ErroranalysisandcompensationfortheIntJAdvManufTechnol(2021)23:495–500DOI10.1007/s00170-003-1662-6ORIGINALARTICLES.-H.YangK.-H.KimY.K.ParkS.-G.LeeErroranalysisandcompensationforthevolumetricerrorsofaverticalmachiningcentreusingahemisphericalhelixballbartestReceived:24July2021/Accepted:29January2021/Publishedonline:14February2021Springer-VerlagLondonLimited2021AbstractMachiningaccuracyisdirectlyinuencedbythequasi-staticerrorsofamachinetool.Sincemachineer-rorshaveadirecteectuponboththesurfacenishandgeometricshapeofthenishedworkpiece,itisimpera-tivetomeasurethemachineerrorsandtocompensateforthem.Alasermeasurementsystemtoidentifygeometricerrorsofamachinetoolhasdisadvantages,suchasahighcost,alongcalibrationtimeandtheusageofavolumetricerrorsynthesismodel.Inthisstudy,wepro-posedanovelanalysisofthegeometricerrorsofamachinetoolusingaballbartestwithoutusingacom-plicatederrorsynthesismodel.Also,astatisticalanalysismethodwasemployedtoderivegeometricerrorsusingahemisphericalhelixballbartest.Accordingtotheexperimentalresult,weobservedthatgeometricerrorsoftheverticalmachiningcentrewerecompensatedby88%.KeywordsMachinetoolerrorsVolumetricerrorsynthesismodelErrorcompensationHemisphericalhelixballbartestRegressionanalysis1IntroductionAsthegeometryandfunctionsofaproductbecomecomplicatedanddiverse,theaccuracyofamachinetoolandtheeciencyofamachiningprocesshavebecomecrucialfactors.Accuracyisthemostsignicantelementinevaluatingthecapabilityofamachinetool.FortheimprovedcapabilityofaCNCmachinetool,therefore,S.-H.Yang()K.-H.KimSchoolofMechanicalEng.,KyungpookNationalUniversityE-mail:syang@knu.ac.krY.K.ParkSchoolofMechanicalandAutomotiveEng.,CatholicUniversityofDaeguS.-G.LeeCollegeofMechanicalandIndustrialSystemEngineering,KyungHeeUniversityanerrorcompensationtechniqueisaveryeectivemethod.Thus,thedevelopmentofanaccurateandeconomicerrormeasurementsystemisessential.Quasi-staticerrors,aectingthedimensionalaccu-racyorthetoleranceofamachinedproduct,occupy40–70%ofmachinetoolerrors.[1]Quasi-staticerrorsaredenedastherelativepositionerrorsbetweentheworkpieceandthetool.Geometricerrorsandthermalerrorsofamachinetoolbelongtoquasi-staticerrorswhichareassociatedwiththestructureofthemachinetoolitself.Thegeometricerrorsofamachinetoolareduetotheshapeerrorofmechanicalelementswhicharekinematicallylinked,andthemisalignmentofmechan-icalelements.Intheend,theerrorisexpressedasavolumetricerror;thediscrepancyofthetoolandtheworkpiece,atthetipofatool.Geometricerrorsofamachinetoolcanbemeasuredbyalasersystem.Itsprimaryforteistheaccuracyoferrormeasurement.However,thelasersystemrequiresalargecapitalinvestmentduetoitshighcost,andtheinstallationiscomplicated.Also,dicultiesinmea-surementandthusaconsiderableamountoftimeforeachmeasurementareunavoidable.Finally,anexperi-encedandskilfuloperatorisabsolutelyrequired.In1982,toovercometheseproblemsassociatedwiththelasersystem,Bryan[2,3,4]proposedthetelescopingballbarsystemfortheaccuracyevaluationofamachinetool.Since1982,theballbarsystemhasbeenfrequentlyadoptedinmanyresearches[5,6,7,8,9,10,11,12,13].Theballbarsystemhasalsobeenwidelyappliedinindustrywheretheaccuracyofamachinetoolshouldbecheckedregularlyandfrequently.Amathematicalmethodexpressingthevolumetricerrorofa3-axismachinetoolinavector,aderivationofamodelusing21geometricerrorcomponentsandamethodofmeasuringthe21errorcomponentswithalaseri...