nedsurface.Severalresearchershavedevelopeddifferentinterpolationalgorithmsforparametriccurvestoimprovemotionspeedaccuracy.Bedietal.[]set△(ui)asaconstanttoformtheuniforminterpolationalgorithmwhichisthesimplestmethodanditschorderrorandcurvespeedhoweverarenotguaranteed.AccordingtotheanalysisofCNCmachinekinematicsandcutterpathgeometry,animprovedinterpolationalgorithminposition,velocity,andaccelerationsplinecurveandB-splinesurfaceinterpolationalgorithmtoobtainbothaccuratecurvesandgougefreesurface.HuangandYang[]developedageneralizedinterpolationalgorithmfordifferentparametriccurveswithimprovedspeedfluctuation.Moreover,YangandKong[]studiedbothlinearandparametricinterpolatorsformachiningprocesses.IntheseCNCsystems,parametriccurvesareprofilesindifferentformatsliketheBeziercurve,B-spline,cubicspline,andNURBS(non-uniformrationalB-spline).Thegeneralparameteriterationmethodusedis错误!未指定书签。ui+=ui+△(ui)whereuiisthepresentparameter,ui+isthenextparameter,and△(ui)istheincrementalvalue.Theinterpolatedpointsarecalculatedbysubstitutinguiintothecorrespondingmathematicalmodeltorecovertheoriginallydesignedcurves.Asthecuttermovesstraightbetweencontiguousinterpolatedpoints,twopositionerrorsmayoccuras:(a)radialerror;and(b)chorderror[]duringmotionforaparametriccurveasshowninFig..CADCNCFig..ThemachiningsystemswithparameterstransmissionParametriccurveCutterpath●DRadialerrorAChorderrorInterpolatedB●CSegmentationParametriccurverepresentedmodelParametriccurveinterpolatorToolmotionMan-MachineinterfacedeviceFig..TheradialerrorandthechorderrorTheradialerroristheperpendiculardistancebetweentheinterpolatedpointsandtheparametriccurve.Basically,theradialerroriscausedbytheroundingerrorofcomputersysterms.Withtherapiddevelopmentofmicroprocessorswithhigherprecision,theradialerrorisnolongeramajorconcerninpresentapplications.Inaddition,thechorderroristhemaximumdistancebetweenthesecantCDandthesecantarcAB.Asmallcurvatureradiuswithafastfeedratecommandmaycausethechorderror.Thus,anadaptivefeedrateisrequiredtokeepthechorderrorwithinanacceptablerange.However,cuttingspeeddominatesthequalityofthemachiningprocess.Toachievethespecifiedfeedrateforparametriccurvesisusuallydifficult.Theundesirablemotionspeedmaydeterioratethequalityofthemachinedsurface.Severalresearchershavedevelopeddifferentinterpolationalgorithmsforparametriccurvestoimprovemotionspeedaccuracy.Bedietal.[]set△(ui)asaconstanttoformtheuniforminterpolationalgorithmwhichisthesimplestmethodanditschorderrorandcurvespeedhoweverarenotguaranteed.AccordingtotheanalysisofCNCmachinekinematicsandcutterpathgeometry,animprovedinterpolationalgorithminposition,velocity,andacceleration是––[],[],[],[],[],[],[](毫米).––●权向量是W=[].●结点矢量是U=[////].插补过程如下:●插补中取样时间Ts=.s●进料速度指令F=毫米/s=m/最小.在许多近年来应用中,机床加工都是以高速机加工这样很高速度进行,比如高速磨[-],直线电动机加工[,],和激光加工[]。在这例子中,提供可造成锐角权向量被用于检测在进料速度指令F=毫米/秒=米/分钟下不同插补运算法则速度偏离。..恒速模式不同插补运算法则切削速度波动按以下方面比较:(a)均匀性,(b)第一位近似值[,,],(c)第二位近似值[,]和(d)被提议速度控制模式。不同插补运算法仿真结果如图-所示,总结如表所示。中间点切削速度变动比通过公式ηi=(F-Vi)/F计算。这里Vi是从插补点C(ui)到C(ui+)切削速度,F是给定进料速度指令。从仿真结果来看,除均匀插补运算法则以外大多数插补运算法则产生导致有相对较小弦误差高度轮廓准确性。如图-所示,所有最大速度偏离都发生在四个锐角转角处。而且,在插补期间速度控制插补机产生最好切削速度准确性。仿真结果表明,现代速度控制插补机应用使切削速度偏离在[-.,.]毫米/秒以内。但是,第二位近似值产生毫米/秒计时(秒)图第一位近似值仿真结果.毫米/秒......计时(秒)图第二位近似值仿真结果毫米/秒.........计时(秒)图当前恒速度插补仿真结果.较大速度偏离在[-.,.]毫米/秒以内,第一位近似值达成最大速度偏离在[-,]毫米/s以内。数量级(ˉ)–.––.––.–计时(秒)图二次方程式根ε,(ui).通过当前运算法则应用,补偿值二次方程根如图所示。图表明,被采用根在零附近,而另一个根是相对较大负数。因为不明确曲线加工真正路径以及参数不均匀,所以通过均匀插补运算法则达到切削速度准确性是最坏情况。虽然现在插补运算法则需要一个比较长时间来计算补偿值,但是通过更新处理器可以明显缩短它处理时间以达到所需要性能。..ACC/DEC模式当开始减慢轴向运动时,为了避免振动或者机械系统波动,在机加工过程中需要ACC/DEC运算法。通常参数曲线ACC/DEC运算法则造成较大径向和弦误差。速度偏离(毫米/秒)..............计时(秒)图加速期间速度第一位近似值误差速度偏离(毫米/秒)ˉ......计时(秒)图加速期间加速第二位近似值误差.Kim[]提出了参数ACC/DEC运算法则。实际上,影射曲线和参数之间绘制不是均匀,ACC/DEC在均匀参数插补运算中不能获得所需加速和减速。不同加速外形如直线,抛物线,指数,它们切削速度误差有不同运算法则,如比较(a)第一位近似值(b)第二位近似值(c)速度控制插补。通过用抛物线ACC/DEC方法切削速度误差如图-所示,总结如表所示。结果表明采用指数ACC/DEC方法产生最大速度误差,而采用抛物线ACC/DEC方法产生最小速度误差,依照模拟结果,在加速过程中,切削速度也是按抛物线形式改变。结果也表明,当前插补运算法则可达到最好速度准确性,误差比其它方法低-个数量级。速度偏离(毫米/秒)ˉ............计时(秒)图加速期间速度控制插补机误差表不同插补计算法则仿真结果类型测量速度误差均方(毫米/秒)最大速度变化比最大弦错差(毫米)MHZ处理器计算时间(微秒)MHZ处理器计算时间(微秒)均匀...第一位近似值[,,]...第二位近似值[,,].ˉ..恒速.ˉ.ˉ.表最大切削速度误差测量插补ACC类型直线(毫米/秒)抛物线(毫米/秒)指数类型(毫米/秒)第一位近似值.ˉ.ˉ.ˉ第二位近似值.ˉ.ˉ.ˉ速度-控制.ˉ.ˉ.ˉ通常,在实际加工不同速度外形机加工中,如直线,抛物线,指数类型,ACC/DEC功能是必须[,]。在这篇论文中,除了在加工过程中,速度是减退以外,减速运算法则和加速运算法则是相同。结果表明现在速度控制插补运算法则通过采用指定ACC/DEC速度类型可达到平滑加速和减速。.结论:被提议速度控制插补运算法则通过包括补偿值办法,已经明显提高了参数曲线切削速度准确性。恒速模式用恒定不变切削速度作用于相邻插补点,ACC/DEC模式产生连续平滑速度变化插补点。在实际机加工过程中,被提议插补运算法则在位置和速度方面都提供了最好准确性。尽管用被提议插补运算法则花费加工时间长一点,但是可以用更快计算机来成功地执行。splinecurveandB-splinesurfaceinterpolationalgorithmtoobtainbothaccuratecurvesandgougefreesurface.HuangandYang[]developedageneralizedinterpolationalgorithmfordifferentparametriccurveswithimprovedspeedfluctuation.Moreover,YangandKong[]studiedbothlinearandparametricinterpolatorsformachiningprocesses.IntheseCNCsystems,parametriccurvesareprofilesindifferentformatsliketheBeziercurve,B-spline,cubicspline附录A:英文资料Thespeed-controlledinterpolatorformachiningparametriccurvesS.-S.Yeh,P.-L.HsuAbstract:ModernCNCsystemsaredesignedwiththefunctionofmachiningarbitraryparametriccurvestosavemassivedatacommunicationbetweenCAD/CAMandCNCsystemsandimprovetheirmachiningquality.AlthoughavailableCNCinterpolatorsforparametriccurvesgenerallyachievecontouringpositionaccuracy,thespecifiedfederate,withdominatesthequalityofthemachiningprocesses,isnotguaranteedduringmotion.Recently,someapproximationresultsconcerningmotionspeedhavebeenreported[ShpitalniM,KorenY,LoCC.Computer-AidedDesign;():-;BediS,AliI,QuanN.TransASMEJEngngIndustry;:-;ChouJJ,YangDCH.Trans.ASMEJEngngIndustry;:-;ChouJJ,YangDCH.TransASMEJEngngIndustry;:-].Inthispaper,byderivingacompensatoryparameter,theproposedinterpolationalgorithmhassignificantlyimprovedcurvespeedaccuracy.Inrealapplications,theproposedalgorithmresultsin:()constantspeed;and()specifiedaccelerationanddecelerationanddeceleration(ACC/DEC)tomeetthefeedratecommands.Themotionaccuracyandfeasibilityofthepresentinterpolatorhavebeenverifiedwithaprovidednon-uniformrationalB-spline(NURBS)example.ElsevierScienceLtd.Allrightsreserved.Keywords:Parametriccurve;CNCinterpolators;Speedaccuracy;NURBS.Introduction:InmodernCAD/CAMsystems,profilesforpartslikedies,vanes,aircraftmodelsareusuallyrepresentedinparametricforms.AsconventionalCNCmachinesonlyprovidelinearandcirculararcinterpolators,theCAD/CAMsystemshavetosegmentacurveintoahugenumberofsmall,linearizedsegmentsandsendthemtoCNCsystems.Suchlinearized-segmentedcontoursprocessedontraditionalCNCsystemsareundesirableinrealapplicationsasfollows:●thetransmissionerrorbetweenCAD/CAMandCNCsystemsforahugenumberofdatamayeasilyoccur,i.e.lostdataandnoiseperturbation;●thediscontinuityofsegmentationdeterioratessurfaceaccuracy;●themotionspeedbecomesunsmoothbecauseofthelinearizationofthecurveineachsegment,especiallyinaccelerationanddeceleration.Asthegeneratedcurvesorprofilesmaybeinaparametricform,onlyparametriccurveinformationisrequiredtobeefficientlytransferredamongCAD/CAM/CNCsystemsasshowninFig.I.Shpitalnietal.[]proposedthecurvesegmentstransferbetweenCADandCNCsystemsandBedietal.[]proposedtheB-splinecurveandB-splinesurfaceinterpolationalgorithmtoobtainbothaccuratecurvesandgougefreesurface.HuangandYang[]developedageneralizedinterpolationalgorithmfordifferentparametriccurveswithimprovedspeedfluctuation.Moreover,YangandKong[]studiedbothlinearandparametricinterpolatorsformachiningprocesses.IntheseCNCsystems,parametriccurvesareprofilesindifferentformatsliketheBeziercurve,B-spline,cubicspline,andNURBS(non-uniformrationalB-spline).Thegeneralparameteriterationmethodusedis错误!未指定书签。ui+=ui+△(ui)whereuiisthepresentparameter,ui+isthenextparameter,and△(ui)istheincrementalvalue.Theinterpolatedpointsarecalculatedbysubstitutinguiintothecorrespondingmathematicalmodeltorecovertheoriginallydesignedcurves.Asthecuttermovesstraightbetweencontiguousinterpolatedpoints,twopositionerrorsmayoccuras:(a)radialerror;and(b)chorderror[]duringmotionforaparametriccurveasshowninFig..CADCNCFig..ThemachiningsystemswithparameterstransmissionParametriccurveCutterpath●DRadialerrorAChorderrorInterpolatedB●CSegmentationParametriccurverepresentedmodelParametriccurveinterpolatorToolmotionMan-MachineinterfacedeviceFig..TheradialerrorandthechorderrorTheradialerroristheperpendiculardistancebetweentheinterpolatedpointsandtheparametriccurve.Basically,theradialerroriscausedbytheroundingerrorofcomputersysterms.Withtherapiddevelopmentofmicroprocessorswithhigherprecision,theradialerrorisnolongeramajorconcerninpresentapplications.Inaddition,thechorderroristhemaximumdistancebetweenthesecantCDandthesecantarcAB.Asmallcurvatureradiuswithafastfeedratecommandmaycausethechorderror.Thus,anadaptiv 附录A:英文资料Thespeed-controlledinterpolatorformachiningparametriccurvesS.-S.Yeh,P.-L.HsuAbstract:ModernCNCsystemsaredesignedwiththefunctionofmachiningarbitraryparametriccurvestosavemassivedatacommunicationbetweenCAD/CAMandCNCsystemsandimprovetheirmachiningquality.AlthoughavailableCNCinterpolatorsforparametriccurvesgenerallyachievecontouringpositionaccura