Efficient estimation by FEA of machine tool distortion due to environmental temperature perturbations

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Precision

Engineering

jou rn a l h o m e pa g e :w w w . e l s e v i e r . c o m / l o c a t e / p r e c i s i o n

Efficient

estimation

by

FEA

of

machine

tool

distortion

due

to

environmental

temperature

perturbations

Naeem

S.

Mian

,

S.

Fletcher,

A.P.

Longstaff,

A.

Myers

CentreforPrecisionTechnologies,UniversityofHuddersfield,Queensgate,HuddersfieldHD13DH,UK

a

r

t

i

c

l

e

i

n

f

o

Articlehistory:

Received14June2012

Receivedinrevisedform5October2012 Accepted12October2012

Available online 24 October 2012

Keywords:

Finiteelementanalysis Precision

Machinetoolaccuracy

Environmentaltemperaturefluctuations Ambienttemperature

Thermalerror

a

b

s

t

r

a

c

t

Machinetoolsaresusceptibletoexogenousinfluences,whichmainlyderivefromvaryingenvironmental conditionssuchasthedayandnightorseasonaltransitionsduringwhichlargetemperatureswingscan occur.Thermalgradientscauseheattoflowthroughthemachinestructureandresultsinnon-linear structuraldeformationwhetherthemachineisinoperationorinastaticmode.These environmen-tallystimulateddeformationscombinewiththeeffectsofanyinternallygeneratedheatandcanresult insignificanterrorincreaseifamachinetoolisoperatedforlongtermregimes.Inmostengineering industries,environmentaltestingisoftenavoidedduetotheassociatedextensivemachinedowntime requiredtomapempiricallythethermalrelationshipandtheassociatedcosttoproduction.Thispaper presentsanovelofflinethermalerrormodellingmethodologyusingfiniteelementanalysis(FEA)which significantlyreducesthemachinedowntimerequiredtoestablishthethermalresponse.Italsodescribes thestrategiesrequiredtocalibratethemodelusingefficienton-machinemeasurementstrategies.The techniqueistocreateanFEAmodelofthemachinefollowedbytheapplicationoftheproposed method-ologyinwhichinitialthermalstatesoftherealmachineandthesimulatedmachinemodelarematched. Anaddedbenefitisthatthemethoddeterminestheminimumexperimentaltestingtimerequiredona machine;productionmanagementisthenfullyinformedofthecost-to-productionofestablishingthis importantaccuracyparameter.Themostsignificantcontributionofthisworkispresentedinatypical casestudy;thermalmodelcalibrationisreducedfromafortnighttoafewhours.Thevalidationworkhas beencarriedoutoveraperiodofoverayeartoestablishrobustnesstooverallseasonalchangesandthe distinctlydifferentdailychangesatvaryingtimesofyear.Samplesofthisdataarepresentedthatshow thattheFEA-basedmethodcorrelatedwellwiththeexperimentalresultsresultingintheresidualerrors oflessthan12␮m.

© 2012 Elsevier Inc. All rights reserved.

1. Introduction

Theshopfloorenvironmentwhere aCNCmachineislocated canbeofparamountimportanceforaccuracyofmanufacturing. Temperaturecontrolledenvironmentsrequirehighcapital invest-mentsand runningcosts,which areundesirableand sometimes impractical.Inenvironmentswherethetemperatureisnot con-trolled,thechangingdayandnightcyclictransitionsandmyriad othersources[1,2]cancauseambienttemperaturestovary sig-nificantlybothinmagnitudeandrate-of-change.Thesetemporal fluctuationscancausespatialthermalgradientsinamachinetool; theheatflowthroughthestructureovertimecausesnon-linear thermaldeformations.Severalresearchprojectshave been con-ductedtoidentify,predictandcompensatetheoveralleffectofthe thermaldistributioninamachinetoolbutwithmainemphasison

∗Correspondingauthor.

E-mailaddress:[email protected](N.S.Mian).

solvingtheeffectofinternallygeneratedheat,particularlyfromthe mainspindleandduringthemachiningprocesses.Forexample, Hao[3]usedageneticalgorithm-basedbackpropagationneural network(GA-BPN)methodusing16thermistorsplacedatthe spin-dle,headstock,axisleadscrewandonthebedofaturningmachine tocompensatedynamicandhighlynonlinearthermalerror.Only oneambienttemperaturesensorwasusedwhichmaynotbe suf-ficient tocapturedetailedenvironmentalbehaviouraround the machinevicinity.Theauthorreportedthethermalerror compen-sationimprovementof63%.Furtherreductioncouldbepossibleif detailedexternalenvironmentaltemperatureswingswere consid-ered.Similarly,researchfromYangetal.[4]testedanINDEX-G200 turningcentreandusedMRAtechniquetopredictitsthermal accu-racy.Theanalysisresultshowedthatthethermalerrorrangefor radiusdirectiononthatmachinewasapproximately18␮m,higher thanexpected.14thermalsensorswereinstalledingroupsand onlyoneambientsensorwasused.Whilemodelling,six temper-aturegroupswithvariableswereconstructedandthemodelwas assumedtobealinearfunctionfortheenvironmentaltemperature

accuracyimprovementsof±10␮mto±3␮m.However,themodel trainingtimesandmachinedowntimeareaccountableissueswith thisresearch.Oneoftheregressiontechniquesknownas ortho-gonalregression techniquewasemployedby Duet al.[6].This techniquewasappliedtomorethan100turningcentresofthesame typeandspecifications.Itwasfoundthatthetechniquewasableto reducethecuttingdiameterthermalerrorfrom35␮mto12␮m. Thetechniquewasstatedasrobustduetoitsyearround repeat-ableimprovementinaccuracy.Theaccuracyisexpectedtoincrease iflongtermshopfloorenvironmentaltemperaturesfluctuations wereconsidered.

Many researchers drew attention towards the environmen-talthermaldriftsinmachinetoolswhicharisefromavarietyof sourceswhiletheyemphasisedthemachinedowntimerequired fordetailedenvironmentaltestingaswellasanalysingthe mod-ellingmethodsandmodellingtime.RakuffandBeaudet[7]drew attentiontotheimportanceandeffectoftheenvironmental tem-peraturevariationerror(ETVE)whileconductingacuttingtestof 24honadiamondturningmachine.Theresearchsuggestedthe provisionoftemperaturecontrolledenclosuresforthemachineto avoidexternalthermaldriftstoimprovetheaccuracyoftheprocess control.Fletcheretal.[8]providedusefulinformationaboutcyclic environmentalfluctuationsanddriftswith50%reductioninerror overa65htest,butdrewattentiontothedetrimentalamountof machinedowntimeforthethermalcharacterisationtests.Longstaff etal.[2]showedseveraltestsconductedforthethermalerror mea-surementsproducedbytheenvironmentalfluctuationscombined withlongtermmachining.Theauthorsalsohighlightedsome unex-pected,rapidfluctuationsoftheenvironmentwithitseffectonthe accuracyofthemachine.Theyalsohighlightedthemachine down-timeissuesrelatedwiththemeasurements.Jedrzejewskietal.[9]

discussesthecomplexitiesinvolvedwithimprovingthedesignof amachinetoolwhenconsiderationsofreducingthermalerrorare infocus.Ahighlyaccuratethermalmodelofthemachineis pre-sentedand consideration ofvarious parameters contributingto thethermalbehaviour.Forexample,thedesigncriteriaconsidered theeffectsofenvironmentalvariationsfor2.5days,thermaleffects aroseduetothepresenceofguardingandbearingsetsofhighspeed spindles.Quartzstraightedgesweremodelledforenvironmental effectaftermountingonthemachinecentresupportbeam.Itwas foundthatthestraightedgefixedontheleftsideproducedthe lowesterroroftheotherthreelocationstested.Theinformation relatedtotheFEAsuchasthemodellingtimewasnotclearandthe operatingconditionswerenotclearlystated.Aconcernshownby BringmannandKnapp[10]abouttheeffectofthermaldriftwhile showinghowincreasingthenumberofmeasurementpoints(from 4to60)canleadtoreduceduncertaintiesandhigheraccuracyfor identifiedlocationerrorsoftherotaryC-axis.Theauthorreported thatthefurtherincreaseinthemeasurementpointsonlyleadsto limitedimprovementsasitcanleadtoextratimeformeasurement whichincreasestheuncertaintyofthethermaleffectarisingfrom environmentalorambienttemperaturechangesuntilthe measure-mentiscomplete.

Itisapparentfromthediscussionthatagreatemphasishasbeen giventocontrolthethermaleffectsmainlyarisingduetointernal

tool.Theproblemisexacerbatedsincethescopeofconditions dur-ingwhichtestdatacanbeacquiredisverylimitedcomparedto truevariationoverfacilityoperationsandnaturalseasons.

Thispaperpresentsanovelofflineenvironmentalthermalerror modelling method based on FEAthat significantly reducesthe machinedowntimerequiredforeffectivethermalcharacterisation. Theproposedmodellingmethodwastestedandsuccessfully vali-datedonaproductionmachinetooloverayearperiodandfound tobeveryrobust(inthispaper,samplesofdatameasuredduring twoseasonsarepresented).Thevalidationconfirmedthepotential ofthismethodtoreducethemachinedowntimenormallyrequired fortheenvironmentaltestingfromafortnighttoafewhours.The paperalsohighlightstheeffectsofseasonalenvironmental tem-peraturechangesinamachinetoolandthepresenceofvertical temperaturegradientswithinashopfloorenvironment.Thepaper alsodescribeson-machinemeasurementmethodstoacquirethe required data efficiently using strategically placed temperature sensorsduringanyconvenientmaintenancescheduleperiod.

2. Proposedmethod

Ingeneral,environmentaltemperaturechangesarenotasrapid asthosefrominternallygeneratedsourcessuchasspindles. Addi-tionally,therecanbeseveraldifferentstructuralresponseswhich requiredifferent metrology equipmentto measure that cannot beusedconcurrently.Therefore,environmentaltestingnormally takesfromtwodaystoseveralweekstoacquiresufficientdata toestablishthevariousrelationshipsbetweenvarying tempera-tureprofilesandtheresponseofthemachine.Toovercomethe machinedowntimeissue,anovelmodellingmethodologybased onatwo-stageFEAisproposedinthispaperwhereaComputer AidedDrawing(CAD)modelofthemachineiscreatedintheFEA software(inthisstudyAbaqus6.7-1/Standardwasused)[11].This isfollowedbyadeterminationoftheinitialthermalstateforthe FEAmodel,akeymethoddevelopedinthisresearch,whichwill establishaclosematchoftherealinitialthermalconditionofthe machinebeforeconductingenvironmentalsimulations.

2.1. FEAmodelling

Fig.1.GeneratedCADmodelofthemachineassemblywithZaxisheadmovedupcomparedto[1]inessencetopresentanewermodelcorrespondingtonewtestconditions.

remainschallenging.Sectioningthemodelledpartsinthesoftware andapplyingindividualtemperaturestothemmayrepresentthe initialthermalstatebutitisastrenuoustaskandmaycause incor-recttemperaturegradientsduetosectionjoints.Thisproblemis solvedbytheproposednovelmethodwhichdeterminestheinitial thermalstatefor themachine modelandalsoprovidesan esti-mateoftheminimumtimerequiredforanenvironmentalteston amachine(Section2.3).

2.1.1. Machinemodel

Amodelofthemachineisrequired.Forthecasestudymachine, amodel describedbytheauthors[1]withrespecttointernally generatedheatwasusedtoestimatethelong-termenvironmental response.Themachinewasaprecision3-axisVerticalMachining Centre(VMC)withaccuracyupto3␮m;testedby manufactur-ingaNAS-979component[12].Simplifiedmodelsofthemachine wereusedtocarryoutofflinesimulationsoftheenvironmental behaviourofthemachine,detailsofwhichareshowninFig.1.

The model was meshed using tetrahedral, hexahedron and hexahedron dominated (hexahedron/wedge) elements where applicableusingAbaqusdefaultmeshingtechniquewhichrevealed thetotalof49,919elementsand20,418nodes.Fig.2showsthe meshedassemblyofthemachine.Allsimulationsareperformed astransientthermalsimulations wherechangingdata fromthe temperaturessensorsisappliedinthesoftwareusingthetabular amplitudetechnique.

2.2. Estimationofinitialthermalstateofthemachine

Generally,priortothestartofanytest,themachineelements exhibitvariationsintemperatureduetotheexistenceoftemporal andspatialthermalgradients.Inparticular,verticaltemperature gradientshavebeenfoundtobesignificant[2,13].Asaresult,it isunfeasibletoaccuratelysetinitialtemperaturesofthe compo-nentsintheFEAsoftwaretomatchreality.Anewtechniqueofa two-stagesimulationinAbaqushasbeendevisedandappliedto solvethis problem.Thefirststagesimulationineffectwill esti-matethetimespanrequiredbyamachineFEAmodelto‘absorb’ theglobally appliedtemperaturefora temperaturechange rep-resentingthemaximumvariationlikelytooccuronthemachine structure.Thistimespanistermedasthe‘settlingtime’and repre-sentsthetemperaturerisetimeforthesteadystatemachinemodel when‘absorbing’theappliedtemperatures.Thesettlingtimeisalso representativeoftheminimumtimerequiredforon-machine test-ingwhichisexplainedinSection2.3.Thisisfollowedbythesecond stageofnormalenvironmentalsimulationthatcanbeusedforerror modellingandcomparedwithexperimentforvalidation.

Tosetupthesimulation, a standardshopfloortemperature of 20◦C was appliedas a uniformparametertothe fullmodel of the machine as a ‘Predefined Field’in theAbaqus software. Since thispaperfocuses onanattempttoprovethe methodol-ogyandmaintainrelativesimplicityintheFEAprocess,theentire modelwasappliedwiththeconvectiveheattransfercoefficientof 6Wm−2◦_C−1_{[1]whichisanaveragedvalueofthevariousheat} transfercoefficientscalculatedexperimentally[1].Itis acknowl-edgedthatmoredetailedapplicationofsurfacespecificcoefficients couldimprovesimulationaccuracy(seeSection4.2).Toestimate thetime,themodelwassimulateduntilitachieveda tempera-turechangeindicativeofthevariationbetweentheglobalassumed 20◦Candtheappliedtemperature.Asimulationwascarriedout with1◦C temperature changetoestimatethetemperaturerise time.

Fig.3. Settlingtimeof12.5hwasrevealedforthismachine’sFEAmodel.

Attheendofthesimulationthetemperaturethroughoutthe machinemodelwasuniform;thisensuredtheselectionofarandom nodetoplotthesettlingtime.Thesimulatedresultrevealedthat themachinemodelachieved99.99%ofthe1◦Ctemperaturechange fromitsinitialtemperatureof20◦Cin12.5hasshowninFig.3. Thissettlingtimesuggeststhatbecausethemachineinitial ther-malstateisunknownatthestartofthesimulation,thismachine FEAmodelrequiresthissettlingtimetoabsorbtheappliedrecorded environmentaltemperaturedataattheendofwhichthe temper-aturedistributionshouldbesynchronisedwiththerealmachine thermalstate.

2.3. Modelcalibration

Themodelcalibrationsequenceswiththedeterminationofthe settlingtimeatthefirstplace.Thesettlingtimesuggeststhe min-imumenvironmentaltestingtimerequiredforthismachinetool whichisanimportantparameterforboth;theproduction man-agementtoestimatethecost-to-productionandfortheaccuracy ofFEAresultsespeciallywhenachievingtheinitialthermalstate ofthemachineFEAmodelbeforeconductingenvironmental sim-ulations.Thereforetheenvironmentaltesttobeconductedonthe machinemustensurethatthesettlingtimeiscovered.Thetestthen mustbecontinuedoveralongperiodsuchastwoorthreedaysto establishtherelationshipbetweenthemachinethermalbehaviour andenvironmentalfluctuations occurringwithintheshopfloor duringthesecondstagesimulation.Theambientsensorsusedto recorddatamustbeleftsituatedinordertorecordcontinuously whilethemachineisinoroffproduction.Sincethedetermination ofthesettlingtimeisanofflineprocessthereforepracticallyno

ationerror(ETVE)[14]testswereconductedonthe3-axisVMCover aperiodofafullyearnotonlytovalidatebuttoconfirmthe robust-nessoftheproposedmethodology;howeversamplesofdatafrom twoseasons(summerandwinter)arepresented.Three-day (con-secutive)testingperiodwasselectedtoensurethesetting time (12.5h)datarecordingaswellastohighlightthermalbehaviour duringnormal24hperiodsonanominallystaticmachinetool.This meansthatthemachinedriveswereinactivetoavoidfeedback cor-rectionfromthepositionencoders;inessencetoobtainthetrue deformationofmachinestructure.Themodelofthemachinewas notmodifiedinanywayduringthisvalidationphase.

3.1. Temperatureanddisplacementsensorlocations

Themachinewasalreadyequippedwith65temperature sur-facesensorsinuniquestrips[15]formeasuringdetailedthermal gradientscausedbytheinternalheatsources.Additionallyseven surfacesensorswereplacedonthecolumntotrackthe environ-mentaltemperaturegradientsdistributioninthistallstructureand onesurfacesensoronthebase.Threeambientsensorswereplaced insidethemachine,atthemachinecolumnandadjacenttothe basetomeasureenvironmentaltemperaturevariations.Five non-contactdisplacementtransducers(NCDTs)wereplacedarounda testmandreltomonitorthedisplacementsandtiltofthetest man-drelin the X, Yand Zaxisdirections. A 400mm postmade of invarwasusedtosupporttheNCDTs.Invarisasteelalloywitha verylowcoefficientofthermalexpansion(1.2␮mm−1_K−1_)which reducestheeffectsofchangingenvironmentaltemperature. Sen-sorplacementsareshown inFig.4.WithreferencetotheBase sensor,theinsideambientsensorwasdisplacedbyapproximately 1mverticallyand0.5mhorizontallywhilethecolumnsensorwas approximately1.2mverticallyand2mhorizontallyapart.

Fig.5. Temperatureprofilesobtainedover3daysperiod(summertest).

3.2. Summertest

Thetemperatureinformationobtainedfromthesurfacesensor ontheSpindleBossandtheambientsensorsfora 3dayperiod areshownintheFig.5.Atthestartofthetest,theexistenceof averticaltemperaturegradientaroundthemachineof1◦Cwas measuredbetweenthebaseambientsensorandthecolumn ambi-entsensorwhichcreatestheaforementionedcomplexinitialstate. Itmayalsobeofinterestthattheverticaltemperaturedifference betweenthecolumnambientsensorandthebaseambientsensor fluctuatedtoapproximately2.5◦Crangeoverthetestspanwhich isfurtherevidenceoftemperatureinstabilitywithintheshopfloor environmentaltemperaturearisingfromvarioussourcessuchas thedayandnighttransitions.Temperaturefluctuationsalsooccur whenopeningandclosingworkshopdoors.

Fig.6showsthemeasuredinsideairtemperatureandthe dis-placement of the mandrel in the Y-axis and Z-axis.The Y-axis displacement followed the temperature variation quite closely whereastheZ-axisdisplacementlaggedthetemperaturebyupto 3.6hatsomeplaces.TheanalysisontheYaxisresults(usingthe topandbottomNCDTs)revealeda30␮m/mtiltpresentwhichis likelytohavebeencausedbynon-uniformdistortionsinthe com-plexgeometryofthestructureresultingintherapidresponseto thetemperaturevariation;comparedwiththeslowresponseof theZ-axiswhichispossiblycontributedfrompureexpansion.The overalldisplacementrangewasapproximately12␮mfortheY -axisandapprox.28␮mfortheZ-axiswiththeoveralltemperature swingofapproximately4◦Cover3days.TheX-axisresultswere negligible,duetothesymmetryofthemachineinthisdirection, andthereforenotpresented.

Thistestvalidatesthehypothesisthatenvironmental fluctua-tioncausesthermal distortionsinmachinestructureandproves thedeteriorationintheaccuracyofamachinetool.Itwasalso iden-tifiedthatverticaltemperaturegradientsinashopfloorvarywith heightwhichcanbecriticaltolargeand/ortallmachines.

Fig.6.YandZaxesdisplacementsandtheenvironmentaltemperaturemeasured insidethemachine(summertest).

Fig.7. Temperaturegradientsacrossthestructureafterthefirststage(12.5h)that representtheactualinitialthermalstate(summertest)– (NT11– nodal tempera-tures–◦_C).

3.3. Validatingsettlingtimemethodology

Thesettlingtimeforthismachinemodelwasdeterminedtobe 12.5hthereforedatacoveringthistimespanwasselectedfromthe measuredambientdataandusedinthefirststagesimulation.As mentionedpreviously,thetemperaturedatawasappliedasa tran-sientfunctioninthesoftwareusingtabularamplitudetechnique forbothsimulationstages.Temperaturedatafromthebasesensor wasappliedtothebase,informationfromtheinside environmen-talsensor wasapplied tothecarrier/spindle/tool and thetable andtemperatureinformationobtainedfromthecolumnambient sensorwasappliedtothecolumn.Theresultfromthefirststage simulationmustprovidenotonlythecorrecttemperatureprofile butalsothecorrectthermal memorytomatchthestarting con-ditionoftherealmachine.Itmustbenotedthatthesimulations werecarriedoutusingonlytheambientdatawhichcanbecaptured withoutmachinedowntime,thesurfacesensorsareonlyusedto compareandcorrelatethesimulatedresults.Fig.7showsthe sim-ulatedtemperaturegradientsacrossthestructureafterthesettling timewhichshouldrepresenttherealsurfacetemperature gradi-entsafterthe12.5hspanwaslapsed.Thepredictedinitialthermal statewasrevealedtobewithin±0.2◦Crangemeasuredatpoints wheresurfacesensorswereplacedandshowninTable1

Afterthesettlingtimesimulation,anormalenvironmental sim-ulationis then runin thesecond stageusing theremainderof therecordedenvironmentaltemperaturedata.Themeasuredand simulatedprofileresultswereplottedforthemainsecondstage simulation.Thesimulatederrorisobtainedasthedifferencein dis-placementbetweenthetableandthetool(testmandrel).Compared

Table1

Comparisonofmeasuredandsimulatedsurfacetemperaturesafter12.5h(summer test).

Structure Measured

temperature (◦C)

Simulated temperature (◦C)

Spindlebosssurface 24.1 24

Columnsurface 24 23.9

Carrierheadsurface 24.2 24.0

Fig.8. CorrelationbetweenthemeasuredandsimulatedYaxisdisplacementwith settlingtimeremoved.

Fig.9. CorrelationbetweenthemeasuredandsimulatedZaxisdisplacementwith settlingtimeremoved.

tothemeasuredresults,thecorrelationswere60%fortheY dis-placementprofiles(Fig.8)and63%fortheZdisplacementprofiles (Fig.9).Theresidualerrorswerelessthan5␮mfortheYaxisand lessthan11␮mfortheZaxis.Includingthesettlingtime,separate simulationsfortemperatureanddisplacementtookapproximately 30and40minrespectively(70minintotal).Thecomputerusedhad typicalPCspecifications:AMDPhenom9950Quadcore2.60GHz processor,4GBRAM,NVIDIAGeForce9400GTgraphicscardand WindowsXP32bitoperatingsystem

4. Wintertest

Tofurthervalidatetherobustnessofthismodelling methodol-ogy,anotherthree-daytestwascarriedouttoobservethemachine behaviourinthewinterseason.Theworkshopexperienced typ-icalsingleshiftworkshopheatingpatternsoftenencounteredto maintaincomfortableenvironmentaltemperatureforthemachine operators.Themachineandmeasurementtestconditionswerethe sameasforthesummerenvironmenttest.

Thetemperatureinformationobtainedfromtheambient sen-sors and thespindle boss surface sensor are shown in Fig. 10. Thistime the verticaltemperature differencebetween the col-umnambientsensorand thebaseambientsensorfluctuatedto

Fig.10. Temperaturedataobtainedover3daysperiod(wintertest).

Fig.11.YandZaxesdisplacementsandtheenvironmentaltemperaturemeasured insidethemachine.

approximately3◦Crangeoverthetestspanwhichelaboratesthat evenverticaltemperaturedifferencechangeswithinsimilar verti-caldistancesindifferentseasons.Thespikesaresuspectedtobe fromtheshortperiodsforopeningofworkshopdoorsfor deliv-erieswhichcausedtheshopfloorenvironmentaltemperatureto decrease.

Fig.11showsthemeasuredinsideairtemperatureand defor-mationof themachine in theYaxis andZaxis directions.The movementofbothaxesfollowedthetemperaturevariationwhile theZaxisdisplacementfollowedbutwithapproximately5hlag thistime.Theoverallmovementis18␮mintheYaxisand35␮m intheZaxisforanoveralltemperatureswingofapproximately 5◦C overthe3days.Thisincreasewasexpectedbecauseofthe exaggerateddayandnightsheatingtransitions.

Fig.12.Temperaturegradientsacrossthestructureafterthefirststage(12.5h)that representtheactualinitialthermalstate(wintertest).

Table2

Comparisonofmeasuredandsimulatedsurfacetemperaturesafter12.5h(winter test).

Structure Measured

temperature(◦C)

Simulated temperature(◦C)

Spindlebosssurface 21.7 21.7

Columnsurface 21 20.9

Carrierheadsurface 21.6 21.6

Table3

Summaryoftheresults.

Ydrift(␮m) Ymodelerror(␮m) Yimprovement(%) Zdrift(␮m) Zmodelerror(␮m) Zimprovement(%)

Summer 12 4.6 60 28 10 63

Winter 18 6.3 63 35 11.7 67

Fig.13.CorrelationbetweenthemeasuredandsimulatedYaxisdisplacementwith settlingtimeremoved.

4.1. FEAsimulations(offlineassessments–wintertest)

Asimilarprocedurewasfollowedforsimulatingthemodel.For thefirststage,12.5hoftherecordeddatawasusedforthesettling timeasbefore,followedbytheenvironmentalsimulationinthe secondstage.Fig.12showsthesimulatedtemperaturegradients acrossthestructureafterthesettlingtimewhichrepresentsthe realsurfacetemperaturegradientsafterthe12.5hspanwaslapsed. Thepredictedinitialthermalstatewasrevealedtobewithin±0.2◦C rangemeasuredatpointswheresurfacesensorswereplacedand showninTable2.

4.1.1. Wintertestcorrelations

Thesimulatedresultscorrelatewellwiththemeasuredprofile being63%fortheYmovementprofiles(Fig.13)and67%forthe Zmovementprofiles(Fig.14).Theresidualerrorswerelessthan 7␮minYandlessthan12␮minZ.

Thewintertestnotonlyvalidatedthecapabilityofthemodelling methodologybutalsoconfirmeditsrobustness.Developmentof theCADmodel,obtainingthesettlingtimeandFEA environmen-talsimulationsareconductedoffline.Thetemperaturesensorscan beinstalledin anyconvenientmaintenance scheduleand envi-ronmentaltemperaturedatacanberecordedwhilethemachine in production therefore is non-invasive to production and cost effectiveasgenerallynomachinedowntimeisinvolved.Itisalso highlightedthat12.5hofsettlingtimecanberepresentativeofa minimumtimerequiredfortemperaturedataacquisitionwhich canberecordedwhilethemachineisinproduction.

Fig.14.CorrelationbetweenthemeasuredandsimulatedZaxisdisplacementwith settlingtimeremoved.

4.2. Summaryofresults

AnFEA-derivedthermalmodelofthemachinewascreatedin thesummerusinga12.5hsettlingtimemethodology.This method-ologyhasbeenvalidatedoverayearperiod,withresultsfromtwo Three-daytests(summerandwinter)presentedhere.Table3 sum-marisestheresults.

Itcanbeobservedthatcomparedtogoodtemperature corre-lations(>90%),thepredictedpositioningofthemachinematched within60–67%rangewiththemeasuredmovement.Thisis sus-pectedtobeduetotheaveragedheattransfercoefficientvalues usedinthis casestudyfortheFEAmodel.Itis anticipatedthat thepositioningresultscancorrelatebetterwhentheFEAmodel isappliedwithsurfacespecificheattransfercoefficientsthatvary aroundenclosedvoidscreatingairpocketsthatwillvaryin tem-peratureindependenttothebulkambienttemperature[1].

5. Conclusions

Environmentalthermaltestingisoftenavoidedinindustriesdue tothecostsandinconvenienceassociatedwithmachinedowntime. Thispaperpresentedanovelofflineenvironmentalthermalerror modellingmethodbasedonFEAthatsuccessfullydealswiththe machine downtimeissueusinga two-stagesimulation method, shorton-linetesting periodand non-disruptiveoffline tempera-turemonitoring.ThesequenceofthemethodistocreateaCAD modelofthemachine,determinethesettlingtimeofthatmachine modelandcreateinitialconditionsinthefirststagefollowedby theenvironmentalsimulationinthesecondstage.Thesettlingtime ensurestheminimumtimeisspentondataacquisition. Tempera-turesensorscanbeinstalledonthemachineduringanyconvenient scheduledmachinemaintenanceandthesimulationscanbedone withinanhourortwo,soitishighlyefficient.Themethodology wassuccessfullyvalidatedona3axisverticalmillingmachinetool overayearperiod;samplesofdatafromtwoETVEtestsduring twoseasons(summerandwinter)arepresentedwherethecritical natureofthefluctuatingshopfloorenvironmentanditseffecton machinetoolprecisionwerealsohighlighted.Theresultsrevealed goodcorrelations betweentheexperimentaland FEAsimulated resultstypicallybetween60%and70%.Themodellingmethodology hassignificantlyreducedthemachinedowntimerequiredfora typ-icalenvironmentaltestingfromafortnighttoonlyhours.Practically nomachinedowntimeisassociatedwiththeapplicationofthis modellingmethodologyexceptforshortvalidations(ifrequired). Additionalusefulinformationcanbeobtainedforpredictingthe effectsofspeculativeconditions.

Acknowledgements

TheauthorsgratefullyacknowledgetheUK’sEngineeringand PhysicalSciences ResearchCouncil(EPSRC) fundingof the Cen-trefor AdvancedMetrology underitsinnovativemanufacturing programme.

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