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外文翻译--研究三次多项式加速和减速控制模型的高速数控加工 英文版.pdf

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外文翻译--研究三次多项式加速和减速控制模型的高速数控加工 英文版.pdf

JOURNALOFZHEJIANGUNIVEM时SCIENCEAISSN1673565XPRINT;ISSN18621775ONLINEWWW.ZJU.EDUCN/IZUS;WWW.SPRINGERLINK.CORNEMAILJZUSZJU.EDU.CNLENGETA1./JZHEJIANGUNIVSCIA2008913358365RESEARCHONCUBICPOLYNOMIALACCELERATIONANDDECELERATIONCONTROLMODELFORHIGHSPEEDNCMACHINING★HONGBINLENGT,YIJIEWU竹,XIAOHONGPANINSTITUTEOFMODERNMANUFACTUREENGINEERING,ZHEFIANGUNIVERS魄HANGZHOU31002LCHINA’EMAILLENGHB2002ZJU.EDU.CN;W埘1116ZJU.EDU.CNRECEIVEDJULY2,2007;REVISIONACCEPTEDNOV.3,2007;PUBLISHEDONLMEDEC.30,2007ABSTRACTTOSATISFYTHENEEDOFHIGHSPEEDNCNUMERICALCONTR01MACHINING,ANACCELERATIONANDDECELERATIONACE/DECCONTROLMODELISPROPOSED。ANDTHESPEEDCURVEISALSOCONSTRUCTEDBYTHECUBICPOLYNOMIAL.THEPROPOSEDCON仃OLMODELPROVIDESCONTINUITYOFACCELERATION.WHICHAVOIDSTHEINTENSEVIBRATIONINHIGHSPEEDNCMACHINING.BASEDONTHEDISCRETECHARACTERISTICOFTHEDATASAMPLINGINTERPOLATION.THEACE/DECCONTROLDISCRETEMATHEMATICALMODELISALSOSETUPANDTHEDISCRETEEXPRESSIONOFTHETHEORETICALDECELERATIONLENGTHISOBTAINEDFURTHERMORE.AIMINGATTHEQUESTIONOFHARDLYPREDETERMININGTHEDECELERATIONPOINTINACC/DECCONTROLBEFOREINTERPOLATION.THEADAPTIVEACE/DECCONTROLALGORITHMISDEDUCEDFROMTHEEXPRESSIONSOFTHETHEORETICALDECELERATIONLENGTH.THEEXPERIMENTALRESULTPROVESTHATTHEACE/DECCONTR01MODELHASTHECHARACTERISTICOFEASYIMPLEMENTATION,STABLEMOVEMENTANDLOWIMPACT.THEMODELHASBEENAPPLIEDINMULTIAXESHIGHSPEEDMICROFABRICATIONMACHININGSUCCESSFULLY.KEYWORDSHI曲SPEEDNCMACHINING,ACCELERATIONANDDECELERATIONACE/DECCONTROLMODEL,CUBICSPEEDCURVE,DISCRETEMATHEMATICALMODEL,ADAPTIVEACCELERATIONANDDECELERATIONCONTROLALGORITHMDNI10.1631/JZUS.A071351DOCUMENTCODEACLCNUMBERU441.4INTRODUCTIONNCNUMERICALCONTR01MACHININGISNOWDE.VELOPINGTOWARDSHIGHSPEEDANDHIGHEFFICIENCY.INHIGHSPEEDMACHINING。EACHMOTIONAXISMUSTACCEL.ERATEINTOMOVINGSTATEANDREALIZEPRECISESTOPINFEWSECONDS.SO,RESEARCHINGONANEFFICIENTACCELERATIONANDDECELERATIONACE/DECCONTROLMETHODTOMEETTHEDEMANDOFHIGHSPEEDMACHININGISONEOFTHECRITICALPROBLEMSINMODEMHIGHPERFORMANCENCSYSTEM.THECOMMONLYUSEDMETHODSINMOSTDOMESTICECONOMICALCNCCOMPUTERNUMERICALCONTR01SYSTERNARELINEARACC/DECMODEANDEXPONENTIALACE/DECMODE.BUTVIBRATIONISEASILYCAUSEDBYDISCONTINUITYOFACCELERATION,WHICHAFFECTSMACHININGQUALITYANDEQUIPMENTLIFEHUETAL,1999;ZHANG,2002.TOLCORRESPONDINGAUTHOR’PROJECTSUPPORTEDBYTHEHI.1’ECHRESEARCHANDDEVELOPMENTPROGRAM863OFCHINANO.2006AA042233,THENATIONALNATURALSCIENCEFOUNDATIONOFCHINANO.50575205ANDTHENATURAISCIENCEFOUNDATIONOFZHEJIANGPROVMCEⅢOS.Y104243ANDY105686,CHINADECREASETHEVIBRATION,THESCURVEACE/DECMOTIONPLANNINGMETHODISADOPTEDINADVANCEDCNCSYSTEM.THEACCELERATIONORDECELERATIONSTAGEINTHESCURVEACC/DECMOTIONPLANNINGMETHODISCOMPOSEDOFIN.CREASINGACCELERATIONPHASE,CONSTANTACCELERATIONPHASEANDDECREASINGACCELERATIONPHASEORINCREAS.INGDECELERATIONPHASE,CONSTANTDECELERATIONPHASEANDDECREASINGDECELERATIONPHASE.THROUGHGRADEDCONTROLOFACCELERATIONINEACHSTAGE.MACHININGFEEDRATECANBECHANGEDSMOOTHLY.HOWEVELTHEA1.GORITHMISTOOCOMPLEXKAANANDYUSUF,200LNAMANDYANG.2004.THETRIGONOMETRICFUNCTIONACE/DECMETHODISMOREFLEXIBLE,BUTTHEALGORITHMISALSOCOMPUTATIONEXTENSIVEANDMORECOMPLEX,WHICHISRELATIVELYDI币CULTTOSATISFYREALTIMEREQUIREMENTGUNANDLI,2003.THEMETHODSELECTINGPOLYNOMIALFUNCTIONSCANGENERATESOMANYKINDSOFACE/DECCHARACTERISTICSAND,FURTHERMORE,CANMAKETHECHARACTERISTICSOFDECELERATIONBEINDEPENDENTFROMTHOSEOFACCELERATION.INORDERTOACHIEVEHIGHPERFORMANCEMOTIONCONTROL,THEMOTIONPROFILESMUSTBEMATCHED堡万方数据LENGETA1./JZHEJIANGUNIVSCIA200893358365TOTHESYSTEMLIMITSSUCHASTHEMAXIMUMACCELERATIONANDTHEMAXIMUMVELOCITY.IFPOSITIONTRAJECTORIESOFWHICHTHEVELOCITYPROFILESARESMOOTHAREGENERATEDBYTHEMETHODSELECTINGPOLYNOMIALFUNCTIONS.ITREQUIRESALOTOFCOMPUTATIONSINABAANDSAKAKIBARA.1985;PARK.1996.THEDIGITALCONVOLUTIONMETHODISMUCHMOREEMCIENLTHANTHEMETHODSELECTINGPOLYNOMIALFUNCTIONSANDISEASILYIMPLE.MENTEDBYHARDWARE.BUT,INTHEVELOCITYPROFILESGENERATEDBYTHEMETHOD.THEACCELERATIONINTERVALISALWAYSTHESAMEASTHEDECELERATIONINTERVALANDTHECHARACTERISTICSOFTHEDECELERATIONAREDEPENDENTONTHOSEOFTHEACCELERATIONKHALSAANDMAHONEY,1990;CHENANDLEE.1998.ASIMPLETOEFFICIENTSSTOREDMETHODFORGENERATINGVELOCITYPROFILESISPROPOSED.ACCORDINGTOTHEDESIREDCHARACTERISTICSOFACC/DEC,EACHSETOFCOEFFICIENTSISCALCULATEDANDSTORED.GIVENAMOVINGDISTANCEANDACE/DECINTERVALS,AVELOCITYPROFILEHAVINGTHEDESIREDCHARACTERISTICSOFACC/DECCANBEE币CIENTLYGENERATEDBYUSINGTHESETOEM.CIENTS.BUTFORLONGANDSHORTDISTANCES.THESAMEACE/DECINTERVALSARESELECTED;THEE币CIENTVELOCITYPROFILECANNOTBECALCULATEDFORTHEVARIEDDISTANCEMOVEMENTSJEONANDHA,2000.THISPAPERISORGANIZEDASFOLLOWS.SECTION2PROPOSESACUBICPOLYNOMIALACE/DECCONTROLMODELFORHIGHSPEEDNCMACHINING.BASEDONTHEDISCRETECHARACTERISTICOFTHEDATASAMPLINGINTERPOLATION,THECUBICPOLYNOMIALACC/DECCONTROLDISCRETEMATHEMATICALMODELISSETUPINSECTION3.THEADAPTIVEACE/DECCONTROLALGORITHMFORPREDETERMININGTHEDECELERATIONPOINTOFARBITRARYROUTESEGMENTISDEDUCEDINSECTION4.EXPERIMENTALRESULTSAREPRESENTEDINSECTION5.ANDCONCLUSIONSARESUMMARIZEDINSECTION6.STRUTTEDBYTHECUBICPOLYNOMIAL,359Y甜Q2A2U3A3U24A4U3/FM.1ITISASSUMEDTHATTMISTHEACCELERATINGORDECELERATINGDURATIONTIME.WHICHISTAKENASSYNCHRONIZEDMOTIONAXESTOACCELERATEORDECELERATEFROMTHEBEGINNINGSPEEDTOTHEENDSPEED,妒T/TM,F∈O,TM.THEOTHERKINETICCHARACTERISTICCURVESOFACCELERATIONANDIERKCANBEOBTAINEDBYDIFFERENTIATINGTHEFEEDRATECURVE,.㈣AU撕2A26ASU12A.46AS24A4U/T铲∥。2【,“.AGAIN,INTEGRATINGEQ.1WITHRESPECTTOTIMEYIELDSTHEDISPLACEMENTCURVEFUNCTIONAS,SZFA0AI.A2U2A3U3A4U4.3THEBOUNDARYCONDITIONSARE,S00,VOK,矿1圪,AOA10,WHEREKAND圪STANDFORTHEBEGINNINGSPEEDINACESTAGEORDECSTAGEANDTHEENDSPEED.THENTHECURVILINEARFUNCTIONSAREDERIVEDAS,‘,“6圪一K12/4,彳U6KV,3KV,一UK甜U2/T2M,VUK一圪材,,4K3KK咖22K一圪弦’,S“TMKU圪一V。TMU30.5KVOTMU4.CUBICPOLYNOMIALACC/DECCONTROLEQUALFTOROMTHEE孟QIMUMUAC0CE5LERATHTEIOANC彳CEML瓤.ERATTIHOENNFMAINS.4,LET.,彳“MODELBEDEDUCEDAS,TOMEETTHENEEDOFHIGHSPEEDMACHINING,THEFEEDRATEMUSTBECHANGEDSMOOTHLYANDTHEACCELERATIONMUSTBECONTINUOUS.THEBOUNDARYCONDITIONSARE1THEDISPLACEMENTATTHEBEGINNINGTIMEIS0;2BOTHTHEBEGINNINGSPEEDANDTHEENDSPEEDARETHESAMEASREQUIRED;3THEACCELERATIONSBOTHATTHEBEGINNINGTIMEANDTHEENDTIMEARE0.THEACC/DECFEEDRATECURVE如NCTIONISCONTM3KKI“24。。NT.5玎ISAREALNUMBER,DENOTINGTHETHEORETICALTIMESOFTHETHEORETICALRUNNINGTIMETMTOINTERPOLATIONPERIODTWHENDECELERATINGORACCELERATINGFROMKTO%.WHENTTM,THETHEORETICALACCELERATIONORDECELERATIONLENGTHSLISOBTAINEDFROMEQ.4AS,万方数据LENGETA1./JZHEJIANGUNIVSCIA200893358365墨圪V。TM/23LK2一曙II4A.。.THERELATIONOFSPEED叻,ACCELERATION0ANDJERK∽ISEXPRESSEDASSHOWNINFIG.1.FROMFIG.1,INTHECUBICPOLYNOMIALACE/DECCONTROLMODEL.THEAC.CELERATIONISCONSECUTIVE。WHICHAVOIDSTHEOCCURRENCEOFINTENSEVIBRATIONINHIGHSPEEDMACHINING.THECALCULATIONSOFJERK,ACCELERATION,SPEEDANDDIS.PLACEMENTINVARYINGSPEEDPROCESSARESIMPLEANDEASYTOREALIZE.BECAUSEOFFEWFOURFUNDAMENTALOP.ERATIONS.矿匕二上二金.一P毒三}\/7L\/一\/一’FIG.1SPEED,ACCELERATION似ANDJERKJOFTHECUBICPOLYNOMIALACC/DECCONTROLMODELCUBICPOLYNOMIALACC/DECCONTROLDISCRETEMODELCHARACTERISTICSOFDATASAMPLINGINTERPOLATIONTHECONTROLLINGWITHDATASAMPLINGINTERPOLATIONISATYPEOFDISCRETECONTROLLINGMODE.THEDATASAM.PIINGINTERPOLATIONISBASEDONAPPROXIMATINGACURVEWITHSTRAIGHTLINESEGMENTS,WHOSELENGTHSAREPROPORTIONALTOTHELOCALAXIALPLANNEDVELOCITIES.THEACE/DECCON仃OLALGORITHMISPERFORMEDONTHEDESIREDFEEDRATECOMMAND矿FIRSTLY.THENTHEFEEDRATECORN.MANDVAFTERACE/DECCONTROLALGORITHMISSENTTOTHEINTERPOLATORTOCOMPUTETHETRAVELINGDISTANEECOM.PONENTFOREACHAXISINTHECARTESIANCOORDINATES△K△YAND△刁.THETRAVELINGDISTANCECOMPONENTS△Z厶YAND觇ALONGTHEX.YANDZAXESARETRANSMITTEDTOTHEMOTIONCONTROLROUTINE邪POSITIONCOMMANDSTOTHEPOSITIONCONTROLLOOPFORTHEDESIREDMACHININGFINALLY.WHENDATASAMPLINGINTERPOLATIONISUSEDINPOSITIONCONTR01.ITISTHECONDITIONTOMAKESURETHATEVERYSYNCHRONIZEDMOTIONAXISREACHESTHEDESTINATIONSIMULTANEOUSLYANDTHEIRMOVEMENTISCONTINUOUSSOTHATEACHAXISRUNNINGTIMETISJUSTINTEGRALTIMESTHATOFTHEINTERPOLATIONPERIOD互I.E.TIMEPARTITIONINGRULE.THISCONDITIONCANBEREALIZEDBYADJUSTINGTHECOMMANDFEEDRATEOFEACHSYNCHRONIZEDMOTIONAXISI.E.ACCELERATINGORDECELERATINGGUOETA1.,2003.THROUGHTHEABOVEANALYSES.NSHOULDBEANIN.TEGER.SETNASTHEMINIMUMINTEGERNOTSMALLERTHAN玎.NCEILN.N≥N.REPLACINGTHEREALNUMBER,1WITHTHEINTEGERNINEQ.5YIELDS,‘3IKKI/24。。NT.6CONSTRUCTIONOFDISCRETEMODELGIVENANYCURVEGIVENBYTHEFUNCTIONYFLT,THEINTERVAL【TO,纠ISDIVIDEDINTONDIVISIONS.PICKINGTHELEFTENDPOINTSTODETERMINETHEHEIGHTSISSHOWNINFIG.2A;THEAPPROXIMATEAREAUNDER少钡DONTHEINTERVALTO,明IS,R儿灿嘻小娟棚孚孚.OTOTLT2R卜L,,L肛LTMTOTOTLT2缸LNTLTUTFIG.2IMPLEMENTCURVEOFJFT.ALEFTENDPOINTSUSEDFORTHEHEIGHTSOFRECTANGLES;BRIGHTENDPOINTSUSEDFORTHEHEIGHTSOFRECTANGLES万方数据LENGETA1./JZHEJIANGUNIVSCIA20089F3J358365THISWAYOFAPPROXIMATINGTHEAREAUNDERTHECURVEISCALLEDTHELEFTSUMMETHOD.CHOOSINGTHEFIGHTENDPOINTSTODETERMINETHEHEIGHTSISSHOWNINFIG.2B;THEAPPROXIMATEAREAUNDER尸砜FONTHEINTERVALTO,明IS,IJⅣ删,≈喜小Z可TNTO警.THISWAYOFAPPROXIMATINGTHEAREAUNDERTHECURVEISCALLEDTHERIGHTSUMMETHOD.SUPPOSETHATTHESLOPEOFIERKISKSANDINITIALVALUESOFJERK,ACCELERATION,SPEEDANDDISPLACEMENTAREJO,AO,GOANDSO,RESPECTIVELY.THEDISCRETEMODELOFJERKCURVE,IMPLEMENTEDBYIEFTSUMMETHOD,IS。JIT厶0F一1T,1≤I≤N.7THEDISCRETEMODELSOFACCELERATION,SPEEDANDDISPLACEMENTCURVE,REALIZEDBYRIGHTSUMMETHOD,ARE,IAIT.40∑,/7’R,IINI,/1I矿F丁VO∑AJTT,JL,SFRSO∑VJTT,JL1≤I≤N.1≤F≤Ⅳ.361州耻器一嘉NN斋‰‘、’Ⅳ1Ⅳ2R21Ⅳ2R2’L≤F≤NTHEDISCRETEMODELSOFACCELERATION,SPEEDANDDISPLACEMENTCURVE,IMPLEMENTEDBYRIGHTSUMMETHOD,ARE,彳FR坠竺二竺F一篁兰二竺2F,、’NN2TNN1Ⅳ2丁71≤I≤N1;YCZR,K;孑糕ZI揣R2一J噪F3,LIN;NN1Ⅳ2’’SFNN33N21V.2N1VE乃、7NN1Ⅳ2竺二竺堕丝12TI24.竺二竺21丝二乃,2NN1Ⅳ2NN1Ⅳ2一旦熹忑巩LIN.2NN1Ⅳ29C8,ME。罢等蠹慧I酱竺罴舞嚣篡。警TOSATISFYTHATTHEACCELERATIONATTHEENDTIMEIS0ANDCONSIDERINGCHARACTERISTICSOFIMPLEMENTINGTHEACCELERATIONCURVEBYFIGHTSUMMETHODTHEHEIGHTOFCORRESPONDINGRECTANGLEAREAATTIME矗IS以廿1,THEBOUNDARYCONDITIONSOFTHEACCELERATIONCURVEARE,40,彳Ⅳ1T0.THEBOUNDARYCONDITIONSOFSPEEDANDDISPLACEMENTCURVEARE,N一1VFF一2210FORTHEACCELERATIONCURVE,WHEN圪刮7MX,THEDISCRETEEXPRESSIONOFTHETHEORETICALACCELERATIONLENGTHIS,只MT1一V,T2FORTHEDECELERATIONCURVE,WHEN圪屯,THEDISCRETEEXPRESSIONOFTHETHEORETICALDECELERATIONLENGTHSDIS,蜀生笋TN1VFF,VOK,VNT圪,SO0.WHERERMISTHEMAXIMUMALLOWEDFEEDRATE,MISSOTHEDISCRETEMODELOFTHEJERKCURVE,IMPLETOTALINTERPOLATIONPERIODSINACCELERATIONPROCESS,NMENTEDBYLEFTSUMMETHOD,IS,ISTOTALINTERPOLATIONPERIODSINDECELERATIONPROCESS.万方数据

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