the bivariate empirical mode decomposition and its contribution to grinding chatter detection 2017 huanguo chen资料.pdf

该【the bivariate empirical mode decomposition and its contribution to grinding chatter detection 2017 huanguo chen资料 】是由【小舍儿】上传分享，文档一共【17】页，该文档可以免费在线阅读，需要了解更多关于【the bivariate empirical mode decomposition and its contribution to grinding chatter detection 2017 huanguo chen资料 】的内容，可以使用淘豆网的站内搜索功能，选择自己适合的文档，以下文字是截取该文章内的部分文字，如需要获得完整电子版，请下载此文档到您的设备，方便您编辑和打印。:..appliedsciencesArticlepositionandItsContributiontoGrindingChatterDetectionHuanguoChen1,*,JianyangShen1,WenhuaChen1,ChuanyuWu1,ChunshaoHuang2,YongyuYi1andJiachengQian11ZhejiangProvince’sKeyLaboratoryofReliabilityTechnologyforMechanicalandElectricalProduct,Hangzhou310018,China;slylgdx1992@(.);******@zstu.(.);******@zstu.(.);yiyongyu123@(.);**********@(.)oolCo.,Ltd.,Hangzhou311305,China;-h-cs@*Correspondence:******@zstu.;Tel.:+86-571-8684-3369AcademicEditor:GangbingSongReceived:2November2016;Accepted:25January2017;Published:8February2017Abstract:Grindingchatterreducesthelong-,,bivariateposition(BEMD),(IMFs)wasalsoinvestigated,,real-,binationofBEMDandHilberttransformwasvalidatedbyexperimentaldataC),:position(BEMD);Hilberttransform;multiplesignals;synchronouscharacteristic;real-timevariance;,whichareoftenhigh-precision,large-tonnagemachines,,whichhasgreatpracticalandeconomicvalue[1,2].Mostnotably,grinderscanentera“chatter”stateduringmachiningoperations,whichcausesaseriesofnegativeeffects[3]suchasmachinedsurfaceundulations,reducedtoollife,poorsurface?nish,noise,,regenerationandmodecouplingarethreewell-,,theamplitudeofvibrationsignalsincreasessubstantiallywhenastablegrindingstateturnsintoachatterstate[4].Additionally,thereisatransitionalphaseinthisprocess,whichcontainsconsiderableinformationaboutgrindingstatus[5].Thus,wecandiscoverthemechanismofgrindingchatterandpredictitbyanalyzingtransition-,7,145;doi::..,7,,reliablechatterdetectionandidenti?cationmethodsareessentialsothateffectivechattersuppressioncanbeappliedinatimelymanner[6].elerometers,acousticemission(AE),,andusedans-transformationtoextractadampingindexasadescriptivefeatureofchatter[7].-dimensionalfeaturevectorsforchatterdetectionbasedonthestandarddeviationofwavelettransformofdrillingmachining,whichallowedrapidchatteridenti?cation[8].Furthermore,[9].Moreover,-grainedentropyrateasachatterindexinacuttingprocess,whichexhibitedadrasticdropattheonsetofchatter[10].,acomputer-based,rapidmeasurementofchatteronsetusingsoundsignalsrecordedbyaunidirectionalmicrophone[11].-stepself-correlationfunctionasachatterindicatorfordetectingcuttingstate[12].;thespeci?cpeculiaritiesofacousticemissionsensorscaneffectivelyrejectexternaldisturbances[13].Insummary,wavelettransform[14,15],s-transformation[16],position(SVD)[17],andarti?cialintelligence[18],,grindervibrationsignalsaremostlynonstationaryandnonlinear,suchthattheseconventionalmethodscannoteffectivelyextractsignalfeatures[19].Subsequently,position(EMD),proposedbyHuangetal.,ingsofconventionaltechniques[20].posesignalsintoseveralintrinsicmodefunctions(IMFs)-,inpractice,grindervibrationsignalsareusuallymultidimensionalsignals,yetcurrentmethodsareonlyusefulwithone-dimensional,real-valuetimeseries[21].Theyareunfavorableforexecutinginformationfusionuratelyre?ectingreal-,,whichgeneralizestherationaleunderlyingEMDtothebivariateframework,namely,position(BEMD)[22].Sincebeingproposed,ithasbeenappliedtoimageprocessingsuchasimagesegmentation[23],imagefusion[24],imagecompression[25]andimagewatermarking[26].AtthethirdsessionoftheHHTInternationalConference,essfullyappliedtowindturbineconditionmonitoring[27].IthasbeenshownthattheBEMDtechniquehasinheritedallthemeritsoftheone-,incontrasttoEMD,posingacomplex-valuedsignalintoacollectionofzero-ponents,[27].parisonbetweentheuseofEMDandBEMDforextractingfeaturesfromgrindingchattersignals,anddemonstratedthesuperiorperformanceofBEMD[28].These?ndingscanbesummarizedasfollows:(1)EMDisinitiallyappliedtoaone-dimensionalsignalandextractszero-ponents,whereasBEMDisappliedtoabivariatesignalandextractszero-ponents;(2)BEMDplex-valuesignals,,posesignalsonebyoneandobtainsbothupperandlowerenvelopesbyconnectingtheextremepoints;(3):..,7,1453of17characteristicsandphaseshifting,,thenumberofIMFsderivedbyBEMDisnormallythesame,andBEMDcanextractaninformationfusionfunctionandpreservephasedifferences;(4)BEMDfacilitatestheestablishmentofpuri?edshaftvibrationorbitsandfullyguaranteesthecorrectnessofresults,’,thealgorithmsofBEMDandHilberttransformarereviewed,,real-,asimulatedchattersignalisgeneratedfromachattersignalgenerator(Simulink,MATLAB,pany,Natick,MA,USA),,,biningBEMDandHilberttransformareexperimentallyvalidatedbyprocessingchattersignalscollectedfromarealgrinder(KD4020X16).(BEMD):,?nedbythelocalmaximumpointsandtheenvelopede?,,s(t)=x(t)+iy(t),andasetofprojectiondirections,jm=2mp/N,1m:(t)ondirectionsjm:pj(t)=Re[eijms(t)],(1)(t):f(tm,pm)g,(tm,eijmpm)gbycubicsplineinterpolationtoobtainthepartialjjenvelopecurveindirectionjmnamedejm(t).–:1Nm(t)=?er(t),(2)Nr=(t)froms(t)toobtaing(t):g(t)=s(t)m(t),(3)(t)isanIMF,ifnot,replaces(t)withg(t)andrepeattheprocedurefromStep1untilg(t),recordtheobtainedIMFandremoveitfromg(t),.,c1(t)=g(t),r1(t)=s(t)c1(t).:..,7,(t)astheoriginalsignalandrepeattheaboveprocedureuntilthesecondIMF,c2(t),isobtained,ponentr2(t)=r1(t)c2(t).,theterms(t)canbeexpressedbytheprocedure:ns(t)=?hk(t)+rn(t),(4)k=1wherehk(t)plex-valuedIMFandrn(t)denotesanon-zeromeanlow-,(IMFs)posedintoexcessiveIMFs,whicharedescribedponentsthatdirectlyaffectresearchers’,re??cienciesisthattheestimationoftheauthenticityofIMFheavilydependsontheuser’,areliableponents,whichisofgreatimportanceinextractingtheactualvibrationmodeandthecorrespondingfeaturesofthetime-:(1)IMFsde?nedbyBEMDalgorithmsarebasedonnumericalanalysisonlyanddonotconsiderthevibrationcharacteristicsofsysteminthephysicalsense;(2)positionandendeffectsarenotwellprocessed;(3),,acorrelationcoef?cientisusedasastatisticalindicatortore?,asshowninEquation(5).Cov(X,Y)E[(XE(X))(YE(Y))]r=pp=pp(5)D(X)D(Y)D(X)D(Y)whereCov(X,Y)denotesthecovariancebetweentheoriginalsignalandtheIMF,E(X)andD(X)denotetheexpectationandvarianceoftheoriginalsignal,respectively,andE(Y)andD(Y)denotetheexpectationandvarianceofthekthIMF,,itisreasonabletoemploytheponentsfromtrueIMFsandthenclassifythemasapartofresidual[16,29].Inviewofthis,ifthecorrelationcoef?cientofeachIMF,rk(k=1,2,...,n),puted,thetrueIMFscanbeextractedbythefollowingmethod(Table1).(IMFs)basedonthecorrelationcoef?l,ReservethekthIMFck,Else,EstimatekthIMF,andrn=rn+?xedthresholdthatisgenerallyadoptedasaratioofthemaximumcorrelationcoef?cient,whereinhisaratiocoef?=max(jrkj/h),k=1,2...n,(6):..,7,,,putationalef?,putationaltimeandstabilitydegree(SD)?nedas,N4?(Xjm)j=1SD=N(7)((Xm)2)2?jj=1whereX={X1,X2,X3,...,XN}T(X2R,j=1,2,...,N,Tisatransposeoperator),Nrepresentsthejsamplingpoints,