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外文翻译加工参数曲线的速度控制插补器.doc

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外文翻译加工参数曲线的速度控制插补器.doc

附录A英文资料THESPEEDCONTROLLEDINTERPOLATORFORMACHININGPARAMETRICCURVESSSYEH,PLHSUABSTRACTMODERNCNCSYSTEMSAREDESIGNEDWITHTHEFUNCTIONOFMACHININGARBITRARYPARAMETRICCURVESTOSAVEMASSIVEDATACOMMUNICATIONBETWEENCAD/CAMANDCNCSYSTEMSANDIMPROVETHEIRMACHININGQUALITYALTHOUGHAVAILABLECNCINTERPOLATORSFORPARAMETRICCURVESGENERALLYACHIEVECONTOURINGPOSITIONACCURACY,THESPECIFIEDFEDERATE,WITHDOMINATESTHEQUALITYOFTHEMACHININGPROCESSES,ISNOTGUARANTEEDDURINGMOTIONRECENTLY,SOMEAPPROXIMATIONRESULTSCONCERNINGMOTIONSPEEDHAVEBEENREPORTEDSHPITALNIM,KORENY,LOCCCOMPUTERAIDEDDESIGN1994;2611832838;BEDIS,ALII,QUANNTRANSASMEJENGNGINDUSTRY1993;115329336;CHOUJJ,YANGDCHTRANSASMEJENGNGINDUSTRY1991;113305310;CHOUJJ,YANGDCHTRANSASMEJENGNGINDUSTRY1992;1141522INTHISPAPER,BYDERIVINGACOMPENSATORYPARAMETER,THEPROPOSEDINTERPOLATIONALGORITHMHASSIGNIFICANTLYIMPROVEDCURVESPEEDACCURACYINREALAPPLICATIONS,THEPROPOSEDALGORITHMRESULTSIN1CONSTANTSPEED;AND2SPECIFIEDACCELERATIONANDDECELERATIONANDDECELERATIONACC/DECTOMEETTHEFEEDRATECOMMANDSTHEMOTIONACCURACYANDFEASIBILITYOFTHEPRESENTINTERPOLATORHAVEBEENVERIFIEDWITHAPROVIDEDNONUNIFORMRATIONALBSPLINENURBSEXAMPLE1999ELSEVIERSCIENCELTDALLRIGHTSRESERVEDKEYWORDSPARAMETRICCURVE;CNCINTERPOLATORS;SPEEDACCURACY;NURBS1INTRODUCTIONINMODERNCAD/CAMSYSTEMS,PROFILESFORPARTSLIKEDIES,VANES,AIRCRAFTMODELSAREUSUALLYREPRESENTEDINPARAMETRICFORMSASCONVENTIONALCNCMACHINESONLYPROVIDELINEARANDCIRCULARARCINTERPOLATORS,THECAD/CAMSYSTEMSHAVETOSEGMENTACURVEINTOAHUGENUMBEROFSMALL,LINEARIZEDSEGMENTSANDSENDTHEMTOCNCSYSTEMSSUCHLINEARIZEDSEGMENTEDCONTOURSPROCESSEDONTRADITIONALCNCSYSTEMSAREUNDESIRABLEINREALAPPLICATIONSASFOLLOWS●THETRANSMISSIONERRORBETWEENCAD/CAMANDCNCSYSTEMSFORAHUGENUMBEROFDATAMAYEASILYOCCUR,IELOSTDATAANDNOISEPERTURBATION;●THEDISCONTINUITYOFSEGMENTATIONDETERIORATESSURFACEACCURACY;●THEMOTIONSPEEDBECOMESUNSMOOTHBECAUSEOFTHELINEARIZATIONOFTHECURVEINEACHSEGMENT,ESPECIALLYINACCELERATIONANDDECELERATIONASTHEGENERATEDCURVESORPROFILESMAYBEINAPARAMETRICFORM,ONLYPARAMETRICCURVEINFORMATIONISREQUIREDTOBEEFFICIENTLYTRANSFERREDAMONGCAD/CAM/CNCSYSTEMSASSHOWNINFIGISHPITALNIETAL1PROPOSEDTHECURVESEGMENTSTRANSFERBETWEENCADANDCNCSYSTEMSANDBEDIETAL2PROPOSEDTHEBSPLINECURVEANDBSPLINESURFACEINTERPOLATIONALGORITHMTOOBTAINBOTHACCURATECURVESANDGOUGEFREESURFACEHUANGANDYANG3DEVELOPEDAGENERALIZEDINTERPOLATIONALGORITHMFORDIFFERENTPARAMETRICCURVESWITHIMPROVEDSPEEDFLUCTUATIONMOREOVER,YANGANDKONG4STUDIEDBOTHLINEARANDPARAMETRICINTERPOLATORSFORMACHININGPROCESSESINTHESECNCSYSTEMS,PARAMETRICCURVESAREPROFILESINDIFFERENTFORMATSLIKETHEBEZIERCURVE,BSPLINE,CUBICSPLINE,ANDNURBSNONUNIFORMRATIONALBSPLINETHEGENERALPARAMETERITERATIONMETHODUSEDIS错误未指定书签。UI1UI△UIWHEREUIISTHEPRESENTPARAMETER,UI1ISTHENEXTPARAMETER,AND△UIISTHEINCREMENTALVALUETHEINTERPOLATEDPOINTSARECALCULATEDBYSUBSTITUTINGUIINTOTHECORRESPONDINGMATHEMATICALMODELTORECOVERTHEORIGINALLYDESIGNEDCURVESASTHECUTTERMOVESSTRAIGHTBETWEENCONTIGUOUSINTERPOLATEDPOINTS,TWOPOSITIONERRORSMAYOCCURASARADIALERROR;ANDBCHORDERROR5DURINGMOTIONFORAPARAMETRICCURVEASSHOWNINFIG2CADCNCFIG1THEMACHININGSYSTEMSWITHPARAMETERSTRANSMISSIONPARAMETRICCURVECUTTERPATH●DRADIALERRORACHORDERRORINTERPOLATEDB●CSEGMENTATIONPARAMETRICCURVEREPRESENTEDMODELPARAMETRICCURVEINTERPOLATORTOOLMOTIONMANMACHINEINTERFACEDEVICEFIG2THERADIALERRORANDTHECHORDERRORTHERADIALERRORISTHEPERPENDICULARDISTANCEBETWEENTHEINTERPOLATEDPOINTSANDTHEPARAMETRICCURVEBASICALLY,THERADIALERRORISCAUSEDBYTHEROUNDINGERROROFCOMPUTERSYSTERMSWITHTHERAPIDDEVELOPMENTOFMICROPROCESSORSWITHHIGHERPRECISION,THERADIALERRORISNOLONGERAMAJORCONCERNINPRESENTAPPLICATIONSINADDITION,THECHORDERRORISTHEMAXIMUMDISTANCEBETWEENTHESECANTCDANDTHESECANTARCABASMALLCURVATURERADIUSWITHAFASTFEEDRATECOMMANDMAYCAUSETHECHORDERRORTHUS,ANADAPTIVEFEEDRATEISREQUIREDTOKEEPTHECHORDERRORWITHINANACCEPTABLERANGEHOWEVER,CUTTINGSPEEDDOMINATESTHEQUALITYOFTHEMACHININGPROCESSTOACHIEVETHESPECIFIEDFEEDRATEFORPARAMETRICCURVESISUSUALLYDIFFICULTTHEUNDESIRABLEMOTIONSPEEDMAYDETERIORATETHEQUALITYOFTHEMACHINEDSURFACESEVERALRESEARCHERSHAVEDEVELOPEDDIFFERENTINTERPOLATIONALGORITHMSFORPARAMETRICCURVESTOIMPROVEMOTIONSPEEDACCURACYBEDIETAL2SET△UIASACONSTANTTOFORMTHEUNIFORMINTERPOLATIONALGORITHMWHICHISTHESIMPLESTMETHODANDITSCHORDERRORANDCURVESPEEDHOWEVERARENOTGUARANTEEDACCORDINGTOTHEANALYSISOFCNCMACHINEKINEMATICSANDCUTTERPATHGEOMETRY,ANIMPROVEDINTERPOLATIONALGORITHMINPOSITION,VELOCITY,ANDACCELERATIONWASPROPOSEDBYCHOUANDYANG6IFTHECNCMACHINEKINEMATICSMODELISKNOWNEXACTLYFURTHER,HOUNGANDYANG3DEVELOPEDTHECUBICSPLINEPARAMETRICCURVEINTERPOLATORBYUSINGTHEEULERMETHODSHPITALNIETAL1DERIVEDTHESAMEINTERPOLATORALGORITHMBYUSINGTAYLOR’SEXPANSIONLOANDCHUNG7PROPOSEDTHECONTOURINGERRORCOMPENSATIONINTERPOLATIONALGORITHMWHICHCONTAINSREALTIMECONTOURINGERRORCALCULATIONSANDASIMPLIFIEDPARAMETERITERATIONMETHODTOACHIEVESATISFACTORYMOTIONACCURACYINACCELERATIONANDDECELERATION,KIM8OBTAINEDASIMPLEMETHODFORPARAMETRICCURVESWHILEITSPOSITIONANDSPEEDERRORSARESIGNIFICANTTHEPRESENTSPEEDCONTROLLEDINTERPOLATIONALGORITHMISPROPOSEDBYDERIVINGASUITABLECOMPENSATORYPARAMETERFORTHEFIRSTORDERAPPROXIMATION1,6,8TOOBTAINDESIRABLEMOTIONSPEEDTHEN,THEPROPOSEDINTERPOLATORISAPPLIEDTOTHECONSTANTSPEEDMODEANDTHEACCELERATION/DECELERATIONMODETOACHIEVECONSTANTFEEDRATEANDTHESPECIFIEDSPEEDPROFILES,RESPECTIVELYTHUS,THEPRESENTCNCINTERPOLATORSRESULTINSTABLEMOTIONANDSMOOTHLYCHANGEDSPEEDTOAVOIDMECHANICALSHOCKORVIBRATIONINMACHININGPROCESSESTHEPROPOSEDSPEEDCONTROLLEDINTERPOLATORSHAVEALSOBEENSUCCESSFULLYAPPLIEDTOANURBSCOMMANDONAPERSONALCOMPUTERTOACHIEVEHIGHMOTIONPRECISION2PARAMETRICCURVEFORMULATIONSUPPOSECUISTHEPARAMETRICCURVEREPRESENTATIONFUNCTIONANDTHETIMEFUNCTIONUISTHECURVEPARAMETERASUTIUIANDUTI1UI1BYUSINGTAYLOR’SEXPANSION,THEAPPROXIMATIONUPTOTHESECONDDERIVATIVEISUI1UIDU/DT│TTITI1–TI1/2D2U/DT2│TTITI1–TI2HOT1ASTHECURVESPEEDVUICANBEREPRESENTEDASVUI‖DCU/DT‖UUI‖DCU/DU‖UUIDU/DT│TTITHEFIRSTDERIVATIVEOFUWITHTISOBTAINEDASDU/DT│TTIVUI/‖DCU/DT‖UUI2BYTAKINGTHEDERIVATIVEOFEQ2,THESECONDDERIVATIVEOFUWITHTISDU/DT│TTI–1/‖DCU/DT‖2UUI{VUID‖DCU/DT‖│UUI/DT}3WHERED‖DCU/DT‖│UUI/DT{D‖DCU/DU‖│UUI/DT}DU/DT│TTI{D‖DCU/DT‖│UUI/DT}{VUI/‖DCU/DU‖UUI}4BYSUBSTITUTINGEQ4INTOEQ3,THESECONDDERIVATIVEOFUISREWRITTENASD2U/DT2│TTI–V2UI/‖DCU/DU‖3UUI{D‖DCU/DU‖│UUI/DU}5WHERED‖DCU/DU‖│UUI/DUDCU/DUD2CU/DU2/‖DCU/DU‖UUI6BYSUBSTITUTINGEQ6INTOEQ5,THESECONDDERIVATIVEOFUBECAMESD2U/DT2│TTI–V2UIDCU/DUD2CU/DU2/‖DCU/DU‖4UUI7LETTHESAMPLINGTIMEININTERPOLATIONBETSSECONDSANDTI1-TITSTHEFIRSTANDSECONDORDERAPPROXIMATIONINTERPOLATIONALGORITHMSAREOBTAINEDBYSUBSTITUTINGEQS2AND7INTOEQ1,RESPECTIVELYBYNEGLECTINGTHEHIGHERORDERTERM,THEINTERPOLATIONALGORITHMSINEQ1CANBEPROCESSEDASFOLLOWSTHEFIRSTORDERAPPROXIMATIONINTERPOLATIONALGORITHM1,6,9UI1UIVUITS/‖DCU/DU‖UUI8THESECONDORDERAPPROXIMATIONINTERPOLATIONALGORITHM6,9UI1UIVUITS/‖DCU/DU‖UUI–{V2UIT2SDCU/DUD2CU/DU2│UUI}/2‖DCU/DU‖UUI9WHEREVUICANBEEITHERTHEFEEDRATECOMMAND,THESPECIFIEDSPEEDPROFILESOFACC/DEC,ORANYDESIREDSPEEDINAGENERALMACHININGPROCESS3THESPEEDCONTROLLEDINTERPOLATIONALGORITHM31THECOMPENSATORYPARAMETERINEQS8AND9,THEFIRSTORDERANDTHESECONDORDERINTERPOLATIONALGORITHMSAREAPPROXIMATEDRESULTSBYNEGLECTINGTHEHIGHERORDERTERMASINEQ1THEREFORE,THE

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