外文翻译 CNC加工加减速平稳变化的方法.docx
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外文翻译 CNC加工加减速平稳变化的方法.docx
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外文翻译CNC加工加减速平稳变化的方法
AGeneralizedApproachforthe
AccelerationandDecelerationofCNCMachineTools
JaeWookJeon
DepartmentofControlandInstrumentationEngineering
SungkyunkwanUniversity
300Chunchun-Dong,Jangan-Gu,SuwonCity,Korea
Abstract—ManytechniquesfortheaccelerationanddecelerationofCNCmachinetoolshavebeenproposedinordertomakeCNCmachinetoolsperformgivenmachiningtasksefficiently.Sincetheyshouldbecalculatedinalimitedtime,mostofthemarenotcomputationallyintensive.However,theseprevioustechniquescannotgeneratevelocityprofileshavingsomekindsofaccelerationanddecelerationcharacteristicsthoughtheycangeneratevelocityprofileshavingvariousaccelerationanddecelerationcharacteristics.Thispaperproposesageneralizedapproachforgeneratingvelocityprofileswhichcannotbegeneratedbyprevioustechniquesaswellasvelocityprofilesgeneratedbythem.Accordingtothedesiredcharacteristicsofaccelerationanddeceleration,eachsetofcoefficientsiscalculatedandisstored.Givenamovingdistance,anaccelerationinterval,andadecelerationintervalforCNCmachinetools,avelocityprofilehavingthedesiredcharacteristicsofaccelerationanddecelerationcanbeefficientlygeneratedbyusingthesecoefficients.Itwillbeshownhowtogeneratetypicalvelocityprofilesbytheproposedtechnique.
I.INTRODUCTION
ThedemandforbetteraccuracyinthemanufacturingofcomplicatedpartsandthedesiretoincreaseproductivityhavedevelopedCNCsystemssothatCNCmachinetoolsmovemoreaccuratelyandmorequickly.SincethecombinedcharacteristicsofthecontrolandthemachinetooldeterminethefinalaccuracyandproductivityoftheCNCsystem,therearemanyfactorstoconsiderforimprovingthesequantities.Oneoftheimportantfactorsisefficientlygeneratingvelocityprofileswhichhavethedesiredaccelerationanddecelerationcharacteristicswhichinturnaredeterminedaccordingtogivenmachiningtasks.ManyresearchershaveproposedtechniquesforgeneratingvelocityprofilesofCNC
machinetools.Oneofthemisgeneratingvelocityprofilesbytheselectionofpolynomialfunctions[1].Thistechniquecangeneratesomanykindsofvelocityprofilesandfurthermorecanmakethecharacteristicsofdecelerationbeindependentfromthatofacceleration.Themajorproblemofthistechniqueiscomputationalloadtoincreasealmostexponentiallywiththeorderofpolynomialintheaccelerationorthatinthedeceleration.Duetotimeconstraints,itisverydifficulttoapplythesetechniquestocontrollingCNCsystems.Otherprevioustechniquesforgeneratingvelocityprofilesisbasedonadigitalconvolution[2-6].Thesetechniquesaremuchmoreefficientthanthetechniquesselectingpolynomialfunctionsandareeasilyimplementedbyahardware.But,invelocityprofilesgeneratedbythesetechniques,theaccelerationintervalisalwayssameasthedecelerationintervalandthecharacteristicsofdecelerationaredependentonthatoftheacceleration.Thus,somevelocityprofilescannotbegeneratedbythesetechniques.
Inthispaper,ageneralizedapproachfortheaccelerationanddecelerationofCNCmachinetoolsisproposed.Theproposedtechniqueisassimpleandefficientasthetechniquesbasedonadigitalconvolutionandcangeneratevelocityprofileswhichhavemorevariouscharacteristicsofaccelerationanddecelerationthanthetechniquesbasedonadigitalconvolutioncan.Thatis,theproposedtechniquecangeneratevelocityprofilesofwhichthedecelerationcharacteristicsareindependentfromtheaccelerationcharacteristics.First,somecoefficientsarecalculatedandarestoredaccordingtotheaccelerationcharacteristic,thedecelerationcharacteristic,andtheaccelerationinterval,andthedecelerationinterval.Thengivenadesiredmovingdistance,avelocityprofilewhichhasthedesiredcharacteristicsisgeneratedbycalculatingthepositionincrementduringeachsamplingtime.Thepositionincrementduringeachsamplingiscalculatedbymultiplyingthestoredcoefficientswiththeproductofonesamplingtimeandthevelocityafteracceleration.
InsectionII,existingtechniquesforgeneratingvelocityprofilesofCNCmachinetoolswillbeexplained.InsectionIII,itwillbeexplainedhowtogenerateadesiredvelocityprofilebytheproposedtechnique.Theproposedtechniqueandotherexistingtechniqueswillbecompared.InsectionIV,itwillbeshownthattheproposedtechniquecangeneratesomeusefulvelocityprofilesforCNCmachinetools.
II.PREVIOUSTECHNIQUES
Fortheillustrationoftheprevioustechniques,letusconsideronesingle-axiscontrolsystemofwhichthemaximumvelocity,themaximumacceleration,andthesamplingtimeareVmax,Amax,andTsrespectively.IfthissystemmovesthegivendistanceSatthemaximumvelocityVmax,thenthemovementtimeT1intherectangularvelocityprofilewillbeT1=S/Vmax=pTs,
(1)
Selectinganintegernwhichisthesmallestintegeramongintegerswhichareequaltoorgreaterthanp,theresultingrectangularvelocityprofileisconstructedasinFig.1.Thevelocityandpositionequationsforthisprofileare
Thepositionincrementduringeachsamplingtimeis
where
and
arethepositioncommandsatthe
andthe
samplingtimesrespectively.Thatis,thepositionincrementduringeverysamplingtimeisthesame.However,sincenophysicalsystemcanachievetheaboverectangularvelocityprofileduetoimpulseacceleration,theaccelerationintervaltoincreasevelocityfromtheresttoaspecifiedvalueandthedecelerationintervaltodecreasevelocityfromthespecifiedvaluetotherestareneeded.
II-A.SelectionofPolynomialFunctions
(5)
GivenanaccelerationintervalTs=naTs,adecelerationintervalTd=ndTswherena=nd,andadistanceS,atrapezoidalvelocityprofilewhichhasthelinearaccelerationanddecelerationcharacteristicscanbeconstructedasinFig.2.Ifthisprofilehastheconstantvelocityinterval,thenn=[S/(VmaxTs)]islargerthanna.Thevelocityandpositionequationsforthisprofileare
And
(6)
Fig.1.ArectangularvelocityprofileformovingadistanceS
Fig.2.AtrapezoidalvelocityprofileformovingadistanceS
Intheabovederivation,itisassumedthattheaccelerationintervalisthesameasthedecelerationintervalandtheconstantvelocityintervalispresent.Inthecasethattheaccelerationintervalisdifferentfromthedecelerationintervalortheconstantvelocityintervalisnotpresent,similarequationsarepossibletoderive.Thistrapezoidalvelocityprofilewhichhasthelinearaccelerationanddecelerationcharacteristicsisparticularlyeffectiveforcontrollingamachinetoolhavingahighdegreeofrigidity.However,largejerkquantityatthestoppointinthetrapezoidalvelocityprofilemaywearoutaleadscrewassemblyveryquicklyandbelikelytomakemachinetoolshavinglittlerigidityvibrate.Sincesmoothvelocityprofileswhichhaveparabolic(second-order)orhigher-orderaccelerationanddecelerationcharacteristicsdonothavelargejerkquantityatthestoppoint,thesevelocityprofilesareveryoftenusedforCNCmachinetools[1-6].Severaltechniqueswhichselectapolynomialfunctionforgeneratingvelocityprofileswithsmall
jerkquantityhavebeenproposed[1].Givenposition,velocity,andaccelerationattheinitialandfinalpositions,aclassofpolynomialfunctionsforsatisfyingtheseconditionsisselected.Oneapproachistospecifyaseventh-degreepolynomialforeachaxis.Anotherapproachistosplittheentiretrajectoryintoseveraltrajectorysegmentssothatdifferentpolynomialsofalowerdegreecanbeusedineachtrajectorysegment.Themostcommonmethodsare4-3-4trajectory,3-5-3trajectory,and5-cubictrajectory.Themajorproblemingeneratingvelocityprofilesbytheselectionofpolynomialfunctionsiscomputationalload.Therequiredtimeforgeneratingasmoothvelocityprofileincreasesalmostexponentiallywithaddedorder.Therefore,itisalmostimpossibletousethesetechniquesforgeneratinganarbitrarysmoothvelocityprofilebecauseoftimeconstraintsincontrollingCNCmachinesystems.
II-B.DigitalConvolutionTechniques
GivenanaccelerationintervalTa=naTs(whichdeterminesthedecelerationintervalTd=ndTs=naTsbecausetwointervalscannotbedifferentinvelocityprofilesgeneratedbydigitalconvolutiontechniques)andadesireddistanceS,atrapezoidalvelocityprofilewhichhasthelinearaccelerationanddecelerationcharacteristicscanbeconstructedbydigitalconvolutiontechniques.ThepositionincrementduringeachsamplingtimeinatrapezoidalvelocityprofileδPl(kTs)isconstructedbytheconvolutionofthepositionincrementδP0(kTs)asin(4)duringeachsamplingtimeinarectangularvelocityprofileandthesequenceH(kTs)givenby
(7)
where
(8)
(9)
asinFig.3.TherelationshipbetweenδP0andδP1isexpressedasthefollowingrecursiveequation[2]
Equation(9)providesthebasicinformationforthetrapezoidalvelocityprofile.Basedon(9),wecandesignthehardwaresystemfortrapezoidalvelocityprofilesasinFig.4,wherebufferregistersactasdelayelements[4].Asecond-ordervelocityprofilewhichhastheparabolicaccelerationanddecelerationcharacteristicscanalsobeconstructedbydigitalconvolutiontechniques.Thepositionincrementinasecond-ordervelocityprofile
canbeobtainedbysuccessiveconvolutionsasinFig.5
Where
.(10)
Theshapeofsecond-ordervelocityprofilecanbedeterminedbythevaluesofm1andm2[2,4].Therelationshipbetween
and
isexpressedasthefollowingrecursiveequations[2].
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