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SCIENCEAISSN1673-565X(Print)；ISSN1862-1775(Online)wwwzjueducnIzus；wwwspringerlinkcornE-mail：jzuszjueducnLengeta1JZhejiangUnivSciA2008913)：358-365ResearchoncubicpolynomialaccelerationanddecelerationcontrolmodelforhighspeedNCmachiningHongbinLENGt,Yi-jieWU竹，XiaohongPAN(InstituteofModernManufactureEngineering,ZhefiangUnivers魄Hangzhou31002LChina)E-mail：lenghb2002zjueducn；w埘1116zjueducnReceivedJuly2，2007；revisionacceptedNov3，2007；publishedonlmeDec30，2007Abstract：TosatisfytheneedofhighspeedNC(numericalcontr01)machining，anaccelerationanddeceleration(acedec)controlmodelisproposed。andthespeedcurveisalsoconstructedbythecubicpolynomialTheproposedcon仃olmodelprovidescontinuityofaccelerationwhichavoidstheintensevibrationinhighspeedNCmachiningBasedonthediscretecharacteristicofthedatasamplinginterpolationtheacedeccontroldiscretemathematicalmodelisalsosetupandthediscreteexpressionofthetheoreticaldecelerationlengthisobtainedfurthermoreAimingatthequestionofhardlypredeterminingthedecelerationpointinaccdeccontrolbeforeinterpolationtheadaptiveacedeccontrolalgorithmisdeducedfromtheexpressionsofthetheoreticaldecelerationlengthTheexperimentalresultprovesthattheacedeccontr01modelhasthecharacteristicofeasyimplementation,stablemovementandlowimpactThemodelhasbeenappliedinmultiaxeshighspeedmicrofabricationmachiningSUCCESSfUllyKeywords：Hi曲speedNCmachining，Accelerationanddeceleration(acedec)controlmodel，Cubicspeedcurve，Discretemathematicalmodel，Adaptiveaccelerationanddecelerationcontrolalgorithmdni：101631jzusA071351Documentcode：ACLCnumber：U441+4INTRODUCTIONNC(numericalcontr01)machiningisnowdevelopingtowardshighspeedandhighefficiencyInhighspeedmachining。eachmotionaxismustaccelerateintomovingstateandrealizeprecisestopinfewsecondsSo，researchingonanefficientaccelerationanddeceleration(acedec)controlmethodtomeetthedemandofhighspeedmachiningisoneofthecriticalproblemsinmodemhighperformanceNCsystemThecommonlyusedmethodsinmostdomesticeconomicalCNC(computernumericalcontr01)sys-ternarelinearaccdecmodeandexponentialacedecmodeButvibrationiseasilycausedbydiscontinuityofacceleration，whichaffectsmachiningqualityandequipmentlife(HuetaL，1999；Zhang，2002)TolCorrespondingauthorProjectsupportedbytheHi1echResearchandDevelopmentPro-gram(863)ofChina(No2006AA042233)，theNationalNaturalScienceFoundationofChina(No50575205)andtheNaturaIScienceFoundationofZhejiangProvmceosY104243andY105686)，Chinadecreasethevibration，thes-curveacedecmotionplanningmethodisadoptedinadvancedCNCsystemTheacceleration(ordeceleration)stageinthes-curveaccdecmotionplanningmethodiscomposedofincreasingaccelerationphase，constantaccelerationphaseanddecreasingaccelerationphase(orincreasingdecelerationphase，constantdecelerationphaseanddecreasingdecelerationphase)ThroughgradedcontrolofaccelerationineachstagemachiningfeedratecanbechangedsmoothlyHoweveLthea1gorithmistoocomplex(KaanandYusuf,200l：NamandYang2004)Thetrigonometricfunctionacedecmethodismoreflexible，butthealgorithmisalsocomputationextensiveandmorecomplex，whichisrelativelydi币culttosatisfyrealtimerequirement(GunandLi，2003)Themethodselectingpolynomialfunctionscangeneratesomanykindsofacedeccharacteristicsand，furthermore，canmakethechar-acteristicsofdecelerationbeindependentfromthoseofaccelerationInordertoachievehighperformancemotioncontrol，themotionprofilesmustbematched堡万方数据Lengeta1JZhejiangUnivSciA200893)：358-365tothesystemlimitssuchasthemaximumaccelera-tionandthemaximumvelocityIfpositiontrajecto-riesofwhichthevelocityprofilesaresmootharegeneratedbythemethodselectingpolynomialfunc-tionsitrequiresalotofcomputations(InabaandSakakibara1985；Park1996)ThedigitalconvolutionmethodismuchmoreemcienlthanthemethodselectingpolynomialfunctionsandiseasilyimplementedbyhardwareBut，inthevelocityprofilesgeneratedbythemethodtheaccelerationintervalisalwaysthesameasthedecelerationintervalandthecharacteristicsofthedecelerationaredependentonthoseoftheacceleration(KhalsaandMahoney,1990；ChenandLee1998)AsimpletoefficientsstoredmethodforgeneratingvelocityprofilesisproposedAccordingtothedesiredcharacteristicsofaccdec，eachsetofcoefficientsiscalculatedandstoredGivenamovingdistanceandacedecintervals，avelocityprofilehavingthedesiredcharacteristicsofaccdeccanbee币cientlygeneratedbyusingthesetoemcientsButforlongandshortdistancesthesameacedecintervalsareselected；thee币cientvelocityprofilecannotbecalculatedforthevarieddistancemovements(JeonandHa，2000)ThispaperisorganizedasfollowsSection2proposesacubicpolynomialacedeccontrolmodelforhighspeedNCmachiningBasedonthediscretecharacteristicofthedatasamplinginterpolation，thecubicpolynomialaccdeccontroldiscretemathe-maticalmodelissetupinSection3TheadaptiveacedeccontrolalgorithmforpredeterminingthedecelerationpointofarbitraryroutesegmentisdeducedinSection4ExperimentalresultsarepresentedinSection5andconclusionsaresummarizedinSection6struttedbythecubicpolynomial，359y(甜)=(q+2a2u+3a3u2+4a4u3)fm(1)Itisassumedthattmistheacceleratingordeceleratingdurationtimewhichistakenassynchronizedmotionaxestoaccelerateordeceleratefromthebeginningspeedtotheendspeed，妒ttm，fO，tmTheotherkineticcharacteristiccurvesofaccel-erationandierkcanbeobtainedbydifferentiatingthefeedratecurve，A(u)撕=(2a2+6asU+12a46as24a4u)t：铲。(2)【，(“)=(+Again，integratingEq(1)withrespecttotimeyieldsthedisplacementcurvefunctionas，S(zf)=a0+aI+a2u2+a3u3+a4u4(3)Theboundaryconditionsare，s(0)=0，v(o)=K，矿(1)=圪，A(O)=A(1)=0，whereKand圪standforthebeginningspeedinacestage(ordecstage)andtheendspeedThenthecur·vilinearfunctionsarederivedas，(“)=6(圪一K)(12-)4，彳(u)=：6K(V+,3-(KV,)一(uK-)甜u：2)+t2m(,V(uK一圪)材，(4)=K+3(KK咖2+2(K一圪弦，s(“)=tmKU+(圪一V。)tmU3+05(K-Vo)tmU4CUBICPOLYNOMIALACCDECCONTROLequalFtoromtheE孟q&imumuac=0ce5lerathteioanc彳ceml瓤eraTtihoennfm：ains(4)，let，彳(“)MODELbededucedas，Tomeettheneedofhighspeedmachining，thefeedratemustbechangedsmoothlyandtheaccelera·tionmustbecontinuousTheboundaryconditionsare：(1)thedisplacementatthebeginningtimeis0；(2)boththebeginningspeedandtheendspeedarethesameasrequired；(3)theaccelerationsbothatthebeginningtimeandtheendtimeare0Theaccdecfeedratecurve如nctioniscontm=3KKI“24。)=nT(5)玎isarealnumber,denotingthetheoreticaltimesofthetheoreticalrunningtimetmtointerpolationperiodTwhendecelerating(oraccelerating)fromKtoWhent=tm，thetheoreticalacceleration(orde-celeration)lengthSlisobtainedfromEq(4)as，万方数据Lengeta1JZhejiangUnivSciA200893)：358-365墨=(圪+V。)tm2=3lK2一曙II(4A。)Therelationofspeed(叻，acceleration0)andjerkisexpressedasshowninFig1FromFig1，inthecubicpolynomialacedeccontrolmodeltheaccelerationiSconsecutive。whichavoidstheOccur-renceofintensevibrationinhighspeedmachiningThecalculationsofjerk，acceleration，speedanddisplacementinvaryingspeedprocessaresimpleandeasytorealizebecauseoffeWfourfundamentaloperations矿匕二上二金一p#毒三7l一一Fig1Speed("，acceleration似)andjerk(J)ofthecubicpolynomialaccdeccontrolmodelCUBICPOLYNOMIALACCDECCONTROLDISCRETEMODELCharacteristicsofdatasamplinginterpolationThecontrollingwithdatasamplinginterpolationisatypeofdiscretecontrollingmodeThedatasampiinginterpolationisbasedonapproximatingacurvewithstraight·linesegments，whoselengthsarepro-portionaltothelocalaxialplannedvelocitiesTheacedeccon仃OlalgorithmiSperformedonthedesiredfeedratecommand矿firstlyThenthefeedratecornmandV(afteracedeccontrolalgorithm)issenttotheinterpolatortocomputethetravelingdistaneecomponentforeachaxisintheCartesiancoordinates(KYand刁ThetravelingdistancecomponentsZ厶Yand觇alongtheXYandZaxesaretransmittedtothemotioncontrolroutine邪positioncommandstothepositioncontrolloopforthedesiredmachiningfinallyWhendatasamplinginterpolationisusedinpo-sitioncontr01itiStheconditiontOmakesurethateverysynchronizedmotionaxisreachesthedestina-tionsimultaneouslyandtheirmovementiScontinuousSOthateachaxisrunningtimetisjustintegraltimesthatoftheinterpolationperiod互ietimepartitioningruleThisconditioncanberealizedbyadjustingthecommandfeedrateofeachsynchronizedmotionaxis(ieacceleratingordecelerating)(Guoeta1，2003)ThroughtheaboveanalysesnshouldbeanintegerSetNastheminimumintegernotsmallerthan玎N=ceil(n)NnReplacingtherealnumber，1withtheintegerNinEq(5)yields，=3IKKI(24。)=NT(6)ConstructionofdiscretemodelGivenanycurvegivenbythefunctiony=flt)，theinterval【to，纠isdividedintoNdivisionsPickingtheleftendpointstodeterminetheheightsisshowninFig2a；theapproximateareaunder少钡Dontheintervalto，明is，r儿灿嘻小娟棚孚)孚Ototlt2r卜l，l肛ltMtOtotlt2缸lnt#-ltutFig2ImplementcurveofJft)(a)Leftendpointsusedfortheheightsofrectangles；(b)Rightendpointsusedfortheheightsofrectangles万方数据Lengeta1JZhejiangUnivSciA20089f3J：358-365ThiswayofapproximatingtheareaunderthecurveiscalledtheleftsummethodChoosingthefightendpointstodeterminetheheightsisshowninFig2b；theapproximateareaunder尸砜f)ontheintervalto，明is，Ij删，喜小+z可tN-to警ThiswayofapproximatingtheareaunderthecurveiscalledtherightsummethodSupposethattheslopeofierkiSKsandinitialvaluesofjerk,acceleration，speedanddisplacementareJo，Ao，goandSo，respectivelyThediscretemodelofjerkcurve，implementedbyIeftsummethod，iS。J(iT)=厶+0(f一1)T，1iN(7)Thediscretemodelsofacceleration，speedanddisplacementcurve，realizedbyrightsummethod，are，iA(iT)=40+，(7)r，I<i<N+I，=1I矿(f丁)=Vo+A(jT)T，j=l，s(fr)=so+V(jT)T，j=l1iN1f361州耻器一嘉N(N斋：、(+1)(+2)r2+1)(+2)r2lfNThediscretemodelsofacceleration，speedanddisplacementcurve，implementedbyrightsummethod，are，彳(fr)：坠竺二竺!f一篁兰二竺2f：，、N(N+2)TN(N+1)(+2)丁71iN+1；yczr，=K+；孑÷糕z+i揣r2一j噪f3，l<i<N；N(N+1)(+2)S(fn：(N3+3N2-1)V+(2N+1)Ve乃、7N(N+1)(+2)+!竺二竺!堕丝±12Ti24!竺二竺21丝二!乃，2N(N+1)(+2)N(N+1)(+2)一旦熹忑巩l<i<N2N(N+1)(+2)(9)c8，me。罢等蠹慧i酱竺罴=：舞嚣篡。警Tosatisfythattheaccelerationattheendtimeis0andconsideringcharacteristicsofimplementingtheaccelerationcurvebyfightsummethod(theheightofcorrespondingrectangleareaattime矗is以廿1)，theboundaryconditionsoftheaccelerationcurveare，4=0，彳(+1)T)=0Theboundaryconditionsofspeedanddisplacementcurveare，(N一1)Vff=一22(10)Fortheaccelerationcurve，when圪刮7-mx，thediscreteexpressionofthetheoreticalaccelerationlength&is，只=(MT-1)一V,T2Forthedecelerationcurve，when圪屯，thediscreteexpressionofthetheoreticaldecelerationlengthSdis，蜀=生笋+T(N+1)Vff，Vo=K，V(NT)=圪，so=0whereRmisthemaximumallowedfeedrate，MisSothediscretemodelofthejerkcurve，impletotalinterpolationperiodsinaccelerationprocess，Nmentedbyleftsummethod，is，istotalinterpolationperiodsindecelerationprocess万方数据