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外文翻译--校准并联机床的不确定参数 英文版.pdf

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外文翻译--校准并联机床的不确定参数 英文版.pdf

UNCERTAINTYPROPAGATIONINCALIBRATIONOFPARALLELKINEMATICMACHINESBERNHARDJOKIELJRA,JOHNCZIEGERTB,LOTHARBIEGCASANDIANATIONALLABORATORIES,ALBUQUERQUE,NM871850958,USABUNIVERSITYOFFLORIDAMACHINETOOLRESEARCHCENTER,237MEB,GAINESVILLE,FL32611,USACSANDIANATIONALLABORATORIES,1ALBUQUERQUE,NM871850958,USAABSTRACTTHISPAPEROUTLINESINDETAILAMETHODFORDETERMININGTHEUNCERTAINTYPRESENTINTHEKINEMATICPARAMETERSJOINTLOCATIONS,INITIALSTRUTLENGTHS,ANDSPINDLELOCATIONANDORIENTATIONFORPARALLELKINEMATICDEVICESAFTERCALIBRATIONTHEUNCERTAINTYESTIMATIONMETHODUSINGMONTECARLOSIMULATIONSWASAPPLIEDTOASEQUENTIALMETHODFORDETERMININGTHEKINEMATICPARAMETERSOFFULLYASSEMBLEDHEXELTORNADO2000A6–3STEWARTPLATFORMMILLINGMACHINERESULTSFORTHEUNCERTAINTYPRESENTINTHEKINEMATICPARAMETERSOFAHEXELTORNADO2000MILLINGKEYWORDSSTEWARTPLATFORM;CALIBRATION;KINEMATICPARAMETERS;UNCERTAINTY1INTRODUCTIONOVERTHELASTDECADE,MULTIAXISMACHINETOOLSBASEDONPARALLELKINEMATICMECHANISMSPKMSHAVEBEENDEVELOPEDANDMARKETEDWORLDWIDEASALTERNATIVESTOTRADITIONALSERIALSTACKEDSLIDE,ORTHOGONALMACHINEARCHITECTURESTHEGENERALDIFFERENCEBETWEENPKMANDORTHOGONALSERIALMECHANISMSISTHEARRANGEMENTOFTHEACTUATORSINORTHOGONALSERIALMECHANISMS,INDIVIDUALACTUATORSRESPONSIBLEFORMOTIONININDIVIDUALCARTESIANDEGREESOFFREEDOMDOFAREJOINEDENDTOENDINASERIALCHAINCONNECTINGTHESTATIONARYGROUNDFRAMETOTHEMOVINGFRAMEINPKMARCHITECTURES,INDIVIDUALACTUATORSARENOTTYPICALLYARRANGEDTOINDEPENDENTLYCONTROLASINGLECARTESIANDOFINSTEADTHEACTUATORSAREARRANGEDSOTHATEACHACTUATORISCONNECTEDBETWEENTHESTATIONARYGROUNDFRAMEANDTHEMOVINGFRAME,SOTHATACOMBINATIONOFACTUATORMOTIONSCONTROLSTHEMOTIONOFTHEMOVINGFRAMEINCARTESIANSPACEAPOPULARTYPEOFPKMISTHESTEWARTPLATFORMFIGURE1THESTEWARTPLATFORMCONNECTSAMOVEABLEPLATFORMTOASTATIONARYGROUNDFRAMEBYSIXEXTENSIBLELINKSORSTRUTS,ALLOWINGFORCONTROLLEDMOTIONOFTHEPLATFORMINALLSIXDOFGENERALLYFORPKMMACHINES,THECARTESIANPOSITIONANDORIENTATIONOFTHETOOLPOINTCARRIEDONTHEPLATFORMISOBTAINEDFROMAKINEMATICMODELOFTHEPARTICULARMACHINEACCURATEPOSITIONINGOFTHESEMACHINESRELIESONTHEACCURATEKNOWLEDGEOFTHEPARAMETERSOFTHEKINEMATICMODELUNIQUETOTHEPARTICULARMACHINETHEPARAMETERSINTHEKINEMATICMODELINCLUDETHESPATIALLOCATIONSOFTHEJOINTCENTERSONTHEMACHINEBASEANDMOVINGPLATFORM,THEINITIALSTRUTLENGTHS,ANDTHESTRUTDISPLACEMENTSTHESTRUTDISPLACEMENTSAREREADILYOBTAINEDFROMSENSORSONTHEMACHINEHOWEVER,THEREMAININGKINEMATICPARAMETERSJOINTCENTERLOCATIONS,ANDINITIALSTRUTLENGTHSAREDIFFICULTTODETERMINEWHENTHESEMACHINESAREINTHEIRFULLYASSEMBLEDSTATETHESIZEANDCOMPLEXITYOFTHESEMACHINEGENERALLYMAKESITDIFFICULTANDSOMEWHATUNDESIRABLETODETERMINETHEREMAININGKINEMATICPARAMETERSBYDIRECTINSPECTIONSUCHASINACOORDINATEMEASURINGMACHINEINORDERFORPKMSTOBEUSEFULFORPRECISIONPOSITIONINGAPPLICATIONS,TECHNIQUESMUSTBEDEVELOPEDTOQUICKLYCALIBRATETHEMACHINEBYDETERMININGTHEKINEMATICPARAMETERSWITHOUTDISASSEMBLYOFTHEMACHINEANUMBEROFAUTHORSHAVEREPORTEDTECHNIQUESFORCALIBRATIONOFPKMS{SOONS1,2,MASORY,3,ZHUANGETAL4,5,ROPPONEN6}INANOTHERPAPER7,THEAUTHORSHAVEREPORTEDONWORKRECENTLYCOMPLETEDBYTHEUNIVERSITYOFFLORIDAANDSANDIANATIONALLABORATORIESONCALIBRATIONOFPKMS,WHICHDESCRIBESANEWTECHNIQUETOSEQUENTIALLYDETERMINETHEKINEMATICPARAMETERSOFANASSEMBLEDPARALLELKINEMATICDEVICECALIBRATIONOFPKMS,ORANYOTHERTYPEOFMACHINE,BEGINSBYCOLLECTINGSETSOFMEASUREMENTSTHECOLLECTEDMEASUREMENTDATAISSUPPLIEDTOANALGORITHM,WHICHCOMPUTESTHEMODELPARAMETERSASWITHANYMETROLOGYTASK,1SANDIAISAMULTIPROGRAMLABORATORYOPERATEDBYSANDIACORPORATION,ALOCKHEEDMARTINCOMPANY,FORTHEUNITEDSTATESDEPARTMENTOFENERGYUNDERCONTRACTDEAC04–94AL85000PRECISIONENGINEERINGJOURNALOFTHEINTERNATIONALSOCIETIESFORPRECISIONENGINEERINGANDNANOTECHNOLOGY25200148–55MACHINEAFTERCALIBRATIONUSINGASMX4,000LASERTRACKERARESHOWNTHEREISUNCERTAINTYPRESENTINTHECOLLECTEDMEASUREMENTDATATHEUNCERTAINTYPRESENTINTHEMEASUREMENTDATAWILLPROPAGATETHROUGHTHEPARAMETERIDENTIFICATIONALGORITHMANDRESULTINERRORSINTHECOMPUTEDKINEMATICPARAMETERSTHEERRORSINTHERECOVEREDKINEMATICPARAMETERSWILLTHENCREATEPOSITIONINGERRORSWHENTHEKINEMATICMODELISUSEDFORMACHINECONTROLTHEPURPOSEOFTHISPAPERISTOEXPLORETHEISSUEOFPROPAGATIONOFUNCERTAINTYINTHECALIBRATIONOFPKMDEVICESWEWILLDESCRIBEAMETHODOLOGYFOREVALUATINGTHEUNCERTAINTYINTHERECOVEREDPARAMETERS,ANDTHERESULTINGERRORBOUNDSINMACHINEPOSITIONINGWEWILLDEMONSTRATETHISMETHODOLOGYFORTHENEWCALIBRATIONMETHODWEHAVEDEVELOPEDANDREPORTEDINANOTHERPAPER7THISPAPERISORGANIZEDINTHEFOLLOWINGMANNERSECTION2DESCRIBESTHEMETHODOLOGYFOREVALUATINGUNCERTAINTYPROPAGATIONINPKMCALIBRATIONSECTION3CONTAINSABRIEFSYNOPSISOFTHECALIBRATIONMETHODOLOGYUSEDINTHISWORKINSECTION4,THEERRORBUDGETFORTHECALIBRATIONMEASUREMENTSISDEVELOPEDSECTION5GIVESTHERESULTSOFTHEUNCERTAINTYPROPAGATIONSIMULATIONSECTION6COMPARESTHESIMULATIONRESULTSTOEXPERIMENTALRESULTSPERFORMEDONTHEMACHINE2METHODOLOGYFOREVALUATINGUNCERTAINTYPROPAGATIONINANYMACHINECALIBRATIONTASK,UNCERTAINTYISINTRODUCEDINTWOWAYSFIRST,THECALIBRATIONMETHODINVOLVESPERFORMINGMEASUREMENTSWITHASPECIFIEDSETOFINSTRUMENTSTHESEMEASUREMENTINSTRUMENTSWILLHAVEANASSOCIATEDUNCERTAINTYINTHEIROUTPUT,WHICHISAFUNCTIONOFTHEPHYSICALPRINCIPALSANDCONSTRUCTIONOFTHEINSTRUMENTSTHEMSELVES,ASWELLASTHEENVIRONMENTINWHICHTHEMEASUREMENTSTAKEPLACEINCONJUNCTIONWITHTHEUNCERTAINTYASSOCIATEDWITHTHEEXTERNALCALIBRATIONINSTRUMENTS,THEREMAYBEADDITIONALUNCERTAINTYINTRODUCEDBYTHEMACHINEITSELFTHEFEEDBACKDEVICESONTHESTRUTSOFPKMMACHINESTYPICALLYCANNOTDIRECTLYMEASURETHEABSOLUTEDISTANCEBETWEENCORRESPONDINGPAIRSOFJOINTCENTERS,ONLYTHECHANGEINLENGTHOFTHESTRUTFROMSOME“HOME”POSITIONATWHICHTHEABSOLUTEJOINTCENTERDISTANCEISASSUMEDTOBEKNOWNCHANGESINTHETHERMALSTATEOFTHEMACHINEMAYCAUSETHISASSUMEDVALUETOBEINCORRECTAND/ORTOFLUCTUATEOVERTIMETHESTRUTDISPLACEMENTFEEDBACKDEVICESALSOHAVEAFINITERESOLUTIONANDSOMEUNCERTAINTYASSOCIATEDWITHTHEIROUTPUTGEOMETRICALEFFECTSNOTINCLUDEDINTHEKINEMATICMODEL,SUCHASNONSPHERICALJOINTMOTION,ALSOCREATEANEFFECTIVESTRUTLENGTHERRORWHICHISNOTSENSEDBYTHESTRUTFEEDBACKDEVICESTHEREFORE,THEMACHINE’SREPEATABILITYANDABSOLUTEPOSITIONINGACCURACYDURINGTHECALIBRATIONMEASUREMENTSCONTRIBUTESTOTHEOVERALLUNCERTAINTYOFTHEBASICDATAUSEDBYTHECALIBRATIONALGORITHMTHEUNCERTAINTIESPRESENTINTHEEXTERNALMEASUREMENTINSTRUMENTCOMBINEWITHTHEUNCERTAINTIESINTHEMACHINEMOTIONSTOCREATEERRORSINTHEDATAUSEDBYTHECALIBRATIONALGORITHMTOCOMPUTETHEPARAMETERSOFTHEMACHINE’SKINEMATICMODELSINCEERRORISPRESENTINTHECOLLECTEDDATA,THEREWILLBEERRORPRESENTINTHECOMPUTEDMODELPARAMETERSASWELLSINCETHESECOMPUTEDMODELPARAMETERSDONOTIDENTICALLYMATCHTHEACTUALPHYSICALPARAMETERSOFTHEREALMACHINE,POSITIONINGERRORSWILLRESULTWHENTHERECOVEREDPARAMETERSAREUSEDDURINGPOSITIONALCONTROLOFTHEMACHINETHESEPOSITIONINGERRORSDUETOINCORRECTPARAMETERIZATIONOFTHEMODELWILLBECOMPOUNDEDWITHTHEUNCERTAINTIESINHERENTTOTHEMACHINEITSELF,RESULTINGINTHEFINALVOLUMETRICACCURACYOFTHEMACHINETHISISANIMPORTANTPOINTTHATSHOULDNOTBEOVERLOOKEDTHEUNCERTAINTIESARISINGFROMTHEMACHINEITSELFIE,REPEATABILITY,SENSORRESOLUTION,UNMODELEDTHERMALANDGEOMETRICEFFECTSAFFECTTHEOVERALLPOSITIONINGPERFORMANCEOFTHEMACHINETWICEFIRST,THEYADDUNCERTAINTYTOTHEBASICMEASUREMENTDATATHATISUSEDBYTHECALIBRATIONALGORITHMSECOND,AFTERTHECALIBRATIONISCOMPLETE,ANDTHENEWLYPARAMETERIZEDKINEMATICMODELISUSEDFORMACHINECONTROL,THESESAMEMACHINEUNCERTAINTIESSTILLEXISTANDCONTRIBUTETOPOSITIONINGERRORSWEPROPOSETHEFOLLOWINGMETHODOLOGYFOREVALUATIONOFUNCERTAINTYPROPAGATIONTHROUGHTHEPKMCALIBRATIONPROCESS1CONSTRUCTANERRORBUDGETFORTHEMEASUREMENTDEVICESUSEDDURINGCALIBRATIONTOPREDICTTHEIRUNCERTAINTYCONTRIBUTIONS2CONSTRUCTANERRORBUDGETFORTHEMACHINEITSELFTOESTIMATETHEMAGNITUDEOFSTRUTLENGTHERRORWHICHCANOCCURDUETOTHERMALEFFECTS,SENSORRESOLUTIONANDUNCERTAINTY,NONSPHERICITYOFTHEJOINTMOTIONS,ANDOTHEREFFECTSINHERENTTOTHEPARTICULARMACHINEWHICHMAYCAUSENONREPEATABILITYOFPOSITIONING3COMBINETHESETWOUNCERTAINTYSOURCESTOESTIMATETHEOVERALLUNCERTAINTYPRESENTINTHECOLLECTEDMEASUREMENTDATAUSEDBYTHECALIBRATIONALGORITHMTOOBTAINMODELPARAMETERSFIG1A12JOINTSIXSIXSTEWARTPLATFORMDEVICE49BJOKIELETAL/PRECISIONENGINEERING25200148–554CONSTRUCTA“PERFECT”DATASETFROMTHEMACHINEMODEL,WHICHASSUMESNOUNCERTAINTIESEXISTINTHEMEASURINGINSTRUMENTSORMACHINE5PERFORMAMONTECARLOSIMULATIONOFTHECALIBRATIONPROCESSBYRUNNINGTHECALIBRATIONALGORITHMMULTIPLETIMES,EACHTIMECORRUPTINGTHE“PERFECT”DATASETWITHRANDOMLYGENERATEDERRORSASSUMINGAUNIFORMDISTRIBUTIONOVERTHEUNCERTAINTYBOUNDSPREDICTEDBYTHECOMBINEDERRORBUDGETANALYSES6ANALYZETHEDISTRIBUTIONOFERRORSINTHEMODELPARAMETERSOBTAINEDFROMTHEMONTECARLOSIMULATION7USINGTHEMACHINEKINEMATICMODELWITHEACHSETOFMODELPARAMETERSOBTAINEDFROMTHECALIBRATIONSIMULATION,SIMULATETHEMACHINEMOTIONSDURINGAPARTICULARMACHINEACCURACYPERFORMANCETESTIE,CIRCULARBALLBARTESTS,LASERINTERFEROMETRICDISPLACEMENTMEASUREMENTS,ETC,BEINGSURETOINCLUDETHEUNCERTAINTYASSOCIATEDWITHTHEMACHINEITSELFINTHESIMULATION8ANALYZETHESIMULATEDPERFORMANCEDATATHERESULTSOFTHISSIMULATIONWILLSHOWTHERANGEOFRESULTSONEISLIKELYTOACHIEVEONTHEFINALMACHINEPOSITIONINGPERFORMANCETESTSFROMAPARTICULARCALIBRATIONPROCEDURETHISPROCEDUREISOUTLINEDINTHEFLOWCHARTINFIGURE2ITISALSOPOSSIBLETOMODIFYTHESESIMULATIONSTOEXAMINETHEEFFECTOFVARIOUSCONTRIBUTORSTOTHEOVERALLPOSITIONINGPERFORMANCEOFTHEMACHINEFOREXAMPLE,ONEMIGHTASSUMETHATTHEMACHINEITSELFISPERFECTTODETERMINEHOWUNCERTAINTIESINTHEEXTERNALCALIBRATIONMEASUREMENTINSTRUMENTSCONTRIBUTETOMACHINEPOSITIONINGERRORSCONVERSELY,ONECANASSUMETHATTHEEXTERNALMEASUREMENTSAREPERFECTANDEXAMINETHEPROPAGATIONOFVARIOUSSOURCESOFMACHINEERROR,SUCHASTHERMALEFFECTSORNONSPHERICITYOFJOINTMOTIONS,TOTHEFINALPOSITIONINGACCURACYPERFORMANCE3CALIBRATIONMETHODOLOGY–SEQUENTIALDETERMINATIONTECHNIQUETHEAPPROACHOUTLINEDINSECTION2WASUSEDTOEVALUATEUNCERTAINTYPROPAGATIONINCALIBRATIONOFPKMDEVICESFORANEWMETHODFORSEQUENTIALDETERMINATIONOFKINEMATICPARAMETERSINPKMSDEVELOPEDBYTHEAUTHORSANDREPORTEDELSEWHERE10ASACONVENIENCETOTHEREADER,THISMETHODISBRIEFLYDESCRIBEDHERETHEPARAMETERIDENTIFICATIONMETHODUSESASPATIALCOORDINATEMEASURINGDEVICESUCHASALASERTRACKERORALASERBALLBARTHECALIBRATIONISPERFORMEDINFOURSTEPS1LOCATIONOFACENTRALREFERENCEFRAMERANDTHEMACHINEFRAMEM2IDENTIFICATIONOFTHESPATIALLOCATIONSOFTHEJOINTS’CENTERSOFROTATION3DETERMINATIONOFTHESPINDLEORIENTATIONANDNOSELOCATION4DETERMINATIONOFTHEINITIALSTRUTLENGTHS31LOCATINGTHECENTRALREFERENCEANDMACH

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