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FORTHERMALERRORS
Abstract:
AmethodforimprovingaccuracyofCNCmachinetoolsthroughcompensationforthethermalerrorsisstudied.Thethermalerrorsareobtainedby1-Dballarrayandcharacterizedbyanautoregressivemodelbasedonspindlerotationspeed.ByrevisingtheworkpieceNCmachiningprogram,thethermalerrorscanbecompensatedbeforemachining.Theexperimentsonaverticalmachiningcentershowthattheeffectivenessofcompensationisgood.
Keywords:
CNCmachinetool Thermalerror Compensation
0 INTRODUCTION
Improvementofmachinetoolaccuracyisessentialtoqualitycontrolinmanufacturingprocesses.Thermallyinducederrorshavebeenrecognizedasthelargestcontributortooverallmachineinaccuracyandareprobablythemostformidableobstacletoobtaininghigherlevelofmachineaccuracy.Thermalerrorsofmachinetoolscanbereducedbythestructuralimprovementofthemachinetoolitselfthroughdesignandmanufacturingtechnology.However,therearemanyphysicallimitationstoaccuracywhichcannotbeovercomesolelybyproductionanddesigntechniques.Soerrorcompensationtechnologyisnecessary.Inthepastseveralyears,significanteffortshavebeendevotedtothestudy.Becausethermalerrorsvarywithtimeduringmachining,mostpreviousworkshaveconcentratedonreal-timecompensation.Thetypicalapproachistomeasurethethermalerrorsandtemperatureofseveralrepresentativepointsonthemachinetoolssimultaneouslyinmanyexperiments,thenbuildanempiricalmodelwhichcorrelatesthermalerrorstothetemperaturestatuesbymulti-variantregressionanalysisorartificialneuralnetwork.Duringmachining,theerrorsarepredictedon-lineaccordingtothepre-establishedmodelandcorrectedbytheCNCcontrollerinreal-timebygivingadditionalsignalstothefeed-driveservoloop.However,veryfewpracticalcasesofreal-timecompensationhavebeenreportedtobeappliedtocommercialmachinetoolstoday.Somedifficultieshinderitswidespreadapplication.First,itistedioustomeasurethermalerrorsandtemperatureofmanypointsonthemachinetools.Second,thewiresoftemperaturesensorsinfluencetheoperatingofthemachinemoreorless.Third,thereal-timeerrorcompensationcapabilityisnotavailableonmostmachinetools.
Inordertoimprovetheaccuracyofproduction-classCNCmachinetools,anovelmethodisproposed.Althoughanumberofheatsourcescontributetothethermalerrors,thefrictionofspindlebearingsisregardedasthemainheatsource.Thethermalerrorsaremeasureedby1-Dballarrayandaspindle-mountedprobe.Anautoregressivemodelbasedonspindlerotationspeedisthendevelopedtodescribethetime-variantthermalerror.Usingthismodel,thermalerrorscanbepredictedassoonastheworkpieceNCmachiningprogramismade.Bymodifyingtheprogram,thethermalerrorsarecompensatedbeforemachining.Theeffortandcostofcompensationaregreatlyreduced.ThisresearchiscarriedonaJCS2018verticalmachiningcenter.
1 EXPERIMENTALWORK
Forcompensationpurpose,theprincipalinterestisnotthedeformationofeachmachinecomponent,butthedisplacementofthetoolwithrespecttotheworkpiece.Intheverticalmachiningcenterunderinvestigation,thethermalerrorsarethecombinationoftheexpansionofspindle,thedistortionofthespindlehousing,theexpansionofthreeaxesandthedistortionofthecolumn.
Duetothedimensionalelongationofleadscrewandbendingofthecolumn,thethermalerrorsarenotonlytime-variantinthetimespanbutalsospatial-variantovertheentiremachineworkingspace.
Inordertomeasurethethermalerrorsquickly,asimpleprotablegauge,i.e.,1-Dballarray,isutilized.1-Dballarrayisarigidbarwithaseriesofballsfixedonitwithequalspace.Theballshavethesamediameterandsmallsphericityerrors.Theballarrayisusedasareferenceforthermalerrormeasurement.Alotofpre-experimentsshowthatthethermalerrorsinz-axisarefarlargerthanthoseinx-axisandy-axis,thereforemajorattentionisdrawnonthethermalerrorsinz-axis.Thermalerrorsintheothertwoaxescanbeobtainedinthesameway.
ThemeasuringprocessisshowninFig.1.Aprobeismountedonthespindlehousingand1-Dballarrayismountedontheworkingtable.Initially,thecoordinatesoftheballsaremeasuredundercoldcondition.Thenthespindleisrunatatestingconditionoveraperiodoftimetochangethemachinethermalstatus.Thecoordinatesoftheballsaremeasuredperiodically.Thethermaldriftsofthetoolareobtainedbysubtractingtheballcoordinatesunderthenewthermalstatusfromthereferencecoordinatesunderinitialcondition.Becauseittakesonlyabout1mintofinishonemeasurement,thethermaldriftsofthemachineunderdifferentzcoordinatescanbeevaluatedquicklyandeasily.Accordingtotherateofchange,thethermalerrorsandtherotationspeedaresampledbyevery10min.Sinceonlythedriftsofcoordinatesdeviatedfromthecoldconditionbutnottheabsolutedimensionsofthegaugeareconcerned,accuracyandpreciseinstrumentsuchasalaserinterferometerisnotrequired.Thereareonlyfourmeasurementpointsz1,z2,z3,z4tocoverthez-axisworkingrangewhosecoordinatesare-50,-150,-250,-350respectively.Thermalerrorsatothercoordinatescanbeobtainedbyaninterpolatingfunction.
Previousexperimentsshowthatthethermallyinduceddisplacementbetweenthespindlehousingandtheworkingtableisthesamewiththatbetweenthespindleandtable.SothethermalerrorsΔzmeasuredreflectthoseinrealcuttingconditionwithnegligibleerror.
Inordertoobtainathoroughimpressionofthethermalbehaviorofthemachinetooland
identifytheerrormodelaccurately,ameasurementstrategyisdeveloped.Variousloadsofthespindlespeedareapplied.Theyaredividedintothreecategoriesasthefollowing:
(1)Theconstantspeed;
(2)Thespeedspectrum;
(3)Thespeedsimulatingrealcuttingcondition.Theeffectoftheheatgeneratedbythecuttingprocessisnottakenintoaccounthere.However,theinfluenceofthecuttingprocessonthethermalbehaviourofthetotalmachinestructureisregardedtobenegligibleinfinishingprocess.
Inthismachine,themostsignificantheatsourcesarelocatedinthez-axis.Thermalerrorsinzdirectionondifferentxandycoordinatesareapproximatelythesame.Itimpliesthatthepositionsofx-carriageandy-carriagehavenostronginfluenceonthez-axisthermalerrors.
Fig.1(L) Thermalerrormeasurement 1.Spindlemountedprobe 2.1-Dballarray
Fig.2(R) Thermalerrorsatdifferentzcoordinates 1.z=-50 2.z=-150 3.z=-250 4.z=-350
Fig.2plotsthetime-historyofthermaldriftΔzatdifferentzcoordinatesunderatest.It
showsthattheresultantthermaldriftsareobviousposition-dependent.Thethermaldriftsatz1,z2,z3,z4arecoincidentinitiallybutseparategraduallyastimepassesandtemperatureincreases.
Thereasonisthat,initiallymostofthermaldriftsresultfromtheposition-independentthermalgrowthofthespindlehousingwhichwouldrisefastandgotothermal-equilibriumquicklycomparedtoothermachinecomponentswithlongerthermal-time-constants.However,astimepasses,thoseposition-dependentthermalerrorssuchastheleadscrewandthecolumncontributetotheresultantthermaldriftsofthetoolmoreandmore.Asaresult,thethermaldriftsatdifferentzcoordinateshavedifferentmagnitudeandthermalcharacteristics.However,thethermalerrorsatdifferentcoodinatesvarywithzcoordinatecontinuously.
2 ARMODELFORTHERMALERROR
Precisepredictionofthermalerrorsisanimportantstepforaccurateerrorcompensation.
Sincetheknowledgeofthemachinestructure,theheatsourceandtheboundaryconditionareinsufficient,aprecisequantitativepredictionbasedontheoreticalheattransferanalysisisquitedifficult.Ontheotherhand,empirical-basederrormodelsusingregressionanalysisandneuralnetworkshavebeendemonstratedtopredictthermalerrorswithsatisfactoryaccuracyinmuchapplication.
Thermalerrorsarecausedbyvariousheatsources.Onlytheinfluenceoftheheatcausedbythefictionofspindlewhichisthemostsignificantheatsourceisconsidered.Theinfluenceofexternalheatsourceonmachiningaccuracycanbediminishedbyenvironmenttemperaturecontrol.
Fromtheobtaineddata,itisfoundthatthermalerrorsvarycontinuouslywithtime.The
valueoferroratonemomentisinfluencedbythatofthepreviousmomentandtherotationspeedofspindle.Soamodelrepresentingthebehaviorofthethermalerrorsaswrittenistheform
where Δz(t)———Thermalerrorattimet
k,m———Orderofthemodel
ai,bi———Coefficientofthemodel
n(t-i)———Spindlerotationspeedattimet-i
Theorderkandmaredeterminedbythefinalprediction-errorcriterion.Thecoefficientsai
andbiareestimatedbyartificialneuralnetworktechnique.Aneuralnetworkisamultiplenonlinearregressionequationinwhichthecoefficientsarecalledweightsandaretrainedwithaniterativetechniquecalledbackpropagation.Itislesssensitivethanothermodelingtechniquetoindividualinputfailureduetothresholdingofthesignalsbythesigmoidfunctionsateachnode.TheneuralnetworkforthisproblemisshowninFig.3.(k=1,m=0).Thenumberofhiddednodesisdeterminedbyatrial-anderrorprocedure.
Usingthedataobtained(thermalerrorsandcorrespondencespeed),fourmodelsfortheerrorsatz1,z