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INTERNATIONALJOURNALOFMACHINETOOLSMANUFACTURE432003687–697IDENTIFICATIONOFCUTTEROFFSETINENDMILLINGWITHOUTAPRIORKNOWLEDGEOFCUTTINGCOEFFICIENTSJJJWANG∗,CMZHENGDEPARTMENTOFMECHANICALENGINEERING,NATIONALCHENGKUNGUNIVERSITY,TAINAN,TAIWAN701RECEIVED28JANUARY2002;ACCEPTED21JANUARY2003ABSTRACTTHISPAPERPRESENTSAMETHODFORTHEIDENTIFICATIONOFCUTTEROFFSETTHROUGHMILLINGFORCEWITHOUTREQUIRINGTHESPECIFICCUTTINGCOEFFICIENTSTOBEKNOWNASPRIORITHETOTALMILLINGFORCEINTHEPRESENCEOFCUTTEROFFSETISFIRSTOBTAINEDONTHEBASISOFDUALCUTTINGMECHANISMS,WHERETHELOCALFORCEISCOMPRISEDOFACONSTANTPLOWINGFORCEANDALINEARSHEARINGFORCEPROPORTIONALTOTHECHIPLOADUNDERTHECUTTEROFFSETTHETOTALMILLINGFORCEISSYNTHESIZEDTHROUGHCONVOLUTIONANDISSHOWNTOBETHESUMOFTHREEFORCECOMPONENTSTHENOMINALCHIPSHEARINGFORCECOMPONENT,THEPLOWINGFORCECOMPONENTSANDTHEOFFSETRELATEDSHEARINGFORCECOMPONENTFOURIERANALYSISOFTHESEFORCECOMPONENTSREVEALSTHEEFFECTSOFOFFSETGEOMETRYANDYIELDSFORMULASFORTHEIDENTIFICATIONOFOFFSETGEOMETRYTHEIDENTIFICATIONPROCESSREQUIRESONLYTWOCUTTINGTESTSANDTHEEVALUATIONOFTWOALGEBRAICEXPRESSIONS;THESHEARINGCONSTANTSAREFOUNDFROMTHEAVERAGEFORCESOFCUTTINGTESTSANDTHEOFFSETGEOMETRYISIDENTIFIEDFROMTHEFORCECOMPONENTATTHESPINDLEFREQUENCYTHROUGHNUMERICALSIMULATIONANDEXPERIMENTALRESULTS,THEEFFICACYOFTHEIDENTIFICATIONMETHODISDEMONSTRATED;THEEFFECTSOFFEEDPERTOOTHANDCUTTINGDEPTHSONTHEACCURACYOFTHEMODELAREINVESTIGATEDANDCRITERIAFORTHEAPPROPRIATESELECTIONOFTHESEPARAMETERSARESUGGESTED2003ELSEVIERSCIENCELTDALLRIGHTSRESERVEDKEYWORDSOFFSETRUNOUT;ENDMILLING;MILLINGFORCE;SHEARING;PLOUGHING1INTRODUCTIONTHEPRESENCEOFCUTTERRUNOUTINMILLINGDEGRADESSURFACEQUALITYANDINCREASESBOTHTHERADIALANDTHRUSTFORCEVARIATIONONTHETOOLS,ASWELLASONTHESPINDLEBEARINGTHUSREDUCINGTOOLANDSPINDLELIFETHEEFFECTOFCUTTERRUNOUTONTHEMILLINGFORCEANDITSIDENTIFICATIONHASBEENTHESUBJECTOFMANYSTUDIESRESEARCHESIN1–4HAVEALREADYPROPOSEDMILLINGFORCEMODELSWITHKNOWNRUNOUTGEOMETRYHOWEVER,CUTTERRUNOUTISGENERALLYDIFFICULTTOPREDICTANDMEASUREBECAUSEITRESULTSFROMTHECOMPLEXINPROCESSINTERACTIONOFTHESTATICRUNOUTANDTHEUNBALANCINGDYNAMICSOFTHEROTATINGASSEMBLYALTHOUGHTHEMEASUREMENTOFSTATICCUTTERRUNOUTCANBECARRIEDOUTOFFLINEWITHADIALINDICATOROROTHERELECTRONICMEANS,THEDYNAMICRUNOUTGEOMETRYDURINGTHE∗CORRESPONDINGAUTHORTEL188662757575EXT62189;FAX188662367231EMAILADDRESSJJWANGMAILNCKUEDUTWJJJWANG08906955/03/SEEFRONTMATTER2003ELSEVIERSCIENCELTDALLRIGHTSRESERVEDDOI101016/S0890695503000282MILLINGPROCESSCOULDBEDIFFERENTANDADIRECTMEASUREMENTWOULDBEVERYDIFFICULTTHEABILITYTOIDENTIFYTHEINPROCESSRUNOUTGEOMETRYWOULDBEUSEFULFORTHEUSERSANDMANUFACTURERSOFMACHINETOOLS,TOOLHOLDERSANDSPINDLESINTHEMONITORINGANDTESTINGOFCUTTERECCENTRICITYWITHINTHEDESIREDRANGEOFOPERATINGSPEEDSINCECUTTERRUNOUTRESULTSINTHEREDISTRIBUTIONOFCHIPLOADAMONGTHECUTTERFLUTES,THEGEOMETRYOFCUTTERRUNOUTISEMBEDDEDINTHEMILLINGFORCEMILLINGFORCETHUSBECOMESACONVENIENTSIGNALSOURCEFORTHEINDIRECTMEASUREMENTORESTIMATIONOFCUTTERRUNOUTARMAREGOETAL4USEDTHEIRRUNOUTFORCEMODELFORTHEESTIMATIONOFCUTTERRUNOUTTHROUGHANITERATIVEBESTFITPROCEDUREGUETAL5PRESENTEDALGORITHMSFORTHEESTIMATIONOFCUTTERRADIALANDAXIALRUNOUTFORTHEFACEMILLINGPROCESSBYFITTINGTHEPEAKANDVALLEYVALUESOFTHECOMPUTEDMILLINGFORCESWITHASSUMEDUNKNOWNCUTTERRUNOUTTOTHEMEASUREDCUTTINGFORCESTHERESULTSSHOWEDAGREATDISCREPANCYBETWEENTHEESTIMATEDRUNOUTANDSTATICALLYMEASUREDCUTTERRUNOUTBASEDONTHECONVOLUTIONANALYSIS,JAYARAMETAL6PRESENTEDAMETHODOLOGYFOR688JJJWANG,CMZHENG/INTERNATIONALJOURNALOFMACHINETOOLSMANUFACTURE432003687–697NOMENCLATUREAN,AOVECTORSOFTHEFOURIERSERIESCOEFFICIENTSFORTHENOMINALMILLINGFORCEANDOFFSETRELATEDFORCEA,N,RHELIXANGLE,NUMBEROFCUTTERFLUTESANDCUTTERRADIUSB,R,HANGULAR,RADIAL,ANDAXIALPOSITIONSFORCUTTINGPOINTSINCUTTERCOORDINATECWD,CWDCCHIPWIDTHDENSITYFUNCTIONOFTHEFIRSTCUTTINGEDGEANDOFTHEENTIRECUTTERBA,BPAXIALIMMERSIONANGLEANDFLUTESPACINGANGLECWDFOURIERTRANSFORMOFTHECHIPWIDTHDENSITYFUNCTION,CWDDA,DRAXIALANDRADIALCUTTINGDEPTHFT,FRLOCALTANGENTIALANDRADIALCUTTINGFORCESPERUNITCHIPWIDTHFCUTTERANGULARDISPLACEMENTGX,GYXANDYCOMPONENTSOFTHELOCALCUTTINGFORCESPERUNITCHIPWIDTHGTOTALCUTTINGFORCEVECTORKTS,KRSSPECIFICSHEARINGFORCECONSTANTSINTHETANGENTIALANDRADIALDIRECTIONSKTP,KRPSPECIFICPLOWINGFORCECONSTANTSINTHETANGENTIALANDRADIALDIRECTIONSLANGULARLOCATIONOFTHECUTTEROFFSETPS,PP,POVECTORSOFLOCALTANGENTIALFORCESPERUNITWIDTHINTHEWORKCOORDINATEDUETOSHEARING,PLOWINGANDAXISOFFSETEFFECTSPS,PP,POFOURIERTRANSFORMSOFPS,PP,POQS,QP,QODIRECTIONALMATRICESFORTHESHEARING,PLOWINGANDAXISOFFSETFORCESQANGULARPOSITIONOFCUTTINGPOINTINTHEWORKQ1,Q2ENTRY/EXITANGLESRMAGNITUDEOFCUTTEROFFSETTTRANSFERMATRIXBETWEENMEASUREDCUTTINGFORCESANDCUTTINGCONSTANTSTXFEEDPERTOOTHWNORMALIZEDFREQUENCYWITHRESPECTTOSPINDLEFREQUENCYDETECTINGPROCESSFAULTSFROMTHESPECTRUMOFTHECUTTINGFORCESIGNALINFACEMILLINGBASEDONTHISWORK,AKSHAYETAL7REPORTEDANOPTIMIZEDAPPROACHTHATUSEDALLTHESPINDLEHARMONICSOFTHECUTTINGFORCESPECTRUMOFYDIRECTIONFORRADIALRUNOUTESTIMATIONINFACEMILLINGITWASSHOWNTHATTHEOPTIMIZEDALGORITHMPERFORMEDWELLEVENWITHTIMEVARYINGSURFACECUTTINGFORCEMODELSANDTHECUTTERRUNOUTESTIMATIONSCHEMESIN4–7HAVERELIEDONNUMERICALANDITERATIVEAPPROACHTOESTIMATETHETOTALMILLINGFORCEANDCUTTERRUNOUTGEOMETRYBYREPRESENTINGTHERADIALRUNOUTOFEACHINDIVIDUALINSERTASADISCRETEFOURIERSERIES,SEETHALERANDYELLOWLEY8DERIVEDTHEFOURIERSERIESCOEFFICIENTSOFTHEOFFSETRELATEDFORCEFORTHEIDENTIFICATIONOFRADIALRUNOUTFORAFACEMILLINGCUTTERHOWEVER,THISMODELISNOTAPPLICABLEWHERETHERUNOUTMAGNITUDEVARIESALONGTHECUTTERHELICALEDGESUCHASTHECASEWITHENDMILLOFFSETFORASOLIDENDMILL,CUTTERRUNOUTVERYOFTENRESULTSFROMACUTTERAXISOFFSETFORTHISTYPEOFRUNOUTGEOMETRY,WANGANDLIANG9ANALYZEDTHECHIPLOADKINEMATICSANDDERIVEDANALYTICEXPRESSIONSFORTHECHIPTHICKNESSANDAVERAGECHIPTHICKNESSCOMBININGTHISCHIPLOADKINEMATICSANDTHECONVOLUTIONINTEGRATIONMETHOD,LIANGANDWANG10FORMULATEDANDANALYZEDTHEINFLUENCEOFCUTTERAXISOFFSETONTHEMILLINGFORCESINTHEFREQUENCYDOMAINBASEDONTHISANALYTICALFORCEMODELANDTHEREQUIREMENTOFAPRIORIKNOWNEXPONENTOFTHECUTTINGCOEFFICIENTFUNCTION,THEMAGNITUDEANDANGULARLOCATIONOFCUTTERAXISOFFSETWEREIDENTIFIEDTHROUGHTHEFOURIERSERIESCOEFFICIENTSOFCUTTINGFORCESATTHESPINDLEFREQUENCYBYEXTENDINGTHEWORKIN10,HEKMANANDLIANG11PRESENTEDARECURSIVESCHEMEFORTHEMOSTRECENTESTIMATESOFTHEDYNAMICRUNOUTMAGNITUDEANDORIENTATIONINTERMSOFTHEPREVIOUSESTIMATESUNDERSIMILARCONVOLUTIONSTRUCTURE,ZHENGANDLIANG12FURTHEREXTENDEDTHECHIPLOADANDFORCEANALYSISFORTHEIDENTIFICATIONOFCUTTERAXISTILTINENDMILLINGESTIMATIONOFENDMILLOFFSETINTHESENUMERICALORANALYTICALMODELSHERETOFOREREQUIRESAPRIORKNOWLEDGEOFTHESPECIFICCUTTINGCOEFFICIENTS,WHICHISUSUALLYNOTAVAILABLEESPECIALLYINANINDUSTRIALENVIRONMENTASERIESOFCUTTINGEXPERIMENTSWOULDHAVETOBECARRIEDOUTINADVANCEFORTHETOOLANDWORKMATERIALOFINTERESTTOESTABLISHADATABASEOREXPRESSIONSFORTHECUTTINGCOEFFICIENTSTHEEFFECTOFONGOINGANDUNKNOWNTOOLWEARADDSUNCERTAINTYTOTHEACCURACYOFTHISPREESTABLISHEDDATAALTHOUGHTHEINSTANTANEOUSTANGENTIALANDRADIALCUTTINGCONSTANTSCANBEESTIMATEDDIRECTLYFROMTHEMEASUREDMILLINGFORCEASIN10–12,THEEXPONENTSOFTHEPOWEREXPRESSIONSFORTHECUTTINGCOEFFICIENTSASFUNCTIONSOFCHIPTHICKNESSWOULDNEEDTOBEKNOWNINADVANCETHISPREREQUISITECOMESFROMTHEFACTTHATTHEMILLINGFORCEVARIATIONDUETOCHIPLOADCHANGEINTHEPRESENCEOFCUTTERRUNOUTISATTRIBUTEDTOTHECHIPSHEAR689JJJWANG,CMZHENG/INTERNATIONALJOURNALOFMACHINETOOLSMANUFACTURE432003687–697INGMECHANISMALONE,WHILETHEESTIMATEDCUTTINGCONSTANTSFROMTHEEXISTINGMODELAREBASEDONTHELUMPEDEFFECTSOFCHIPSHEARINGANDEDGEPLOWINGCUTTINGMECHANISMSTHESELUMPEDCONSTANTSDEPENDGREATLYONCHIPTHICKNESSANDAREGENERALLYEXPRESSEDASPOWERFUNCTIONSOFCHIPTHICKNESSORAVERAGECHIPTHICKNESSITWOULDBEMOREAPPROPRIATEANDHASSTRONGERBEARINGONTHEPHYSICALGROUNDSTOUSEONLYSHEARINGRELATEDCUTTINGCOEFFICIENTSINMODELINGTHEFORCEVARIATIONDUETOCUTTERRUNOUTRESEARCHESIN4,8,13–16HAVEUSEDAREFINEDCUTTINGFORCEMODELTHATEXPLICITLYINCLUDESTHESEPARATEANDSIMULTANEOUSEFFECTSOFCHIPSHEARINGANDEDGEPLOWINGMECHANISMSINTHECUTTINGPROCESSYELLOWLEYASSUMEDACONSTANTPRESENCEOFPLOWINGFORCEANDALINEARSHEARINGFORCEPROPORTIONALTOTHEINSTANTCHIPTHICKNESSANDSHOWEDTHATSUCHAMODELISACCURATEFORTHEIDENTIFICATIONOFINSERTRUNOUTIN8ANDFORTHEPREDICTIONOFAVERAGECUTTINGFORCE13ARMAREGO4,14PROPOSEDTHATTHESHEARINGCOEFFICIENTSBEEXPRESSEDASFUNCTIONSOFNORMALRAKEANGLE,TOOLINCLINATIONANGLE,NORMALSHEARANGLE,SHEARSTRESS,FRICTIONANGLEANDCHIPFLOWANGLE,ANDTHEPLOWINGCOEFFICIENTSEXPRESSEDASFUNCTIONSOFNORMALRAKEANGLEANDCUTTINGVELOCITYBASEDONWORKSIN4,14,BUDAKETALESTABLISHEDAPREDICTIVEMODELFORTHEDUALCUTTINGCOEFFICIENTSIN15ANDSHOWEDTHATTHESHEARINGCOEFFICIENTSANDPLOWINGCOEFFICIENTSCANBETREATEDASCONSTANTSWITHOUTLOSSOFACCURACYITISTHEREFOREPROPOSEDINTHISPAPERTHATTHEENDMILLINGFORCEWITHCUTTEROFFSETBEFORMULATEDUSINGCONSTANTPLOWINGANDSHEARINGCUTTINGCOEFFICIENTSFORCECOMPONENTSDUETOTHECUTTEROFFSETCANTHENBEAPPROPRIATELYACCOUNTEDFORBYTHESHEARINGCUTTINGCONSTANTSTHEUSEOFCONSTANTCOEFFICIENTSWITHDUALCUTTINGMECHANISMSWILLBESHOWNHEREINTONOTONLYSIMPLIFYTHETASKFORTHEIDENTIFICATIONOFTHEOFFSETGEOMETRYBUTALSOYIELDMOREACCURATERESULTSINTHENEXTSECTIONTHEANALYTICALFORCEMODELWITHCUTTEROFFSETISFIRSTESTABLISHEDSECTION3PRESENTSTHEMETHODSFORTHEESTIMATIONOFCUTTINGCONSTANTSANDTHEOFFSETGEOMETRYFOLLOWEDBYTHENUMERICALANDEXPERIMENTALVERIFICATIONSINSECTION4ANDCONCLUSIONSINSECTION52MILLINGFORCESWITHCUTTERAXISOFFSETTHECUTTERANDWORKCOORDINATESWITHTHEOFFSETGEOMETRYARESETUPSIMILARLYTOTHOSEIN9ANDARESHOWNINFIG1THEPOSITIONSOFCUTTINGEDGESAREREPRESENTEDINTHERBHCOORDINATETHEBOTTOMOFANARBITRARILYCHOSENCUTTINGEDGEISLOCATEDATB0ANDCOINCIDESWITHQ0INTHEWORKCOORDINATEWHENTHECUTTERDISPLACEMENTFIS0ASTHECUTTERROTATES,THESETHREEANGULARVARIABLESTAKEONTHEFOLLOWINGRELATIONSHIPFIG1ATHECUTTERANDWORKGEOMETRYANDCOORDINATESINTHEMILLINGPROCESSANDBCUTTEROFFSETGEOMETRYQH11005FH11002B1THEOFFSETGEOMETRYSHOWNINFIG1BHASTHEGEOMETRICALCENTEROFTHECUTTERSHIFTEDADISTANCEOFRFROMTHEROTATIONCENTERINANANGULARDIRECTIONOFLFROMB0THEREVISEDCHIPTHICKNESSWITHCUTTEROFFSETISSHOWNIN9,18TOBEAPPROXIMATEDBYTCQ,BH11005TXSINQH11001TOB2WHERETOBH11005H110022RSINPNSINBH11002LH11002PN3CONSIDERINGTHESHEARINGANDPLOWINGCUTTINGMECHANISMS,THELOCALCUTTINGFORCEPERUNITCHIPWIDTHISASSUMEDTOTAKETHEFOLLOWINGLINEARFORMWITHFOURCUTTINGCONSTANTS,H20873GTQ,BGRQ,BH20874H11005H20873KTSKRSKTSH20874TCQ
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