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http//pib.sagepub.com/ManufactureEngineers,PartBJournalofEngineeringProceedingsoftheInstitutionofMechanicalhttp//pib.sagepub.com/content/224/12/1784TheonlineversionofthisarticlecanbefoundatDOI10.1243/09544054JEM193220102241784ProceedingsoftheInstitutionofMechanicalEngineers,PartBJournalofEngineeringManufactureTKalvoda,YRHwangandMVrabecCuttertoolfaultdetectionusinganewspectralanalysismethodPublishedbyhttp//www.sagepublications.comOnbehalfofInstitutionofMechanicalEngineerscanbefoundatManufactureProceedingsoftheInstitutionofMechanicalEngineers,PartBJournalofEngineeringAdditionalservicesandinformationforhttp//pib.sagepub.com/cgi/alertsEmailAlertshttp//pib.sagepub.com/subscriptionsSubscriptionshttp//www.sagepub.com/journalsReprints.navReprintshttp//www.sagepub.com/journalsPermissions.navPermissionshttp//pib.sagepub.com/content/224/12/1784.refs.htmlCitationsWhatisThisDec1,2010VersionofRecordbyguestonJanuary9,2013pib.sagepub.comDownloadedfrom1784CuttertoolfaultdetectionusinganewspectralanalysismethodgTKalvoda1,YRHwang1,2,andMVrabec31DepartmentofMechanicalEngineering,NationalCentralUniversity,ChungLi,Taiwan,RepublicofChina2DepartmentofMechanicalEngineeringandtheInstituteofOptoMechatronicsEngineering,NationalCentralUniversity,ChungLi,Taiwan,RepublicofChina3FacultyofMechanicalEngineering,CzechTechnicalUniversityofPrague,Prague,CzechRepublicThemanuscriptwasreceivedon10December2009andwasacceptedafterrevisionforpublicationon22March2010.DOI10.1243/09544054JEM1932AbstractAninvestigationofmillingendcuttertoolfaultmonitoringbasedondynamicforceinthefrequencydomainandtimefrequencydomainispresentedinthispaper.Anewdataanalysistechnique,theHilbert–HuangtransformHHT,isusedtoanalysethisprocessinthefrequencydomainandtimefrequencydomain.ThistechniqueisalsocomparedwiththetraditionalWelchsmethodpowerspectrabasedontheFouriertransformFTinthefrequencydomainapproach.Thenonlinearityandnonstationarityofthecuttingprocessaretakenintoaccount.ThismethodisdesignedtotrackthemainpeakinthefrequencydomainandtimefrequencydomainHHT.Themaintoolbreakindicatoristheappearanceofnewfrequencyasaresultofthecuttertoolfault.TheHHTanalysistechniquecoversthephysicalnatureofthecuttingprocess.Thecuttingprocessisnottreatedlikeatheoreticalprocess,whichisobviousbytheoscillationofthefrequencyaroundthefundamentalfrequencyofthecuttertool.Thebreakofthecuttertoolisobviousinthepresentedresults.Keywordscuttertoolfault,spectralanalysis,millingprocessmonitoring,Hilbert–Huangtransform1INTRODUCTIONThecomputernumericalcontrolCNCmachinescannotdetectcuttertoolconditionsinanonlinemanner.Becauseabrokentoolmaycontinuefunctioningwithoutbeingdetected,thematerialscostswillincreaseandthequalityofproductswilldiminishaserrorsaremadebythebrokentoolinprocess.Toreducethematerialscostsandpreventdamagetothecuttingtool,detectingtechnologyofanunmanned,onlinetoolbreakagedetectionsystemisnecessary1.Thetoolwearmonitoringhasbeenwidelystudiedbymanydifferentapproaches.Therearetwomajorapproachesusingsensingtechnologyfordetectingtoolbreakageoneisthedirectmethod,whichmeasuresandevaluatesthevolumetricchangeintheCorrespondingauthorDepartmentofMechanicalEngineering,NationalCentralUniversity,No.300,JhongdaRoad,No.300,JhongdaRoad,ChungLi,Taiwan,RepublicofChina.emailkalvodagmail.comtool,andtheotheristheindirectmethod,whichmeasuresthecuttingparametersduringtheoperationprocess2.Thedisadvantageofthedirectprocessesisobviousintermsoftheinterruptionofthecuttingprocessaswellasinthepresenceofthecoolantfluidsonacuttertool.TheFouriertransformFTanditsmodifiedshorttimeFouriertransformhasbeenwidelystudiedinordertodetectcuttertoolwearorcuttertoolbreak3.Thelackofthismethodleadstotheassumptionthattheprocesseddataarestrictlylinearandstationary,whichisimpossibleowingtothenatureofthecuttingprocess.AnothershortcomingoftheFTisthepresenceofharmonicsasamultipleoffundamentalfrequency,whichmakesitdifficulttorecognizetherealfrequencyfromharmonic.TheFouriertransformpresentationislimitedtothefrequencydomain.Thepossibledirectionofthestudytoolwearprocessorcuttertoolbreakprovidesthewaveletstransform3,4,buttheassumptionofthedatalinearityforwavelettransformmakesitdifficultytoreliablyProc.IMechEVol.224PartBJ.EngineeringManufactureJEM1932byguestonJanuary9,2013pib.sagepub.comDownloadedfromCuttertoolfaultdetectionusinganewspectralanalysismethod1785analysethedynamiccuttingforcesignalinordertomonitorthecuttingprocess.ThenewmethodHilbert–HuangtransformHHTfortimeseriesanalysiswasproposed5,6.Themethodovercomestheshortcomingsofnonlinearityandnonstationarityofthetimeseriesdatasets.TheHHTwassuccessfullyappliedformanysolutionsoftimeseriesanalysisstructuralhealthmonitoring,vibration,speech,biomedicalapplications,andsoon6.TheHHTconsistsoftwofundamentalstepssignaldecompositionsusingempiricalmodedecompositionEMD,whichisactuallyadyadicfilterbank,andtheinstantaneousfrequencycomputation7.2EXPERIMENTALMETHODS2.1ToolwearrecognitionThetoolwearisgenerallycausedbyacombinationofvariousprocesses.Toolwearcanoccurgraduallyorindrasticbreakdowns.Gradualwearmayoccurbyadhesion,abrasion,ordiffusion,anditmayappearintwowayswearonatoolsfaceorwearonitsflank.Contactwiththechipproducesacraterinthetoolface.Flankwear,ontheotherhand,iscommonlyattributedtofrictionbetweenthetoolandtheworkpiecematerial.Ingeneral,increasingthecuttingspeedincreasesthetemperatureatthecontactzone,leadingtoadrasticreductionofthetoolslife.Themillingcuttingprocessisspecifiedbytheintensivecontactbetweenthecuttertoolandtheworkpieceanditleadstothetoolwearortoolbreakage.Thedescribedprocessischaracterizedbythechangeofthecuttertoolgeometry.Thecuttingtoothinducesthefluctuationpartinthecuttingforceasaresultoftheforcedvibration.Thechangetoolwearortoolbreakofthecuttinggeometrycanbeobservedinthespectralanalysis.Thephysicalessenceofthecuttertoolwearwillbeneglectedinthefollowingpartsofthisstudy.2.2TheHilbert–HuangtransformasamethodofanalysisThelimitationofuseofthetraditionalmethodssuchFourierandwavelettransformswaspresentedabove.Recentresearch5,6hasbroughtanewapproachfornonlinearandnonstationarydata.TheHHThasbeenshowntoperformwellforthesekindofdata.TheHHThasbeensuccessfullyappliedformanysolutionsofnonlinearandnonstationarydata.Thepresentationinbothfrequencyandtimefrequencydomainsshowstheadvantageoftheothertransforms.Theimportanteventinthecuttingprocessmaybeattributedtogiventime.TheEMDmethodisfundamentaltoHHT.UsingtheensembleempiricalmodedecompositionEEMDmethod,anycomplicateddatasetcanbedecomposedintoafiniteandoftensmallnumberofcomponentsacollectionofintrinsicmodefunctionsIMF.AnIMFrepresentsagenerallysimpleoscillatorymodeasacounterparttothesimpleharmonicfunction.Inordertoavoidmodemixingbetweentheindividualcomponents,thewhitenoiseofthegivenvalueisaddedintotheinvestigatedsignalthisprocessisreferredtoasEEMD.Bydefinition,anIMFisanyfunctionwiththesamenumberofextremaandzerocrossings,withitsenvelopesbeingsymmetricwithrespecttozero5,6.TheprocessofEMDisasfollowsaidentifyminimaandmaximabconnectlocalminimaandmaximausingthesplinecfindthemeanm1oftheupperandbottomenvelopeidentification.Themeanisdesignatedasm1,andthedifferencebetweenthedataandm1inthefirstcomponenth1ish1xt−m11Inthesecondsiftingprocess,h1istreatedasthedata,thenh1−m11h112Thissiftingprocedurecanberepeatedktimes,untilh1kisanIMF,thatish1k−1−m1kh1kthenitisdesignatedasc1h1k,thefirstIMFcomponentfromthedata.Tocheckifh1kisanIMF,thefollowingconditionsmustbefulfilled5,6athedifferencebetweenthenumbersofextremaandzerocrossingsislessorequalslant1bthemeanoftheupperenvelopelinkedbylocalmaximaandthelowerenvelopelinkedbylocalminimaiszeroateverypoint.ThefirstIMFc1issubtractedfromtheoriginalsignalr1s−c1.Thisdifferenceiscalledtheresiduer1.Itisnowtreatedasthenewsignalandsubjectedtothesamesiftingprocess.ThedecompositionprocessfinallystopswhentheresiduernbecomesamonotonicfunctionorafunctionwithonlyoneextremumfromwhichnomoreIMFcanbeextracted.Decompositionoftheoriginalsignalintonempiricalmodesandaresidueisthenachievedbyxtnsummationdisplayj1cjrn3AnotherstepistoapplytheHilberttransformtothedecomposedIMFs.EachcomponenthasitsHilberttransformyiyit1π∞integraldisplay−∞cjτt−τdτ4JEM1932Proc.IMechEVol.224PartBJ.EngineeringManufacturebyguestonJanuary9,2013pib.sagepub.comDownloadedfrom1786TKalvoda,YRHwang,andMVrabecFig.1CuttingforcesignalanalysedbyusingofvariousapproachesaoriginaldatasetbFouriertransformofthesignalcwavelettransformdHHToftheoriginalsignalWiththeHilberttransform,theanalyticsignalisdefinedasztxtiytateiθt5whereatradicalBigx2y2,6andθtarctany/x7Here,atistheinstantaneousamplitudeandθtisthephasefunction,andtheinstantaneousfrequencyissimplyωdθdt8AfterperformingtheHilberttransformoneachcomponent,theoriginaldatacanbeexpressedastherealpartRinthefollowingformxtRfractur⎧⎨⎩nsummationdisplayj1ajtexpbracketleftbiggiintegraldisplayωjtdtbracketrightbigg⎫⎬⎭9WiththeHilbertspectrumdefined,themarginalspectrumcanbedefinedashωTintegraldisplay0Hω,tdt10Themarginalspectrumoffersameasureofthetotalamplitudeorenergycontributionfromeachfrequencyvalue.Thisspectrumrepresentstheaccumulatedamplitudeovertheentiredataspaninaprobabilisticsense.AlldetailsofHHTaregiveninreferences5and6.TheperformanceoftheFouriertransform,wavelet,andHHTcanbedemonstratedbyanartificialsignal.ThesignalcorrespondstothecuttingforceinthexaxisFig.1a.ThecuttingconditionscorrespondProc.IMechEVol.224PartBJ.EngineeringManufactureJEM1932byguestonJanuary9,2013pib.sagepub.comDownloadedfrom
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