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AnoverhungboringbarservosystemforonlinecorrectionofmachiningerrorsW.M.Chiua,,F.W.Lama,D.GaobaDepartmentofManufacturingEngineering,TheHongKongPolytechnicUniversity,HungHom,Kowloon,HongKongbDepartmentofMechanicalEngineering,HarbinInstituteofTechnology,Harbin,PRChinaReceived17June2001AbstractInthispaper,anewlydesignedoverhungboringbarservosystemequippedwithanonlinecompensationfunctionformachiningerrorsispresented.Theoverhungboringbarthathasbeendevelopedismadewithapairofconcentricbarswithanouterdiameterof14mmandanoverhungratioof81.ApiezoelectricPZTactuatorwasincorporatedintheboringbarservosystemtoachieveonlinecompensation.Acontroltechnique,forecastingcompensatorycontrolFCCwasimplementedintheboringbarservosystemtoperformanonlinepredictionofthemachiningerrorsencountered.AnofflinesimulationwasperformedtotesttheadequacyoftheparametersbeingusedintheFCCmodelsadopted.Resultsofthecuttingtestswiththeboringbarservosystemshowthattotheextentlimitedbytheinstrumentcapability,aboringbarservosystemusinganFCCmethodologycanbeaverycosteffectivetoolforonlinecompensationofmachiningerrorsintheprecisionboringofholeswithhighaspectratios.KeywordsRealtimeerrorcompensationPrecisionboringForecastingcompensatorycontrol1.IntroductionThegenerallevelofworkaccuracyandsurfacefinishrequiredofmachinedpartsisbecomingincreasinglymorestringentinmodernindustry.Therearetwogeneralapproaches,commonlyknownaserroravoidanceanderrorcompensationmethods,availableforreducingtheerrorsthatadverselyaffecttheformaccuracyofamachinedpart.Undoubtedly,therealtimeerrorcompensationmethodisprobablythemostdirectandcosteffectivewaytodealwithexternaldisturbancesofunpredictablenaturesuchasnonuniformdepthsofcut,spindlemotionerrors,dynamicvibrations,etc.Overtheyears,realtimeerrorcompensationmethodologyhasfoundmanyfruitfulapplicationsinindustryduetoitsreadinesstohandlesituationsinvolvingdisturbancesofdynamicandnonrepetitivenature.Althoughaconsiderablevolumeofresearchworkhasbeenreportedintheareaofonlineactiveerrorcompensationformachiningoperationsinthelasttwodecades1–3,therewereonlyafewattemptsthatwerefocusedontheoverhungboringofdeepholes.Beingtheweakestlinkintheforceloopwithinthemachine–toolstructure,aboringbarplaysadominantroleindeterminingtheoverallformaccuracyandcuttingproductivitywithinthewholemachine–toolsystem.Unlikeotherremovalprocesses,theimplementationofactiveerrorcompensationforoverhungboringposessomerealchallengesinmoderndaymachinecontroltechnologybecausesmallsensorsthatcanbeattachedtosmallsizedboringbarsformonitoringformerrorsinsmallholesareextremelyrare.Anothermajordifficultycomesfromtheinaccessibilityofthecuttingpointthatpreventssensorsfrombeingmountedclosetothepointofcuttingforrealtimemeasurement.Further,actuatorsthatareuseabletoeffectthenecessarycompensatoryactionaremostlytoolargetofitinsidesmalloverhungboringbars.Hence,conventionalsensorsandactiveactuators,whicharesuccessfulforrealtimemeasurementandcompensationinmuchexternalmachining,areoflittleusewheninternalsurfacesareencountered.Severalboringbardesignsforonlineactiveerrorcompensationhavebeenreported4–6.Inthesesystemsreported,theactuatorsforcompensationareinstalledinsidetheboringbarandclosetothecuttingtool.Althoughthemachiningerrorscanbecontrolledbysensorsandactuatorsincloseproximitytothecuttingzone,theboringbarsdesignedinsuchawayarelargeindimensionssoastoaccommodatethesefitteddevices,hencerenderingthemselvesunsuitableforuseinsmallerholes.JournalofMaterialsProcessingTechnology1222002286–292Correspondingauthor.Tel.þ85227666590faxþ85223625267.Emailaddressmfwmchiuinet.polyu.edu.hkW.M.Chiu.Inthispaper,aboringbarservosystemof14mmdiameterand81overhungratiowhichincorporatesapiezoelectricPZTactuatorforonlineerrorcorrectionispresented.Theboringbarconsistsoftwoconcentricbars,oneofwhichisusedforerrordetectionandtheotherforerrorcompensation.Ananalyticalandexperimentalstudyhasbeenconductedtoshowhowthisboringbarservosystemcanbeusedtocompensatefortheinstantaneousmachiningerrorsduringtheboringprocess.2.Boringbarservosystem2.1.OperatingprincipleAschematicdiagramoftheboringservosystemisshowninFig.1.ThedualconcentricboringbaradoptsaleverstructurewithaPZTactuatorandaboringcutterinstalledattheoppositeendsofthebar.ByapplyingasuitablevoltagetothePZTamplifier,theactuatorstackwillcontract.Thecontractionoftheactuatorstackcanbetransferredintoamicrofeedingmotionoftheboringcutterbyrotatingthecontrolouterbararoundtheflexuralpivot.Themeasuringinnerbarisofacantileverstructurewithstraingagesattachedformeasuringtheforceinduceddeflectionsinthebar.Theamountofmicrofeedingoftheboringcutteriscalculatedaccordingtothemeasuredstrainsignalsinthemeasuringbar.Asaresult,theboringbarsodesignedcanbemadewithamuchsmallerouterdiametereventhoughthePZTactuatorandstraingageshavebeenincorporated.Thesequenceofstepsinoperatingtheboringbarservosystemisoutlinedasfollows1.Theinstantaneousdeflectionoftheboringtoolactedbythecuttingforceismeasuredbythestraingagesattachedtothemeasuringbar.2.ThevoltagesignalfromthestraingagesisdigitizedbyanA/Dconverterfordatalogging.3.Thesamplederrordataisprocessedinthecontrolcomputer.4.AnoutputcontrolcommandistransformedbyaD/Aconverterintoananalogsignalwhichisusedtodrivethepiezoactuatorthroughitspoweramplifier.5.ThedeflectionoftheboringtoolissuppressedthroughthecorrectiveactionofthePZTactuator,hencemaintainingaconstantnominalcutterpositionandneutralizingthedetrimentaleffectsofcuttingforcesontheformaccuracy.AsshowninFig.2,beforethecuttingforceFcisappliedi.e.Fc¼0,boththecontrolandmeasuringbarsremainstraightFig.2a.AsthecuttingforceFcactsontheboringbar,theboringbarasawholeisdeflecteddownwardsFig.2bresultinginanincreaseofstraininthemeasuringbarandgeneratingaproportionalanalogsignalfromthestraingages.ThisanalogsignalissampledbythecontrolcomputerthroughtheA/Dconverterandusedtogenerateacontrollingaction.ThePZTactuatorthenexpandsbyincreasingtheappliedvoltagetothepoweramplifierthroughtheD/Ainterface.Asaresult,thecontrolbarrotatesaroundtheflexuralhingeinaclockwisedirectionsuppressingthedownwarddeflectionofthecutteruntilthemeasuringbarbecomesstraightagain.AscanbeseeninFig.2c,therestorationofthecuttertoitsequilibriumpositionisachievedwithgreaterdeformationinthecontrolbar.Ontheotherhand,iftheexternalforceismomentarilyreduced,thedeflectionoftheboringbarbecomeslessastheforcewithinthesystemislower.AnoppositecontrolactionwillbeissuedtothePZTactuatorinordertooffsetthechange.Inthisway,nomatterhowthecuttingforcevariesinthecourseofcutting,theboringtoolwilltendtoreturntothepresetposition,thusforcingtheboringtooltoundergocuttingateffectivelyzerodeflection.Therefore,theforceinducedeffectsonthemachinedsurfacewouldthenbecancelledoutandtheoverallformaccuracyshouldbeimproved.2.2.ModelingoftheboringbarservosystemFortheanalysisofthedynamicbehavioroftheboringbarservosystem,theequationofmotionisformulatedasshowninFig.3.Forthispurpose,elementsoftheboringbarservosystemaremodeledbyasingledegreeoffreedomsystemFig.1.Aschematicdiagramoftheboringbarservosystem.Fig.2.Theinteractionofdeflectionandcorrectioninacompensationcycle.W.M.Chiuetal./JournalofMaterialsProcessingTechnology1222002286–292287withlumpedmasses,stiffnessandviscousdampingcoefficients.VariableystandsfortheradialdeflectionofthecutteryfortheangularrotationaboutpointOofthecontrolbarjfortheangularrotationaboutbasepointO0ofthemeasuringbarIystandsforthemomentofinertiaofthecontrolbaraboutpointOIjforthatofthemeasuringbaraboutpointO0Cy,Kyarethedampingcoefficientandstiffness,respectively,ofthecontrolbarCj,Kjarethedampingcoefficientandstiffness,respectively,forthemeasuringbarFcandFprepresentstheradialcuttingforceandthecompressiveforce,respectively,ofthePZTactuator.Forsmalldeparturesfromequilibrium,anglesjandycanbeassumedtobesmallsothattheequationofmotioncanbesimplifiedtoMC127yþC_yþKy¼FcþL1L2Fp1whereM¼IyþIjþL21MpL22C¼CyþCjþL21CpL22K¼KyþKjþL21KpL22TwoequationsgoverningthedesignoftheboringbarsystemcanbeobtainedfromEq.1.InEq.2,themaximumunconstrainedradialtooltravel,ymax,isexpressedintermsofDmax,themaximumunconstrainedexpansionforthePZTactuator.Similarly,theundampednaturalfrequencyoftheboringsystem,on,isshowninEq.3ymax¼L1L2KpKyþKjþL21KpDmax2on¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiKyþKjþL21KpIyþIjþL21Mps32.3.ForecastingcompensatorycontrolFCCmodelTocarryoutonlinecontrol,itisimportanttoselectasuitablecontrolschemethatiscomputationallysimple,yetsophisticatedenoughtotrackanyrapidlychangingcomponentsofthecontrolledvariable.AtimeseriesapproachbasedonFCCmethodologywhichhasbeensuccessfullyimplementedinmanymachinecontrolproblems7hasbeenadoptedinthiswork.ThestreamoftooldeflectionsfromtheboringbarservosystemoccurringwithinagivensequenceoftimemaybetreatedasatimeseriesthatcanbemodeledbyanautoregressiveandmovingaverageARMAseries.Theadvantageofthetimeseriesapproachisitsversatilityinpredictingfuturevaluesoftheoutputvariablewithoutgoingthroughtheprocessofestablishingthecauseandeffectrelationshipsamongvariousinputparametersandtheiroutputs.Moreimportantly,itispossibletoaccountfortherandompartofthecontrolledvariablesaswellastheirdeterministicpart.Duetothemeritsofbeinglessdemandingintermsofthecomputingpowerrequiredforimplementation,anautoregressiveARmodel,asimplifiedversionofanARMAmodel,hasbeenselectedtomodelthedeflectionerrorsyt¼f1ytC01þf2ytC02þC1C1C1þfpytC0pþd4whereytstandsforthetooldeflectionerrorobservedatdifferenttimeinstancest,fjtheARparametersanddaseriesofwhitenoiserepresentingtherandomdisturbances.TheparametersoftheARmodeloforderpcanbedeterminedrecursivelyonline.Ateachsamplingtime,theparametersoftheARmodelwillbeupdatedasthelatestytbecomesavailable.ThiswillallowtheARmodeltoadaptitselfintrackingtheprocessvariability.OneofthemostimportantfeaturesoftheFCCtechniqueliesinitsforecastingcapability.Basedonthepastandcurrentmeasurements,thecontrolledvariableforthenextsamplingintervalcanbepredictedbyusingtheconstructedARmodelandcompensatedbeforethecutteractuallycutsthework.Thisforecastingcapabilitytendstoovercomethetimelagproblembetweenthemomentoferrormeasurementandthatoftakingcorrectiveaction.Itallowsextratimeforacontrollertogenerateacontrolcommandandtheeffectertorespondtothatcommand.FromEq.4,aqstepaheadforecastingmodelinytðqÞisexpressedasytðqÞ¼XqC01i¼1fiytðqC0iÞþXpi¼qfiytþqC0i5TheforecastingvalueinytðqÞmadeattimetforq¼123...canbeupdatedwhenanewlyobservedytþ1becomesavailable.AblockdiagramoftheclosedloopcontrolsystemforthemicroboringservosystemisshowninFig.4.Toovercomethetimelagbetweenmeasurementandcorrectiveaction,thepredictionofdeflectionerrorsofthecutterisbasedonanARmodelasmentionedabove.Inthechosenmodel,thedeflectionerrorsaresampledsequentiallyandsavedinthecontrolcomputer.ThepositionofthecutterisforecastedbytheARmodel,theparametersofwhichareupdatedrecursively.Fig.3.Dynamicmodeloftheboringbarservosystem.288W.M.Chiuetal./JournalofMaterialsProcessingTechnology1222002286–292Then,theforecastedvalueisusedtocontrolthecontractionofthePZTactuatortoachievecompensation.AsimulationisthenperformedtoassesstheeffectivenessoftheARmodelintrackingrandomerrors.Theactualandforecastedvalueswerecompared,asshowninFig.5.ItcanbeseenthattheforecastingerrorsarenormallydistributedaboutazeromeanandthattheARmodelisreasonablyaccuratefortrackingtherandomerrorsignalsonhand.2.4.PerformancesofboringbarservosystemSeveraltestswereconductedtoassessthestaticanddynamiccharacteristicsoftheboringbarservosystem.2.4.1.ResonantfrequencyTheresonantfrequencyoftheboringbarsetupwasdeterminedbytheimpacthammermethod.Animpulsiveforcewasappliedtotheoverhungendofboringbarwhileadigitaloscilloscopeisusedtocapturethevibrationsignalsfromtheboringbarsetup.InFig.6,theresultsofanimpacttestontheboringbararepresented.Theuppercurveshowsthetimeresponseandtheloweronethefrequencyresponse.Itcanbeconcludedfromthetestresultsthattheresonantfrequencyoftheboringbarisabout440Hz.2.4.2.StaticcalibrationoftheboringbarsystemTherelationshipbetweenthedeflectionoftheboringcutterandthecontrolvoltageappliedtothepiezoactuatorpoweramplifierisshowninFig.7.Themaximumcorrectivemovementoftheboringcutterisabout20mm.DuetotheinherentcharacteristicsofPZTmaterials,aslighthysteresisloopcanbeobservedbetweentheappliedvoltageandtheactuatorsexpansion.ThisphenomenonisfrequentlyobservedinmanyPZTdevicesandcouldbecorrectedinthecontrolprogram.Fig.4.TheblockdiagramoftheFCCcontroller.Fig.5.Resultsoftheforecastingsimulation.Fig.6.Theresonantfrequencyoftheboringbar.W.M.Chiuetal./JournalofMaterialsProcessingTechnology1222002286–292289