Skin-pass rolling II—Studies of roughness transfer under combined normal and tangential loading

InternationalJournalofMachineTools&Manufacture48(2008)1308–1312

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InternationalJournalofMachineTools&Manufacture

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Skin-passrollingII—Studiesofroughnesstransferundercombinednormalandtangentialloading

HideoKijimaa,Ã,NielsBayb,1

ab

RollingandProcessingResearchDepartment,JFESteelCorporation,1,Kokancho,Fukuyama,Hiroshima721-8510,Japan

DepartmentofMechanicalEngineering,TechnicalUniversityofDenmark,ProductionstorvetDTU,Bygning425,DK2800,Kgs.Lyngby,Denmark

articleinfo

Articlehistory:

Received10December2007Receivedinrevisedform11June2008

Accepted11June2008

Availableonline18June2008Keywords:

Skin-passrollingTemperrollingRoughness

Finiteelementanalysis

abstract

Thein uenceoftoolroughnessonroughnesstransferinskin-passortemperrollingofsteelstripisinvestigated,focusingonloadingundercombinednormalandtangentialdisplacementoftoolrelativetotheworkpiece.Thecalculatedroughnesstransferbyanelasto-plastic niteelement(FE)simulationofplanestrainindentationinauthors’previouspaper[H.Kijima,N.Bay,Skin-passrollingI—studiesonroughnesstransferandelongationunderpurenormalloading,InternationalJournalofMachineToolsandManufacture,May2008,acceptedforpublication]isveri edbyexperimentalmeasurementsinthispaper.Theexperimentshowsasigni cantin uenceonroughnesstransferoftangentialdisplacementofworkpieceinthestickingandtheslidingregion.TheFEcalculationsmodellingthestickingandslidingregionrevealthemechanismsofplasticdeformationandroughnesstransfer.

&2008ElsevierLtd.Allrightsreserved.

1.Introduction

Thepresentpaperisthesecondinaseriesoftwo.The rstpaper,[1],describesthebackgroundforthestudy,includingearlierworkinliteraturethatisfocussedonexperimentalinvestigationswithlittleemphasisontheoreticalornumericalanalysis.In[1]a niteelement(FE)analysisoftheroughnesstransferandstripelongationispresented,showingsigni cantin uenceoftoolroughnessontooltransferandelongation.EarlierworkbyKijimaandBay[2,3]hasshownthatitisfeasibletosimplifytheskin-passrollingtoplanestrainupsettingwithsmallreduction,inthiswayclarifyingthebasicmechanismscontrollingtheformationofanextendedstickingregioninthecaseofhighfrictionandsmoothtoolsurfaces.

In[1]thisisutilizedtoinvestigatethein uenceoftoolroughnessonroughnesstransferandelongationnumericallyforthecaseofpurenormalloading,i.e.withnotangentialslidingbetweentoolandworkpiece.ThetoolroughnessisidealizedasaseriesofcirclesegmentswithdifferentaverageroughnessRaandpitchlp.Inthepresentpaperthenumericalresultsareveri edbyplanestrainupsettingexperiments.Theexperimentsshowthatlocaltangentialdisplacementofthebulkworkpiecesigni cantlyin uencestheroughnesstransfer.Thisobservationis

con rmedbyFEanalysismodellingthestickingaswellastheslidingregion.

2.ExperimentalinvestigationsandcomparisonwithFEcalculations

2.1.Experimentalprocedure

Inordertoverifytheresultsobtainedbynumericalmodellinginthepreviouspaper,anexperimentalsetupwasdesignedtostudyroughnesstransferinplanestrainupsettingwithlong,narrowtoolsmountedinasub-presswithlowfriction,highaccuracyguidesina60tonf(588kN)universal,hydraulicpress.Toollengthwas150mmandthewidthwas5mm,seeFig.1a.ThetoolsweremadeofpowdermetallurgicalhighspeedsteelAISIM3:2,hardenedandtemperedto62HRC.Thetoolsurfacewas negrindedandsubsequentlyroughenedbyelectricaldischargetexturingtoaroughnessRaE3.25mmandRzE21.0mmmeasuredinlongitudinal(transverse)directionofthetoolinordertoensuresuf cientmeasuringlength(seeFig.1).Sincetheelectricaldischargetexturinggivesarandomthree-dimensional(3D)structureitisacceptabletomeasureinthelongitudinal(transverse)directioninsteadofthelateralone,althoughthisisdirectionofworkpiecedeformationandthusthemostrelevanttomeasure.

TheworkpiecematerialwasannealedlowC-steelwithstripdimensions200Â50Â0.75mm3.Priortoeachexperimentthetoolandworkpiecesurfaceswerecarefullydegreasedwith

ÃCorrespondingauthor.Tel.:+81849454154;fax:+81849453840.

1

E-mailaddresses:h-kijima@jfe-steel.co.jp(H.Kijima),nbay@ipl.dtu.dk(N.Bay).Tel.:+4545254764;fax:+4545930190.

0890-6955/$-seefrontmatter&2008ElsevierLtd.Allrightsreserved.doi:10.1016/j.ijmachtools.2008.06.006

H.Kijima,N.Bay/InternationalJournalofMachineTools&Manufacture48(2008)1308–1312

1309

Nomenclatureh0WwpLwpLtWtHtrlppE

initialthicknessofworkpiece(mm)

lengthoftheworkpieceintransversedirection(mm)lengthoftheworkpieceinlateraldirection(mm)lengthofthetoolintransversedirection(mm)lengthofthetoolinlateraldirection(mm)lengthofthetoolinverticaldirection(mm)roughnesspro leradiusontoolsurface(mm)pitchofmodelledpro leontoolsurface(mm)

averagepressureasloadingintheexperiment(MPa)Young’smodulusofworkpiece(GPa)Poisson’sratio

n

initialyieldstressofworkpiece(MPa)yieldstressofworkpiece(MPa)

Raaverageroughnessofsurface(mm)Ra,toolaverageroughnessoftoolsurface(mm)Rzmaximumroughnessofsurface(mm)Rz,toolmaximumroughnessoftoolsurface(mm)Rz,wpmaximumroughnessofworkpiecesurface(mm)

Rz,wp/Rz,tooltransferratioofmaximumroughnessfromtoolto

workpiece

Dxapplieddisplacementoftoolmovementinhorizontal

(lateral)direction(mm)

Dhapplieddisplacementoftoolmovementinvertical

direction(mm)

sy0s

acetonetoachievehighfrictioncondition.Loadingwasdonetodifferentpressuresintherange400opo1000MPa.Afterloadingeachspecimen,threerepeatedroughnesspro les,each4mmlong,weremeasuredinthetransversedirectionofindentationat12differentpositionsinthelateraldirection,seeFig.1b,inordertohaverepresentativevaluesformaximumroughnessRzinthese12locations.

2.2.Resultsanddiscussion

Fig.2showsthepressuredistributioninlateraldirectionofthetoolcontactlengthforseveralaveragepressurelevels,calculatedbytheFEanalysiswithsmoothtoolsurface[3].Duetohighfrictionandlargeratiobetweencontactlengthandstripthicknessatypicalfrictionhillisseenwithitspeakatthecentreofcontact.

Fig.3showsthemeasuredroughnessasthetransferratioRz,wp/Rz,toolfortwonormalpressurelevelsinthe12differentlaterallocationsdiscussedabove.Theaverage,maximum,andminimumvaluesofthreemeasurementsonthesameworkpieceareshown.TheextensionofthestickingregiondeterminedbytheFEanalysis[3]isalsoshown.Fig.4showstherelationshipbetweenthepeakpressureshowninFig.2andthemeasuredroughnesstransferratioatthecentreofcontactinFig.3,comparedwiththecalculatedroughnesstransferratioforvaryingpitch/stripthicknessratiodeterminedinthepreviouspaper[1].

AlthoughtheFEanalysiswasbasedontwo-dimensional(2D)toolasperities,whereastheexperimentsaredonewithrandom3Dasperities,theagreementisrathergood,implyingthattheroughnesstransferatthecentreofcontactmaybedeterminedbythesimpleindentationmodelappliedinthepreviouspaper,constraininglateraldeformationoftheworkpiece.

atdireralection

Tran

e disvers

rectio

n

h0 = 0.75mm

Lt = 150mm

Lwp = 200mm

Wt = 5mm

3.Thein uenceoftangentialshearbetweentoolandworkpiecesurface

Wwp = 50mm

Ht = 40mm

3.1.Introduction

ItshouldbenoticedthatthedistributionofroughnesstransferseeninFig.3doesnotfollowthepressuredistributionseenin

Center

4mm

Ditch

Edge

932.2[MPa]

885.8

830.4

748.8509.7

1400Vertical pressure [MPa]

120010008006004002000

Wwp = 50mm

5mm

00.511.522.5

Longitudinal position [mm]

Fig.2.Calculatedpressuredistribution.

Fig.1.Experimentalprocedure:(a)schematicoutlineofplanestrainindentationsetupand(b)positionsformeasuringworkpieceroughness.

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H.Kijima,N.Bay/InternationalJournalofMachineTools&Manufacture48(2008)1308–1312

rgeroughnesstransfercanbeseenintheslidingregion,althoughthepressureissmallcomparedtothatinthecentre.Theroughnesstransferreachesamaximumattheboundarybetweentheslidingandthestickingregion.ThistendencyissimilartothejunctiongrowthphenomenonpointedoutbyMcFarlaneandTabor[4]intheiranalysisoffrictionbystudyingplasticdeformationofsurfaceasperities,andthefrictionmodelofBayandWanheim[5]athighnormalpressuresbasedon atteningofworkpieceasperitiesinslidingcontactwithasmoothtoolsurface.Itissimilarlyexpectedinanelasto-plasticdeforma-tionofskin-passrollingthattheroughnesstransferisin uencedbythetangentialshearofthebulkworkpiece[2,3],causingfurthersurfacedeformationintheslidingregionbetweentoolandworkpiecesurfaces.Theshearstresswasearliershowntoreach

1.2]

-[ loo1t,zR/p0.8w,zR 0.6oitar 0.4Sticking regionrefsn0.2aContact region

Tr00.0

1.0

2.0

3.0

4.0

5.0

Lateral position [mm]

1.2]

-[ loo1t,zR/p0.8w,zR 0.6

oitar 0.4Sticking region

refsn0.2

aContact region

Tr00

1

2

3

4

5

Lateral position [mm]

Fig.3.Measuredroughnessdistribution:(a)averagenormalpressure¼901.6MPaand(b)averagenormalpressure¼588.0MPa.

]

1-[ loot,z0.8R/FEMpw,z0.6lp/h0R 1.0oita0.40.75r re0.5Experiment

fsn0.20.25

aTr00

200

400

600

800

1000

1200

Normal pressure [MPa]

parisonbetween

measuredandcalculatedroughnesstransferatthecentreofthecontactlength.itsmaximumattheboundarybetweenstickingandsliding[3].Inthefollowingthein uenceofthetangentialshearonroughnesstransferisanalysed.3.2.Analyticalconditions

Inordertomodelthedifferenceinroughnesstransferinthestickingandtheslidingregion,amodelwiththelengthofthreeroughnesspitchesisanalysed.Figs.5aandbshowtheFEmodelforthestickingregionandtheslidingregion,respectively.Inthecaseofsticking,thetoolisassumedtomoveinnormaldirectiononly,andthehorizontalortangentialdisplacementoftheworkpieceisassumedtobedistributedasahyperbolicfunction,Fig.5a,withmaximumdisplacementatthemiddleofthestripandzerodisplacementatthetoolsurface.Theassumptionofahyperbolicdisplacementpro leisbasedonearliercalculationsofthedeformationpatternbytheauthors[2].TheamountofindentationDh/2,seeFig.5,wasvariedtoachieveappropriateaveragepressuresonthecentretargetregion.Inthecaseofsliding,thetoolisassumedtomovealonganinclinedlinetowards

r

Rigid tool roughness

2

/h Δ2

/0hΔ x

lp

Δ x

r

Rigid tool roughness

x

2

/h 2

/0hlp

Fig.5.SchematicoutlineoftheFEmodel:(a)stickingfrictionwithhyperbolicdeformationand(b)slidingfriction.

]

1-[ loot,z0.8R/pwΔ x[µm]

,z0.6R25 oit12.5a0.4r6 re3

fsn0.20

aTr00

200

400

600

800

1000

1200

Average pressure [MPa]

Fig.6.Calculatedroughnesstransferandcontactareaforvaryingtangentialdisplacementinthestickingregion.

H.Kijima,N.Bay/InternationalJournalofMachineTools&Manufacture48(2008)1308–1312

1311

Transfer ratio Rz,wp/Rz,tool [-]

thesurface,implyingverticalaswellashorizontalmovementsimultaneously,whereastheworkpieceisstationary.Theincre-mentoftoolmovementinhorizontaldirection,Dx,seeFig.5b,waschosenasaparameterandthecorrespondingvaluesofDh/2werechosentoensureappropriatenormalpressures.Thecentralpartofonepitchlengthoftheworkpieceisthetargetofevaluation.Theadjacenttwopitchlengths,oneoneachside,areintroducedtoreducetheeffectofboundaryconditionsontheworkpiece.Thetoolroughnesspro lewasmodelledasaseriesofcirclesegmentswithradiusr.Thefollowinggeometricalpara-metervalueswerechosen:toolroughnessRa¼1mm(r¼0.322mmandRz¼3.91mm),pitchlp¼0.1mm,workpiecethicknessh0¼0.2mm.Theanalysiswascarriedoutwiththe2D,planestrain,staticimplicitmethodinELFEN[6]assumingthetooltoberigid.Theworkpiecematerialwasassumedtobeelasto-plasticwithYoung’smodulusE¼205.8GPa,Poisson’sration¼0.3,initialyieldstresssy0¼170.8MPa,andastress–straincurvedeterminedbytensiletestingas

interface.Ateachreduction,themaximumroughnessRzwascalculated.

3.3.Stickingregion

Fig.6showsthecalculatedroughnesstransferinthecaseofstickingfrictionasafunctionofaveragenormalpressurewiththetangentialdisplacementDxasaparameter.ThecurvesforDx¼0mmcorrespondtothepurenormalloadingwithouttangentialdisplacementstudiedinthepreviouspaper[1].Theresultsclearlyindicatetheincreaseinroughnesstransferwhen

10.80.60.40.200

200

400

600

800

1000

1200

Average pressure [MPa]

Δ x[µm]

2010

520

s¼552:1ð Pþ0:003Þ0:202½MPa

(1)

whereePistheaverageeffectiveplasticstrain.VonMisesyieldcriterionwasused.AdoptingCoulomb’slaw,whichistheonlyfrictionmodelavailableinELFEN,thecoef cientoffrictionbetweentoolandworkpiecewaschosenasm¼0.3.Thecontactproblembetweentoolandworkpiecewassolvedbythepenaltymethodfornormalpenetrationaswellastangentialsliding.Themeshwasrectangularanditsmaximumsizewas1/20ofhalftheworkpiecethickness,h0/2.Finermeshwasappliednearthe

Fig.9.Calculatedroughnesstransferandcontactareaforvaryingtangentialdisplacementintheslidingregion.

3Vertical position y [μm]

210-1-20

Δ x[µm]

Vertical position y [μm]

3210-1-2

Originalsurface

10

5

2

0Δ x[µm]

2512.5

60

Original surface

0.020.040.060.080.100.020.040.060.080.1

Longitudinal position x [mm]

Fig.7.Calculatedsurfacepro leinthestickingregionat500MPaaveragepressure.

Longitudinal position x [mm]

Fig.10.Calculatedsurfacepro leintheslidingregionat500MPaaveragepressure.

0.18950.17370.15790.14210.12630.11050.09470.07890.06310.04730.03150.01570.0000

Fig.8.Effectiveplasticstraindistributioninworkpiece(averagepressure:500MPa,tangentialdisplacementDx¼12.5mm).

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H.Kijima,N.Bay/InternationalJournalofMachineTools&Manufacture48(2008)1308–1312

0.49270.45160.41050.36940.32830.28730.24630.20510.16410.12310.08200.0409

0.0000

Fig.11.Effectiveplasticstraindistributioninworkpiece(averagepressure:500MPa,tangentialdisplacementDx¼10mm).

tangentialdisplacementoccurseventhoughnoslidingappearsbetweentoolandworkpiece.Fig.7showsthecalculatedsurfacepro leatanaveragepressureof500MPa.IncreasingtangentialdisplacementDxleadstoincreasedroughnessoftheworkpiecesurface.Fig.8showstheeffectiveplasticstraindistributionat500MPaaveragepressureandatangentialdisplacementDx¼rgeplasticdeformationoccursunderthetoolasperity,whereastheworkpiecesurfacesextrudedintothevalleysofthetoolsurfacemoveasalmostrigidbodieswithnodeformation.3.4.Slidingregion

Fig.9showsthecalculatedroughnesstransferasafunctionoftheaveragenormalpressurewiththetangentialdisplacementDxasaparameterinthecaseofslidingfriction,whereasFigs.10and11showthesurfacepro leandeffectiveplasticstraindistributionintheworkpieceat500MPaaveragepressure.

ComparingFigs.9–11withthecorrespondingFigs.6–8,itisseenthatrelativeslidingbetweentoolandworkpieceleadstosigni cantlylargerplasticstrainsunderthetoolasperities,implyingsomewhatlargerroughnesstransfer.

Ingeneralaclearin uenceisnoticedoftangentialdisplace-mentontheroughnesstransferfromtooltoworkpiece,implyingthatthepurenormalloadinginthemiddleofthecontactlengthmayunderestimatetheroughnesstransferindryskin-passrolling,wheretangentialdisplacementscauselargeshearstressesinthesurface,leadingtoincreasedroughnesstransfer.Asshownin[3]theextensionofthestickingregionchangeswiththeactualcontactlength,whichdependsontheworkrollradius.Thisimpliesthattheroughnesstransferinlaboratoryrollingmillswithsmallworkrollradiusisdifferentfromtheoneobtainedwithproductionmillswithlargeworkrollradius.4.Conclusion

Anexperimentalinvestigationofroughnesstransferbyplanestrainupsettingwithtoolsofdifferentsurfaceroughnesswascarriedouttocon rmthecalculatedroughnesstransferbyFEanalysis,modellingthecentreofthecontactregion,wherenormalloadingwithnotangentialdisplacementwasassumedtooccur.Evenina2Dmodel,thecalculatedmaximumroughnesstransferofatoolroughnesspro lemodelledbyaseriesofcirclesegmentsshowedgoodagreementwiththeexperimentalmeasurements.

Theresultsfurthermoreshowthatthepressuredistributioncanbecalculatedwithasmoothtoolsurfacemodelandthattangentialdisplacementcanbeneglectedatthecentreofthecontactregion.

Experimentalresultsshowedlargeroughnesstransferintheslidingregion,especiallyattheboundarybetweentheslidingandstickingregion,althoughthepressureissmallertherethanatthecentre.InanextendedFEanalysiscarriedouttomodeltheslidingandstickingfriction,asigni cantin uenceoftangentialloadingbetweentoolandworkpieceonroughnesstransferwasshownforbothcasescomparedtopurenormalloading.Theconclusionisthatjunctiongrowthoccursundertheseelasto-plasticconditions.Theexperimentalandnumericalresultsofplanestrainup-settingwithsmallreductionshownaboveimplythatpurenormalloadinginthemiddleofthecontactlengthmayunderestimatetheroughnesstransferindryskin-passrolling,andthespecialconditionsinskin-passrollingwithanextendedstickingregionandslidingneartheinletandexitzonesoftherollgapfacilitateroughnesstransfer.Sincetheextensionofthestickingregiondependsonthecontactlength,theroughnesstransferinlaboratoryrollingmillswithsmallworkrollradiusisdifferentfromtheoneobtainedwithproductionmillswithlargeworkrollradius.Acknowledgements

TheauthorsareindebtedtoJFESteelCorporation,whichsupportedH.Kijimawitha2-yearresearchgrantattheTechnicalUniversityofDenmark.FurthermoretheauthorsaregratefulforthehelpfromengineeringassistantReneSobieckiforassistancewithroughnessmeasurements.References

[1]H.Kijima,N.Bay,Skin-passrollingI—studiesonroughnesstransferand

elongationunderpurenormalloading,InternationalJournalofMachineToolsandManufacture2008,inpress,doi:10.1016/j.ijmachtools.2008.06.005.

[2]H.Kijima,N.Bay,Modellingofskinpassrollingbyelasto-plasticanalysisof

planestrainupsetting,JournalofMaterialsProcessingTechnology177(2006)509–512.

[3]H.Kijima,N.Bay,Contactconditionsinskin-passrolling,AnnalsofCIRP56

(2007)301–306.

[4]J.MacFarlane,D.Tabor,Relationbetweenfrictionandadhesion,Proceedingsof

theRoyalSocietyofLondon202A(1069)(1950)244–253.

[5]N.Bay,T.Wanheim,Realareaofcontactandfrictionstressathighpressure

slidingcontact,Wear38(1076)201–209.

[6]ELFENVersion3.7.0,Rock eldSoftwareLtd.,Technium,Swansea,UK.

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