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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ThespeedcontrolledinterpolatorformachiningparametriccurvesS.S.Yeh,P.L.HsuAbstractModernCNCsystemsaredesignedwiththefunctionofmachiningarbitraryparametriccurvestosavemassivedatacommunicationbetweenCAD/CAMandCNCsystemsandimprovetheirmachiningquality.AlthoughavailableCNCinterpolatorsforparametriccurvesgenerallyachievecontouringpositionaccuracy,thespecifiedfederate,withdominatesthequalityofthemachiningprocesses,isnotguaranteedduringmotion.Recently,someapproximationresultsconcerningmotionspeedhavebeenreportedShpitalniM,KorenY,LoCC.ComputerAidedDesign19942611832838BediS,AliI,QuanN.TransASMEJEngngIndustry1993115329336ChouJJ,YangDCH.Trans.ASMEJEngngIndustry1991113305310ChouJJ,YangDCH.TransASMEJEngngIndustry19921141522.Inthispaper,byderivingacompensatoryparameter,theproposedinterpolationalgorithmhassignificantlyimprovedcurvespeedaccuracy.Inrealapplications,theproposedalgorithmresultsin1constantspeedand2specifiedaccelerationanddecelerationanddecelerationACC/DECtomeetthefeedratecommands.ThemotionaccuracyandfeasibilityofthepresentinterpolatorhavebeenverifiedwithaprovidednonuniformrationalBsplineNURBSexample.©1999ElsevierScienceLtd.Allrightsreserved.KeywordsParametriccurveCNCinterpolatorsSpeedaccuracyNURBS1.IntroductionInmodernCAD/CAMsystems,profilesforpartslikedies,vanes,aircraftmodelsareusuallyrepresentedinparametricforms.AsconventionalCNCmachinesonlyprovidelinearandcirculararcinterpolators,theCAD/CAMsystemshavetosegmentacurveintoahugenumberofsmall,linearizedsegmentsandsendthemtoCNCsystems.SuchlinearizedsegmentedcontoursprocessedontraditionalCNCsystemsareundesirableinrealapplicationsasfollows●thetransmissionerrorbetweenCAD/CAMandCNCsystemsforahugenumberofdatamayeasilyoccur,i.e.lostdataandnoiseperturbation●thediscontinuityofsegmentationdeterioratessurfaceaccuracy●themotionspeedbecomesunsmoothbecauseofthelinearizationofthecurveineachsegment,especiallyinaccelerationanddeceleration.Asthegeneratedcurvesorprofilesmaybeinaparametricform,onlyparametriccurveinformationisrequiredtobeefficientlytransferredamongCAD/CAM/CNCsystemsasshowninFig.I.Shpitalnietal.1proposedthecurvesegmentstransferbetweenCADandCNCsystemsandBedietal.2proposedtheBsplinecurveandBsplinesurfaceinterpolationalgorithmtoobtainbothaccuratecurvesandgougefreesurface.HuangandYang3developedageneralizedinterpolationalgorithmfordifferentparametriccurveswithimprovedspeedfluctuation.Moreover,YangandKong4studiedbothlinearandparametricinterpolatorsformachiningprocesses.IntheseCNCsystems,parametriccurvesareprofilesindifferentformatsliketheBeziercurve,Bspline,cubicspline,andNURBSnonuniformrationalBspline.Thegeneralparameteriterationmethodusedis错误未指定书签。ui1ui△uiwhereuiisthepresentparameter,ui1isthenextparameter,and△uiistheincrementalvalue.Theinterpolatedpointsarecalculatedbysubstitutinguiintothecorrespondingmathematicalmodeltorecovertheoriginallydesignedcurves.Asthecuttermovesstraightbetweencontiguousinterpolatedpoints,twopositionerrorsmayoccurasaradialerrorandbchorderror5duringmotionforaparametriccurveasshowninFig.2.CADCNCFig.1.ThemachiningsystemswithparameterstransmissionParametriccurveCutterpath●DRadialerrorAChorderrorInterpolatedB●CSegmentationParametriccurverepresentedmodelParametriccurveinterpolatorToolmotionManMachineinterfacedeviceFig.2.TheradialerrorandthechorderrorTheradialerroristheperpendiculardistancebetweentheinterpolatedpointsandtheparametriccurve.Basically,theradialerroriscausedbytheroundingerrorofcomputersysterms.Withtherapiddevelopmentofmicroprocessorswithhigherprecision,theradialerrorisnolongeramajorconcerninpresentapplications.Inaddition,thechorderroristhemaximumdistancebetweenthesecantCDandthesecantarcAB.Asmallcurvatureradiuswithafastfeedratecommandmaycausethechorderror.Thus,anadaptivefeedrateisrequiredtokeepthechorderrorwithinanacceptablerange.However,cuttingspeeddominatesthequalityofthemachiningprocess.Toachievethespecifiedfeedrateforparametriccurvesisusuallydifficult.Theundesirablemotionspeedmaydeterioratethequalityofthemachinedsurface.Severalresearchershavedevelopeddifferentinterpolationalgorithmsforparametriccurvestoimprovemotionspeedaccuracy.Bedietal.2set△uiasaconstanttoformtheuniforminterpolationalgorithmwhichisthesimplestmethodanditschorderrorandcurvespeedhoweverarenotguaranteed.AccordingtotheanalysisofCNCmachinekinematicsandcutterpathgeometry,animprovedinterpolationalgorithminposition,velocity,andaccelerationwasproposedbyChouandYang6iftheCNCmachinekinematicsmodelisknownexactly.Further,HoungandYang3developedthecubicsplineparametriccurveinterpolatorbyusingtheEulermethod.Shpitalnietal.1derivedthesameinterpolatoralgorithmbyusingTaylorsexpansion.LoandChung7proposedthecontouringerrorcompensationinterpolationalgorithmwhichcontainsrealtimecontouringerrorcalculationsandasimplifiedparameteriterationmethodtoachievesatisfactorymotionaccuracy.Inaccelerationanddeceleration,Kim8obtainedasimplemethodforparametriccurveswhileitspositionandspeederrorsaresignificant.Thepresentspeedcontrolledinterpolationalgorithmisproposedbyderivingasuitablecompensatoryparameterforthefirstorderapproximation1,6,8toobtaindesirablemotionspeed.Then,theproposedinterpolatorisappliedtotheconstantspeedmodeandtheacceleration/decelerationmodetoachieveconstantfeedrateandthespecifiedspeedprofiles,respectively.Thus,thepresentCNCinterpolatorsresultinstablemotionandsmoothlychangedspeedtoavoidmechanicalshockorvibrationinmachiningprocesses.TheproposedspeedcontrolledinterpolatorshavealsobeensuccessfullyappliedtoaNURBScommandonapersonalcomputertoachievehighmotionprecision.2.ParametriccurveformulationSupposeCuistheparametriccurverepresentationfunctionandthetimefunctionuisthecurveparameterasutiuianduti1ui1ByusingTaylorsexpansion,theapproximationuptothesecondderivativeisui1uidu/dt│ttiti1–ti1/2d2u/dt2│ttiti1–ti2HOT1AsthecurvespeedVuicanberepresentedasVui‖dCu/dt‖uui‖dCu/du‖uuidu/dt│ttithefirstderivativeofuwithtisobtainedasdu/dt│ttiVui/‖dCu/dt‖uui2BytakingthederivativeofEq.2,thesecondderivativeofuwithtisd²u/dt²│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}4BysubstitutingEq.4intoEq.3,thesecondderivativeofuisrewrittenasd2u/dt2│tti–V2ui/‖dCu/du‖3uui{d‖dCu/du‖│uui/du}5whered‖dCu/du‖│uui/dudCu/dud2Cu/du2/‖dCu/du‖uui6BysubstitutingEq.6intoEq.5,thesecondderivativeofubecamesd2u/dt2│tti–V2uidCu/dud2Cu/du2/‖dCu/du‖4uui7LetthesamplingtimeininterpolationbeTssecondsandti1-tiTsThefirstandsecondorderapproximationinterpolationalgorithmsareobtainedbysubstitutingEqs.2and7intoEq.1,respectively.Byneglectingthehigherorderterm,theinterpolationalgorithmsinEq.1canbeprocessedasfollowsThefirstorderapproximationinterpolationalgorithm1,6,9ui1uiVuiTs/‖dCu/du‖uui8Thesecondorderapproximationinterpolationalgorithm6,9ui1uiVuiTs/‖dCu/du‖uui–{V2uiT2sdCu/dud2Cu/du2│uui}/2‖dCu/du‖uui9whereVuicanbeeitherthefeedratecommand,thespecifiedspeedprofilesofACC/DEC,oranydesiredspeedinageneralmachiningprocess.3.Thespeedcontrolledinterpolationalgorithm3.1.ThecompensatoryparameterInEqs.8and9,thefirstorderandthesecondorderinterpolationalgorithmsareapproximatedresultsbyneglectingthehigherordertermasinEq.1.Therefore,the

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