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

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Mian, Naeem S., Fletcher, Simon, Longstaff, Andrew P. and Myers, Alan

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

perturbations

Original Citation

Mian, Naeem S., Fletcher, Simon, Longstaff, Andrew P. and Myers, Alan (2013) Efficient

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

Precision Engineering, 37 (2). pp. 372-379. ISSN 0141-6359

This version is available at http://eprints.hud.ac.uk/16209/

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ContentslistsavailableatSciVerseScienceDirect

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.

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

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rise.Thepredictedthermalerrorbetweenthespindleandthecutter revealedaresidualerrorof5␮mfromamaximumerrorof approx-imately18␮mfor atest lengthof 4h. Modellingtime wasnot mentioned.TsengandChen[5]proposedathermalerrorprediction modelderivedfromtheneural-fuzzytheory.IC-typetemperature sensorsandaRenishawMP4probesystemwereusedtomeasure thetemperaturechangesandthermaldeformationsrespectively. Sensorswereattachedtothespindlemotor,spindlesleeveside withonesensormeasuringenvironmentalvariations.The predic-tionmodelimprovedthemachiningaccuracyfrom80␮mto3␮m. ThepredictionmodelwasfurthercomparedwithMRArevealing 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

heating.Asaresult,mostexistingcommercialerrorcompensation systemsdealwithaxisgrowthandspindleheatingwhileneglecting ambienteffectsontheremainderofthestructure.Itisalso appar-entthatasignificantamountofmachinedowntimeisassociated withenvironmentaltestingparticularlywhenthedominantcycles aredailyorevenweekly;Longstaffetal.[2]reportedasignificant issueformachinesthatexperienceaweekendshutdown.Inmost casesenvironmentaltestingtoestablisharelationship between temperatureandresponseisavoidedduetothecosttoproduction associatedwithmachinedowntime.However,thisomissioncanbe criticalwhenstrivingforthebestpossibleaccuracyofthemachine 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

Amachine toolis, inpractice,rarelyatthermal equilibrium. Consequently,establishingtheinitialconditionsfortheFEA sim-ulationofenvironmentalchangepresentsa significantproblem asitadverselyaffectsthecomparisonoftheFEAand experimen-talresults.To representtherealistic initialthermalstateofthe machine structure isa challenging taskif therealtemperature gradientsaretobemeasuredandappliedtothemodel. Experi-mentally,theapplicationoftheindividualtemperaturesensorsat locationswithinthemachinestructuralloopislaboriousandprone touncertainty inlocatingsensitiveareas.In contrasttothermal errorfromrunningthemachinewheretheheatsourcesareeasy toidentifyforapplicationofthesensors,environmentalchanges affectthewholestructure.However,evenifthisisachieved, mod-ellingtheinitialthermalstateofthemachineintheFEAsoftware

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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 _applied_as _a _uniform_parameter_to_the _full_model

of the machine as a ‘Predefined Field’in theAbaqus software. Since thispaperfocuses onanattempttoprovethe methodol-ogyandmaintainrelativesimplicityintheFEAprocess,theentire modelwasappliedwiththeconvectiveheattransfercoefficientof 6Wm−2◦_C−1_[1]_which_is_an_averaged_value_of_the_various_heat

transfercoefficientscalculatedexperimentally[1].Itis acknowl-edgedthatmoredetailedapplicationofsurfacespecificcoefficients couldimprovesimulationaccuracy(seeSection4.2).Toestimate thetime,themodelwassimulateduntilitachieveda tempera-turechangeindicativeofthevariationbetweentheglobalassumed 20◦_C_and_the_applied_temperature._A_simulation_was_carried_out

with1◦_C _temperature _change_to_estimate_the_temperature_rise

time.

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Fig.3. Settlingtimeof12.5hwasrevealedforthismachine’sFEAmodel.

Attheendofthesimulationthetemperaturethroughoutthe machinemodelwasuniform;thisensuredtheselectionofarandom nodetoplotthesettlingtime.Thesimulatedresultrevealedthat themachinemodelachieved99.99%ofthe1◦_C_temperature_change

fromitsinitialtemperatureof20◦_C_in_12.5_h_as_shown_in_Fig.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

machinedowntimeisrequiredduringthemodelcalibrationand fortheapplicationofthismodellingmethodology.The tempera-turesensorscanbesituatedonthemachineduringanyconvenient maintenanceschedule.

3. Validationofthemethod

Thecasestudymachine,describedin2.1.1,wasmodelledand calibratedasdescribed.Standardenvironmentaltemperature vari-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−1K−1)which reducestheeffectsofchangingenvironmentaltemperature. Sen-sorplacementsareshown inFig.4.WithreferencetotheBase sensor,theinsideambientsensorwasdisplacedbyapproximately 1mverticallyand0.5mhorizontallywhilethecolumnsensorwas approximately1.2mverticallyand2mhorizontallyapart.

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Fig.5. Temperatureprofilesobtainedover3daysperiod(summertest).

3.2. Summertest

Thetemperatureinformationobtainedfromthesurfacesensor ontheSpindleBossandtheambientsensorsfora 3dayperiod areshownintheFig.5.Atthestartofthetest,theexistenceof averticaltemperaturegradientaroundthemachineof1◦_C_was

measuredbetweenthebaseambientsensorandthecolumn ambi-entsensorwhichcreatestheaforementionedcomplexinitialstate. Itmayalsobeofinterestthattheverticaltemperaturedifference betweenthecolumnambientsensorandthebaseambientsensor fluctuatedtoapproximately2.5◦_C_range_over_the_test_span_which

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␮mforthe Y-axisandapprox.28␮mfortheZ-axiswiththeoveralltemperature swingofapproximately4◦_C_over₃_days._The_X-axis_results_were

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◦_C_range_measured_at_points

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

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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◦_C_range_over_the_test_span_which_elaborates_that

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 _over_the₃_days._This_increase_was_expected_because_of_the

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 Basesurface 21.9 21.9

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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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