Anoverhungboringbarservosystemforon-linecorrectionofmachiningerrorsW.M.Chiua,*,F.W.Lama,D.GaobaDepartmentofManufacturingEngineering,TheHongKongPolytechnicUniversity,HungHom,Kowloon,HongKongbDepartmentofMechanicalEngineering,HarbinInstituteofTechnology,Harbin,PRChinaReceived17June2001AbstractInthispaper,anewlydesignedoverhungboringbarservosystemequippedwithanon-linecompensationfunctionformachiningerrorsispresented.Theoverhungboringbarthathasbeendevelopedismadewithapairofconcentricbarswithanouterdiameterof14mmandanoverhungratioof8:1.Apiezoelectric(PZT)actuatorwasincorporatedintheboringbarservosystemtoachieveon-linecompensation.Acontroltechnique,forecastingcompensatorycontrol(FCC)wasimplementedintheboringbarservosystemtoperformanon-linepredictionofthemachiningerrorsencountered.Anoff-linesimulationwasperformedtotesttheadequacyoftheparametersbeingusedintheFCCmodelsadopted.Resultsofthecuttingtestswiththeboringbarservosystemshowthattotheextentlimitedbytheinstrumentcapability,aboringbarservosystemusinganFCCmethodologycanbeaverycost-effectivetoolforon-linecompensationofmachiningerrorsintheprecisionboringofholeswithhighaspectratios.Keywords:Real-timeerrorcompensation；Precisionboring；Forecastingcompensatorycontrol1.IntroductionThegenerallevelofworkaccuracyandsurfacefinishrequiredofmachinedpartsisbecomingincreasinglymorestringentinmodernindustry.Therearetwogeneralapproaches,commonlyknownaserroravoidanceanderrorcompensationmethods,availableforreducingtheerrorsthatadverselyaffecttheformaccuracyofamachinedpart.Undoubtedly,thereal-timeerrorcompensationmethodisprobablythemostdirectandcost-effectivewaytodealwithexternaldisturbancesofunpredictablenaturesuchasnon-uniformdepthsofcut,spindle-motionerrors,dynamicvibrations,etc.Overtheyears,real-timeerrorcompensationmethodologyhasfoundmanyfruitfulapplicationsinindus-tryduetoitsreadinesstohandlesituationsinvolvingdis-turbancesofdynamicandnon-repetitivenature.Althoughaconsiderablevolumeofresearchworkhasbeenreportedintheareaofon-lineactiveerrorcompensationformachiningoperationsinthelasttwodecades13,therewereonlyafewattemptsthatwerefocusedontheoverhungboringofdeepholes.Beingtheweakestlinkintheforceloopwithinthemachinetoolstructure,aboringbarplaysadominantroleindeterminingtheoverallformaccuracyandcuttingpro-ductivitywithinthewholemachinetoolsystem.Unlikeotherremovalprocesses,theimplementationofactiveerrorcom-pensationforoverhungboringposessomerealchallengesinmoderndaymachinecontroltechnologybecausesmallsen-sorsthatcanbeattachedtosmall-sizedboringbarsformonitoringformerrorsinsmallholesareextremelyrare.Anothermajordifficultycomesfromtheinaccessibilityofthecuttingpointthatpreventssensorsfrombeingmountedclosetothepointofcuttingforreal-timemeasurement.Further,actuatorsthatareuseabletoeffectthenecessarycompensa-toryactionaremostlytoolargetofitinsidesmalloverhungboringbars.Hence,conventionalsensorsandactiveactuators,whicharesuccessfulforreal-timemeasurementandcom-pensationinmuchexternalmachining,areoflittleusewheninternalsurfacesareencountered.Severalboringbardesignsforon-lineactiveerrorcom-pensationhavebeenreported46.Inthesesystemsreported,theactuatorsforcompensationareinstalledinsidetheboringbarandclosetothecuttingtool.Althoughthemachiningerrorscanbecontrolledbysensorsandactuatorsincloseproximitytothecuttingzone,theboringbarsdesignedinsuchawayarelargeindimensionssoastoaccommodatethesefitteddevices,hencerenderingthem-selvesunsuitableforuseinsmallerholes.JournalofMaterialsProcessingTechnology122(2002)286292*Correspondingauthor.Tel.:852-27-666-590；fax:852-23-625-267.E-mailaddress:.hk(W.M.Chiu).Inthispaper,aboringbarservosystemof14mmdiameterand8:1overhungratiowhichincorporatesapiezo-electric(PZT)actuatorforon-lineerrorcorrectionispre-sented.Theboringbarconsistsoftwoconcentricbars,oneofwhichisusedforerrordetectionandtheotherforerrorcompensation.Ananalyticalandexperimentalstudyhasbeenconductedtoshowhowthisboringbarservosystemcanbeusedtocompensatefortheinstantaneousmachiningerrorsduringtheboringprocess.2.Boringbarservosystem2.1.OperatingprincipleAschematicdiagramoftheboringservosystemisshowninFig.1.Thedual-concentricboringbaradoptsaleverstructurewithaPZTactuatorandaboringcutterinstalledattheoppositeendsofthebar.ByapplyingasuitablevoltagetothePZTamplifier,theactuatorstackwillcontract.Thecontractionoftheactuatorstackcanbetransferredintoamicro-feedingmotionoftheboringcutterbyrotatingthecontrol(outer)bararoundtheflexuralpivot.Themeasuring(inner)barisofacantileverstructurewithstraingagesattachedformeasuringtheforce-induceddeflectionsinthebar.Theamountofmicro-feedingoftheboringcutteriscalculatedaccordingtothemeasuredstrainsignalsinthemeasuringbar.Asaresult,theboringbarsodesignedcanbemadewithamuchsmallerouterdiametereventhoughthePZTactuatorandstraingageshavebeenincorporated.Thesequenceofstepsinoperatingtheboringbarservosystemisoutlinedasfollows:1.Theinstantaneousdeflectionoftheboringtoolactedbythecuttingforceismeasuredbythestraingagesattachedtothemeasuringbar.2.ThevoltagesignalfromthestraingagesisdigitizedbyanA/Dconverterfordatalogging.3.Thesamplederrordataisprocessedinthecontrolcomputer.4.AnoutputcontrolcommandistransformedbyaD/Aconverterintoananalogsignalwhichisusedtodrivethepiezo-actuatorthroughitspoweramplifier.5.ThedeflectionoftheboringtoolissuppressedthroughthecorrectiveactionofthePZTactuator,hencemaintainingaconstantnominalcutterpositionandneutralizingthedetrimentaleffectsofcuttingforcesontheformaccuracy.AsshowninFig.2,beforethecuttingforceFcisapplied(i.e.Fc0),boththecontrolandmeasuringbarsremainstraight(Fig.2(a).AsthecuttingforceFcactsontheboringbar,theboringbarasawholeisdeflecteddownwards(Fig.2(b)resultinginanincreaseofstraininthemeasuringbarandgeneratingaproportionalanalogsignalfromthestraingages.ThisanalogsignalissampledbythecontrolcomputerthroughtheA/Dconverterandusedtogenerateacontrollingaction.ThePZTactuatorthenexpandsbyincreasingtheappliedvoltagetothepoweramplifierthroughtheD/Ainterface.Asaresult,thecontrolbarrotatesaroundtheflexuralhingeinaclockwisedirectionsuppressingthedownwarddeflectionofthecutteruntilthemeasuringbarbecomesstraightagain.AscanbeseeninFig.2(c),therestorationofthecuttertoitsequilibriumpositionisachievedwithgreaterdeformationinthecontrolbar.Ontheotherhand,iftheexternalforceismomentarilyreduced,thedeflectionoftheboringbarbecomeslessastheforcewithinthesystemislower.AnoppositecontrolactionwillbeissuedtothePZTactuatorinordertooffsetthechange.Inthisway,nomatterhowthecuttingforcevariesinthecourseofcutting,theboringtoolwilltendtoreturntothepre-setposition,thusforcingtheboringtooltoundergocuttingateffectivelyzerodeflection.Therefore,theforce-inducedeffectsonthemachinedsurfacewouldthenbecancelledoutandtheoverallformaccuracyshouldbeimproved.2.2.ModelingoftheboringbarservosystemFortheanalysisofthedynamicbehavioroftheboringbarservosystem,theequationofmotionisformulatedasshowninFig.3.Forthispurpose,elementsoftheboringbarservosystemaremodeledbyasingledegreeoffreedomsystemFig.1.Aschematicdiagramoftheboringbarservosystem.Fig.2.Theinteractionofdeflectionandcorrectioninacompensationcycle.W.M.Chiuetal./JournalofMaterialsProcessingTechnology122(2002)286292287withlumpedmasses,stiffnessandviscousdampingcoeffi-cients.Variableystandsfortheradialdeflectionofthecutter；yfortheangularrotationaboutpointOofthecontrolbar；jfortheangularrotationaboutbasepointO0ofthemeasuringbar；IystandsforthemomentofinertiaofthecontrolbaraboutpointO；IjforthatofthemeasuringbaraboutpointO0；Cy,Kyarethedampingcoefficientandstiffness,respectively,ofthecontrolbar；Cj,Kjarethedampingcoefficientandstiffness,respectively,forthemea-suringbar；FcandFprepresentstheradialcuttingforceandthecompressiveforce,respectively,ofthePZTactuator.Forsmalldeparturesfromequilibrium,anglesjandycanbeassumedtobesmallsothattheequationofmotioncanbesimplifiedtoMC127yC_yKyFcL1L2Fp(1)whereMIyIjL21MpL22；CCyCjL21CpL22；KKyKjL21KpL22TwoequationsgoverningthedesignoftheboringbarsystemcanbeobtainedfromEq.(1).InEq.(2),themaximumunconstrainedradialtooltravel,ymax,isexpressedintermsofDmax,themaximumunconstrainedexpansionforthePZTactuator.Similarly,theundampednaturalfrequencyoftheboringsystem,on,isshowninEq.(3):ymaxL1L2KpKyKjL21KpDmax(2)onKyKjL21KpIyIjL21Mps(3)2.3.Forecastingcompensatorycontrol(FCC)modelTocarryouton-linecontrol,itisimportanttoselectasuitablecontrolschemethatiscomputationallysimple,yetsophisticatedenoughtotrackanyrapidlychangingcompo-nentsofthecontrolledvariable.Atime-seriesapproachbasedonFCCmethodologywhichhasbeensuccessfullyimplementedinmanymachinecontrolproblems7hasbeenadoptedinthiswork.Thestreamoftooldeflectionsfromtheboringbarservosystemoccurringwithinagivensequenceoftimemaybetreatedasatime-seriesthatcanbemodeledbyanauto-regressiveandmovingaverage(ARMA)series.Theadvantageofthetime-seriesapproachisitsversatilityinpredictingfuturevaluesoftheoutputvariablewithoutgoingthroughtheprocessofestablishingthecause-and-effectrelationshipsamongvariousinputparametersandtheiroutputs.Moreimportantly,itispossibletoaccountfortherandompartofthecontrolledvariablesaswellastheirdeterministicpart.Duetothemeritsofbeinglessdemand-ingintermsofthecomputingpowerrequiredforimple-mentation,anauto-regressive(AR)model,asimplifiedversionofanARMAmodel,hasbeenselectedtomodelthedeflectionerrors:ytf1ytC01f2ytC02C1C1C1fpytC0pd(4)whereytstandsforthetooldeflectionerrorobservedatdifferenttimeinstancest,fjtheARparametersanddaseriesofwhitenoiserepresentingtherandomdisturbances.TheparametersoftheARmodeloforderpcanbedeterminedrecursivelyon-line.Ateachsamplingtime,theparametersoftheARmodelwillbeupdatedasthelatestytbecomesavailable.ThiswillallowtheARmodeltoadaptitselfintrackingtheprocessvariability.OneofthemostimportantfeaturesoftheFCCtechniqueliesinitsforecastingcapability.Basedonthepastandcurrentmeasurements,thecontrolledvariableforthenextsamplingintervalcanbepredictedbyusingtheconstructedARmodelandcompensatedbeforethecutteractuallycutsthework.Thisforecastingcapabilitytendstoovercomethetimelagproblembetweenthemomentoferrormeasurementandthatoftakingcorrectiveaction.Itallowsextratimeforacontrollertogenerateacontrolcommandandtheeffectertorespondtothatcommand.FromEq.(4),aq-stepaheadforecastingmodelinytqisexpressedasytqXqC01i1fiytqC0iXpiqfiytqC0i(5)Theforecastingvalueinytqmadeattimetforq1；2；3；.canbeupdatedwhenanewlyobservedyt1becomesavailable.Ablockdiagramoftheclosed-loopcontrolsystemforthemicroboringservosystemisshowninFig.4.Toovercomethetimelagbetweenmeasurementandcorrectiveaction,thepredictionofdeflectionerrorsofthecutterisbasedonanARmodelasmentionedabove.Inthechosenmodel,thedeflec-tionerrorsaresampledsequentiallyandsavedinthecontrolcomputer.ThepositionofthecutterisforecastedbytheARmodel,theparametersofwhichareupdatedrecursively.Fig.3.Dynamicmodeloftheboringbarservosystem.288W.M.Chiuetal./JournalofMaterialsProcessingTechnology122(2002)286292Then,theforecastedvalueisusedtocontrolthecontractionofthePZTactuatortoachievecompensation.AsimulationisthenperformedtoassesstheeffectivenessoftheARmodelintrackingrandomerrors.Theactualandforecastedvalueswerecompared,asshowninFig.5.ItcanbeseenthattheforecastingerrorsarenormallydistributedaboutazeromeanandthattheARmodelisreasonablyaccuratefortrackingthera