杆与蜗轮的旋转角度.doc

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外文翻译--应用参数动力学研究蜗杆与蜗轮的旋转角度.doc

翻译部分英文原文ParametricstudyofdynamicsofwormandwormgearsetundersuddenlyappliedrotatingangleM.Y.Chung,D.ShawDepartmentofPowerMechanicalEngineering,NationalTsingHuaUniversity,No.101KungFuRoadSectionII,HsinChu,Taiwan,ROCReceived13September2006receivedinrevisedform23January2007accepted25February2007Availableonline17April2007AbstractThedynamicsofawormgearsetunderinstantlyappliedrotatingangleareaffectedbyseveralfactorsincludingthefrictionforceandelasticdeformationofthesurfacebetweengearteeth.Itisfoundthatthosefactorscauseanonnegligiblerotationalpositioningerror.Thegoalsofthisstudyareto1setupamathematicmodel,2carryoutanumericalsimulation,and3carryoutanexperimentandcompareitwiththenumericalresults.Theexperimentsandnumericalresultshaveverygoodagreement.Inthisresearch,themomentinertiaofflywheel,friction,rigidityofshaftandrigidityofgeartootharealsostudied.Theresultscanbeusedaserrorestimationsofrelevantangles,angularspeedandangularaccelerationunderasuddenlyappliedrotationalangle,andareusefulforestablishingtheerrorcompensationrequiredforpositioncontrol.1.IntroductionWhenradartracksanaircraftwhichturnsatasharpangletheradarmaynotbeabletolockontothetargetduetothesmalloscillationoftheantenna.Sometimes,theoscillationevencausesafailureoftheradarsystem.Accuratepositioningisacrucialsubjectinatrackingsystem.However,duetothedesignofthetrackingtransmissionmechanismisrestrictedbybothspaceandweight,thevolumeandtheweightofthetransmissionmechanismmustbelimited.Thewormgearsetisagoodchoiceduetoitssmallvolumeandhighreductionratio.Owingtotheoscillationoftheantennaisanimportantdynamicsbehaviorforhighprecisionpositioningofradarsystem,thedynamicsofawormgearsetunderinstantlyappliedlargetorqueisveryimportanttounderstandthisbehavior.Thisbehaviorisaffectedbyseveralfactorsincludingthefrictionforceandelasticdeformationofthesurfacebetweengearteeth.Tounderstandtheeffectofthosefactors,alotofresearchhasbeenconducted.YukselandKahraman1studiedthein.uenceofsurfacewearonthedynamicbehaviorofatypicalplanetarygearset.ThewearmodelemployedaquasistaticgearcontactmodeltocomputecontactpressuresandArchardswearmodeltodeterminetheweardepthdistributions.Parkeretal.2analyzedthedynamicresponseofaspurpairofawiderangeofoperatingspeedsandtorques.Comparisonsweremadetootherresearcherspublishedexperimentsthatrevealcomplexnonlinearphenomena.Thedynamicresponseofaspurpairwasinvestigatedusinga.niteelement/contactmechanicsmodelthatofferssigni.cantadvantagesfordynamicgearanalyses.Maliha3createdanonlineardynamicmodelofaspurgearpair,whichwascoupledwithlinear.niteelementmodelsoftheshaftscarryingthem,andwithdiscretemodelsofbearingsanddisks.Theexcitationsconsideredinthemodelwereexternalstatictorqueandinternalexcitationcausedbymeshstiffnessvariation,gearerrorsandgeartoothpro.lemodi.cation.Britton4producedasuper.nishedgearteethwithaapproximately0.05mmRaFilmandthefrictiontractionintheexperimentsweresimulatedtheoreticallyusingathin.lmnonNewtonianmicroelastohydrodynamiclubricationsolverandencouragingagreementbetweenfrictionmeasurementsandtheoreticalpredictionswasobtained.Kong5predictedelasticcontactandelastohydrodynamic.lmthicknessinwormgears.Usingtheundeformedgeometryofthegapbetweengearteethincontactathreedimensionalelasticcontactsimulationtechniquehadbeendevelopedforcalculationofthetrueareaofelasticcontactunderloadrelativethewheelandwormsurfaces.Tuttle6studiedtheharmonicdrives,whichexhibitedverynonlineardynamicbehavior,inhismodelnotonlydynamicmodelsincludeaccuraterepresentationoftransmissionfriction,complianceandkinematicalerrorwereunderstand,butalsoimportantfeaturesofharmonicdrivegeartoothgeometryandinteraction.Experimentalobservationswereusedtoguidethedevelopmentofamodeltodescribeharmonicdriveoperation.Itisimportanttobeawarethatwormgearperformanceisin.uencedbythelubricantappliedandmaintained.Helouvry7discussedtheissueoftheservoorientationcontrolbeingaffectedbyasurgeofbothmaximumstaticfrictionforceanddynamicfrictionforce.Theyreportedtheoccurrenceofastablepositioningerror,aswellasthestoppingorstokingduringtrackingattheturningpointofalimitingloopofthetrackingsystem.Whenthesystemwasinaonedirectionallowspeedtracking,itwaspossibleforthestick–slipphenomenontooccurduetothefactthatthefrictionalforcetovelocitycurveappearstobeanegativeslopeandin.uencesthestaticfrictionforce.Itwasalsofoundthatasimilarphenomenonoccursathighspeedtracking.Doupont8proposedafrictionalforcemodelwithnegativeslope.Inthereference,relativemotionfromstatictohighspeedslidingwasdividedintofourstages.Inthe.rststage,theexternalforcewaslessthanthemaximumstaticfrictionforce.Inthesecondstage,twocontactingsurfacesstartedtodevelopasmallrelativevelocity.Inthethirdstage,therelativevelocitystartedtoincreasebetweentwoobjects,andlubricantgotintothecontactareaanddecreasedthefrictionalforce.Inthefourthstage,thelubricanthadfully.lledthecontactarea,andtheviscouscharacteristicandthefrictionalforceincreasedwiththevelocity.Oguridesignhandbook9includedseveralempiricalchartsandcalculationformulaeofthefrictioncoef.cientvs.slidingvelocity,theallowableerrorofmanufacturing,therecommendedvalueforthegapsbetweentwoteeth,andtheallowablecontactpressure.Shigley10discussedthewormspitchcirclelinevelocityaswellasthetransmissionfrictionalcoef.cient.Inthisstudy,onlythefrictionforceandelasticdeformationofthesurfacebetweengearteethareinterested.TheZKtypewormgearsetisusedtoeliminatethebacklash.Previousresearchworksongearsandgearsetswerefocusedonthelimitingloading,pressuredistributionandallowablepressureloadingofgears,andontherelationshipbetweenfrictioncoef.cientandslidingvelocity.Mostinvestigationsarebaseontheassumptionthatthetoothisrigid.Thisstudyisfocusedontheeffectsoftheelasticdeformationofthegeartoothsurfaceandthenonlinearfrictioncoef.cientonthesystemdynamics.Tostudythedynamicsofthewormgearset,adynamicmodelofthewormgearsetisdevelopedandthecomparisonbetweentheexperimentalresultsandthenumericalresultsisalsostudied.Theparametersofthedynamicmodelareadjustedbythe.ndingsofthecomparisonoftheanalysisandtheexperiment.Finally,theeffectsofmomentinertiaof.ywheel,friction,rigidityofshaftandrigidityofgeartoothonthenonlinearbehaviorofthetransmissionmechanismarealsostudied.2.Thedynamicmodelsofthewormgearset2.1.TheequilibriumequationsofthewormandwormgearsetThegeometricofwormgearsetisshowninFig.1.Thereareaworm,awormgear,twoshafts,fourbearingsanda.ywheel.Theshaftofwormisdrivenbyanangley1.Therotationalangleofthe.ywheelisy4.Therotationalangleofthewormsbodyisy2duetotheelasticdeformationofthewormshafty16¼y2.Therotationangleofwormgearbodyisy3.ThemomentofinertiaofthewormisJw.Thepitchradiusofthewormshelicaltoothisrw.ThewormsrotationalinertiaasarigidbodyisJg.Thepitchradiusofthewormgearisrg.Themomentinertiaofthe.ywheelisJ4.Inthisstudy,toneglecttheeffectofbacklash,ZKtypewormandwormgearareusedbothinanalysisandexperiment.Tosimplifythetheoreticalmodel,thebasicassumptionsarelistedasfollows1The.ywheelisrigid.2Thewormsandwormgearteethareelastic.3Thebodyofthewormgearisrigid.4Wormandwormgearareperpendiculartoeachother.5Theclearancebetweenteethisignored.6Noerroronthegeartoothpro.le.7Thewormissinglethread.8Thewormshaftandwormgearshaftaretworotationalspring.Thedynamicbehaviorisneglected.9Translationaldegreeoffreedomforalltheelementsisnotconsidered.10Onlyfrictionisconsidered,nootherdampingeffectisconsidered.2.2.Theaxialspringconstantofbearings,wormshaftandwormgearshaftTheresultsofexperimentto.ndtherelationbetweenloadandtheaxialdisplacementofbearingareshowninFig.2.TheaxialspringconstantofwormbearingKbTwsandwormgearbearingKbTgsareobtainedbyusingFig.2.Furthermore,KLwsandKbTwscanbetreatastwoseriesconnectedspring.AswellasKLgsandKbTgscanalsobetreatastwoseriesconnectedspring.Therefore,kwscanbeexpressedintermsofKLwswithKbTwsandkgscanalsobeexpressedintermsofKLgswithKbTgs.TheequationsarelistedasfollowingLwsbTwswsLwsbTwsLgsbTgsgsLgsbTgsKKKKKKKKKK

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