/ManufactureEngineers,PartB:JournalofEngineeringProceedingsoftheInstitutionofMechanical/content/224/12/1784Theonlineversionofthisarticlecanbefoundat:DOI:10.1243/09544054JEM19322010224:1784ProceedingsoftheInstitutionofMechanicalEngineers,PartB:JournalofEngineeringManufactureTKalvoda,Y-RHwangandMVrabecCuttertoolfaultdetectionusinganewspectralanalysismethodPublishedby:Onbehalfof:InstitutionofMechanicalEngineerscanbefoundat:ManufactureProceedingsoftheInstitutionofMechanicalEngineers,PartB:JournalofEngineeringAdditionalservicesandinformationfor/cgi/alertsEmailAlerts:/subscriptionsSubscriptions:/journalsReprints.navReprints:/journalsPermissions.navPermissions:/content/224/12/1784.refs.htmlCitations:WhatisThis?-Dec1,2010VersionofRecordbyguestonJanuary9,2013Downloadedfrom1784CuttertoolfaultdetectionusinganewspectralanalysismethodgTKalvoda1*,Y-RHwang1,2,andMVrabec31DepartmentofMechanicalEngineering,NationalCentralUniversity,Chung-Li,Taiwan,RepublicofChina2DepartmentofMechanicalEngineeringandtheInstituteofOpto-MechatronicsEngineering,NationalCentralUniversity,Chung-Li,Taiwan,RepublicofChina3FacultyofMechanicalEngineering,CzechTechnicalUniversityofPrague,Prague,CzechRepublicThemanuscriptwasreceivedon10December2009andwasacceptedafterrevisionforpublicationon22March2010.DOI:10.1243/09544054JEM1932Abstract:Aninvestigationofmillingendcuttertoolfaultmonitoringbasedondynamicforceinthefrequencydomainandtime-frequencydomainispresentedinthispaper.Anewdataanalysistechnique,theHilbertHuangtransform(HHT),isusedtoanalysethisprocessinthefrequencydomainandtime-frequencydomain.ThistechniqueisalsocomparedwiththetraditionalWelchsmethodpowerspectrabasedontheFouriertransform(FT)inthefrequencydomainapproach.Thenon-linearityandnon-stationarityofthecuttingprocessaretakenintoaccount.Thismethodisdesignedtotrackthemainpeakinthefrequencydomainandtime-frequencydomain(HHT).Themaintoolbreakindicatoristheappearanceofnewfrequencyasaresultofthecuttertoolfault.TheHHTanalysistechniquecoversthephysicalnatureofthecuttingprocess.Thecuttingprocessisnottreatedlikeatheoreticalprocess,whichisobviousbytheoscillationofthefrequencyaroundthefundamentalfrequencyofthecuttertool.Thebreakofthecuttertoolisobviousinthepresentedresults.Keywords:cuttertoolfault,spectralanalysis,millingprocessmonitoring,HilbertHuangtransform1INTRODUCTIONThecomputernumericalcontrol(CNC)machinescannotdetectcuttertoolconditionsinanon-linemanner.Becauseabrokentoolmaycontinuefunc-tioningwithoutbeingdetected,thematerialscostswillincreaseandthequalityofproductswilldimin-ishaserrorsaremadebythebrokentoolinprocess.Toreducethematerialscostsandpreventdam-agetothecuttingtool,detectingtechnologyofanunmanned,on-linetoolbreakagedetectionsystemisnecessary1.Thetoolwearmonitoringhasbeenwidelystudiedbymanydifferentapproaches.Therearetwomajorapproachesusingsensingtechnologyfordetectingtoolbreakage:oneisthedirectmethod,whichmea-suresandevaluatesthevolumetricchangeinthe*Correspondingauthor:DepartmentofMechanicalEngineer-ing,NationalCentralUniversity,No.300,JhongdaRoad,No.300,JhongdaRoad,Chung-Li,Taiwan,RepublicofChina.email:tool,andtheotheristheindirectmethod,whichmeasuresthecuttingparametersduringtheoperationprocess2.Thedisadvantageofthedirectprocessesisobviousintermsoftheinterruptionofthecuttingprocessaswellasinthepresenceofthecoolantfluidsonacuttertool.TheFouriertransform(FT)anditsmodifiedshort-timeFouriertransformhasbeenwidelystudiedinordertodetectcuttertoolwearorcuttertoolbreak3.Thelackofthismethodleadstotheassumptionthattheprocesseddataarestrictlylinearandstationary,whichisimpossibleowingtothenatureofthecut-tingprocess.AnothershortcomingoftheFTisthepresenceofharmonicsasamultipleoffundamentalfrequency,whichmakesitdifficulttorecognizetherealfrequencyfromharmonic.TheFouriertransformpresentationislimitedtothefrequencydomain.Thepossibledirectionofthestudytoolwearprocessorcuttertoolbreakprovidesthewaveletstrans-form3,4,buttheassumptionofthedatalinearityforwavelettransformmakesitdifficultytoreliablyProc.IMechEVol.224PartB:J.EngineeringManufactureJEM1932byguestonJanuary9,2013DownloadedfromCuttertoolfaultdetectionusinganewspectralanalysismethod1785analysethedynamiccuttingforcesignalinordertomonitorthecuttingprocess.ThenewmethodHilbertHuangtransform(HHT)fortimeseriesanalysiswasproposed5,6.Themethodovercomestheshortcomingsofnon-linearityandnon-stationarityofthetimeseriesdatasets.TheHHTwassuccessfullyappliedformanysolutionsoftimeseriesanalysis:structuralhealthmonitoring,vibration,speech,bio-medicalapplications,andsoon6.TheHHTconsistsoftwofundamentalsteps:signaldecompositionsusingempiricalmodedecom-position(EMD),whichisactuallyadyadicfilterbank,andtheinstantaneousfrequencycomputation7.2EXPERIMENTALMETHODS2.1ToolwearrecognitionThetoolwearisgenerallycausedbyacombinationofvariousprocesses.Toolwearcanoccurgraduallyorindrasticbreakdowns.Gradualwearmayoccurbyadhesion,abrasion,ordiffusion,anditmayappearintwoways:wearonatoolsfaceorwearonitsflank.Contactwiththechipproducesacraterinthetoolface.Flankwear,ontheotherhand,iscom-monlyattributedtofrictionbetweenthetoolandtheworkpiecematerial.Ingeneral,increasingthecut-tingspeedincreasesthetemperatureatthecontactzone,leadingtoadrasticreductionofthetoolslife.Themillingcuttingprocessisspecifiedbytheintensivecontactbetweenthecuttertoolandtheworkpieceanditleadstothetoolwearortoolbreak-age.Thedescribedprocessischaracterizedbythechangeofthecuttertoolgeometry.Thecuttingtoothinducesthefluctuationpartinthecuttingforceasaresultoftheforcedvibration.Thechange(toolwearortoolbreak)ofthecuttinggeometrycanbeobservedinthespectralanalysis.Thephysicalessenceofthecuttertoolwearwillbeneglectedinthefollowingpartsofthisstudy.2.2TheHilbertHuangtransformasamethodofanalysisThelimitationofuseofthetraditionalmethodssuchFourierandwavelettransformswaspresentedabove.Recentresearch5,6hasbroughtanewapproachfornon-linearandnon-stationarydata.TheHHThasbeenshowntoperformwellforthesekindofdata.TheHHThasbeensuccessfullyappliedformanysolutionsofnon-linearandnon-stationarydata.Thepresentationinbothfrequencyandtime-frequencydomainsshowstheadvantageoftheothertransforms.Theimportanteventinthecuttingprocessmaybeattributedtogiventime.TheEMDmethodisfundamentaltoHHT.Usingtheensembleempiricalmodedecomposition(EEMD)method,anycomplicateddatasetcanbedecomposedintoafiniteandoftensmallnumberofcomponents:acollectionofintrinsicmodefunctions(IMF).AnIMFrepresentsagenerallysimpleoscillatorymodeasacounterparttothesimpleharmonicfunction.Inordertoavoidmodemixingbetweentheindividualcompo-nents,thewhite-noiseofthegivenvalueisaddedintotheinvestigatedsignal(thisprocessisreferredtoasEEMD).Bydefinition,anIMFisanyfunctionwiththesamenumberofextremaandzerocrossings,withitsenvelopesbeingsymmetricwithrespecttozero5,6.TheprocessofEMDisasfollows:(a)identifyminimaandmaxima；(b)connectlocalminimaandmaximausingthespline；(c)findthemean(m1)oftheupperandbottomenvelopeidentification.Themeanisdesignatedasm1,andthedifferencebetweenthedataandm1inthefirstcomponenth1ish1=x(t)m1(1)Inthesecondsiftingprocess,h1istreatedasthedata,thenh1m11=h11(2)Thissiftingprocedurecanberepeatedktimes,untilh1kisanIMF,thatish1(k1)m1k=h1k；thenitisdesignatedasc1=h1k,thefirstIMFcompo-nentfromthedata.Tocheckifh1kisanIMF,thefollowingconditionsmustbefulfilled5,6:(a)thedifferencebetweenthenumbersofextremaandzero-crossingsislessorequalslant1；(b)themeanoftheupperenvelope(linkedbylocalmaxima)andthelowerenvelope(linkedbylocalminima)iszeroateverypoint.ThefirstIMFc1issubtractedfromtheoriginalsig-nalr1=sc1.Thisdifferenceiscalledtheresiduer1.Itisnowtreatedasthenewsignalandsubjectedtothesamesiftingprocess.Thedecompositionprocessfinallystopswhentheresiduernbecomesamono-tonicfunctionorafunctionwithonlyoneextremumfromwhichnomoreIMFcanbeextracted.Decom-positionoftheoriginalsignalinton-empiricalmodesandaresidueisthenachievedbyx(t)=nsummationdisplayj=1cj+rn(3)AnotherstepistoapplytheHilberttransformtothedecomposedIMFs.EachcomponenthasitsHilberttransformyiyi(t)=1integraldisplaycj()td(4)JEM1932Proc.IMechEVol.224PartB:J.EngineeringManufacturebyguestonJanuary9,2013Downloadedfrom1786TKalvoda,Y-RHwang,andMVrabecFig.1Cuttingforcesignalanalysedbyusingofvariousapproaches:(a)originaldataset；(b)Fouriertransformofthesignal；(c)wavelettransform；(d)HHToftheoriginalsignalWiththeHilberttransform,theanalyticsignalisdefinedasz(t)=x(t)+iy(t)=a(t)ei(t)(5)wherea(t)=radicalB