外文翻译--在端面铣削过程中刀具偏移量的识别没有先验知识的切削系数 英文版.pdf

InternationalJournalofMachineTools&Manufacture43(2003)687697IdentificationofcutteroffsetinendmillingwithoutapriorknowledgeofcuttingcoefficientsJ.-J.J.Wang,C.M.ZhengDepartmentofMechanicalEngineering,NationalChengKungUniversity,Tainan,Taiwan701Received28January2002；accepted21January2003AbstractThispaperpresentsamethodfortheidentificationofcutteroffsetthroughmillingforcewithoutrequiringthespecificcuttingcoefficientstobeknownaspriori.Thetotalmillingforceinthepresenceofcutteroffsetisfirstobtainedonthebasisofdualcuttingmechanisms,wherethelocalforceiscomprisedofaconstantplowingforceandalinearshearingforceproportionaltothechiploadunderthecutteroffset.Thetotalmillingforceissynthesizedthroughconvolutionandisshowntobethesumofthreeforcecomponents:thenominalchipshearingforcecomponent,theplowingforcecomponentsandtheoffsetrelatedshearingforcecomponent.Fourieranalysisoftheseforcecomponentsrevealstheeffectsofoffsetgeometryandyieldsformulasfortheidentifi-cationofoffsetgeometry.Theidentificationprocessrequiresonlytwocuttingtestsandtheevaluationoftwoalgebraicexpressions；theshearingconstantsarefoundfromtheaverageforcesofcuttingtestsandtheoffsetgeometryisidentifiedfromtheforcecomponentatthespindlefrequency.Throughnumericalsimulationandexperimentalresults,theefficacyoftheidentificationmethodisdemonstrated；theeffectsoffeedpertoothandcuttingdepthsontheaccuracyofthemodelareinvestigatedandcriteriafortheappropriateselectionoftheseparametersaresuggested.2003ElsevierScienceLtd.Allrightsreserved.Keywords:Offsetrunout；Endmilling；Millingforce；Shearing；Ploughing1.IntroductionThepresenceofcutterrunoutinmillingdegradessur-facequalityandincreasesboththeradialandthrustforcevariationonthetools,aswellasonthespindlebearingthusreducingtoolandspindlelife.Theeffectofcutterrunoutonthemillingforceanditsidentificationhasbeenthesubjectofmanystudies.Researchesin14havealreadyproposedmillingforcemodelswithknownrun-outgeometry.However,cutterrunoutisgenerallydiffi-culttopredictandmeasurebecauseitresultsfromthecomplexin-processinteractionofthestaticrunoutandtheunbalancingdynamicsoftherotatingassembly.Althoughthemeasurementofstaticcutterrunoutcanbecarriedoutoff-linewithadialindicatororotherelec-tronicmeans,thedynamicrunoutgeometryduringtheCorrespondingauthor.Tel.:+1-886-6275-7575Ext62189；fax:+1-886-6236-7231.E-mailaddress:jjwangmail.ncku.edu.tw(J.-J.J.Wang).0890-6955/03/$-seefrontmatter2003ElsevierScienceLtd.Allrightsreserved.doi:10.1016/S0890-6955(03)00028-2millingprocesscouldbedifferentandadirectmeasure-mentwouldbeverydifficult.Theabilitytoidentifythein-processrunoutgeometrywouldbeusefulfortheusersandmanufacturersofmachinetools,toolholdersandspindlesinthemonitoringandtestingofcuttereccen-tricitywithinthedesiredrangeofoperatingspeed.Sincecutterrunoutresultsintheredistributionofchiploadamongthecutterflutes,thegeometryofcutterrun-outisembeddedinthemillingforce.Millingforcethusbecomesaconvenientsignalsourcefortheindirectmeasurementorestimationofcutterrunout.Armaregoetal.4usedtheirrunoutforcemodelfortheestimationofcutterrunoutthroughaniterativebest-fitprocedure.Guetal.5presentedalgorithmsfortheestimationofcutterradialandaxialrunoutforthefacemillingprocessbyfittingthepeakandvalleyvaluesofthecomputedmillingforceswithassumedunknowncutterrunouttothemeasuredcuttingforces.Theresultsshowedagreatdiscrepancybetweentheestimatedrunoutandstaticallymeasuredcutterrunout.Basedontheconvolutionanaly-sis,Jayarametal.6presentedamethodologyfor688J.-J.J.Wang,C.M.Zheng/InternationalJournalofMachineTools&Manufacture43(2003)687697NomenclatureAn,AovectorsoftheFourierseriescoefficientsforthenominalmillingforceandoffsetrelatedforcea,N,Rhelixangle,numberofcutterflutesandcutterradiusb,r,hangular,radial,andaxialpositionsforcuttingpointsincuttercoordinatecwd,cwdcchipwidthdensityfunctionofthefirstcuttingedgeandoftheentirecutterba,bpaxialimmersionangleandflutespacingangleCWDFouriertransformofthechipwidthdensityfunction,cwdda,draxialandradialcuttingdepthft,frlocaltangentialandradialcuttingforcesperunitchipwidthfcutterangulardisplacementgx,gyXandYcomponentsofthelocalcuttingforcesperunitchipwidthgtotalcuttingforcevectorkts,krsspecificshearingforceconstantsinthetangentialandradialdirectionsktp,krpspecificplowingforceconstantsinthetangentialandradialdirectionslangularlocationofthecutteroffsetps,pp,povectorsoflocaltangentialforcesperunitwidthintheworkcoordinateduetoshearing,plowingandaxis-offseteffectsPs,Pp,PoFouriertransformsofps,pp,poqs,qp,qodirectionalmatricesfortheshearing,plowingandaxis-offsetforcesqangularpositionofcuttingpointintheworkq1,q2entry/exitanglesrmagnitudeofcutteroffsetTtransfermatrixbetweenmeasuredcuttingforcesandcuttingconstantstxfeedpertoothwnormalizedfrequencywithrespecttospindlefrequencydetectingprocessfaultsfromthespectrumofthecuttingforcesignalinfacemilling.Basedonthiswork,Akshayetal.7reportedanoptimizedapproachthatusedallthespindleharmonicsofthecuttingforcespectrumofY-directionforradialrun-outestimationinfacemilling.Itwasshownthattheoptimizedalgorithmperformedwellevenwithtimevaryingsurface.Cuttingforcemod-elsandthecutterrunoutestimationschemesin47havereliedonnumericalanditerativeapproachtoesti-matethetotalmillingforceandcutterrunoutgeometry.ByrepresentingtheradialrunoutofeachindividualinsertasadiscreteFourierseries,SeethalerandYel-lowley8derivedtheFourierseriescoefficientsoftheoffsetrelatedforcefortheidentificationofradialrunoutforafacemillingcutter.However,thismodelisnotapplicablewheretherunoutmagnitudevariesalongthecutterhelicaledgesuchasthecasewithendmilloffset.Forasolidendmill,cutterrunoutveryoftenresultsfromacutteraxisoffset.Forthistypeofrunoutgeometry,WangandLiang9analyzedthechiploadkinematicsandderivedanalyticexpressionsforthechipthicknessandaveragechipthickness.Combiningthischiploadkinematicsandtheconvolutionintegrationmethod,LiangandWang10formulatedandanalyzedtheinfluenceofcutteraxisoffsetonthemillingforcesinthefrequencydomain.Basedonthisanalyticalforcemodelandtherequirementofaprioriknownexponentofthecuttingcoefficientfunction,themagnitudeandangularlocationofcutteraxisoffsetwereidentifiedthroughtheFourierseriescoefficientsofcuttingforcesatthespindlefrequency.Byextendingtheworkin10,HekmanandLiang11presentedarecursiveschemeforthemostrecentestimatesofthedynamicrunoutmag-nitudeandorientationintermsofthepreviousestimates.Undersimilarconvolutionstructure,ZhengandLiang12furtherextendedthechiploadandforceanalysisfortheidentificationofcutteraxistiltinendmilling.Estimationofendmilloffsetinthesenumericaloranalyticalmodelsheretoforerequiresapriorknowledgeofthespecificcuttingcoefficients,whichisusuallynotavailableespeciallyinanindustrialenvironment.Aser-iesofcuttingexperimentswouldhavetobecarriedoutinadvanceforthetoolandworkmaterialofinteresttoestablishadatabaseorexpressionsforthecuttingcoef-ficients.Theeffectofongoingandunknowntoolwearaddsuncertaintytotheaccuracyofthispre-establisheddata.Althoughtheinstantaneoustangentialandradialcuttingconstantscanbeestimateddirectlyfromthemea-suredmillingforceasin1012,theexponentsofthepowerexpressionsforthecuttingcoefficientsasfunc-tionsofchipthicknesswouldneedtobeknowninadvance.Thisprerequisitecomesfromthefactthatthemillingforcevariationduetochiploadchangeinthepresenceofcutterrunoutisattributedtothechipshear-689J.-J.J.Wang,C.M.Zheng/InternationalJournalofMachineTools&Manufacture43(2003)687697ingmechanismalone,whiletheestimatedcuttingcon-stantsfromtheexistingmodelarebasedonthelumpedeffectsofchipshearingandedgeplowingcuttingmech-anisms.Theselumpedconstantsdependgreatlyonchipthicknessandaregenerallyexpressedaspowerfunctionsofchipthicknessoraveragechipthickness.Itwouldbemoreappropriateandhasstrongerbearingonthephysi-calgroundstouseonlyshearingrelatedcuttingcoef-ficientsinmodelingtheforcevariationduetocutterrun-out.Researchesin4,8,1316haveusedarefinedcuttingforcemodelthatexplicitlyincludestheseparateandsim-ultaneouseffectsofchipshearingandedgeplowingmechanismsinthecuttingprocess.Yellowleyassumedaconstantpresenceofplowingforceandalinearshear-ingforceproportionaltotheinstantchipthicknessandshowedthatsuchamodelisaccuratefortheidentifi-cationofinsertrunoutin8andforthepredictionofaveragecuttingforce13.Armarego4,14proposedthattheshearingcoefficientsbeexpressedasfunctionsofnormalrakeangle,toolinclinationangle,normalshearangle,shearstress,frictionangleandchipflowangle,andtheplowingcoefficientsexpressedasfunc-tionsofnormalrakeangleandcuttingvelocity.Basedonworksin4,14,Budaketal.establishedapredictivemodelforthedualcuttingcoefficientsin15andshowedthattheshearingcoefficientsandplowingcoef-ficientscanbetreatedasconstantswithoutlossofaccu-racy.Itisthereforeproposedinthispaperthattheendmill-ingforcewithcutteroffsetbeformulatedusingconstantplowingandshearingcuttingcoefficients.Forcecompo-nentsduetothecutteroffsetcanthenbeappropriatelyaccountedforbytheshearingcuttingconstants.Theuseofconstantcoefficientswithdualcuttingmechanismswillbeshownhereintonotonlysimplifythetaskfortheidentificationoftheoffsetgeometrybutalsoyieldmoreaccurateresults.Inthenextsectiontheanalyticalforcemodelwithcutteroffsetisfirstestablished.Section3presentsthemethodsfortheestimationofcuttingcon-stantsandtheoffsetgeometryfollowedbythenumericalandexperimentalverificationsinSection4andcon-clusionsinSection5.2.MillingforceswithcutteraxisoffsetThecutterandworkcoordinateswiththeoffsetgeometryaresetupsimilarlytothosein9andareshowninFig.1.Thepositionsofcuttingedgesarerep-resentedinther-b-hcoordinate.Thebottomofanarbi-trarilychosencuttingedgeislocatedatb=0andcoincideswithq=0intheworkcoordinatewhenthecutterdisplacementfis0.Asthecutterrotates,thesethreeangularvariablestakeonthefollowingrelation-ship:Fig.1.(a)Thecutterandworkgeometryandcoordinatesinthemill-ingprocessand(b)cutteroffsetgeometry.qH11005fH11002b(1)TheoffsetgeometryshowninFig.1.bhasthegeo-metricalcenterofthecuttershiftedadistanceofrfromtherotationcenterinanangulardirectionoflfromb=0.Therevisedchipthicknesswithcutteroffsetisshownin9,18tobeapproximatedby:tc(q,b)H11005txsinqH11001to(b)(2)whereto(b)H11005H110022rsinpNsin(bH11002lH11002pN)(3)Consideringtheshearingandplowingcuttingmech-anisms,thelocalcuttingforceperunitchipwidthisassumedtotakethefollowinglinearformwithfourcut-tingconstants,H20873gt(q,b)gr(q,b)H20874H11005H20873ktskrsktsH20874tc(q,b)H11001H20873ktpkrpktpH20874(4)wherektsandkrsaretheshearingconstantsrepresenting,respectively,thetangentialspecificshearingconstantandtheratioofradialtothetangentialshearingforce.ktpandkrparetheplowingconstantsrepresentingthetangentialplowingconstantandtheratioofradialtothetangentialplowingforcerespectively.Intheworkcoor-dinate,thelocalforcebecomesH20873gx(q,b)gy(q,b)H20874H11005H20875cosqsinqsinqH11002cosqH20876H20873gt(q,b)gr(q,b)H20874(5)690J.-J.J.Wang,C.M.Zheng/InternationalJournalofMachineTools&Manufacture43(2003)687697CombiningEqs.(2)(5)andrearrangingEq.(5),thelocalforcescanbeexpressedasthesuperpositionofanominalcuttingforceandaforcecontributionfromthecutteroffset:H20873gx(q,b)gy(q,b)H20874H11005H20873fx(q)fy(q)H20874H11001H20873fxo(q,b)fyo(q,b)H20874(6)inwhichH20873fx(q)fy(q)H20874H11005qsps(q)H11001qppp(q)andH20873fxo(q,b)fyo(q,b)H20874(7)H11005to(b)qopo(q)whereps(q)H11005ktstxH20873p1p2H20874H11005ktstxH20873sinqcosqsin2qH20874w(q),pp(q)H11005ktpH20873p3p4H20874H11005ktpH20873cosqsinqH20874w(q),po(q)H11005ktsH20873p3p4H20874(8)H11005ktsH20873cosqsinqH20874w(q)andqsH11005qoH11005H208751krsH11002krs1H20876,qpH11005H208751krpH11002krp1H20876(9)ThenominallocalforceinEq.(7)isexpressedasthesumoftheshearingandtheplowingcomponentsasindi-catedbytheirsubscripts.Matricesqs,qpandqoreflecttheeffectsofradialcuttingconstantsonthelocalforce.Forcevectors,ps,ppandpoinEq.(8)arethelocaltan-gentialforcesperunitwidthduetotheshearing,plowingandaxis-offseteffectsrespectively.Aunit-heightpulsefunctionw(q)isincludedinEq.(8)torepresenttheactualradialrangeofcuttingbetweentheentryangle,q1,andtheexitangle,q2.Althoughtheentryandexitanglesarefunctionsofbasshownin9,theyareapproximatedasconstantsheretoreducethemathemat-icalcomplexityoftheforcemodel.Thetotalforcecanbeobtainedbyintegratingthelocalforcealongthehdirectionwithintheaxialdepthofcut.WithachangeofvariableasinEq.(1),thetotalforcecanbeshowntotakeonaconvolutionintegralform:g(f)H11005H20873gx(f)gy(f)H20874H11005H20885da0H20873gx(q)gy(q)H20874dhc(10)H11005H20885H11009H11002H11009H20873gx(fH11002b)gy(fH11002b)H20874cwdc(b)dbH11005g(f)cwdc(f)wheredenotestheconvolutionoperation.hc(b)inEq.(10)representstheaxialpositionoftheactivecuttingpointsfortheperiodicsequenceofcutterflutesandcwdcisthechipwidthdensityfunctiondefinedbydhc/db,thechipwidthperradianinb.ThesetwofunctionsareshowninFig.2andtheirexpressionsare:hc(b)H11005H20913H11009iH11005H11002H11009h(bH11002ibp)withh(b)(11)H11005H20902Rtanab,0H11349bH11349ba0,otherwisecwdc(b)H11005dhcdbH11005H20888H11009iH11005H11002H11009cwd(bH11002ibp)(12)withcwd(b)H11005dhdbH11005H20902Rtana,0H11349bH11349ba0,otherwisewherebp=2p/Nistheangularspacingbetweenneighb-oringflutesandba=datana/Rrepresentstheaxialimmersionangleofthecutter.Indexiisthesequencenumberofthecutterflutes.SubstitutingEqs.(7)(9)into(10)resultsinaconvolutionformintermsofthreedif-ferentforcegeneratingmechanisms:Fig.2.(a)Theaxialpositionfunctionoftheactivecuttingpointsand(b)thechipwidthdensityfunction.