外文翻译--二级齿轮减速器的球手万向节的间隙计算 英文版.pdf

INTJADVMANUFTECHNOL200321604–611OWNERSHIPANDCOPYRIGHT2003SPRINGERVERLAGLONDONLIMITEDBACKLASHESTIMATIONOFASEEKERGIMBALWITHTWOSTAGEGEARREDUCERSJHBAEK,YKKWAKANDSHKIMDEPARTMENTOFMECHANICALENGINEERING,KOREAADVANCEDINSTITUTEOFSCIENCEANDTECHNOLOGY,3731GUSUNGDONGYUSUNGGUDAEJON,KOREAANOVELTECHNIQUEFORESTIMATINGTHEMAGNITUDEORCONTRIBUTIONRATIOOFEACHSTAGEBACKLASHINASYSTEMWITHATWOSTAGEGEARREDUCERISPROPOSEDTHECONCEPTISBASEDONTHECHANGEOFFREQUENCYRESPONSECHARACTERISTIC,INPARTICULAR,THECHANGEOFANTIRESONANTFREQUENCYANDRESONANTFREQUENCY,DUETOTHECHANGEOFTHEMAGNITUDEOFTHEBACKLASHOFEACHSTAGE,EVENTHOUGHTHETOTALMAGNITUDEOFTHEBACKLASHOFASYSTEMWITHATWOSTAGEGEARREDUCERISCONSTANTTHEVALIDITYOFTHETECHNIQUEISVERIFIEDINASEEKERGIMBALANDSATISFACTORYRESULTSAREOBTAINEDITISTHOUGHTTHATTHEDIAGNOSISANDMAINTENANCEOFMANUFACTURINGMACHINESANDSYSTEMSWITHTWOSTAGEGEARREDUCERSWILLBECOMEMOREEFFICIENTANDECONOMICALBYVIRTUEOFPROPOSEDTECHNIQUEKEYWORDSANTIRESONANTFREQUENCY；BACKLASHESTIMATION；CONTRIBUTIONRATIO；FREQUENCYRESPONSECHARACTERISTIC；RESONANTFREQUENCY；SEEKERGIMBAL1INTRODUCTIONTHEAUTOMATIONOFMANUFACTURINGMACHINESANDTHEFREQUENTUSEOFROBOTSANDSERVOSYSTEMSHAVEGREATLYINCREASEDTHEDEMANDFORSERVOSYSTEMSWITHSERVOMOTORSWITHTHEADVANCEOFMOTORMANUFACTURINGTECHNIQUES,SERVOSYSTEMSHAVEBEENDEVELOPEDWITHDIRECTDRIVETYPEMOTORSTHATDONOTREQUIREGEARREDUCERSHOWEVER,THUSFAR,SERVOSYSTEMSWITHGEARREDUCERSHAVEBEENUSEDEXTENSIVELYINMANUFACTURINGMACHINESINMANYFIELDS,BECAUSETHESERVOSYSTEMVOLUMEANDWEIGHTISLARGERTHANTHATOFTHEGEARREDUCER,WHILEITSTORQUEISRELATIVELYSMALLINCOMPARISONSERVOSYSTEMSWITHGEARREDUCERSHAVEHADPROBLEMSRELATEDTOGEARBACKLASHSINCETHEIRINCEPTIONACCORDINGLY,MANYSTUDIESHAVEBEENPERFORMEDINORDERTODEALWITHTHEPROBLEMSCORRESPONDENCEANDOFFPRINTREQUESTSTOJHBAEK,RESEARCHANDDEVELOPMENT7GROUP,LGINNOTEKCO,LTD,148–1MABUKRIGUSUNGEUPYONGINCITYKYONGGIDO,449–910,KOREAEMAILJHBAEKBLGINNOTEKCOMRECEIVED5FEBRUARY2002ACCEPTED29MARCH2002INORDERTODIAGNOSEANDMAINTAINTHEPERFORMANCEOFTHEROBOTSANDSERVOSYSTEMS,AMETHODOFMONITORINGANDDETECTINGTHEMAGNITUDEANDCHANGEOFBACKLASHHASBEENDEVELOPEDDAGALAKISANDMYERSUSEDACOHERENCEFUNCTIONANDTHEMAGNITUDEOFRESONANTPEAKINTHEFREQUENCYRESPONSEBETWEENTHEMOTORVOLTAGEANDTHEACCELERATIONOFAROBOTLINKASMEASURES1STEINANDWANGDEVELOPEDATECHNIQUEBASEDONMOMENTUMTRANSFERANALYSISINORDERTODETECTANDESTIMATETHEBACKLASHOFASERVOSYSTEMWITHAGEARREDUCERTHEYFOUNDTHATTHESPEEDCHANGEOFTHEPRIMARYGEARDUETOIMPACTWITHTHESECONDARYGEARISRELATEDTOTHEMAGNITUDEOFTHEBACKLASH2SAKERETALDEVELOPEDATECHNIQUETOCOMPLEMENTTHEWORKOFSTEINANDWANGUSINGTHEIMPULSIVETORQUEDUETOIMPACT,INSTEADOFTHESPEEDCHANGEOFTHEPRIMARYGEAR3PANETALDEVELOPEDATECHNIQUEFORDETECTINGANDCLASSIFYINGTHEBACKLASHOFAROBOTBYUSINGWIGNER–VILLEDISTRIBUTIONSCOMBINEDWITHATWODIMENSIONALCORRELATIONOFTHERELATIONSHIPBETWEENTHESINUSOIDALJOINTMOTIONANDTHEACCELERATIONOFTHEROBOTLINK4HOWEVER,THEREISNOTECHNIQUEFORESTIMATINGTHEMAGNITUDEORCONTRIBUTIONRATIOOFEACHSTAGEOFTHEBACKLASHINASERVOSYSTEMWITHAMULTISTAGEGEARREDUCER,WHICHISOFTENUSEDINMANUFACTURINGMACHINESANDROBOTSITISVERYIMPORTANTTOKNOWTHEMAGNITUDEOFEACHSTAGEBACKLASHOFSYSTEMINORDERTOOBTAINTHEDESIREDMAGNITUDEOFBACKLASHANDTOMAINTAINTHATMAGNITUDEINACORRECTRANGETHEPURPOSEOFTHISPAPERIS,THEREFORE,TOPRESENTATECHNIQUEFORESTIMATINGTHEMAGNITUDEORCONTRIBUTIONRATIOOFEACHSTAGEBACKLASHOFASERVOSYSTEMWITHATWOSTAGEGEARREDUCERTHECONTRIBUTIONRATIOISDEFINEDASTHERATIOOFTHEMAGNITUDEOFTHEFIRSTSTAGEBACKLASHTOTHATOFTHETOTALBACKLASHTHECONCEPTFORESTIMATINGTHEMAGNITUDEOFEACHSTAGEBACKLASHISBASEDONTHECHANGEOFANTIRESONANTFREQUENCYARFANDRESONANTFREQUENCYRFINTHEFREQUENCYRESPONSECHARACTERISTICOFASERVOSYSTEM,ACCORDINGTOTHECHANGEOFTHEMAGNITUDEOFEACHSTAGEOFBACKLASH,EVENTHOUGHTHETOTALBACKLASHOFTHESERVOSYSTEMISCONSTANTINORDERTOVERIFYTHEVALIDITYOFTHEPROPOSEDTECHNIQUE,TWODRIVINGSERVOSYSTEMSOFASEEKERGIMBAL,WHICHAREUSEDINORDERTOSTABILISETHEORIENTATIONOFANOBJECT,ARECONSIDEREDONEISANAZIMUTHDRIVINGSERVOSYSTEMADSS；THEOTHERISANELEVATIONDRIVINGSERVOSYSTEMEDSSBOTHSERVOSYSTEMSHAVETWOSTAGEGEARREDUCERSBACKLASHESTIMATIONOFASEEKERGIMBAL6052MODELOFSEEKERGIMBAL21MODELOFTHEADSSINTHESEEKERGIMBALAPHOTOGRAPHOFTHESEEKERGIMBALWITHTWOSTAGEGEARREDUCERSWHICHISCONSIDEREDINTHISPAPERISPRESENTEDINFIG1ATHEADSSANDEDSSCORRESPONDTOTHETWODRIVINGPARTSOFTHESEEKERGIMBALINTHECASEOFTHEADSS,THEHATCHEDCOMPONENTS,PINION2,SHAFT1,GEAR1,PINION1,MOTORANDBEARINGSROTATEWITHRESPECTTOTHEAAH11032AXISEXCEPTTHATGEAR2ISATTACHEDONAFIXEDSHAFTASSHOWNINFIG1BITISASSUMEDTHATBEARINGSSUPPORTEACHSHAFTWITHOUTANYCLEARANCE,DUETOTHEPRELOADALSO,THEINFLUENCEOFTHEDAMPINGCHARACTERISTICISNEGLECTEDTHEMODELOFTHEADSSOBTAINEDUNDERTHESEASSUMPTIONSISPRESENTEDINFIG1CTHEMOMENTOFFIG1ASEEKERGIMBAL；BSTRUCTUREOFADSS；CMODELOFADSS；DSTRUCTUREOFEDSS；EMODELOFEDSSINERTIAOFPINION1ISINCLUDEDWITHTHATOFTHEMOTORTHETORSIONSPRINGREPRESENTEDATTHERIGHTSIDEOFGEAR1INDICATESTHETORSIONSTIFFNESSDUETOTOOTHSTIFFNESSBETWEENPINION1ANDGEAR1INTHECASEOFSHAFT1,THEMOMENTOFINERTIAISLUMPEDATTHECENTREOFTHEDISTANCEBETWEENGEAR1ANDPINION2ANDTORSIONSPRINGS,WITHTWICETHEVALUEOFTORSIONSTIFFNESSOFSHAFT1,ARECONNECTEDWITHGEAR1ANDPINION2BECAUSETHEYAREFIXED,GEAR2ANDTHEFIXEDSHAFTAREMODELLEDSOTHATTHEYHAVEONLYTORSIONSPRINGSWITHOUTMOMENTOFINERTIAEACHBACKLASHISREPRESENTEDASTHEANGLESOFROTATIONOFTHEGEARSWHENTHEPINIONSAREFIXEDCOMPONENTSENCLOSEDBYAPHANTOMDOUBLEDOTLINEINFIG1CINDICATETHELOADOFTHEADSSTHEADSSCONSIDEREDCONSISTSOFATACHOMETERFILTER,AMOTORAMPLIFIERANDTHEAFOREMENTIONEDSTRUCTURETHEMOTORAMPLIFIERISUSEDTOAMPLIFYTHEINPUTVOLTAGEOFMOTORAPERMANENT606JHBAEKETALMAGNETICFIELDTYPEDCMOTORWITHATACHOMETERISUSEDASANACTUATORINORDERTOFILTERTHEOUTPUTVOLTAGEOFTHETACHOMETER,ASECONDORDERLOWPASSFILTERISUSEDTHEGOVERNINGELECTRICEQOFTHESECOMPONENTSAREASFOLLOWS5VMKAVI1LADIADTRMIAKBH9258˙MVM2ATMKTIA2BVTKTSH9258˙M3VOSGFSVTS4THEEQOFMOTIONFORTHEMOTORISASFOLLOWSJMH9258MBMH9258˙MTMH11002TG1N1H11002TF,MSIGNH9258˙M5THETORQUETRANSMITTEDTOGEAR1ISREPRESENTEDASANONLINEAREQ,PRESENTEDINEQ6,DUETOTHEBACKLASHBETWEENPINIONFIG2THEBODEDIAGRAMVO/VIOFADSSACCORDINGTOCONTRIBUTIONRATIOACASE1；BCASE2；CCASE3；DCASE4；ECASE5SIMSIMULATION；EXPEXPERIMENT1ANDGEAR1THEMODELOFTHEDEADZONEISUSEDASTHEMODELOFTHEBACKLASH6TG1H20902KG1H9258D1H11002H92541,H9258D1H11022H925410,H20841H9258D1H20841H11021H92541KG1H9258D1H92541,H9258D1H11021H11002H92541H209036WHEREH9258D1H9258M/N1H11002H9258G17THEEQOFMOTIONFORGEAR1ISASFOLLOWSJG1H9258G1TG1H110022KS1H9258G1H11002H9258S18THEEQOFMOTIONFORSHAFT1ISASFOLLOWSJS1H9258S12KS1H9258G1H9258P2H110024KS1H9258S19BESIDES,THEEQUATIONOFMOTIONFORPINION2ISASFOLLOWSJP2H9258P22KS1H9258S1H11002H9258P2H110021NRTL10BACKLASHESTIMATIONOFASEEKERGIMBAL607THETORQUEOFTHELOADISREPRESENTEDINEQ11,LIKEEQ6TLH20902K2H9258D2H11002H92542,H9258D2H11022H925420,|H9258D2|H11021H92542K2H9258D2H92542,H9258D2H11021H11002H92542H2090311WHEREH9258D2H9258P2/NRH11002H9258L12HERE,THEEQUIVALENTTORSIONSTIFFNESSBETWEENGEAR2ANDSHAFT2ISASFOLLOWS7K2KG2KS2KG2KS213FINALLY,THEEQUATIONOFMOTIONFORTHELOADISASFOLLOWSJLH9258LTLH11002TF,LSIGNH9258˙L14THERESPONSEOFTHEOUTPUTVOLTAGEOFTHETACHOMETERFILTERWITHRESPECTTOTHEINPUTVOLTAGEOFTHEMOTORAMPLIFIERISOBTAINEDFROMTHESEEQINADDITION,THERELATIONBETWEENTHETOTALBACKLASHANDEACHSTAGEBACKLASHISASFOLLOWSBTB21NRB115WHEREBI360H9254I/H9266I1,21622MODELOFTHEEDSSINTHESEEKERGIMBALINTHISSUBSECTION,THEEDSSMODELSANDEQOFMOTIONAREDERIVEDTHESTRUCTUREOFTHEEDSSISPRESENTEDINFIG1DBECAUSEGEAR2ISDIRECTLYATTACHEDTOTHELOAD,THEMOMENTOFINERTIAOFGEAR2ISINCLUDEDWITHTHATOFTHELOADANDGEAR2HASONLYATORSIONSPRINGMODEL,ASSHOWNINFIG1ETHEEQOFMOTIONFORTHEEDSSBETWEENTHEMOTORAMPLIFIERANDTACHOMETERFILTERARETHESAMEASTHOSEOFTHEADSS,EXCEPTFORREPLACINGEQS10–13ANDEQ15WITHEQS17–20ASFOLLOWSJP2H9258P22KS1H9258S1H11002H9258P2H110021N2TL17TLH20902KG2H9258D2H11002H92542,H9258D2H11022H925420,|H9258D2|H11021H92542KG2H9258D2H92542,H9258D2H11021H11002H92542H2090318WHEREH9258D2H9258P2/N2H11002H9258L19BTB21N2B120FROMEQS1–9,EQ14ANDEQS17–20,THERESPONSEOFTHEOUTPUTVOLTAGEOFTHETACHOMETERFILTERWITHRESPECTTOTHEINPUTVOLTAGEOFTHEMOTORAMPLIFIERISOBTAINED3SIMULATIONITISWELLKNOWNTHATANINCREASEINTHETOTALBACKLASHINASYSTEMCAUSESTHEFREQUENCYRESPONSECHARACTERISTIC,OFTHEOUTPUTVOLTAGEOFTHETACHOMETERFILTERWITHRESPECTTOTHEINPUTVOLTAGEOFTHEMOTORAMPLIFIER,TOCHANGEBECAUSEITREDUCESTHEEFFECTIVEEQUIVALENTTORSIONALSTIFFNESSOFTHESYSTEM8HOWEVER,ITHASNOTBEENREPORTEDYETTHATALTHOUGHTHETOTALBACKLASHMAGNITUDEISCONSTANT,ASERVOSYSTEMWITHADIFFERENTBACKLASHMAGNITUDEATEACHSTAGEHASDIFFERENTFREQUENCYRESPONSECHARACTERISTICINTHISWORK,EACHSTAGEOFBACKLASHOFASERVOSYSTEMISEXAMINEDBYTHISPHENOMENONANDHYPOTHESISINORDERTOVERIFYTHISHYPOTHESIS,THEFREQUENCYRESPONSECHARACTERISTICOFADSSISINVESTIGATEDACCORDINGTOTHECONTRIBUTIONRATIOTHEBODEDIAGRAMSOFADSSOBTAINEDFROMTHESIMULATIONAREREPRESENTEDINFIG2THESPECIFICATIONSUSEDFORTHESIMULATIONAREPRESENTEDINTABLE1THECOMBINATIONSOFTHEMAGNITUDEOFBACKLASHOFEACHSTAGEOBTAINEDACCORDINGTOTHECHANGEOFCONTRIBUTIONRATIOARELISTEDINTABLE2THEYAREOBTAINEDFROMEQS15AND20INORDERTOOBTAINTHESIMULATIONRESULTSOFFIG2,THEEQUATIONOFMOTIONOUTLINEDINTHEPREVIOUSSECTIONARECONVERTEDINTOABLOCKDIAGRAMTHESIMULATIONISTHENPERFORMEDUSINGMATLABSIMULINKV61SOFTWARETHEPEAKAMPLITUDEOFTHESINUSOIDALVOLTAGESUPPLIEDTOTHEMOTORAMPLIFIERIS25VANDTHESAMPLINGTIMEUSEDIS10H9262SECBODEDIAGRAMSOFFIG2AREMADEFROMTHEFREQUENCYANALYSISTOEXTRACTONLYTHEEXCITEDFREQUENCYCOMPONENTFROMTHEOUTPUTVOLTAGEOFTHETACHOMETERFILTERWITHRESPECTTOTHESINUSOIDALVOLTAGESUPPLIEDTOTHEMOTORAMPLIFIERTHEARFANDRFOBTAINEDARESUMMARISEDINTABLE2ANDAREREPRESENTEDINFIG3ATHEDIFFERENCEBETWEENTHEARFANDRFISSHOWNINFIG3BFROMFIG3AANDB,ITISFOUNDTHATTHEFREQUENCYRESPONSECHARACTERISTICOFASERVOTABLE1SPECIFICATIONSFORADSSANDEDSSPARAMETERADSSEDSSGEARRATIO1,N1594641TORSIONSTIFFNESS,KG1MH11554N/RAD340E4474E4MOMENTOFINERTIAOFGEAR1,JG1KGH11554M2234E5369E5TORSIONSTIFFNESSOFSHAFT1,KS1MH11554N/RAD228154E2MOMENTOFINERTIAOFSHAFT1,JS1KGH11554M2830E8204E7MOMENTOFINERTIAOFPINION2,JP2KGH11554M2221E7484E7GEARRATIO,NR,N2105775EQUIVALENTTORSIONSTIFFNESS,K2,KG2MH11554N/RAD774E4254E5MOMENTOFINERTIAOFLOAD,JLKGH11554M2275E3144E2STATICFRICTIONTORQUEOFLOAD,TF,LMH11554N70E371E3TOTALBACKLASH,BTDEG00660276MOTORINDUCTANCE,LAH850E4MOTORRESISTANCE,RMH9024410BACKEMFCONST,KBVH11554S/RAD344E2TORQUESENSITIVITY,KTMH11554N/A349E2MOMENTOFINERTIAOFMO