数控机床的带限运动控制

ZhangXinmei(Autor)

BandlimitedMotionControlofCNCMachineTools

https://cuvillier.de/de/shop/publications/725

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CuvillierVerlag,InhaberinAnnetteJentzsch-Cuvillier,Nonnenstieg8,37075Göttingen,Germany

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Chapter1

Introduction

Motivation

Goodqualityandlowcostofaproductarealwaysrequiredbyallcustomers.Thosetwofactorsofaproductaremainlydeterminedbytheproductionmachines.Goodqualityofaproductisassuredbyhighprecisionofthemachinetools.Lowpriceofaproductcanbeachievedbyincreasedproductivitythroughhighmanufacturingspeedtogetherwithminimizedauxiliaryprocesstimesandprocessstability.Therefore,highprecisionandspeedaretwodemandsformodernmachinetoolstoprovideproductsthatsatisfycustomers[76].

Byrnepresentedcurvesin[8],asshowninFigure1.1,tracingthedevelopmentinman-ufacturingcapabilityintermsofachievablemachiningaccuracyduringthelast60years.Ultra-precisionmachinetoolsundercomputercontrolcanpositionthetoolrelativetotheworkpiecetoaresolutionandpositioningaccuracyintheorderof1nm.For“precisionma-chining”,theaccuracycouldnowachieve10nmwiththehelpofaccuratemachineelements.In“normalmachining”,e.g.CNCturningandmillingmachines,accuraciesof10to100μmcanbeachieved.Besidesknowingthoseconcretevaluesofaccuraciesthatmachinetoolscanachieve,thetendenciestohigheraccuraciesofmachinetoolsalsocatchtheeyes.

Precisionmanufacturingrelies,toasignificantextent,onthequalityandaccuracyofama-chinetool.Oneimportantfactorwhichaffectstheaccuracyofamachinedcomponentistheerrorcausedbythevibrationofthemachinetool.Thecommonlyapprovedsolutionistouserigidcomponentstoimprovetheaccuracyofthemachinesystem.

HighSpeedMachining(HSM)isalsoamainstreamtrend.OriginofinterestinHSMwastheworkdonebySalomonin1931[20].HisdefinitionofHSMisbasedonchipremovaltemperaturereductionwithhighcuttingspeed(5-10timeshigherthaninconventionalma-chining)inamachiningprocess.Thoughlaterresearchershaveunfortunatelynotbeenable

1.1.MOTIVATION

1.2.PROBLEMDESCRIPTIONANDAIMS

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2

PAGE

3

TurningandMillingMachines

100

NormalMachining

10

1(1μm)

PrecisionMachining

GrindingMachinesCNCMachines

Lapping,Honing,BoringandGrindingMachines

PrecisionGrindingandTurningMachines

0.1

HighPrecisionand

UltraPrecisionMachines

0.01

UltraPrecisionMachining

(1nm)

FreeAbrasiveMachining

0.001

IonBeamMachining

0.0001

1940

1960

1980

2000

Figure1.1:Developmentofachievable“Machining”accuracyoverthelastsixtyyears[8]

toverifythistheorytoitsfullextent,theyalsoconfirmthatthereisarelativedecreaseofthetemperatureatthecuttingedgethatstartsatcertaincuttingspeedsfordifferentmateri-als[20].Table1.11givesanexampleofsomecuttingspeeds[3]forgeneralknowledgeofnormalandhighspeedincuttingprocess.Thecuttingspeedisdependentonthecharacteroftheworkpiecematerial.Forinstance,forcuttinggraycastiron,figuresgreaterthan6m/smightbehigh-speedmachining,whereasforsofteraluminumalloys,50m/sishigh-speed.

ToperformHSMapplicationsitisnecessarytouselight,butrigidmachinetooltoachievehighspeedandminimizeproblematicvibrations.Lightandrigidmachinetoolassureshighacceleration,higheigenfrequencyofthesystem,thereforhighspeed.Rigidmachinetoolassuresnoloweigenfrequencyintheaxis,thereforehighaccuracy.

Therefore,bothprecisionandhighspeedmachiningrequirerigidmachinesystem.How-everprimarilyduetospace,weight,andpowerconstraints,thisisnotalwayspossible.Elasticityisunavoidableinsomemechanicalsystemssuchas:highspeedpickandplacerobots,coordinatemeasurementmachines,harddrivetestingmachines,gantrycranesandsoon.Inmachinetools,duetothepowertrainselementssuchasbelts,spindles,gearsandsoon,therigidityofthemachinetoolisalsolimited.Allthosekindsofmechanismssufferfromvibrationrelatedproblemsundergoingpoint-to-point,trajectoryfollowing,andothercommonmotiontasks.Theeffectiveuseofsuchsystemscanonlybeachievedwhensuchvibrationscanbeproperlyhandled.

Thusthedemandsofhighqualityandlowcostofproductmotivateresearcherstofinda

1WC:TungstenCarbide;PCD:polycrystallinediamond;CBN:cubicboronnitride;sia.:sialon;cer.:ceramic;

+:morethan

Workmaterial

Solidtool-endmill,drill

WC,coatedWC,PCD,ceramic

Indexabletool-shellandfacemill

WC,ceramic,sialon,CBN,PCD

Typicalvelocity

(m/s)

HighSpeed

(m/s)

Typicalvelocity

(m/s)

HighSpeed

(m/s)

aluminum

5+

(WC,PCD)

50+

(WC,PCD)

10+

60+

(WC,PCD)

castiron

softductile

2.5

1.75

6

4

6

4

20(sia.,cer.)15(cer.)

steel

freemachiningsteelalloy

stainlesshardnessRC65

1.75

1.25

1.75

0.4

6

4

2.5

2

6

3.5

2.5

0.5(WC)

1.5(CBN,cer.)

10

6

4.5

0.75(WC)

3(CBN,cer.)

titanium

0.625

1

0.75

1.5

superalloy(Iconel)

0.75

1.25

1.3(WC)

3.5(sia.)

6(sia.,cer.)

Table1.1:Exampleofsomecuttingspeeds[3]

waytogetridofvibrationformachinetools,oratleastreducethemtoaninsignificantdegree,especiallythosehaveinherentstructureflexibility,sothattheaimsofhighaccuracyandhighspeedcanbeachieved.

ProblemDescriptionandAims

Theproblemofreducingvibrationsisacomplexonethatcanbeapproachedinmanyways.Kozak[30]presentsasimplemannertocategorizethoseapproachesbylookingataflexibledynamicsystemundercontrolasshowninFigure1.2,whichcanbefoundineverycontroltextbook.

FeedforwardController

Desired

motion Command

Generator

FeedbackController

output

Plant

Figure1.2:Blockdiagramofatypicalclosedloopcontrol

Therearefourprimaryblocksintheabovesystem.Researchershavemadedifferenteffortstoreducesystemvibrationthroughthosefourblocks.Theyarethe

1.2.PROBLEMDESCRIPTIONANDAIMS

1.2.PROBLEMDESCRIPTIONANDAIMS

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4

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5

Plant,

CommandGenerator,

FeedbackController,

andtheFeedforwardController.

ThePlantBlock

Theplantisnormallythefirstconcernforaresearchertothinkaboutwhenvi-brationreductiontaskispresented.Theelasticstructureoftheplantisasourceofvibrations.Therefore,makingtheplantsystemmorerigidand/oraddingdampertotheplantaretwomainapproaches.

Theincreasingoftherigiditysometimescomeswiththeincreaseoftheinertiaormassofthecomponentsoftheplant.Thisresultsinareducedpayload,worsedy-namicbehaviorandincreasedcost.Thereareusuallymanytrade-offsthatmustbeconsideredinordertoproduceaphysicallyandeconomicallyviablemecha-nism.Moreover,theelasticitythatcomesfrompowertrainsinthemechanicalplantrestrictsthelevelofrigiditythatcanbereached.

Addingdampertotheplantisusuallydonebyaddingdampingmaterialtoamechanism.However,modifyingapre-existingplantcanbecostlyanddifficult,andmakingmodificationstoreducevibrationcanpotentiallychangetheperfor-manceofotheraspectsofthemechanism,e.g.thestiffness.

Inthiswork,theplantisnottargetedforeliminatingvibrations,becausetheaimedsolutionistoreducethevibrationforanyplant.Buttheknowledgeofpa-rametersoftheplantisasimportantasgettingridofvibrationsitself.Therefore,parameteridentificationisthefirststep.Twomaindomainsofidentificationex-ist:frequencydomainandtimedomainidentification[1,19,36,42].Thetimedomainidentificationistheclassicalapproachtosystemidentification.Inthefrequencydomainidentification,thefrequencyresponseofthesystemisusedtoestimatetheplantparameters.However,theexistingmethodsofparametersidentificationareeithertoocomplicatedornotsuitableforhighordersystems.Asthecharacteristicparametersoftheplanthavetobeknownforthefinalsolu-tion,thefirstaimofthisworkisparameteridentificationformachinetoolsystemofanyorder.

Aim1:Identifyingparametersoftheplantforanyorderofthesystem.

TheCommandGeneratorBlock

Systemvibrationscomeinmainlytwoforms.Firstformofvibrationsaretran-sientanddieoutafteraperiodoftime.Thesecondformofvibrationsaresteadystatevibrations,whichareconstantinmagnitudeandfrequency,anddonotdieout.Thissecondformofvibrationsaregenerallycausedbysomeperiodicex-citation.Ingeneral,vibrationscancomeinanycombinationofthesetwotypes.Vibrationscanbecausedbymanydifferentsources.Commandgeneratorisoneofthesources.Typicalexampleofcommandthatbringsthetransientvibrationisastepinput.

Alotofeffortsarededicatedtocreateormodifycommandsthatcausethesys-temresponsetosatisfydesiredtransient/steadystateperformancecharacteris-tics[46,47,56,57].Thereisatleastonedistinctadvantageofusingthecommandgenerationapproachovertheotherapproaches:systemsthatsufferfromtrouble-somedynamicbehavior,suchasvibrations,canberetrofittedtotakeadvantageofcommandgenerationschemesatlowcostandwithgenerallynomodificationsneedingtobemadetothemechanicalsystemandcontroller.

Limitingjerk,thederivativeofaccelerati