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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PARAMETRICSTUDYOFDYNAMICSOFWORMANDWORMGEARSETUNDERSUDDENLYAPPLIEDROTATINGANGLEMYCHUNG,DSHAWDEPARTMENTOFPOWERMECHANICALENGINEERING,NATIONALTSINGHUAUNIVERSITY,NO101KUNGFUROADSECTIONII,HSINCHU,TAIWAN,ROCRECEIVED13SEPTEMBER2006;RECEIVEDINREVISEDFORM23JANUARY2007;ACCEPTED25FEBRUARY2007AVAILABLEONLINE17APRIL2007ABSTRACTTHEDYNAMICSOFAWORMGEARSETUNDERINSTANTLYAPPLIEDROTATINGANGLEAREAFFECTEDBYSEVERALFACTORSINCLUDINGTHEFRICTIONFORCEANDELASTICDEFORMATIONOFTHESURFACEBETWEENGEARTEETHITISFOUNDTHATTHOSEFACTORSCAUSEANONNEGLIGIBLEROTATIONALPOSITIONINGERRORTHEGOALSOFTHISSTUDYARETO1SETUPAMATHEMATICMODEL,2CARRYOUTANUMERICALSIMULATION,AND3CARRYOUTANEXPERIMENTANDCOMPAREITWITHTHENUMERICALRESULTSTHEEXPERIMENTSANDNUMERICALRESULTSHAVEVERYGOODAGREEMENTINTHISRESEARCH,THEMOMENTINERTIAOFFLYWHEEL,FRICTION,RIGIDITYOFSHAFTANDRIGIDITYOFGEARTOOTHAREALSOSTUDIEDTHERESULTSCANBEUSEDASERRORESTIMATIONSOFRELEVANTANGLES,ANGULARSPEEDANDANGULARACCELERATIONUNDERASUDDENLYAPPLIEDROTATIONALANGLE,ANDAREUSEFULFORESTABLISHINGTHEERRORCOMPENSATIONREQUIREDFORPOSITIONCONTROL1INTRODUCTIONWHENRADARTRACKSANAIRCRAFTWHICHTURNSATASHARPANGLE;THERADARMAYNOTBEABLETOLOCKONTOTHETARGETDUETOTHESMALLOSCILLATIONOFTHEANTENNASOMETIMES,THEOSCILLATIONEVENCAUSESAFAILUREOFTHERADARSYSTEMACCURATEPOSITIONINGISACRUCIALSUBJECTINATRACKINGSYSTEMHOWEVER,DUETOTHEDESIGNOFTHETRACKINGTRANSMISSIONMECHANISMISRESTRICTEDBYBOTHSPACEANDWEIGHT,THEVOLUMEANDTHEWEIGHTOFTHETRANSMISSIONMECHANISMMUSTBELIMITEDTHEWORMGEARSETISAGOODCHOICEDUETOITSSMALLVOLUMEANDHIGHREDUCTIONRATIOOWINGTOTHEOSCILLATIONOFTHEANTENNAISANIMPORTANTDYNAMICSBEHAVIORFORHIGHPRECISIONPOSITIONINGOFRADARSYSTEM,THEDYNAMICSOFAWORMGEARSETUNDERINSTANTLYAPPLIEDLARGETORQUEISVERYIMPORTANTTOUNDERSTANDTHISBEHAVIORTHISBEHAVIORISAFFECTEDBYSEVERALFACTORSINCLUDINGTHEFRICTIONFORCEANDELASTICDEFORMATIONOFTHESURFACEBETWEENGEARTEETHTOUNDERSTANDTHEEFFECTOFTHOSEFACTORS,ALOTOFRESEARCHHASBEENCONDUCTEDYUKSELANDKAHRAMAN1STUDIEDTHEINUENCEOFSURFACEWEARONTHEDYNAMICBEHAVIOROFATYPICALPLANETARYGEARSETTHEWEARMODELEMPLOYEDAQUASISTATICGEARCONTACTMODELTOCOMPUTECONTACTPRESSURESANDARCHARD’SWEARMODELTODETERMINETHEWEARDEPTHDISTRIBUTIONSPARKERETAL2ANALYZEDTHEDYNAMICRESPONSEOFASPURPAIROFAWIDERANGEOFOPERATINGSPEEDSANDTORQUESCOMPARISONSWEREMADETOOTHERRESEARCHERS’PUBLISHEDEXPERIMENTSTHATREVEALCOMPLEXNONLINEARPHENOMENATHEDYNAMICRESPONSEOFASPURPAIRWASINVESTIGATEDUSINGANITEELEMENT/CONTACTMECHANICSMODELTHATOFFERSSIGNICANTADVANTAGESFORDYNAMICGEARANALYSESMALIHA3CREATEDANONLINEARDYNAMICMODELOFASPURGEARPAIR,WHICHWASCOUPLEDWITHLINEARNITEELEMENTMODELSOFTHESHAFTSCARRYINGTHEM,ANDWITHDISCRETEMODELSOFBEARINGSANDDISKSTHEEXCITATIONSCONSIDEREDINTHEMODELWEREEXTERNALSTATICTORQUEANDINTERNALEXCITATIONCAUSEDBYMESHSTIFFNESSVARIATION,GEARERRORSANDGEARTOOTHPROLEMODICATIONBRITTON4PRODUCEDASUPERNISHEDGEARTEETHWITHAAPPROXIMATELY005MMRAFILMANDTHEFRICTIONTRACTIONINTHEEXPERIMENTSWERESIMULATEDTHEORETICALLYUSINGATHINLMNONNEWTONIANMICROELASTOHYDRODYNAMICLUBRICATIONSOLVERANDENCOURAGINGAGREEMENTBETWEENFRICTIONMEASUREMENTSANDTHEORETICALPREDICTIONSWASOBTAINEDKONG5PREDICTEDELASTICCONTACTANDELASTOHYDRODYNAMICLMTHICKNESSINWORMGEARSUSINGTHEUNDEFORMEDGEOMETRYOFTHEGAPBETWEENGEARTEETHINCONTACTATHREEDIMENSIONALELASTICCONTACTSIMULATIONTECHNIQUEHADBEENDEVELOPEDFORCALCULATIONOFTHETRUEAREAOFELASTICCONTACTUNDERLOADRELATIVETHEWHEELANDWORMSURFACESTUTTLE6STUDIEDTHEHARMONICDRIVES,WHICHEXHIBITEDVERYNONLINEARDYNAMICBEHAVIOR,INHISMODELNOTONLYDYNAMICMODELSINCLUDEACCURATEREPRESENTATIONOFTRANSMISSIONFRICTION,COMPLIANCEANDKINEMATICALERRORWEREUNDERSTAND,BUTALSOIMPORTANTFEATURESOFHARMONICDRIVEGEARTOOTHGEOMETRYANDINTERACTIONEXPERIMENTALOBSERVATIONSWEREUSEDTOGUIDETHEDEVELOPMENTOFAMODELTODESCRIBEHARMONICDRIVEOPERATIONITISIMPORTANTTOBEAWARETHATWORMGEARPERFORMANCEISINUENCEDBYTHELUBRICANTAPPLIEDANDMAINTAINEDHELOUVRY7DISCUSSEDTHEISSUEOFTHESERVOORIENTATIONCONTROLBEINGAFFECTEDBYASURGEOFBOTHMAXIMUMSTATICFRICTIONFORCEANDDYNAMICFRICTIONFORCETHEYREPORTEDTHEOCCURRENCEOFASTABLEPOSITIONINGERROR,ASWELLASTHESTOPPINGORSTOKINGDURINGTRACKINGATTHETURNINGPOINTOFALIMITINGLOOPOFTHETRACKINGSYSTEMWHENTHESYSTEMWASINAONEDIRECTIONALLOWSPEEDTRACKING,ITWASPOSSIBLEFORTHESTICK–SLIPPHENOMENONTOOCCURDUETOTHEFACTTHATTHEFRICTIONALFORCETOVELOCITYCURVEAPPEARSTOBEANEGATIVESLOPEANDINUENCESTHESTATICFRICTIONFORCEITWASALSOFOUNDTHATASIMILARPHENOMENONOCCURSATHIGHSPEEDTRACKINGDOUPONT8PROPOSEDAFRICTIONALFORCEMODELWITHNEGATIVESLOPEINTHEREFERENCE,RELATIVEMOTIONFROMSTATICTOHIGHSPEEDSLIDINGWASDIVIDEDINTOFOURSTAGESINTHERSTSTAGE,THEEXTERNALFORCEWASLESSTHANTHEMAXIMUMSTATICFRICTIONFORCEINTHESECONDSTAGE,TWOCONTACTINGSURFACESSTARTEDTODEVELOPASMALLRELATIVEVELOCITYINTHETHIRDSTAGE,THERELATIVEVELOCITYSTARTEDTOINCREASEBETWEENTWOOBJECTS,ANDLUBRICANTGOTINTOTHECONTACTAREAANDDECREASEDTHEFRICTIONALFORCEINTHEFOURTHSTAGE,THELUBRICANTHADFULLYLLEDTHECONTACTAREA,ANDTHEVISCOUSCHARACTERISTICANDTHEFRICTIONALFORCEINCREASEDWITHTHEVELOCITYOGURIDESIGNHANDBOOK9INCLUDEDSEVERALEMPIRICALCHARTSANDCALCULATIONFORMULAEOFTHEFRICTIONCOEFCIENTVSSLIDINGVELOCITY,THEALLOWABLEERROROFMANUFACTURING,THERECOMMENDEDVALUEFORTHEGAPSBETWEENTWOTEETH,ANDTHEALLOWABLECONTACTPRESSURESHIGLEY10DISCUSSEDTHEWORM’SPITCHCIRCLELINEVELOCITYASWELLASTHETRANSMISSIONFRICTIONALCOEFCIENTINTHISSTUDY,ONLYTHEFRICTIONFORCEANDELASTICDEFORMATIONOFTHESURFACEBETWEENGEARTEETHAREINTERESTEDTHEZKTYPEWORMGEARSETISUSEDTOELIMINATETHEBACKLASHPREVIOUSRESEARCHWORKSONGEARSANDGEARSETSWEREFOCUSEDONTHELIMITINGLOADING,PRESSUREDISTRIBUTIONANDALLOWABLEPRESSURELOADINGOFGEARS,ANDONTHERELATIONSHIPBETWEENFRICTIONCOEFCIENTANDSLIDINGVELOCITYMOSTINVESTIGATIONSAREBASEONTHEASSUMPTIONTHATTHETOOTHISRIGIDTHISSTUDYISFOCUSEDONTHEEFFECTSOFTHEELASTICDEFORMATIONOFTHEGEARTOOTHSURFACEANDTHENONLINEARFRICTIONCOEFCIENTONTHESYSTEMDYNAMICSTOSTUDYTHEDYNAMICSOFTHEWORMGEARSET,ADYNAMICMODELOFTHEWORMGEARSETISDEVELOPEDANDTHECOMPARISONBETWEENTHEEXPERIMENTALRESULTSANDTHENUMERICALRESULTSISALSOSTUDIEDTHEPARAMETERSOFTHEDYNAMICMODELAREADJUSTEDBYTHENDINGSOFTHECOMPARISONOFTHEANALYSISANDTHEEXPERIMENTFINALLY,THEEFFECTSOFMOMENTINERTIAOFYWHEEL,FRICTION,RIGIDITYOFSHAFTANDRIGIDITYOFGEARTOOTHONTHENONLINEARBEHAVIOROFTHETRANSMISSIONMECHANISMAREALSOSTUDIED2THEDYNAMICMODELSOFTHEWORMGEARSET21THEEQUILIBRIUMEQUATIONSOFTHEWORMANDWORMGEARSETTHEGEOMETRICOFWORMGEARSETISSHOWNINFIG1THEREAREAWORM,AWORMGEAR,TWOSHAFTS,FOURBEARINGSANDAYWHEELTHESHAFTOFWORMISDRIVENBYANANGLEY1THEROTATIONALANGLEOFTHEYWHEELISY4THEROTATIONALANGLEOFTHEWORM’SBODYISY2DUETOTHEELASTICDEFORMATIONOFTHEWORMSHAFT;Y16Y2THEROTATIONANGLEOFWORMGEARBODYISY3THEMOMENTOFINERTIAOFTHEWORMISJWTHEPITCHRADIUSOFTHEWORM’SHELICALTOOTHISRWTHEWORM’SROTATIONALINERTIAASARIGIDBODYISJGTHEPITCHRADIUSOFTHEWORMGEARISRGTHEMOMENTINERTIAOFTHEYWHEELISJ4INTHISSTUDY,TONEGLECTTHEEFFECTOFBACKLASH,ZKTYPEWORMANDWORMGEARAREUSEDBOTHINANALYSISANDEXPERIMENTTOSIMPLIFYTHETHEORETICALMODEL,THEBASICASSUMPTIONSARELISTEDASFOLLOWS1THEYWHEELISRIGID2THEWORMSANDWORMGEARTEETHAREELASTIC3THEBODYOFTHEWORMGEARISRIGID4WORMANDWORMGEARAREPERPENDICULARTOEACHOTHER5THECLEARANCEBETWEENTEETHISIGNORED6NOERRORONTHEGEARTOOTHPROLE7THEWORMISSINGLETHREAD8THEWORMSHAFTANDWORMGEARSHAFTARETWOROTATIONALSPRINGTHEDYNAMICBEHAVIORISNEGLECTED9TRANSLATIONALDEGREEOFFREEDOMFORALLTHEELEMENTSISNOTCONSIDERED10ONLYFRICTIONISCONSIDERED,NOOTHERDAMPINGEFFECTISCONSIDERED22THEAXIALSPRINGCONSTANTOFBEARINGS,WORMSHAFTANDWORMGEARSHAFTTHERESULTSOFEXPERIMENTTONDTHERELATIONBETWEENLOADANDTHEAXIALDISPLACEMENTOFBEARINGARESHOWNINFIG2THEAXIALSPRINGCONSTANTOFWORMBEARINGKBTWSANDWORMGEARBEARINGKBTGSAREOBTAINEDBYUSINGFIG2FURTHERMORE,KLWSANDKBTWSCANBETREATASTWOSERIESCONNECTEDSPRINGASWELLASKLGSANDKBTGSCANALSOBETREATASTWOSERIESCONNECTEDSPRINGTHEREFORE,KWSCANBEEXPRESSEDINTERMSOFKLWSWITHKBTWSANDKGSCANALSOBEEXPRESSEDINTERMSOFKLGSWITHKBTGSTHEEQUATIONSARELISTEDASFOLLOWINGLWSBTWSWSLWSBTWSLGSBTGSGSLGSBTGSKKKKKKKKKK

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