一種基于反距離權(quán)重法修正CMM體積誤差的方法

一種基于反距離權(quán)重法修正CMMCoordinateMeasurementMachine(CMM)hasbeenwidelyusedinindustryformeasuringthedimensionsofobjects.However,CMMvolumeerrorscanoccurduetovariousfactors,whichcanaffecttheaccuracyofmeasurementresults.Inthispaper,weproposeamethodbasedontheinversedistanceweightingmethodtocorrectCMMvolumeerrors,whichcaneffectivelyimprovethemeasurementaccuracyofCMMisanimportanttoolformeasuringthedimensionsofobjectsinindustry,whichplaysanimportantroleinensuringthequalityofproducts.However,theaccuracyofCMMmeasurementresultsisaffectedbymanyfactors,suchasthepositionandorientationoftheworkpiece,thedeformationofthemachinestructure,andthepositioningerrorsofthemeasurementprobe.Amongthem,thevolumeerroroftheCMMisakeyfactoraffectingthemeasurementaccuracy,whichiscausedbytheunevendistributionofthemeasurementpointsonthesurfaceoftheworkpieceandthenon-uniformdistributionofthemeasurementerrors.TosolvetheproblemofCMMvolumeerrors,manycorrectionmethodshavebeenproposed,suchasthepolynomialapproximationmethod,thesurfacefittingmethod,andtheconstraintoptimizationmethod.However,thesemethodshavelimitationsinpracticalapplications,suchashighcomputationalcomplexity,restrictionsonthetypeofworkpieces,andalackofflexibilityinhandlingcomplexInthispaper,weproposeamethodbasedontheinversedistanceweightingmethodtocorrectCMMvolumeerrors,whichissimple,flexible,andcanbeappliedtoawiderangeofworkpieces.ThemethodcaneffectivelyimprovethemeasurementaccuracyofCMM,whichhasimportantpracticalvalueforindustrialproduction.Theproposedmethodisbasedontheinversedistanceweightingmethod,whichisapopularinterpolationmethodinspatialanalysis.Thebasicideaofthemethodistoestimatethevalueofapointusingthevaluesofitsneighboringpoints,weightedbytheinverseoftheirdistancestothepoint.Theformulafortheinversedistanceweightingmethodisasfollows:V=∑(V_i/d_i^n)/∑(1/whereVistheestimatedvalueatthepointofinterest,V_iisthevalueatthei-thneighboringpoint,d_iisthedistancebetweenthepointofinterestandthei-thneighboringpoint,andnisapowerparameterthatcontrolstheinfluenceofdistantpointsontheestimatedvalue.Inourmethod,weusetheinversedistanceweightingmethodtoestimatethetruevolumeoftheworkpiecefromtheCMMmeasurementdata,whichcanbeexpressedasfollows:V_true=∑(V_i/d_i^n)/∑(1/whereV_trueisthetruevolumeoftheworkpiece,V_iistheCMMmeasurementvolumeatthei-thmeasurementpoint,d_iisthedistancebetweenthei-thmeasurementpointandtheneighboringpoints,andnisauser-definedparameterthatdeterminestheinfluenceofdistantmeasurementpointsontheestimatedvolume.Thekeystepoftheproposedmethodistoselecttheneighboringpointsforeachmeasurementpoint.Weuseacircularsearchwindowcenteredateachmeasurementpointtofindtheneighboringpointswithinthewindow.Theradiusofthesearchwindowcanbedeterminedbasedonthesizeoftheworkpieceandthedensityofthemeasurementpoints.Alargersearchwindowcancapturemoreinformationaboutthelocalgeometryoftheworkpiece,butitmayalsointroducemorenoiseanderrorsintotheestimation.Anotherimportantissueintheproposedmethodistheselectionofthepowerparametern.Asmallvalueofngivesmoreweighttothedistantmeasurementpoints,whichcanleadtoasmootherestimationbutalsoreducetheaccuracy.Alargevalueofngivesmoreweighttothenearbymeasurementpoints,whichcanimprovetheaccuracybutalsoincreasethefluctuationandnoiseoftheestimation.Therefore,theselectionoftheoptimalvalueofndependsonthecharacteristicsoftheworkpieceandthemeasurementdata,anditmayneedtobefine-tunedthroughexperiments.ExperimentalToevaluatetheperformanceoftheproposedmethod,weconductexperimentsonasetofworkpieceswithdifferentshapesandsizes.TheCMMmeasurementdataareobtainedusingahigh-precisionCMMmachine,andthetruevolumesoftheworkpiecesaremeasuredusingadisplacementsensorwithsub-micronaccuracy.Wecomparetheresultsoftheproposedmethodwiththoseofthesurfacefittingmethodandtheconstraintoptimizationmethod,whicharetwocommonlyusedmethodsforcorrectingCMMvolumeerrors.Figure1showsthecomparisonoftheestimationerrorofthethreemethodsonacylinderworkpiece.Itcanbeseenthattheproposedmethodachievesasmallerestimationerrorthantheothertwomethods,especiallyinthemiddlepartoftheworkpiecewherethecurvatureislargeandthemeasurementdensityislow.Thisdemonstratesthesuperiorityoftheproposedmethodinhandlingcomplexgeometryandsparsemeasurementdata.Figure2showsthecomparisonoftheestimationerrorofthethreemethodsonarectangularworkpiece.Itcanbeseenthatthesurfacefittingmethodandtheconstraintoptimizationmethodbothgivelargeestimationerrorsatthecornersandedgesoftheworkpiece,wherethesurfacecurvaturechangesrapidlyandthemeasurementerrorsaresignificant.Incontrast,theproposedmethodgivesamuchsmootherandmoreaccurateestimation,whichisconsistentwiththetruevolumemeasuredbythedisplacementsensor.Inthispaper,weproposeamethodbasedontheinversedistanceweightingmethodtocorrectCMMvolumeerrors,whichcaneffectivelyimpro