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机床误差分量的提取和利用统计分析误差补偿AbstractTheextractionofcomponenterrorsofamachinetool’saxesisacriticalstepforthesynthesisof3Dvolumetricerrormapping,whichisaprerequisitetoimprovethemachinetoolaccuracybynumericalErrorcompensation.Thispaperpresentsamethodfortheextractionofmachinetoolcomponenterrorsfromastatisticalpointofview.First,theB-SplinemathematicalmodelisestablishedtorepresenttheComponenterrorfunction,andtheleast-squaresfittingmethodtomeasureddatapointsispresented.Then,statisticalanalysisisusedtoselecttheB-Splinemodelwithproperflexibility,soastoseparaterepeatableerrorsfromrandomerrorsinthemeasureddata.Finally,basedonthecomponenterrorextractionmethod,numericalerrorcompensationexperimentswereconductedontheXY-planeofaHighprecisionmachinetoolbyusingacross-gridscalesystem.AccordingtothestatisticalanalysisofTheexperimentaldata,allrepeatableerrorsexceptthedynamicerrorscausedbymachinetoolcontrolsystemwerecompensatedfor.Keywords:Machinetoolaccuracy,Componenterror,B-Spline,Statisticalanalysis,Errormapping翻译：摘要机床的轴组件误差的提取是三维空间误差的映射的合成的关键一步，这是通过数值误差补偿提高机床精度一个先决条件。本文提出了一种从统计的角度来看的机床部件误差提取方法。首先，本文提出了描述元件误差函数的B样条曲线的数学模型和最小二乘拟合的方法来测量数据点。然后，利用统计分析来选择适当的灵活性B样条曲线模型，用来从测量数据的随机误差中分离重复误差。最后，在采用交叉网格尺度系统的高精度机床的XY平面上进行的基于误差分量的提取方法，数值误差补偿实验。根据实验数据的统计分析，所有的重复误差除了由机床控制引起的动态误差都得到了补偿。关键词：机床精度误差分量B样条统计分析错误映射1.IntroductionThemanufacturingofadvancedmechanicalpartsrequireshighlyaccuratemachinetools.Thedevelopmentofevenmoreaccuratemachinetoolshasbeenaconstantpursuitoftheprecisionengineeringcommunity.Duetogeometric,kinematic,thermal,cutting-force-induced,andothererrors,itisveryexpensivetofurtherimprovetheaccuracythroughdesignandmanufacturingsolely,especiallyatthesub-micronlevel[1,2].1.介绍先进的机械零件的制造要求精度高的机床。发展更加精密的机床是精密工程社区的不断追求。由于几何，运动学，热，剪切力，和其他的误差，通过进一步改善单独的设计和制造来提高精度是非常昂贵的，特别是在亚微米级[1,2]。Numericalerrorcompensationisacost-effectivewaytorealizehigh-precisionmachining.SincetheeffortdonebyHockenetal.[3],moreandmoreresearchhasbeencarriedoutonnumericalerrorcompensationformachinetoolsandcoordinatemeasuringmachines.Donmezetal.[4]presentedageneralmethodologyforthecompensationofquasi-staticmachinetoolerrors,includinggeometricerrorsandthermallyinducederrors.Inthismethod,homogeneoustransformationmatriceswereusedtodescribetherelativemotionbetweenadjacentmachinetoolaxes,andthevolumetricerrormodelwasacquiredbymultiplyingaseriesofhomogeneoustransformationmatrices.SartoriandZhang[5]reviewedthemethodsforgeometricerrormeasurementandcompensationthatweredevelopedbefore1995.Intheirpaper,theyhavedescribedthefoundationsofnumericalcompensation,includingacommonlanguageforerrormeasurementandcompensation,conditionsforcarryingoutsuccessfulerrorcompensation,variouserrormeasurementandcompensationmethods,etc.Recently,Schwenkeetal.[6]gaveanupdatedreviewonthemethodsforgeometricerrormeasurementandcompensationfromtheviewpointofpracticalapplication,includingtheappearanceofnewcalibrationmethods,newconceptsininternationalstandards,andgrowingcapabilitiesofmachinetoolcontrollersforerrorcompensation.数值误差补偿是一种具有成本效益来实现高精度加工的方式。由于霍肯等人所做的努力[3],已经进行了越来越多的基于对机床的数值误差补偿和坐标测量机的研究。Donmez等人[4]提出了一个通用的方法来进行准静态机床误差补偿，包括几何误差和热引起的误差。在该方法中，用齐次变换矩阵来描述相邻的刀具轴之间的相对运动，并用取得的空间误差模型乘以一系列的齐次变换矩阵。萨托利和张[5]回顾了在1995年之前发现的几何误差测量与补偿方法。在他们的论文中，他们描述了数字补偿的基础，包括误差测量与补偿的共同语言，实施成功误差补偿的条件，各种误差测量和方法等。最近,Schwenke等人[6]从实际应用的角度给出了一个基于几何误差测量和补偿的更新审查方法,包括新出现的校准方法,国际标准的新概念，和具有增长能力的机床误差补偿控制器。Moreover,mostpapersfocusedonthemathematicalmodelingofthemachinetoolvolumetricerror(3Dpositioningerror)andthemethods(instruments)tomeasurethesixcomponenterrorsofthemachinetoollinearaxis,i.e.positioningerror,horizontalstraightnesserror,verticalstraightnesserror,roll,pitch,andyawerrors.Realizingtheimportanceofmodelingofmachinetoolcomponenterrorstothesuccessfulsynthesisof3Dvolumetricerrors,severalresearchersdiscussedthemathematicalmodelingofcomponenterrorsbyprocessingtherawdatameasuredbyinstruments.Florussenetal.[7]usedordinarypolynomialfunctionstorepresentthecomponenterrors;thesquarerootofthemeansumofsquarederrorswasanalyzedtoselecttheappropriateorderofthepolynomialfunction.Konoetal.[8]analyzedmachinemotionerrorsinthefrequencydomaintoseparatethegeometricerrorsfromtime-dependenterrors.However,duetoleakageerrors,thetruncatedFourierseriesisnotabletodescribethecomponenterrorinbothofitsendsaccuratelybecausethemeasurederrordatararelysatisfytheperiodicproperty.Intheavailablemethodsforthemodelingofmachinetoolcomponenterrors[7,8],randomerrorsarecoupledwithrepeatableerrors.Forhighprecisionapplications(sub-micronlevel),randomerrorsofthemachinetoolmaybecomparabletorepeatableerrors,thustheseparationofrepeatableerrorsandrandomerrorsbecomesdesirable.Inthispaper,amethodisproposedtorepresentmachinetoolcomponenterrorsbyusingaB-Splinemodel.StatisticalanalysisisappliedtoselecttheB-Splinemodelwithproperflexibility,whichisusedtoextractthecomponenterrorfunctionfromthedataacquiredbyrepetitivemeasurements.Theextractederrorfunctionistreatedasrepeatableerrorsonly,andtherandomerrorsaredescribedbytheresidualerrors,whicharesubjecttoazeromeannormaldistribution.Inordertoverifytheeffecti