mechanical performances of dies

8/12/2019 Mechanical Performances of Dies

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Final Technical Report

ESMART Subtask 5.8: Mechanical Performance of Dies

AwardNumberDEFC3604GO14230

CoOpAgreementNo.2005307

OSURFProjectNumber746200

ProjectPeriod: January2004June2011

R.AllenMiller,PrincipalInvestigator

Phone: 6145811754

Email: [email protected]

OhioStateUniversity

210BakerSystemsEngineering

1971NeilAve.

Columbus,OH43210

Contributors:

KhalilKabiri Bamoradian,ResearchEngineer

AbelardoDelgadoGarza,PhDStudent

KarthikMurugesan,PhDStudent

AdhamRagab,PostdoctoralResearcher

PartnerOrganization: NorthAmericanDieCastingAssociation

September13,2011


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i

Acknowledgement/Disclaimer

Acknowledgement: ThisreportisbaseduponworksupportedbytheUS.Departmentof

Energy

under

Award

No.

DOE

award

DE

FC36

04GO14230.

Disclaimer: Anyopinions,findings,andconclusionsorrecommendationsexpressedinthis

materialarethoseoftheauthoranddonotnecessarilyreflecttheviewsoftheDepartment

ofEnergy.

ProprietaryDataNotice: Thisreportdoesnotcontainanyproprietarydata.

DocumentAvailability: ReportsareavailablefreeviatheU.S.DepartmentofEnergy(DOE)

InformationBridgeWebsite:http://www.osti.gov/bridge

ReportsareavailabletoDOEemployees,DOEcontractors,EnergyTechnologyDataExchange

(ETDE)representatives,andInformationalNuclearInformationSystem(INIS)representatives

fromthefollowingsource:

OfficeofScientificandTechnicalInformation

P.O.Box62

OakRidge,TN37831

Tel:(865)5768401

FAX:(865)5765728

Email:[email protected]

Website:http://www.osti.gov/contract.html


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TableofContentsAcknowledgement/Disclaimer................................................................................. i

Table

of

Contents

....................................................................................................

ii

ListofFigures......................................................................................................... iv

ListofTables............................................................................................................ v

ListofAcronyms..................................................................................................... vi

ListofAppendices..................................................................................................vii

ExecutiveSummary............................................................................................... viii

1. Introduction...................................................................................................... 1

2. Background....................................................................................................... 2

2.1 SummaryofPreviousWork.............................................................................. 2

2.2 SummaryoftheStateoftheArt................................................................... 10

2.3 Objectives....................................................................................................... 11

2.4 TasksandApproach........................................................................................ 12

3. ResultsandDiscussion.................................................................................... 14

3.1 AnalysisofDiePositionEffects....................................................................... 14

3.1.1 ComputationalExperiments 16

3.1.2 DimensionalAnalysis 17

3.1.3 ModelAdequacy,FEAResults 21

3.1.4ModelAdequacy,ExperimentalMeasurements 22

3.2 DieFailureCaseStudy.................................................................................... 27

3.3 CavityPressureModelingMethods...............................................................29

3.3.1 FluidStructureInteraction(FSI)Model 30

3.3.2 AlternativetoFSI 32

3.3.3 TrackingofCavityDistortion 33

3.4 EvaluationofEjectorSideandSlideDesign...................................................35

3.4.1 DesignofExperiments 35

3.4.2

Dimensional

Analysis

37

3.4.3 CoverSidePartingSurfaceSeparation 43

3.5 ModelingandDesignGuidelines.................................................................... 44

4. BenefitsAssessment....................................................................................... 45

5. Commercialization.......................................................................................... 46

6. Accomplishments............................................................................................ 46


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7. Conclusions..................................................................................................... 48

8. Recommendations.......................................................................................... 48

9. References...................................................................................................... 49

10.AppendicesAE............................................................................................. 55


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iv

ListofFiguresFigure1 TypicalDieCastingSystemModelUsedbyOSU...........................................10

Figure2 FreeBodyDiagramoftheMechanicalLoads................................................15

Figure3 DepictionofSystemResponse...................................................................... 15

Figure4 CoordinateSystemandTiebarLabels..........................................................17

Figure5 Schematicofthetestdieonthemachineplatens.......................................23

Figure6 Schematicofstraingaugesandcoordinatesystem......................................23

Figure7 TiebarLoadMeasurementsvs.Predictions.................................................26

Figure8 TheCasting.................................................................................................... 28

Figure9 Defects........................................................................................................... 28

Figure10 FSIcavitydisplacementpredictions............................................................31

Figure11Castingfiniteelementmesh........................................................................ 33

Figure12 Shellelementmesh..................................................................................... 35

Figure13 SchematicofPillarPatternsusedintheStudy...........................................37

Figure14LengthScalesRepresentingUnsupportedSpan..........................................42


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v

ListofTablesTable1 DescriptionofVariables................................................................................. 17

Table2:ParameterEstimatesforTopTieBarModelFit.............................................19

Table3:ParameterEstimatesforBottomTieBarModelFit.......................................20

Table4:SummaryofFiniteElementModels...............................................................21

Table5:ComparisonofModelPredictionsfora3500TonMachine..........................21

Table6:ComparisonofModelPredictionsfora1000TonMachine..........................22

Table7:ComparisonofModelPredictionsfora250TonMachine............................22

Table8:ExperimentalArray......................................................................................... 24

Table9:ComparisonofMeasurementsandPredictions.............................................25

Table10:DifferencebetweenMeasurementsandModelPredictions.......................27

Table11 FactorsusedinDesignofExperiments........................................................36

Table12NonDimensionalStructuralDesignParameters..........................................39

Table13ParameterEstimatesforEjectorSideFit......................................................41

Table14 ParameterEstimatesforCoverSideFit.......................................................44


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vi

ListofAcronymsNADCA NorthAmericanDieCastingAssociation

DOE DepartmentofEnergy,alsoDesignofExperiments

FEA FiniteElementAnalysis

FSI FluidStructureInteraction

SPSS Statisticalanalysissoftware


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ListofAppendicesAppendixA: K.KabiriBamoradianDieandDieCastingMachineForceandDeflection

Predictions,,ReportpreparedforNADCA,July2010.

AppendixB:A.Ragab,K.KabiriBamoradian,DoorCloserDieCaseStudy,May2004.

AppendixC: R.A.Miller,K.KabiriBamoradian,andA.Garza,FiniteElementModelingof

CastingDistortioninDieCasting,NADCATransactions2009,NorthAmerican

DieCastingAssociation,Wheeling,Illinois,April2009

AppendixD: AbelardoGarzaDelgado,K.KabiriBamoradian,R.A.Miller,Determinationof

ElevatedTemperatureMechanicalPropertiesofanAluminumA380.0Die

CastingAlloyintheAsCastCondition",NADCATransactions2008,North

AmericanDieCastingAssociation,Wheeling,Illinois,May2008.

AppendixE: DieandDieCastingMachineComputerSimulations: Modeling,Meshing,

BoundaryConditions,andAnalysisProcedures


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ExecutiveSummaryAsanetshapeprocess,diecastingisintrinsicallyefficientandimprovementsinenergy

efficiencyarestronglydependentondesignandprocessimprovementsthatreducescrap

ratessothatmoreofthetotalconsumedenergygoesintoacceptable,usablecastings. A

castingthatisdistortedandfailstomeetspecifieddimensionalrequirementsistypically

remeltedbutthisstillresultsinadecreaseinprocessyield,lostproductivity,andincreased

energyconsumption. Thisworkfocusesondeveloping,andexpandingtheuseof,computer

modelingmethodsthatcanbeusedtoimprovethedimensionalaccuracyofdiecastingsand

producediedesignsandmachine/diesetupsthatreducerejectionratesduetodimensional

issues.

Amajorfactorcontributingtothedimensionalinaccuracyofthecastingistheelastic

deformationsofthediecavitycausedbythethermomechanicalloadsthediesaresubjected

to

during

normal

operation.

Although

thermal

and

die

cavity

filling

simulation

are

widely

usedintheindustry,structuralmodelingofthedie,particularlyformanagingpartdistortion,

isnotyetwidelypracticed.Thismaybedueinparttotheneedtohaveathorough

understandingofthephysicalphenomenoninvolvedindiedistortionandthemathematical

theoryemployedinthenumericalmodelstoefficientlymodelthediedistortion

phenomenon.Therefore,twoofthegoalsofthisworkaretoassistineffortstoexpandthe

useofstructuralmodelingandrelatedtechnologiesinthediecastingindustryby1)

providingadetailedmodelingguidelineandtutorialforthoseinterestedindevelopingthe

necessaryskillsandcapabilityand2)bydevelopingsimplemetamodelsthatcapturethe

resultsandexperiencegainedfromseveralyearsofdiedistortionresearchandcanbeused

topredictkeydistortionphenomenaofrelevancetoadiecasterwithaminimumof

backgroundandwithouttheneedforsimulations. Theseobjectivesweremet. Adetailed

modelingtutorialwasprovidedtoNADCAfordistributiontotheindustry. Powerlawbased

metamodelsforpredictingmachinetiebarloadingandforpredictingmaximumparting

surfaceseparationweresuccessfullydevelopedandtestedagainstsimulationresultsfora

widerangeofmachinesandexperimentaldata. Themodelsprovedtoberemarkably

accurate,certainlywellwithintherequirementsforpracticalapplication.

Inadditiontomakingdiestructuralmodelingmoreaccessible,theworkadvancedthestate

oftheartbydevelopingimprovedmodelingofcavitypressureeffects,whichistypically

modeledasahydrostaticboundarycondition,andperformingasystematicanalysisofthe

influenceofejectordiedesignvariablesondiedeflectionandpartingplaneseparation. This

cavitypressuremodelingobjectivemetwithlessthancompletesuccessduetothelimitsof

currentfiniteelementbasedfluidstructureinteractionanalysismethods,butanimproved

representationofthecasting/dieinterfacewasaccomplishedusingacombinationofsolid


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ix

andshellelementsinthefiniteelementmodel. Thisapproximationenabledgoodprediction

offinalpartdistortionverifiedwithacomprehensiveevaluationofthedimensionsoftest

castingsproducedwithadesignexperiment. Anextradeliverableoftheexperimentalwork

wasdevelopmentofhightemperaturemechanicalpropertiesfortheA380diecastingalloy.

Theejectorsidedesignobjectivewasmetandtheresultswereincorporatedintothemeta

modelsdescribedabove.

Thisnewtechnologywaspredictedtoresultinanaverageenergysavingsof2.03trillion

BTUs/yearovera10yearperiod.Current(2011)annualenergysavingestimatesoveraten

yearperiod,basedoncommercialintroductionin2009,amarketpenetrationof70%by

2014is4.26trillionBTUs/yearby2019. Alongwiththeseenergysavings,reductionofscrap

andimprovementincastingyieldwillresultinareductionoftheenvironmentalemissions

associatedwiththemeltingandpouringofthemetalwhichwillbesavedasaresultofthis

technology.TheaverageannualestimateofCO2reductionperyearthrough2020is0.085

MillionMetricTonsofCarbonEquivalent(MMTCE).


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1

1. IntroductionDiecastingisanearnetshapemanufacturingprocessinwhichpartswithcomplex

geometriesareproducedbyinjectingmoltenmetalintosteelmolds/diesunderhigh

pressure.Themoltenmetalisheldinthediecavityuntilitsolidifiesandpartiallycooled,the

dieisopenedandthepartisejected,andtheprocessisrepeatedthousandsoftimes. The

processofferscompetitiveadvantagesovermanyothernetshapemanufacturingprocesses

suchasforgingandstampingwithitsabilitytoproducepartswithcomplexgeometric

features,highsurfacefinishandtightdimensionaltolerances.

Asanetshapeprocess,diecastingisintrinsicallyefficientandimprovementsinenergy

efficiencyarestronglyrelatedtodesignandprocessimprovementsthatreducescraprates

sothatmoreofthetotalconsumedenergygoesintoacceptable,usablecastings. Acasting

thatisdistortedandfailstomeetthespecifieddimensionalrequirementsisscrappedand

remeltedbutthisstillresultsinadecreaseinprocessyield,lostproductivity,andincreasedenergyconsumption. Thisworkfocusesondevelopingandexpandingtheuseofcomputer

modelingmethodsthatcanbeusedtoimprovethedimensionalaccuracyofdiecastingsand

producediedesignsandprocesssetupsthatreducerejectionratesduetodimensional

issues.

Oneofthemajorfactorsthatcontributetothedimensionalinaccuracyofthecastingisthe

elasticdeformationsofthediecavitycausedbythethermomechanicalloadsthediesare

subjectedtoduringnormaloperation.Diecastingdiesareexpectedtorunseveralmillion

cyclesduringtheirlifetime.Highmanufacturingcostsprohibitprototypingandanyserious

diedeformationordiefailureproblemsarenotnoticeduntilthefirstproductionrun.Adie

cancostanywherebetween$50,000to$1,000,000andthedeliverytimesrangesfrom312

monthsdependinguponthecomplexityofthedies.Thereforeitisextremelyimportantthat

thediedistortionbepredictedandcontrolledatthedesignstage.

Althoughthermalanddiecavityfillingsimulationarewidelyusedintheindustry,structural

modelingofthedie,particularlyformanagingpartdistortion,isnotyetwidelypracticed.

Thismaybedueinparttotheneedtohaveathoroughunderstandingofthephysical

phenomenoninvolvedindiedistortionandthemathematicaltheoryemployedinthe

numericalmodelstoefficientlymodelthediedistortionphenomenon.Therefore,twoofthegoalsofthisworkaretoassistineffortstoexpandtheuseofstructuralmodelingand

relatedtechnologiesinthediecastingindustry. Specificallyto

1. Provideadetailedmodelingguidelineandtutorialforthoseinterestedindevelopingthe

necessaryskillsandcapabilityand


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2

2. developsimplemetamodelsthatcapturetheresultsandexperiencegainedfromseveral

yearsofdiedistortionresearchandcanbeusedtopredictkeydistortionphenomenaof

relevancetoadiecasterwithaminimumofbackgroundandwithouttheneedfor

simulations.

Inadditiontheworkisintendedtoadvancethestateoftheartbydevelopingimproved

modelingofcavitypressureeffectswhichistypicallymodeledasahydrostaticboundary

conditionandtoperformasystematicanalysisoftheinfluenceofejectordiedesign

variablesondiedeflectionandpartingplaneseparation.

Intermsofcommercialization/disseminationofthemethodology,thetutorialmentioned

aboveisnowavailableinelectronicformfromtheNorthAmericanDieCastingAssociation

(NADCA)websiteandislinkedtoothermaterialrelatedtodistortion. Twometamodels

(onefortiebarbalanceusedformachinesetuptominimizedistortionandoneforparting

planeseparation(flash)prediction)havealsobeentransferredtoNADCAandavailableto

theindustry. Themetamodelsaredimensionlesspowerlawmodelsthatencapsulate

resultsfromsimulationsperformedinthisprojectandinprecedingprojectsinaformthat

canbeusedwithouttheneedforacomplexFEAsimulation. Eachmetamodelhasbeen

convertedtoasimpleapplicationthatcanbedownloadedfromtheNADCAwebsite. Thetie

barbalanceresultshavealsobeenimplementedasamodulewithinversion4ofthePQ2

softwareprogramthatisdistributedbyNADCA. Thissoftwareisusedtohelpfindthebest

matchofdie,machine,andprocesssetupwithpartdesignrequirements. Includingthetie

barbalancemodelinthissoftwareenablesbasicdistortionconsiderationstobeconsidered

alongwithmachinepoweranddiefillingconditions.

2. BackgroundThepurposeofthissectionistoprovideasummaryofpreviousworkperformedonthe

mechanicalperformanceofdiesandtooutlinetheobjectivesofthisproject.

2.1 SummaryofPreviousWorkTodateonlytwogroupsintheworldhavesystematicallyaddressedthemechanical

performanceofthedieandmachinesystemindiecasting.OneofthegroupsisOSU,

supportedthroughpreviousDOEfundedwork.ThesecondisDaveCaulkandhiscolleagues

atthe

General

Motors

Tech.

Center

when

they

developed

the

Die

Cast

software

(e.g.,

[25]).

Othersaroundtheworldhaveperformedexperimentalworkandgenerallyoverlysimplified

staticanalyses,butonlythesetwogroupshavelookedatthefundamentalprinciplesthat

underliethebehaviorofthedieinresponsetothemachineclampingforces,cyclicheat

loads,andhighcavitypressuresduringfillandintensification.Perhapsbecauseonlyhigh

pressureprocessesareimpactedbytheseadditionalloads(sand,investment,permanent

moldsystemsarenotsubjecttothesameclampingandpressureloadsandonlypermanent


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3

moldissubjecttocyclicheatloads),theproblemsarefarlesswidelystudiedthanthermal

andfillrelatedissuesforcastingprocesses.

Thefocusofthediecastingresearchcommunityhasbeenmostlyondeveloping

numerical/computationalmethodstosolveheattransfer,fluidflow,solidificationand

thermaldistortionrelatedproblems.Veryfewresearchershavepaidattentiontotheroleof

mechanicalloadssuchasclampingforceandcavitypressureindieandcastingdistortion.

Eveninthemodelswheremechanicalloadsareconsidered,notallofthemaccountforthe

stiffnessofthemachinepartssuchastheplatens,tiebarsandthetogglemechanism.

AhuettGarza[21]and[22],conductedanelaboratestudyoftheloadsinvolvedindiecasting

processandheconcludedthatdiedeflectionsimulationswithreasonableresolutioncanbe

carriedoutbyaccountingfortheclampingload,heatreleasedduringsolidification,the

intensificationpressure,andtheheatremovedduringlubricantspray.Hisstudyshowedthat

theheat

released

during

fill,

the

momentum

during

filling

and

the

pressure

surge

atthe

end

offillcanbeignoredinthediedeflectionsimulationsandstillresultswithreasonable

accuracyandresolutioncanbeachieved.Byanorderofmagnitudeanalysisitwasshown

thattheheatreleasedduringfillcanbeignoredwhentheratiobetweenhalfthethicknessof

thepartandthefilltimeisgreaterthanorequaltooneseventh.Thiscorrespondstoacase

wherethesolidificationtimeisatleastanorderofmagnitudegreaterthanthefilltime.The

detailsofthescaleanalysisarealsoprovidedin[23].

Basedontheresultsofhisstudyaninitialfiniteelementmodelingprocedurewasdeveloped

andtested[21],[24]and[25].Thepreliminarymodelconsistedofonlythecoverdie,ejector

dieandtheejectorsupportblock.Firstathermalanalysiswascarriedouttoobtainthe

nodaltemperaturevaluesonthedies,whichwerelaterusedinthestressanalysis. The

cavitypressurewasmodeledasahydrostaticpressurewithmagnitudeequaltothatof

intensificationpressure.Theclamploadwasmodeledasapressureboundarycondition

behindtheejectorsupportblock.Arigidsupportwasassumedbehindthecoverdieand

nodesonthebacksurfaceofthediewereconstrainedinalldirections.Thestiffnessofthe

machinewasnotaccountedforinthismodel.

InasubsequentstudyDedhia[26]comparedthepartingplaneseparationpredictionsofa

modelwithrigidsupportbehindthecoverdieversusthepartingplaneseparationpredictionsfromamodelthataccountedforthemachinestiffness.Springelementswere

usedtoaccountforthestiffnessoftheplatensandthetogglemechanism.Theclampload

wasmodeledbyapplyingappropriatedisplacementboundaryconditionstothespring

elementsthatrepresentedthetogglemechanism.Theseparationvaluesatseverallocations

alongtheedgesofthecavitywereusedasameasureofdiedeflection.Themaximum


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separationvaluewasabout12%to20%higherinthemodelwithspringelementsthanthe

valuesfromthemodelwithrigidsupport,dependinguponthedesignfeaturesofthedie.

Choudhary[27]developedafiniteelementmodelinwhichthethreemachineplatens,theC

frameandthetiebarsweremodeledexplicitly.Thediewasadummystructurethat

consistedoftwoparallelplatesconnectedbypillarsonthefourcornersoftheplates.A

rollersupportwasmodeledatthebottomofcoverandejectorplatens.Asupportblockwas

modeledatthebottomoftherearplatentopreventdisplacementintheverticaldirection.A

smallslidingcontactwasdefinedatallinterfaces.Thenodesontheeitherendofthetiebars

weretiedtocorrespondingnodesontheejectorandrearplaten.Theclamploadwas

appliedasapressureboundaryconditiononthetoggleblocksonthecoverandrearplatens.

Thermalloadsandcavitypressurewereignoredinthemodel.Thedeflectionofthecover

platenwaspredictedateightdifferentlocationsbehindthecoverplatenandtheresults

werecomparedwithcorrespondingvaluesfromthefielddata.Thedeflectionpatternfrom

thesimulationswassimilartothepatternobservedonthefielddata.Buttheindividual

deflectionvaluesfellintherangeof10%to15%oftheobservedfielddata.Thismodelwas

fairlyaccurategiventhevariousapproximationstotheboundaryconditionsinthemodel

andtheprocedurefollowedtomodeltheclampload.

Inanotherdiedistortionmodelingstudy,Chayapathi[28]usedafiniteelementmodelin

whichthetiebarswereexplicitlymodeledandthetogglemechanismwasrepresentedby

linearspringelements.Thenodesononeendofthetiebarthatareincontactwiththe

nodesinthecoverplatenweretiedtothecorrespondingnodesonthecoverplaten.The

nodes

on

the

other

end

of

the

tie

bar

were

constrained

in

all

six

degrees

of

freedom.

The

cornernodesonthebottomofthecoverplatenwereconstrainedinverticaldirectionto

preventrigidbodymotion.Theclamploadwasappliedbyspecifyingdisplacementsonthe

freeendofthespringelements.Theintensificationpressureloadwasappliedasapressure

boundaryconditiononthecavitysurfaces.

Ragabetal[29]experimentallyverifiedtheadequacyofthisfiniteelementmodelfor

predictingthecontactloadsbetweenthediesandplatensonthecoverandejectorsides.

Thecontactloadbetweentheplatensandthediesweremeasuredusingatotalof35load

cells,18loadcellsonthecoversideand17loadcellsontheejectorside.Thecontactload

wasmeasuredundertwodifferentloadingconditions,underclamploadonlyandduring

actualcastingoperation.Theloadcellsandthefixturesusedintheexperimentswerealso

explicitlyincludedinthefiniteelementmodel.Thesummationofcoversideloadcell

measurementsdecreasedby7%afterintensificationwhereasthesummationofcoverside

loadcellpredictionsfromsimulationremainedconstant.Ontheejectorsidethesummation

ofloadcellmeasurementsandpredictionsremainedconstant.Thedifferencebetween


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modelpredictionsandmeasurementsonthecoversidewereattributedtothefactthatthe

modelisstifferthanthedie/machineactuallyis.

Toaddresstheseobserveddifferencesbetweenthemodelpredictionsandmeasurements

onthecoversidefurthermodelingimprovementsweretestedbyArrambide[30].Various

machinecomponentswereincludedinthefiniteelementmodelsandthepredictionswere

comparedagaintotheexperimentalloadcellmeasurements.Fourdifferentmodelswere

tested.Thefirstmodelincludedthecoverandejectorplaten,dies,inserts,theloadcellsand

fixturesallofthemmodeledusingquadratictetrahedralelements.Thetiebarswere

modeledusingbeamelements,withtheoneendofthebeamelementsconstrainedtothe

coverplatenandtheotherendwasfixedinspace.Severalnodesonthebottomofthecover

platenwasconstrainedinverticalandtiebardirections.Theclamploadwasappliedasa

pressureboundaryconditionbehindtheejectorplaten.Inthesecondmodeltherearplaten

wasalsoincludedandthetwoendsofthetiebarswereconstrainedtothecoverandrear

platens.Thetogglemechanismwasrepresentedbybeamelementsandtheclamploadwas

appliedbyspecifyingappropriatetemperatureonthesebeamelements.Inthethirdand

fourthmodelsthefrontsupportframewasaddedtotheprevioustwomodels.

Comparisonbetweenloadcellmeasurementsandloadcellpredictionsbetweensimulations

showedthatthefrontsupportframedidnothaveanyeffectonthecontactloadbetween

thediesandtheplatens.Includingtherearplatenandtogglemechanisminthemodel

alteredtheloaddistributiononvariousloadcellpredictionsby2 34%,withanaverageof

11%.Alsothefullmodelshowedgoodcorrelationwiththeexperimentalmeasurements.To

test

the

adequacy

of

the

full

model

to

predict

parting

plane

separation,

a

simplified

model

withdies,insertsandloadcellsonlywasbuilt.Theclamploadwasappliedbehindtheload

cellsdirectlyusingthepredictionsfromthefullmodelandalsotheloadsfromthe

experimentalmeasurements.Themaximumseparationshowedadifferenceof0.001which

fallswithintheresolutionofthenumericalsimulation.

Inallofthediedistortionmodelingstudiesdiscussedabove,theintensificationpressurewas

assumedtobehydrostaticanditwasmodeledasapressureboundaryconditiononthe

cavitysurfacesinthefiniteelementmodels.Inrealitytheliquidmetalcarriesthehydrostatic

pressurefromtheplungermechanismandtransfersittothecavitysurfaces.Butthesolid

elementsusedinthestructuralfiniteelementmodelscannotcarrythishydrostaticpressure

tothecavity.

GarzaDelgado[31]developedatwodimensionalfluidstructureinteraction(FSI)finite

elementmodelusingADINAtopredictdiedistortion.Itwasafullycoupledthermo

mechanicaltestmodelthatwasdevelopedtogainanunderstandingofthecapabilityofthe

fluidstructureinteractionmodeltopredictdiedistortion.AnFSIboundaryconditionwas


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definedattheinterfacebetweenthesolidandliquiddomain.Asoliddomainwasusedto

representthediesandaliquiddomainwasusedtorepresentthecastingandthepressure

loadwassimulatedbyspecifyinganodalpressureboundaryconditioninthegateareaofthe

fluiddomain.TheFSImethodusesaconjugateheattransfertocalculatetheheatfluxes

acrosstheinterfaceandhencenointerfacialheattransfercoefficientshadtobedefined

betweentheliquidandthesoliddomain.Latentheateffectswereincludedinthemodelby

specifyingtemperaturedependentspecificheatcurve.Thismodelwasdevelopedfor

demonstrationpurposesanditisyettobeimplementedincomplexdiedistortion

simulations.

Anotherimportantdynamicloadthathasbeenignoredindiedistortionsimulationsisthe

impactloadcausedbythesuddendecelerationoftheplungermechanismattheendoffill.

Xueetal[32],attemptedtopredictthepressuredistributioninthediecavityduetothis

impactloadingusingaCFDmodel.Thegoalwastousethepressurepredictionsfromthis

CFDmodeltoapproximatethedynamiccavitypressureinstructuraldiedistortion

simulations.FLOW3Dwasusedtosimulatethemetalflowintheshotsleeve,runnerand

thedies.Themoltenaluminumwastreatedasslightlycompressiblefluidwithtemperature

independentmaterialpropertiesandaK turbulentmodelwasusedinthesimulation.Heat

transferbetweenthemetalandthedieswasincludedinthemodelandtheheatconduction

inthediewasneglected.Pressurehistoryatdifferentcavitylocationswasinvestigated.The

pressurespikewasfoundtobemorethantwiceoftheintensificationpressurethatis

normallyusedintheproductionofthisexperimentalcastpartusedinthisstudy.Itwasalso

observedthatthepressurewithinthecavitywasalmostuniformandthemaximumpressure

differenceinthecavitywasalsoverysmall(about50PSI)attheinstanttheimpactoccurs. It

wasalsoobservedfromthepredictionsthatthepressureinthecavitywaszeroduringthe

slowshotphaseanditreachedthepeakatdifferentlocationsatdifferentinstantsoftime

duringthefastshot.Themaximumpressureoccurredduringthedecelerationphasethrough

outthecavity.

Milleratal[33],developedafiniteelementmodeltopredictthedeflectionoftheslidesin

nonopenclosediesandtheresultsfromthemodelwerecomparedwithfielddata.Thefield

dataconsistedoftheslideblowbackandtiltvaluesfromnominalpositionunderdifferent

pressureloadsfordifferentslidedesign.Thesimplefiniteelementmodelassumedarigid

supportbehindthecoverdie.Themodelpredictionsshowedagoodcorrelationwiththe

experimentaldataexceptforthehighpressurecases.Thiswasduetotheassumptionof

rigidsupportbehindthecoverdie.

Vashist[34]studiedtheeffectofdifferentsupportstructuresforthedieonthepartingplane

separation.Thegoalwastostudythepartingplaneseparationpatternsonaproductiondie


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thatflashedseverelyafteritwasmovedfroma1000tonmachinetoa2500tonmachine.

Thediehadtobemountedloweronthe2500tonmachineduetothelocationoftheshot

hole.Therefore,toevenlyspreadouttheclampload,thediefootprintwasincreasedonthe

coveronthemachineplatenbyaddingsupportstructurestothedies.Thisstudyanalyzed

theeffectofdifferenttypesofsupportstructuresanddifferentclamploads.Theresults

showedthattheaddedsupportsstiffenedthedie/machinestructureandincreasedthe

platencoveragearea,buttheydidnotaidintransferringtheclamploadtothediefaces.

Flynnetal[35]measuredthedeflectionofthesameproductiondieatvariouslocationsof

thedieusingLVDTsandtheyreportedagoodmatchbetweenthemodelpredictionsby

Vashist[34]andtheexperimentalmeasurements.

GarzaDelgado[36]studiedthefailureoftieboltsthatoccurredonahotchambermachine,

usingasequentiallycoupledthermomechanicalmodel.Thiscasestudyshowedthatnon

uniformheatgrowthonthepartingsurfaceofthedieresultedinunequaldistributionof

loadsonthetieboltsandresultedintieboltsfailure.Themachineframe,shankandbracket

weremodeledexplicitlyinthestructuralmodel.Thetogglemechanismandthetiebolts

weremodeledusing3Dbeamelements.

BaroneandCaulk[39]presentedamethodtopredicttheultimatedistortionofboththe

castingandthedieduetothermalandmechanicalloadsinthediecastingprocess.They

formulatedthediedistortionproblemasanonlinearthermoelasticcontactproblemsolved

byiterativeboundaryelementmethod.Butthecastingdistortionwasanalyzedasan

unconstrainedthermoelasticshrinkageusingfiniteelementmethod.Theirmodelincluded

the

dies,

the

ejector

support,

and

cover

and

ejector

platens.

The

tie

bars

and

toggle

mechanismswererepresentedbyspringelementsbehindtheejectorandcoverplaten

respectivelywithappropriatestiffnessvalues.Suitabledisplacementconstraintswere

providedonselectednodesonthebottomofthecoverplatentopreventrigidbodymotion

oftheentirestructure.Thisboundaryconditionisanapproximationofanchoringthe

machinetothebase.Theunevencontactonthepartingsurfacewashandledusing

contact/gapelementswhoseformulationprovidesforloadtransferbetweenthedie

componentsonlywhenthemutualsurfacetractioniscompressive.Frictionbetweenthe

contactsurfaceswereignoredinthismodel.Thecavitypressurewasmodeledasa

hydrostaticpressurewithamagnitudeequaltothatoftheintensificationpressure.The

modelingapproachwastestedonafrontdrivetransmissioncasedieandtheresultswere

presented.Theadvantageofthismethodasclaimedbytheauthorsisthatthecastingand

diedistortioncanbeanalyzedsimultaneouslyandtheshrinkageallowanceforthediecavity

canbeestimated.


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8

Ragabetal[40]studiedtheeffectofcastingmaterialconstitutivemodelonthedeflection

andresidualstresspredictionsonthecasting.Thecoverandejectorplatenswereincludedin

themodelandthetiebarswererepresentedusingspringelements.Theclamploadwas

appliedbyspecifyingdisplacementboundaryconditiononthespringelementsrepresenting

thetogglemechanism.Thecavitypressurewasmodeledasapressureboundarycondition.

Acontactconstraintwasusedbetweenthedieandthecasting.Afullycoupledthermo

mechanicalanalysiswasconducted.Threedifferentmaterialmodelswereconsideredforthe

casting,viz.,elastic,elasticplasticandelasticviscoplastic.Theresidualstresspredictions

wereaffectedsignificantlybythematerialmodels. Thedistortionpredictionswereless

affected.Theelasticmodeloverestimatedthestressesandtheviscoplasticmodellacked

therequiredmaterialpropertydata.ThereforeinafurtherstudyRagab,[41]usedthe

elasticplasticmodeltopredicttheeffectofkeymodelingfactorsoncastingdistortion

predictions.Thefactorsconsideredweretheyieldstrengthandstrainhardeningofthe

castingmaterial,theheattransfercoefficientbetweenthedieandthecastingandthe

injectiontemperatureofthemetal.Thestudyconcludedthattheyieldstrengthhadamajor

effectonresidualstressesatejectionwhiletheinjectiontemperatureandtheheattransfer

coefficienthadamajoreffectontheresidualstressesatroomtemperature.The

disadvantageofthemodelusedinRagabsstudywasthatthesolidcastingcouldnotfollow

thedistortedshapeofthecavityduetotheuseofsolidelementsforthecastingsandhence

itmightaffectthecastingdistortionprediction.

GarzaDelgado[42]addressedthisissuebyusingashellmeshrepresentingthecasting

surfaceinthesequentiallycoupledthermomechanicalmodelthatincludedtheclamploads,

intensificationpressureloadandthethermalload.Thenodaldistortionvaluesoftheshell

meshwerethenmappedontothesurfacenodesofasolidmeshforthecasting.Thenthe

solidcavitywastiedtothedistortedshapeofthedieusingtiedcontactandthecooling

stagesofthecastingweresimulatedusingafullycoupledelasticplasticthermomechanical

model.Modelingthetiebarsexplicitlyandapplyingtheclamploadsthroughspring

elementscausedproblemsinestablishingcontactbetweenthedieandthecasting.

Thereforetheclampforcewasmodeledasapressureboundaryconditionbehindtheejector

plateninthiswork.

NumerousparametricdiedesignstudieshasbeenconductedattheCenterforDieCastingat

OhioStateUniversitytounderstandtheroleofstructuraldiedesignparametersondie

deflection.Someoftheseparametricdiedesignstudiesarereviewedhere.

Jayaraman[43],conductedaparametricstudyoftheslidedesignvariablesforaninboard

lockdesignandtheworkwascontinuedbyChakravarti[44,45]usingarefinedmodel.The

variablesconsideredwerethepreload,theangleofthelockingsurfaceandthepivot.Results


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9

suggestedthatthepreloadhadnoeffectontheblowbackandtiltvaluesbutitaffectedthe

fatiguelifeoftheslides.Thetrendsalsoshowedthatthetipseparationincreasedwith

lockingfaceangleandslideswithhighpivotwerebettersupportedbytheejectorplaten.

Therewasnegligibleeffectonthepartingplaneseparationwithintherangeofdesign

variables.

TheeffectofproudinsertsonthepartingplaneseparationwasfirstanalyzedbyDedhia[26],

[46].Thestudyconcludedthatusingproudinsertsresultedinalowerseparationduringthe

initialcyclesbutatthelaterstagesasthediewarmsupandgrowstheseparationvalues

weresimilartothecaseswithflushinserts(insertpartingsurfaceinlinewiththedieparting

surface).AmuchrefinedmodelwaslaterusedbyTewari[3],[45]tostudytheeffectof

proudinsertsonthepartingplaneseparation.Thecontactpressurebetweenthediesand

theplatensandthecompressivestressesinthediepocketwerealsostudied.Itwas

observedthatthepartingplaneseparationwasreducedaroundthecavitybyhavingaproud

insertandthecontactpressurebetweenthediesandtheplatenswasnotaffecteddueto

theuseofproudinserts.Theproudinserthadnegligibleeffectonthecompressivestresses

inthediepocket.

Tewari[3],[45],analyzedtheeffectofaddingabackplatebehindtheejectorsupportbox.

Resultsfromhisstudyindicatethatthebackplatehasnegligibleeffectonboththeparting

planeseparationandthecontactpressurebetweentheejectordieandtheplaten.

AparametricstudyconductedbyDedhiaetal[26],[46],showedthatusingproudpillarshad

noeffectonthepartingplaneseparation.Thedifferenceinpartingplaneseparationvalues

betweenthecaseswithproudpillarsandflushpillarswaslessthan5%.

Aseriesofparametricstudies[13],[28]wereconductedtogainunderstandingoftheeffect

ofimportantstructuralvariablesofthediesandthemachineonthediedistortion.The

summaryoftheworkwaspublishedin[4],[45].

Thevariablesinvestigatedwerediesize(%ofplatenareacovered),insertthickness,

thicknessofdiesteelbehindtheinsertanddielocationontheplaten.Responsesurface

modelsbasedondesignofexperimentswereusedtostudytheinteractionbetweenthe

variablesandtheireffectofpartingplaneseparation.Theapproachforthesensitivity

analysiswasdevelopedbyChayapathi[1],[28]andtheinitialexperimentaldesignarray

consistedof15experimentalruns. Anadditional16runswerefurtheraddedbyKulkarni

andTewari[2],[3]toascertaintheresults.Thestudyhasshownthatthedominantfactor

thataffectsthediedistortiononthecoversideisthecoverplatenthickness.Thindies

performedbetterthanthickdies.Themorethesteelbehindthediesthelesserwasthe

partingplaneseparationobserved.Smallormediumsizeddies(covering40%to50%of


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10

platenarea)performedbetter.Kulkarni[2]attemptedtostudythecoverandejectorside

performancesseparately.Buttheejectorsidedesignvariablessuchastherailsize,number,

sizeandlocationofthesupportpillarswerenotcontrolledinthecomputational

experiments.Thereforethestudywasinconclusiveaboutthecontributionofejectorside

design

to

the

ejector

side

separation.

2.2 SummaryoftheStateoftheArtThestateoftheartinmodelingthediecastingdie/machinesystemisbrieflysummarizedin

thissectiontoplacetheworkperformedinthisprojectincontext.

Thevastmajorityofdiecastingmodelingworkperformedinindustryaddressesflow

modelingofdiefillingandthermalmodelingofthepartanddieasthediecools. Invirtually

everycasethemachineisignoredexceptasthesourceofthemetalspeedduringfillingand

thedieisassumedtobecompletelyrigidexceptpossiblyforthermalgrowth. Thereis

generallyno

consideration

of

the

mechanical

forces

and

pressures

at

work

in

the

system.

Asdescribedintheprevioussection,theworkatOhioStateoverthepastseveralyearshas

addressedanddevelopedstructuralmodelingtechniquesandboundaryconditionssuitable

tomodelmanyaspectsofthesystemresponsetothemachineclampingforces,cavityand

injectionpressure,aswellasthethermalloadsthatmostmodelingconsiders. Adepictionof

themajorcomponentsofthesystemastypicallymodeledisshowninFigure1.

Figure1 TypicalDieCastingSystemModelUsedbyOSU


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11

Themachinebase,allthreeplatens(assumingathreeplatensystem),thecoverandejector

diecomponents,andthetiebarsareexplicitlymodeled. Themachineclampingmechanism

isrepresentedwithbeamelementswhoselengthisadjustedtoprovidetheproperclamp

magnitude.

Thepartanddiecavityaretypicallymodeledindependentlyandthesystemisanalyzedin

quasisteadystatebymodeling50ormorethermalcyclesofthediesothatthetimevarying

dietemperaturefieldisconsistentfromonecycletothenext. Thestructuralanalysisis

staticandthecavitypressureisnotexplicitlymodeledbutaddressedwithahydrostatic

boundarycondition. Theinabilitytoexplicitlymodelthepressureattheinterfacebetween

thecastingandthedieisoneofthelimitingfactorsindevelopingrobustmodelsofpart

distortion. Overall,themodelingapproachhasproventobequiterobustandusefulbutit

doesrequireconsiderableunderstandingofthemechanicsofthesystemandofstructural

modeling. Consequently,structuralmodelingofthesystemisnotyetwidelypracticedin

industryasadesigntool. Itis,however,beginningtobeusedfortroubleshootingsystem

failures.

2.3 ObjectivesIngeneralterms,theobjectivesofthisprojectaretomaketheprinciplesandmethodsof

systemstructuralmodelingmoreaccessibletotheindustrythroughthedevelopmentof

detailedtutorialmaterialandthroughtheuseofmetamodels(modelsofmodels)that

capturetheresultsofsimulationsinrelativelysimpledimensionlessequationsthatcanbe

programmedonaspreadsheetorinasimplecomputerapplication. Inaddition,theissueof

thepressure

boundary

condition

mentioned

above

isexplored

insome

detail

and

areas

of

themodelingthatarelesswelldeveloped,specificallythedesignoftheejectorsideofthe

die,areexplored.

Severaloftheindustrialcasestudiessummarizedintheprevioussectionshowthateven

veryexperiencedprocessengineersandtoolingdesignersoftenincorrectlypredicthowthe

diewillrespondtochangestothestructuralelementsinthedieassembly. Industrydoesnot

alwaysapplybasicengineeringprincipleswhenconsideringdiemechanicalperformance.As

aconsequenceconsiderabletimeandmoneyisspenttryingoutdiedesignoptionsthat

ultimatelydonotwork.Thisprocessresultsinverylongtryoutswithmanyscrapped

castings.Theseproblemscanbeavoidedoratleastminimizedwithcorrespondingsavingsof

wastedenergy.

Specificgoalsincluded:

Systematicallyaddressingdesignoftheejectorsideofthediecastingdie.

Developparametricinformationabouttherelationshipbetweendieshoedesign,

slidecarrierdesign,andthemachine.


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12

Analyzingtherelationshipbetweenthediecenterofpressure,diegeometriccenter,

andplatencenterofpressureinthepursuitofbettersetupguidelines.

Examinethepossibilityofexplicitlymodelingthecasting/dieinterfacewiththe

objectiveofeliminatingtheneedtouseapressureboundarycondition

Providedesign

guidelines

for

the

industry

addressing

the

mechanical

design

ofdies

andtherelationshipbetweendieandmachine.

2.4 TasksandApproachThetaskstomeetthesegoalsinclude:

1. AnalysisofDiePositionEffects

ApproachAcollectionofcomputationalexperimentsdesignedusingdesignof

experimentsprincipleswasusedtodevelopFEAmodelsofdiesinvariousconfigurations

onthediecastingmachine. Thenthroughtheapplicationofdimensionalanalysis,the

dataproducedalongwithdatafromotherexperimentsperformedbythegroup,werethenusedtoconstructadimensionlesspowerlawmodeltopredictingtiebarbalanceas

afunctionofdieconfigurationparameters. Thistaskiscloselyrelatedtotask4

describedbelow.

2. DieFailureCaseStudy

ApproachAstudywasperformedinconjunctionwithanindustrypartnerthatanalyzed

therootcauseofprematurecrackingofadieusedtoproduceadoorcloserhousing.

Thecrackresultedinasurfaceblemishthatresultedincastingsbeingrejected. The

primarypurposeofthistaskwastogainmoremodelingexperiencewithfailuresandto

extendthemodelingprocedurestoconsidertheseissues.

3. CavityPressureModelingMethods

ApproachAcomprehensiveFEAmodelingstudysupportedwithresultsfromcasting

experimentsandaseparatesetofexperimentstoobtainhightemperaturestressstrain

propertieswasused.

4. EvaluationofEjectorSideandSlideDesign

Approach Acollectionofcomputationalexperimentsdesignedusingdesignof

experimentsprincipleswasusedtodevelopFEAmodelsofvariousdieshoeandpillar

configurations. Thenthroughtheapplicationofdimensionalanalysis,thewereusedto

constructadimensionlesspowerlawmodeltopredictingmaximumpartingplane

separationasafunctionofdesignparameters. Thistaskiscloselyrelatedtotask1

describedabove.

5. ModelingandDesignGuidelines


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ApproachDrawingonexperienceswithmodelingperformedaspartofthisprojectand

withthepreviousworksummarizedintheprevioussection,acomprehensivemodeling

tutorialwasdeveloped. Inaddition,averyshortsummaryofkeyprincipleswas

developedasanintroductiontothearea.


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3. ResultsandDiscussion3.1 AnalysisofDiePositionEffects

Abriefdescriptionofthemodelingandanalysisperformedforthistaskispresentedbelow.

AsummaryreportthatdescribesthediepositionanalysisworkispresentedinAppendixA.

ThisreportwasprovidedtoNADCAfordistributiontotheindustryandalsocontainsthe

summaryfortheejectorsidedesignwork.

Asimplifiedrepresentationofadiecastingmachineanddieusedformodelingwasshownin

Figure1previously.

Thedieisclampedandheldclosedbythecombinationofatogglemechanism(represented

asbeamelementsinthefigure)andtiebarsthatareanchoredtothecoverandrearplaten.

Theejectorplatenmoveswiththetoggletoopenthedie. Thetiebarsactmuchlikeboltsor

aclampinprovidingtherestrainingforceneededtokeepthedieclosed. Thedegreeto

whichthedieisheldclosedandpressureonthepartingsurfacesofthediearerelatively

uniformdependsonthethermalgrowthofthedie,thecavityshapeandtheplacementof

thepositionofthedieontheplatens.

AsimplifiedfreebodydiagramofthemechanicalloadsinthesystemisshowninFigure2. In

acompletelybalancedcase,eachtiebarcarries1/4thoftheclampforceandprovidesthe

restrainingforcetokeepthedieclosed. Fromtheclampforceappliedatthebackofthe

ejectorplaten,theloadpathisthroughtheejectorplaten,throughtheejectordie,across

thediepartingsurface,throughthecoverdietothecoverplatenandtothetiebars. Again

inaperfectlybalancedsituation,asthecavitypressureisapplied,theforcesacrossthepartingsurfacedropwhiletheforcesbetweenthediesandplatensandtheforcesinthetie

barsremainunchanged.

Figure3illustratesthecharacteristicsoftheresponseofthesystemtotheclampand

pressureloads(theblacklinesdenotethesystempriortotheapplicationofloads,thegreen

linesareamagnifieddepictionofthesystemafterloading). Notethattheplatens(anddie)

distortandthetiebarsstretchresultinginapseudorigidbodymotion. Theactualdistortion

patterninaparticularcasedependsonthemagnitudeoftheloadsandthegeometryofthe

systemandthedistortionpatterncanchangesignificantlyifthediepositionontheplaten

changes.

Inunbalancedsituationswherethedieand/orthediecavityareoffcenter,thedistortionof

thesystemismoresevereandthetiebarloadingwillnotbebalancedwithsomebars

carryingmorethanthenominalandsomecarryingless.


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Figure2 FreeBodyDiagramoftheMechanicalLoads

Figure3 DepictionofSystemResponse

Ifthefourtiebarsdonotcarryequalloads,thediescloseunevenlyatthediepartingsurface

anddieflashingmayoccur.Inextremecases,poorlybalancedtiebarloadscouldalsoleadto

tiebarfailure.Thecommonpracticetoovercomethetiebarloadimbalanceproblemisto

adjustthelengthofthetiebarsbetweentheplatenssothatallthefourtiebarscarryequal


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loads.Insuchacasetheminimumclamploadrequiredtoholdthediestogetherwillbe

higherthantheonethatwouldbeneededifthedieswerecenteredontheplatenthus

limitingthecapacityofthemachine.

Thecurrentapproachusedinindustrytopredictthetiebarloadsbalancesthemomentsdue

tothecavitypressurebutignoresthelocationofthediewithrespecttotheplatencenter

anditassumesthatthemachineandthediesareperfectlyrigidandconsequentlycanbe

quiteinaccurate.

Toaddresstheseissues,anonlinearpowerlawmodelwasdevelopedtopredictthetiebar

loadsofthediecastingmachinebasedonthelocationofthedieandcavitycenterof

pressurewithrespecttothetiebars.Themodelwasobtainedbycurvefittotiebarload

predictiondatafromcomputationalexperiments.Thecomputationalexperimentswere

conductedusingthefiniteelementmodeling.Anexperimentaldesignwasdevelopedbased

onthe

horizontal

and

vertical

dimension

ofthe

die,

the

locations

ofthe

die

and

cavity

center

ofpressurewithrespecttotheplatencenterandthemagnitudeofcavitycenterofpressure.

Dimensionalanalysiswasusedtoincorporateotherimportantscalefactorsandobtainthe

nondimensionalparameters.Thenonlinearmodelwasthenfittothenondimensional

formofthelocation,scaleandloadvariables.Experimentaltiebarloadmeasurementswere

thencomparedtothepowerlawmodelpredictionstochecktheadequacyofthepowerlaw

models.

3.1.1 ComputationalExperimentsThefactorsthatwereconsideredarethedielength,diewidth,locationofthediewith

respecttotheplatencenterandthelocationofthecavitycenterofpressurewithrespectto

theplatencenterandthemagnitudeofthecavitypressure.Thedescriptionofthevariables

andtheirlevelsareshowninTable1.Thelocationvariablesaredefinedwithrespecttoa

coordinatesystemwithoriginonthecenteroftheplatenareabetweenthetiebars.The

schematicofthecoordinatesystemandthetiebarlabelsareshowninFigure4.


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Factor FactorDescription Level1

Level

2Level

3Level

4Level

5LX DieWidth(inches) 26.49 30.4 32.6 34.6 36.5

LY DieHeight(inches) 26.49 30.4 32.6 34.6 36.5

DPX Dielocation

inX

direction(inches)4 2 0 2 4

DPYDielocationinY

direction(inches)4 2 0 2 4

CPX

Locationofcenterof

pressurein X

direction(inches)

4 2 0 2 4

CPY

Locationofcenterof

pressurein Ydirection

(inches)

4 2 0 2 4

CPR CavityPressure(KSI) 2 4 6 8 1

Table1 DescriptionofVariables

Figure4 CoordinateSystemandTiebarLabels

Afewadditionalcaseswerealsoaddedtotheexperimentalarraytoincludecaseswitha

cavityloadequalto100%ofclamploadandafewcaseswithnocavitypressureload.

3.1.2 DimensionalAnalysisDimensionalanalysisandananalysisofthephysicalphenomenainvolvedleadtoapower

lawformshownin(1)


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c1 c2

tb tb

tb tb

Tie bar load DPX DPY=c0 1 1+

Nominal Load 0.5L 0.5L

CPRA CPX CPY CPRA 1+c3 exp 1 +c4 1+

CLAMP 0.5L 0.5L CLAMP

CPRA CPRA 1-c5 exp

CLAMP

CLAMP

(1)

Thisformwasassumedforeachindividualtiebarandparametersselectedtofitthepower

lawtothepredictedloadsforeachofthefourtiebarsforallofthe70casesinthe

experimentalarray. TheSPSSstatisticalsoftwarepackagewasusedtoperformthenon

linearregressionandthesequentialquadraticprogrammingalgorithminSPSSwasusedto

solvethenonlinearregressionproblem.

Thesamemodelformwasobtainedforallthefourtiebarsandthemagnitudesofthe

coefficientsandexponentsforthetwotoptiebarswereapproximatelyequalwithdifferent

signs.Similarlythemagnitudesoftheexponentsandcoefficientsforthetwobottomtiebars

werenearlythesame.Thereforetheloaddataforthetoptiebarswerepooledandthedata

forthebottomtiebarswerepooledandthesamemodelformwasfittothepooleddata.

Theresultsaregivenbyequations(2)and(3)respectively.Thetermswith+/ signsare

reversedbetweenthetwoequations.Theseparametersrepresenttheverticallocationof

thedieandcenterofpressurerespectivelyandhencetheirsignsarepositiveforthetoptie

barsandnegativeforthebottomtiebars.

Theparameterestimates,thestandarderrorintheestimatesandtheconfidenceintervals

fortheestimatesforthetopandbottomtiebarsareprovidedinTable2andTable3

respectively. Thequalityofthefitisclearlyverygood.

Theresultingequationsareasfollows:

0.354 0.303

tb t b

tb t b

Top Tie bar load DPX DPY=1.005 1 1+


CPRA CPX CPY CPRA 1+0.063 exp 1 +0.886 1+


1-0.

CPRA CPRA098 exp

CLAMP CLAMP

(2)


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0.294 0.256

tb t b

t b tb

Bottom Tie bar load DPX DPY=1.04 1 1-


CPRA CPX CPY CPRA 1+0.062 exp 1 +1.03 1-


1-0

CPRA CPRA.106 exp

CLAMP CLAMP

(3)

ParameterEstimates

Parameter Estimate

Std.

Error

95%Confidence

Interval

Lower

Bound

Upper

Bound

c0 1.005 0.002 1.001 1.009

c1 0.354 0.011 0.333 0.374

c2 0.303 0.012 0.279 0.327

c3 0.063 0.005 0.052 0.074

c4 0.886 0.045 0.796 0.976

c5 0.098 0.006 0.109 0.086

AdjustedRsquare=0.96

Table2:ParameterEstimatesforTopTieBarModelFit


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ParameterEstimates

Parameter Estimate

Std.

Error

95%Confidence

Interval

Lower

Bound

Upper

Bound

c0 1.04 0.002 1.036 1.044

c1 0.294 0.012 0.271 0.318

c2 0.256 0.014 0.228 0.284

c3 0.062 0.005 0.051 0.073

c4 1.025 0.052 0.922 1.128

c5 0.106 0.005 0.117 0.095

AdjustedRSquare=0.95

Table3:ParameterEstimatesforBottomTieBarModelFit

Thetermnominalloadonthelefthandsidesoftheequationsisdefinedasonefourthofthe

totalclampload.ThesignbeforethetermsinvolvingDPXandCPXindicatesthatthesigns

ofthesevariablesdependonthelocationofthedie/cavityandalsoonthetiebarforwhich

theloadiscalculated.Ifthedieand/orcavityispositionedtowardsthetiebarforwhichthe

loadistobepredicted,apositivesignshouldbechosenforthecorrespondingvariablesand

ifthedieand/orcavityispositionedawayfromthetiebarforwhichtheloadistobepredictedanegativesignshouldbechosen.Forexample,ifthedieishorizontallyoffcenter

towardsthehelperside,apositivesignshouldbeusedbeforethevariableDPXtopredict

theloadsonthehelpersidetiebarsandanegativesignshouldbeusedbeforeDPXto

predicttheloadsontheoperatorsidetiebarsandviceversa.Thesamesignconvention

appliestothetermsinvolvingthehorizontalcavitylocationCPX.

Thethirdtermintheequationrepresentsthemomentscausedbythecavitypressureload.

Themomenttermsandtheloadtermappearasexponentialtermsinthemodel.This

indicatesthatthetiebarloadsincreaseordecreaseinanexponentialfashionasthecavity

centerofpressureismovedtowardsorawayfromtherespectivetiebars. Theparameters

involvingthediedimensions,Lx/AandLy/Awerefoundtohaveanegligibleeffectonthe

modelpredictionsandhencetheywereignoredinthemodel.Thesenondimensional

parameterswereincludedintheinitialmodelfitting.Buttheerrorinvolvedintheir

estimatesforthecorrespondingexponentsweremuchhigherthanthevalueofthe

exponentsitself.Thereforethismodelbehavesasalumpedmodelwheretheclampand


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pressureloadsareapproximatedbypointloadsactingonthediecenterandcavitycenterof

pressurerespectively.

3.1.3 ModelAdequacy,FEAResultsThepowerlawmodelsshowninequations(2)and(3)wereobtainedbycurvefittingtotie

datafroma800tonfourtogglemachine. Tostudytheadequacyofthemodeltopredictthe

tiebarloadsonmachinesofotherdesignsandclampingcapacity,thepowerlawmodel

predictionswerecomparedagainstthefiniteelementmodelpredictionsoftiebarloadon

machinesofotherdesignsandtonnages.Threedifferentmachinefiniteelementmodels

wereconsidered,viz,a3500tonfourtogglemachine,1000tonfourtogglemachineanda

250tontwotogglemachines.Thedielocation,cavitylocation,theclamploadand

magnitudeofcavitypressureforthesethreecasesaresummarizedinTable4. TheFEAand

powerlawpredictions,presentedasthedifferencefromnominal,forthesamefourcases

areshowninTable5,Table6,andTable7respectively.

Machine

Design

DPX

(in)

DPY

(in)

CPX

(in)

CPY

(in)

CPR

(PSI)

Ltb

(in)

Cavity

Load

(tons)

Clamp

Load

(tons)

3500ton4

toggle4 0 4 0 0 84.25 0 3500

1000ton

4toggle0 1.25 0 3.63 10000 44 602 722

250ton2

toggle

0 3.14 0 0.423 10000 21.75 135 250

Table4:SummaryofFiniteElementModels

TieBarLoad/NominalLoadPrediction

FEA PowerLaw

TopTieBar1 3.8% 3.0%


BottomTieBar1 2.9% 2.6%


Table5:ComparisonofModelPredictionsfora3500TonMachine

(DPX=4,DPY=0,CPX=4,CPY=0,CPR=0PSI)


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FEA PowerLaw






(DPX=0,DPY=1.25,CPX=0,CPY=3.63,CPR=10000PSI)


FEA PowerLaw



BottomTieBar1 8.2% 14%

BottomTieBar2 8.2% 14%


(DPX=0,DPY=3.14,CPX=0,CPY=0.423,CPR=10000PSI)

The1000and250tonmachineshaveverydifferentdesignscomparedtothe800and3500

tonmachinesandtheFEAanalysesinthesecasesusedsimplifiedboundaryconditionson

thecoverplaten. Thedifferenceinboundaryconditions,andnotthedifferenceindesign,is

largelyresponsiblefortheconstantmagnitudeFEAresultsinthetwocasesinquestion.

Theresultsshowreasonablygoodpredictivecapabilityacrossavarietyofdesignsas

expectedofadimensionlessmodel.

3.1.4ModelAdequacy,ExperimentalMeasurementsExperimentswereconductedona250tontwotogglemachinebyvaryingthedielocation

andobtainingthetiebarloadsunderclamploadonly.Theschematicofthetestdieonthe

machineplatensisshowninFigure5. Thetestdiemeasures13.38inchesby18inchesand

thedistancebetweenthetiebarcentersis21.75inches.Fouruniaxialstraingaugeswere

attachedtoeachtiebartomeasurethelongitudinalstrains.Thestraingaugeswere

attachedtothetiebarsatadistanceof267mm(10.5in)fromtheinsidefaceofthe

stationaryplatensothatthestraingaugesarehalfwaybetweenthestationaryandmovable

platenswhenthetestdieisclosed.Theschematicofthestraingaugelocationsisshownin


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Figure6. Thefourstraingaugesoneachtiebarare90apart.Thirteendifferentdiesetups

werestudied,onewithadiecenteredontheplaten,fourcaseswithverticallyoffcenter

dies,fourcaseswithhorizontallyoffcenterdiesandfourcaseswithdiagonallyoffcenter

dies.ThethirteencasesaresummarizedinTable8.Notallcombinationsofdiagonallyoff

centerdiescouldbestudiedduetothelimitationofthespaceavailablebetweenthetie

bars.

Figure5 Schematicofthetestdieonthemachineplatens

Figure6 Schematicofstraingaugesandcoordinatesystem


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RunDPX

(inches)DPY(inches)

1

0 02 0 2

3 0 4

4 2 0

5 4 0

6 0 2

7 0 4

8 2 0

9 4 0

10 2 1.87511 4 1.875

12 2 1.875

13 4 1.875

Table8:ExperimentalArray

Eachcasewasrepeatedthreetimesandaconstantclamploadof2500KNwasappliedinall

cases.Thoughthemachinewasprogrammedtoapplyaclampingloadof2500KN,theactual

clamploadappliedbythemachinevariesslightlyfromthenominal.Themetalinjection

stagewasignoredintheseexperimentsduetothepracticaldifficultyofmovingtheshot

sleeveforeachtest.Thestrainsoneachtiebarwereobtainedunderclamploadonly.The

averageofthestrainsmeasuredbythefourstraingaugesoneachtiebarwascalculatedto

obtainthestrainoneachtiebar. Thetiebarloadswerethencalculatedfromthestrain

values.Thenominalclamploadpertiebarwasassumedtobetheaverageofthefourtiebar

loadsandtheloadoneachtiebarwasestimatedastheratiobetweenthetiebarloadand

thenominalload.

Theexperimentalmeasurementsandpowerlawpredictionsoftiebarloadsforthethirteen

casesareshowninTable9andFigure7. Ideallytheloadsonallfourtiebarsshouldbeequal

forcase1wherethediesarecenteredontheplaten.Howeverthemeasurementsshowthattheloadsonbottomtiebarsarelowerthanonthetoptiebars.Thiscouldbedueto

inaccuracyinpositioningthediesontheplatencausingthemeasurementstobebiased

towardsthetoptiebars. Lackofsquarenessandperfectflatnessoftheplatenscouldalso

contributetothisobserveddifference.


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Case DPX DPYExperimental

Measurements PowerLawPredictionsT1 T2 B1 B2 T1 T2 B1 B2

1 0 0 1.03 1.02 0.99 0.97 1.00 1.01 1.04 1.04

2

0

2

1.10 1.09 0.92 0.90 1.05 1.06

0.99

0.993 0 4 1.16 1.15 0.85 0.83 1.10 1.11 0.93 0.93

4 2 0 0.99 1.09 0.90 1.02 0.94 1.07 0.98 1.09

5 4 0 0.94 1.14 0.85 1.07 0.86 1.12 0.91 1.13

6 0 2 0.96 0.95 1.05 1.04 0.94 0.95 1.08 1.08

7 0 4 0.92 0.90 1.10 1.08 0.87 0.88 1.12 1.12

8 2 0 1.09 0.98 1.03 0.91 1.06 0.94 1.09 0.98

9 4 0 1.16 0.92 1.09 0.83 1.11 0.86 1.13 0.92

10 2 1.875 1.06 1.15 0.84 0.95 0.98 1.12 0.93 1.04

11 4 1.875 1.03 1.22 0.76 1.00 0.90 1.17 0.87 1.0812 2 1.875 1.02 0.90 1.11 0.97 1.00 0.89 1.13 1.02

13 4 1.875 1.08 0.84 1.17 0.91 1.05 0.82 1.18 0.95

Table9:ComparisonofMeasurementsandPredictions

Thedatashowthatthemodelpredictionsareconsistentlyslightlylowerthanthe

experimentalmeasurementsforthetoptiebarsandtheyareconsistentlyslightlyhigher

thanthemeasurementsforthebottomtiebarsinallofthe13cases. Thiscanbeattributed

totheconstrainttypeusedbetweenthecoverplatenandthemachinebasefortheFEA

modelusedtoconstructthemetamodel.Theedgenodesofthecoverplatenandthebase

weretiedusingamultipointconstraintinthecomputational(FEA)experimentsthatcreated

thedataforthemetamodel.Thoughthe250tonmachineusedfortheexperimentshasa

weldedjointthemultipointconstraintusedintheFEAmightbestifferthantheactual

weldedjointonthemachine.Thelackofflatnessandsquarenessofthediescouldalsohave

contributedtosomeofthesedifferences.


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Figure7 TiebarLoadMeasurementsvs.Predictions

ThedifferencesbetweenthemeasurementsandmodelpredictionsareshowninTable10.

Thedifferencesbetweenthemodelpredictionsandtheloadmeasurementsvaryfrom0.1%

to12%dependingonthedielocation.Asexpected,theworstcasesarethediagonallyoff

centercases,case10andcase11,wherethemeasurementsshowthattheloadonthetop

tiebar1(T1)ishigherthanthenominalandthemodelpredictionsshowthattheloadson

toptiebar1(T1)islowerthanthenominal.Similarlytheloadmeasurementsonbottomtie

bar1(B2)arelowerthanthenominalincase10andcase11,andthemodelpredictions

showthattheyarehigherthanthenominal.Overall,thepatternofresultsisverygood.

Noteagainthatthepowerlawwasderivedfromsimulationdatabasedonan800ton,4

togglemachineandtheexperimentaldataisfroma250ton,2togglemachineadding

credibilitytotheclaimthatthepowerlawproducesreasonablepredictionsforawide

varietyofmachinedesignsandsizes.


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Case DPX DPYDifferencebetweenMeasurementsandModel

Predictions(%)T1 T2 B1 B2

1 0 0 2.54% 1.26% 4.83% 7.40%

2 0 2 4.50% 2.84% 6.77% 9.17%

3 0 4 6.52% 4.59% 7.20% 9.76%

4 2 0 5.40% 2.03% 7.72% 6.95%

5 4 0 7.63% 2.24% 6.75% 6.03%

6 0 2 1.98% 0.10% 2.75% 4.90%

7 0 4 4.28% 2.13% 1.80% 4.32%

8 2 0 2.80% 3.37% 5.10% 7.81%

9 4 0 5.19% 5.90% 3.89% 9.10%

10 2 1.875 8.15% 3.25% 9.65% 9.23%

11 4 1.875 12.33% 4.66% 11.54% 8.60%

12 2 1.875 2.49% 1.02% 2.25% 5.41%

13 4 1.875 3.39% 2.29% 0.91% 4.14%

Table10:DifferencebetweenMeasurementsandModelPredictions

3.2 DieFailureCaseStudyThedieusedtoproducethehousingofadoorclosingmechanismsufferedprematurecracksontheejectordiecavitysurface.Thesecracksledtovisiblemarksonthecastingsurface

makingthecastingunacceptable. Theonsetofthecracksintheejectordieoccurredat

approximately20,00040,000shots,muchbelowthedesignexpectationleadingto

unexpectedcostelevation. Severaltechniquesweretriedbythediecastertofixthe

problem,butwithnosuccess. Sincethecauseoftheproblemwasthoughttobeflexingof

thedie,theCenterforDieCastingatOhioStateUniversitywasaskedtoanalyzethedie

usingdiedistortionmodelingtechniquesdevelopedoverthepastseveralyears. The

problemwasexpectedtoprovideagoodcasestudyfortestingtheanalysisprocedures.

Figure8andFigure9illustratethecastingandthesurfacedefect. Severalmodifications

weremadetothecastingandtheejectorinserttoavoidthecrackformationwithlittle

success.Themodificationsincludedchangesinthecastinggeometryandaddingcooling

linestotheejectorinsert.Thelastmodificationwastosplittheejectorinsertintotwopieces

tominimizethebendingstrains.


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Figure8 TheCasting

Figure9 Defects

ThisproblemwasprovidedtoOSUbyDCDTechnologiesandBlueRidgePressureCastings.

Thegoalwastosimulatethedieandthecastingprocessusingthetechniquesdevelopedin

theCenterforDieCastingattheOhioStateUniversityinordertoinvestigatethereasonfor

thecracksandtoproposeappropriatediemodificationstominimizeit.

Asequentiallycoupledthermomechanicalanalysiswasconductedandthemodelpredicted

strainswere

used

to

calculate

the

fatigue

cycle

life

in

the

ejector

insert

cavity

surface.

The

modelpredictedstrainscancausefatiguefailurewithin13,00023,000cyclesattheactual

cracklocationssomewhatearlierthanhasbeenobserved.Thismaybeduetothelackoftwo

featuresinthestructuralmodel,namely,thecastingandtheslides.Theinteractionbetween

theinsertsandboththecastingandslidescanchangethestrainpatternanddecrease,to

someextent,thetensilestrainsresultingfromthethermalloads.Includingthecastingand


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slidesinthestructuralmodelwasnotpossibleduetotheneedtokeepcomputational

resourcesmanageable.

Theresultsshowthatthehighstrainsarelocalizedtoafewlocationssuggestingthat

modifyingthediestructuredoesnotsolvetheproblem.Insteadchangingthepartgeometry

toreducethestressconcentratoratthecracklocationscouldmakeadifference.The

analysiswasrerunagainwithmodifiedfilletradiiatcrackslocationsandtheresultsshowed

muchbetterresultsattwoofthefourlocations.

Insummary,thecasestudyturnedouttobeausefultestofthemodelingprocedures,but

sincetheproblemwasdeterminedtobethepartdesignandnotthedieormachine,the

opportunitytorepresentdiechangesandperformbeforeandaftertestsdidnot

materialize.

AreportprovidingmoredetailaboutthisworkisfoundinAppendixB.

3.3 CavityPressureModelingMethodsAsmentionedintheintroduction,ashortcominginthediestructuralmodelingprocedures

currentlyusedisthepressureboundaryconditionusedtorepresentthemechanical

interfacebetweenthecastingandthedie. Thistendsnottobeaproblemiftheissuesare

structuraldesignofthediebutitmaybeanissueifaccuratepartdistortionmodelsare

sought.

Thedistorteddiecavityattheendoffillingrepresentstheinitialshapeconditionsforthe

castingattheonsetofsolidification. Thisdistorteddiecavityshaperesultsfromtheeffects

ofmainlythreeprocessloads:clamping,temperaturegrowthandintensificationpressure.

Accuratepredictionsofcastingfinaldimensionsrequiremodelingthedistorteddiecavity

shapeadequately,sincetheelasticdeflectionsexperiencedproduceddimensionalchanges

inthediecavitythataffectthecastingdimensions.

Indiedistortionmodelstheintensificationpressureeffectshavebeentraditionally

representedbyusingaconstantpressureboundaryconditionappliedtothediecavity

surface. Ideally,theintensificationpressureshouldbetheresultoftheloadingactionofthe

pressurizedcastingactingontothediecavitysurfaces. However,thishydrostaticloading

cannotbemodeledbecausecontinuumsolidelementslackahydrostaticpressuredegreeoffreedomandarerenderedinadequateforthesepurposes.

Thelatestdevelopmentsinfiniteelementmodelingalgorithmsallowmodelingthe

interactionoffluidandstructuralelements. Thesemodelingcapabilitiesrepresentthestate

oftheartinfiniteelementcodesandwereinitiallyadoptedformodelingcastinganddie


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distortion. ThefiniteelementpackageADINAwasselectedbecauseitallowsmultiphysics

modelinginonesingleintegratedcode.

Theadoptionofthismodelingtechniquewasthoughttoaugmentcastinganddiedistortion

modelingeffortsduetothefollowing. First,sincethecastingcouldberepresentedusing

liquidelementsthatpossessapressuredegreeoffreedom,modelingintensification

pressureeffectscouldbereadilydonebyapplyingapressureloadtothebiscuitandletting

thecastingfluidelementsloadthedeformabledie. Second,thedistorteddiecavityshapeat

theendoffillingcouldbereadilyobtainedfromthedistortedcastingmeshbecausethe

fluidstructureinteractionalgorithmrequirestheliquidelementstoalwaysfollowthe

distortedshape. Therefore,theinitialcastingshapeattheonsetofsolidificationcouldbe

readilyobtainedfromthedistortedfluidmesh.

3.3.1 FluidStructureInteraction(FSI)ModelThe

model

was

divided

into

solid

and

liquid

domains.

The

solid

domain

was

comprised

of

thestructuralelementswhichincludedtheinserts,die,ejectorsupportblock,ejectorand

coverplatensandtiebars. Theliquiddomainwascomprisedofonlythecasting. Inthe

structuralelementstheusualboundaryconditionsappliedtodiedistortionmodelswere

considered. Contactbetweenallthedeformablebodieswasincorporatedaswell. Inthe

fluiddomain,thecastingwasrepresentedwithliquidelements,whichhavepressureand

velocitydegreesoffreedom. Afluidstructureinteractionboundaryconditionwasspecified

forallthesurfacesinboththecastingandthediewheretheywereexpectedtointeract.

Clampingandthermalforcewassimulatedbyapplyingapressureloadontheejectorplaten.

Thermal

load

was

modeled

by

prescribing

a

temperature

load

on

the

inserts

and

die.

Intensificationpressurewasmodeledbynormalsurfacetractionloadonthebiscuitregionof

thecasting. Theloadswereappliedsequentiallyinatotalofthreesteps.

Thedisplacementsonthecastingmeshwereextractedattheendoftheanalysis. Figure10

showsthepredictionsgivenbytheFSImodel. Theseresultsshowthatthecavitydistortion

isnotnegligibleandthepredicteddisplacementmagnitudesemphasizetheimportanceof

incorporatingthecontributionsofthediedeflectionsincastingdistortionanalyses.

Thisdisplacementfieldrepresentedthedistortedcavityshapeattheendoffillingandwas

consideredastheinitialcastingshapeforsubsequentthermalmechanicalsolidification/coolingmodeling. Thesamemeshforallthedifferentcomponentsusedinthe

FSImodelwasusedinafullycoupledthermalmechanicalmodel. Themodelwascomprised

ofthesamestructuralcomponentsasbeforewiththeadditionofthecasting. Thefinal

coordinatesofthecastingintheFSImodelweretakenastheinitialcoordinatesforthe

thermalmechanicalmodel.


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Figure10 FSIcavitydisplacementpredictions

Sincemodelingcastingsolidification/coolingmustconsidertheinteractionbetweenthe

castingandthedie,thedeformedstatepredictedintheFSImodelhadtobereproduced

usingthesameloadingconditions. Clampingandthermalloadsweremodeledasdescribed

andtheintensificationpressurewasnowmodeledasapressureloadappliedtothedie

cavitysurfaces. Contactbetweenthecastingandthediewasnotenableduntilthe

deformationwasreproduced. Allthefiniteelementsusedtorepresentallthecomponents

hadtemperatureanddisplacementsdegreesoffreedom. ThemodelwasruninAbaqus,

usingtheC3D8Tcoupledtemperaturedisplacementthreedimensionalelements.

Whilerunningthismodelconvergencedifficultieswereexperienced. Examinationofthe

resultsshowedamismatchbetweenthecastingshapeanddiecavitysurfacesafter

applicationoftheinitialloading. Thesemirigidbodymotionduetotiebarstretchingafter

clampingwasidentifiedasthesourceofdivergenceinthethermalmechanicalmodel. The

displacementpredictionsafterclampingbetweentheFSIandthethermalmechanicalmodel


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differedbyasmuchas0.07mmandthisdifferencewaslargeenoughtopreventproper

establishmentofcontact.

Itwasconjecturedthatthedifferentcontactalgorithmsusedbyeachcodeproduced

differentdisplacements. Sincecoupledthermalmechanicalmodelscanbeanalyzedin

ADINAitwasdecidedtosetupthesolidificationmodelandrunitallinADINA. Thesame

loadingandboundaryconditionsasdescribedbeforewerereproducedinanADINAthermal

mechanicalmodel. Theresultsshowedthatthedisplacementpredictionsofthethermal

mechanicalmodelweredifferentwhencomparedwiththeFSIpredictions. Themagnitude

ofthesedifferenceswascloseto0.07mmaswell. Thesedifferencesindisplacement

predictionswithinADINApreventedfurthermodelingeffortsusingthecodeanditwas

abandoned.

3.3.2 AlternativetoFSIThe

modeling

ofpart

distortion

was

divided

into

three

different

models.

The

first

model

determinestheinitialcastingshapeafterthemetalhasfilledthediecavity. Thesecond

modelsimulatesthecoolingofthecastinginsidethedie. Thethirdmodelsimulatesthe

coolingofthecastingafterejection. Themodelsareruninthedescribedsequenceandthe

resultsprovidedbyeachmodelaresubsequentlyusedbythefollowingone.

Figure11showsthecastingusedforthisresearchproject. Thegeometryofthecastingwas

designedforaprocesscontrolstudydonebyOsborne[42]aspartofhisresearchwork. All

ofthecastingribsareformedintheejectorhalf,withthecovercontributingonlytoform

thebackoftheplate. Thedesignofthiscastingwasdoneinordertousethedistance

betweentheribsasameasureforincavitydistortion,whereasthedepthoftheribswas

usedtoprovideameasureforacrosspartingplanedistortion.


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Figure11Castingfiniteelementmesh

3.3.3 TrackingofCavityDistortion

Thepredictionsobtainedbythediedistortionmodelrepresentthefirststeptowardsthe

modelingof

casting

distortion.

As

has

been

already

described,

the

die

experiences

elastic

deflectionsresultingfromthecombinedeffectsofthedifferentprocessloads. These

deflectionscausesmallbutimportantdimensionalchangesinthediecavity,changesthat

mustbecapturedsincetheyrepresenttheinitialshapetheliquidcastingacquiresattheend

ofthefilling.

Inordertoknowwhattheinitialcastingshapeispriortotheonsetofcooling,anaccurate

descriptionofthedeformeddiecavityshapemustbeobtainedfirst. Ragab[35]

experimentedtrackingthedistorteddieshapebytyingthecastingsurfacestothediecavity

surfaces. Themodelincludedthecasting,die,platens,ejectorsupportblock. Allpartsinthe

modelwere

discretized

using

solid

brick

finite

elements.

It

was

reported

that

because

the

castingwasrepresentedbysolidelements,limitationsintheelementdeformations

preventeditfromaccuratelytrackingthedieshapeasthedifferentloadswereapplied.

Themethodologyusedinthisresearchworkreliesintheuseofashellmeshtotrackthe

distortionsinthecavity. Thesamestructuralcomponentsforthediedistortionmodelare

usedinthismodel. Theapplicationofthethreedifferentprocessloadsissequentiallydone


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asdescribedbefore. Inordertoavoidhavingasolidcastingtrackingthecavitydistortions,a

shellmeshisusedinstead. Theshellmeshisbuiltusingthesurfaceelementsofthecasting

mesh,sharingthesamenodesasthecastingsurfaceelements. Bysharingthesamenodes,

thedisplacementsobtainedfromtheshellmeshcanbereadilymappedontothecasting

meshsurface.

Thedimensionalchangesinthecavityaretrackedbytyingtheshellmeshtothediecavity

mesh. Tyingtheshelltothediecavityprovidesadescriptionofthedistorteddiecavity

shapeaftertheapplicationofthealreadymentionedstaticloads. Afterthediehasbeen

distorted,thepredicteddisplacementsoftheshellmeshcanbeappliedtothecastingmesh,

providingacastingshapethatmatchesthatofthedeformeddiecavity. Theunderlying

assumptioninthisprocedureisthatthedistortionsinthecavityaresmallenoughthatthey

canbemappedonlytothecastingsurfacewithoutaffectingitsinteriorstructure.

Figure12

shows

the

shell

mesh

used

for

this

model.

With

athree

dimensional

mesh

ofthe

casting,theshellmeshcanbereadilyobtainedusingthemeshingcapabilitiesofanypre

processor. Forthismodel,ashellthicknessof0.0254mmwasspecified. Toavoidany

modelinglimitationsduetorigidityontheshell,theYoungsModulusoftheshellmaterial

wasspecifiedtobethreeordersofmagnitudesmallerthanthatofregularsteel.

Themodelisrunasastaticanalysis. Ashasbeenalreadydescribed,clamping,thermaland

pressureloadaresequentiallyappliedinthreedifferentsteps. Attheendoftheanalysis,

thedisplacementpredictionsfromtheshellareextractedandusedinthefollowingmodel.

Thedescriptionformodelingthecoolingofcastinginsidethedieisprovidedinthenext

section.

Twopapers,onedescribingapartdistortionstudybasedonthisworkandonedetailing

worktoobtainthehightemperaturepropertiesofthediecastingalloyA380arepresented

inAppendicesCandDrespectively.


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Figure12 Shellelementmesh

3.4 EvaluationofEjectorSideandSlideDesignTheapproachtotheejectorsidedesigntaskcloselyfollowsthatusedfortiebarloading.

Powerlaw

models

were

developed

to

predict

maximum

parting

plane

separation

on

the

coverandejectorside.Adesignofexperimentswasdevelopedbasedonthemajor

structuralvariablesofthediecastingdieandthemachine.Astaticfiniteelementanalysis

wasconductedateachdesignpointspecifiedinthedesignarrayusingourbasicstructural

modelingmethodology. Thepredictedmaximumseparationofthecoverandejectorside

partingsurfacesfromtheirnominallocationwasobtainedfromthefiniteelementmodels.

Powerlawmodelswerefittothepartingplaneseparationdataandthenondimensional

structuraldesignparameters.Thenondimensionalparameterswereobtainedusing

dimensionalanalysisbasedonBuckinghampitheorem.Thedesignofexperiments,thenon

dimensionalparameters

and

the

power

law

models

are

summarized

below.

More

details

canbefoundinAppendixA.

3.4.1 DesignofExperiments

Thedesignvariablesincludedinthestudyarethediewidth,dielength,diethickness,

thicknessofthediesteelbehindtheinsert(dieshoulderthickness),pillardiameterandthe


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patternofejectorpillarsupports.Thedescriptionofthefactorsalongwiththeirhighandlow

valuesisshowninTable11.

Factor Description HighLevel LowLevelPt Platenthickness 9 13

Lx Horizontaldimensionof 24 38

LyVerticaldimensionofthe

die24 38

t Diethickness 5 10

TR Diethicknessratio 0.4 0.5

PD Pillardiameter 1.5 4

X PillarPattern(discrete 4Levels/Patterns

Table11 FactorsusedinDesignofExperiments

Thesixthfactor,pillarpattern,isadiscretefactor.Theschematicofthefourdifferentpillar

arrangementsbehindtheejectordiethatwereanalyzedisshowninFigure13whichshows

therearviewofanejectordie.Thebacksurfaceoftherailsishatchedinthefigure.Therails

are3incheswideinallofthecases.Therailsandpillarsare6incheslonginallofthecases.

Inpillarpattern1thereareatotalofninepillars,onedirectlybehindthecenterofpressure

andtheouterpillarsarelocatedataradialdistanceof6.75inchesfromthecenterpillar.In

pattern1theouterpillarsare45apartfromeachother.Inpattern2,therearenopillars

andtheejectordiehasonlyrailsupport.Inpattern3andpattern4therearefivepillars,one

onthecenterandfourouterpillarseach90apart.Thedifferencebetweenpattern3andpattern4isintheorientationoftheouterpillars.A58runcentralcompositeresponse

surfaceexperimentaldesignwaschosenbasedonthefivecontinuousfactors.Thenthe58

runswererepeatedforeachlevelofthediscretefactor.


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Figure13 SchematicofPillarPatternsusedintheStudy

Pattern1,9pillars,(b)Pattern2,Nopillars,(c)Pattern3,FivePillars,(d)Pattern4,5pillars

Themaximumcoverandejectorsidepartingplaneseparationwerepredictedforeachcase

intheexperimentalarrayusingthefiniteelementmodelingmethodology

3.4.2 DimensionalAnalysisTheobjectiveofthecomputationalexperimentsistodevelopempiricalcorrelationsto

predictthemaximumpartingplaneseparationasafunctionofthedesignvariablesinvolved.

Dimensionalanalysiswasusedtodeterminethenondimensionalparametersfortheempiricalcorrelations.Dimensionalanalysisisbasedontheprinciplethatanyvalidphysical

relationshipshouldbedimensionallyhomogeneous.BasedonthisprincipleBuckingham[58]

showedinhisfamousPitheoremthatanyequationdescribingthephysicalrelationship

betweenthevariablescanbereformulatedasafunctionofdimensionlessproductsof

variables.


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Thechoiceofvariablestobeusedinthedimensionalanalysisandthegroupingofvariables

thatformthenondimensionalgroupscanbedeterminedusingtheknowledgeofthe

physicalphenomenonandengineeringjudgment.Thediesandinsertsareassumedaspre

stressedflatplatesthatarerestingonelasticsupportsandsubjectedtouniformloading.The

semianalyticalempiricalequationforpredictingmaximumdeflectionofaflatplatunder

uniformloadingisgivenby[60].

4

3

WLMaximum deflection

Et (4)

Wistheuniformlydistributedload,listhelengthoftheplate,Eistheyoungsmodulus,tis

theplatethicknessandisaconstantthatdependsontheaspectratioandboundary

conditions.Theunsupportedspanbehindthecoverdieischaracterizedbythelengthand

widthofthedieandamodelforcoversideseparationwilltakeaformsimilartothe

deflectionequationabove.Howeverontheejectorsidetheunsupportedspanischaracterizedbythedistancebetweenthepillarsandrailsupports.Jofreit[61]developeda

semiempiricalequationtopredictthemaximumdeflectionofconcreteflatplatessupported

onstraightbeamsaroundtheperipheryandagridofpillarsinbetweenthebeamsupports.

Theequationtopredictthemaximumdeflectionwithinanyinnergridofpillarsisgivenby

4

3

3

4

s nl lW

Maximum deflectionEt

(5)

wherelsandlnarethelongspanandtheshortspanbetweenthepillarsupports.Itcanbe

observedthatthespanvariableLinequation(4)isreplacedbytheweightedaverageofthe

shorterandlongerspanbetweenthepillarsupports.Thereforeamodelfortheejectorside

separationwilltakeasimilarform. Basedonthestructureoftheequations(4)and(5),the

physicalrelationbetweenthemaximumpartingplaneseparationandthedesignvariables

canbewrittenasfollows:

max , , , , , , , , , , 0 tb nf Pt L t TR L l PD RW DistributedLoad E (6)

where,max

isthemaximumpartingplaneseparation,Ltbisthedistancebetweenthetiebar

centers,Listhelengthscalerepresentingthelengthandwidthofthedieorthespan

betweenthepillars,lnisthelengthscaleforspanbetweenpillars,PDisthepillardiameter,

RWisthewidthofthedieandEistheyoung'smodulusofthediematerial.Theterm

DistributedLoaddenotesthedistributedcontactloadatthepartingsurfaceanditis

approximatesasfollows:


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Pr Pr

-

x y x y

TotalClamp Load Cavity essure ojectedAreaofCavityDistrubted Contact Load

L L L L(7)

ThenondimensionalparametersselectedaresummarizedasshowninTable12.Detailscan

befoundinAppendixA.

DimensionlessParameter

Description

1 (Ltb/t)or(Distancebetweentiebarcenters/Diethickness)

2 (Pt/t )or(Platenthickness/Diethickness)

3 (TR)or(Dieshoulderthickness/Diethickness)

4 (L/t )or(Span/Diethickness)

5 (MaxSeparation/t)(Youngs Modulus/Distributedcontactload)

6 (Lx/Ly)or(Aspectratioofthedie)

7 (Lcx/Lcy)or(Aspectratioofthecavity)

Table12NonDimensionalStructuralDesignParameters

Theparameter1,indicatesthatincreasingthedistancebetweenthetiebarcenterhasthe

sameeffectasdecreasingthediethickness.Ifthedistancebetweenthetiebarsincreases

foragivenplatenthickness,theplatenbendsmoreandthesupportavailableforthediesis

reducedandthediesdeflectmore.Decreasingthediethicknesswillalsoresultinanincreaseinthedeflectionofthedie.ThoughthevariableLtbwasnotexplicitlyvariedinthe

computationalexperiments,theparameter1variesamongtheexperimentalcasesdueto

thevariationindiethicknessamongtheexperimentalcasesandtheeffectofLtbcanbe

capturedfromthecomputationalexperiments.

Thesecondparameter2canbecombinedwiththefirstparameter1,toobtainanewnon

dimensionalparameter,say,12,whichisgivenby

11 2

2

tb

Pt

L

(8)

Theparameter12,aboveshowsthatthereisalwaysacombinationofvaluesofplaten

thicknessanddistancebetweentiebarcentersforwhichtheplatenstiffnessremainsa

constant.Themostimportantnondimensionalparameteris4whichrepresentstheratio

betweentheunsupportedspanandthediethickness.Thisparametersuggeststhatlarger

thespanbehindthedie,thickershouldbethedie.Acombinationofthespananddie


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thicknesscanalwaysbechosentoobtainadesiredmagnitudeofpartingplaneseparation.

Ontheejectorside,theparameter4representstheratioofthespanbetweenthepillar

supportstothediethickness.Inourexperimentsthepillarlocationswithrespecttothe

centerofpressurewerefixed.Butthethicknessofthediewasvar

mechanical performances of dies

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