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Analysis of Temperature Field and Thermal Crown of Roll During Hot Rolling by Simplified FEM

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Analysis of Temperature Field and Thermal Crown of Roll During Hot Rolling by Simplified FEM

    Analysis of Temperature Field and Thermal

    Crown of Roll During Hot Rolling by

    Simplified FEM

    Availableonlineatwww.sciencedirect.com

    ……?

    @.cT?

    JOURNALOFIRONANDSTEELRESEARCH.INTERNATIONAL.2006,13(6):27-30,

    48

    AnalysisofTemperatureFieldandThermalCrownof

    RollDuringHotRollingbySimplifiedFEM

    GUOZhongfeng,LIChangsheng,XUJian-zhong,LIUXianghua.WANGGuo

    dong

    (StateKeyLaboratoryofRollingandAutomation,NortheasternUniversity.Shenyang110004,Liaoning,China)

    Abstract:Thermalcrownofrollisanimportantfactor,whichaffectsstripprofile.Itisnecessarytoanalyzethetem

    peraturefieldandthermalcrownofrollforhotstripmil1.Anewsimplifiedfiniteelementmethod(FEM)wasused

    toanalyzethetemperaturefieldandthermalcrownofroll,andcorrespondingmodelswerebuiltaccordingtothe

    practicalboundaryconditions.TransientrolltemperaturefieldandthermalcrownweresimulatedbvANSYSFEM

    softwarewithconsideringtransientthermalcontactandcomplexboundarycondition.Temperatureandthermal

    crownvariationsonrollsurfacenodeswereobtained.ThethermalcrownresultsofrollobtainedbyFEMsimulation

wereingoodagreementwiththemeasureddata,indicatingthatsimplifiedFEMmodelsandre

    sultswerecorrect.

    Keywords:temperaturefield;thermalcrowntFEM;roll Itisnecessarytopredictthethermalcrownof workrollforimprovingstripprofile.However,the predictionisdifficultduetothecomplexityofheat exchangeconditionsandthedifficultyofonline

    measurement['

    .Thoughmuchprogressofmeas

    uringthetemperaturefieldandthermalcrownofthe workrollhasbeenmadebyFEMandFiniteDiffer

    enceMethod(FDM)L1,ittookmuchmoretime toobtainthetransienttemperaturefieldby3D FEML4,53,andthe2DFEManalysisisnotverysatis

    factoryformanysimplifications.Therefore,anew simplificationmethodwaspresentedtosimulatethe temperaturefieldandthermalcrownoftheworkroll byANSYSFEMsoftware,andinfluencingfactors areconsidered.Thetemperaturevariationofdiffer

    entdepthnodesinacycletimeandthermalcrownat differenttimeareobtained.

    1BoundaryConditions

    TheboundaryconditionsareshowninFig.1 andFig.2.Thesurfaceofworkrollwasdividedinto eightboundaryregionsaccordingtotheformofheat exchange(Fig.1).

    ABsectionistheintenseconvectionzoneof rollandstrip;

    5

    1W0rkroll;2--Backuproll;3Nozzlel 4Watercollectingpipe;5--Splashplate Fig.1Sketchmapofboundaryconditionsincrosssection

    Coolingno"-zzle

    iIg0.IIll

    ll

    J?qb.J

    6lIl7

    V/////.///////////////A'

    Strip

    Fig.2Sketchmapofthermalboundaryconditionsof workrolIinradlaldirection

    FoundationItem:ItemSponsoredbyMajorStateBasicResearchDevelopmentProgramofC

    hina(G20000672084)

    Biography:GUOZhongfeng(1978),Male,DoctorCandidateIE-mail:zfguo@126.com;RevisedDate:November28?2005 f__^i

JournalofIronandSteelResearch.InternationalVol_13

    BCsectionisthestripradiationzoneaten- trance;

    C_Dsectionisthewater-coolingzoneaten

    trance;

    DEsectionistheairnatura1convectionzone atentrance;

    E_Fsectionisthecontactzoneofworkrol1 andbackuproll;

    FGsectionistheairnatura1convectionzone atexit;

G_Jsectionisthewatercoolingzoneatexit;

    JAsectionisthestripradiationzoneatexit. Dots(18)showninFig.2werethefeature

    pointsofboundarycondition.W0rkrollwasincon

    tactwithstripandbackuprollinthesurfacethat wascomposedofdots2-376,whereheatpassedin

    toworkrol1byconductionandradiation,anditwas thentakenawaybyconvectionofcoolingwaterand conductionofbackupro11.Theareacomposedof dots3487anddots12-6-5didnothavecontactwith strip,buthadcontactwithcoolingwaterandair. Somesimplificationwasrequiredbecauseitwas notnecessarytodescribeeachkindofheatconduc

    tion.Somekindsofheatexchangeswereignoredbe

    causetheyhad1ittleeffect,suchastheheatbetween workrollandbackupro11,andtheheatgeneratedby bearing.

    2BasicHypotheses

    Thetemperaturechangeincircumferentialdi

    rectionoftherollwasignoredbecausero11cycle timewasmuchsmallerthantheresponsetimeof therma1crownandrollingconditionvariations.For thesymmetryofgeometricalshapeoftherollandto savethecalculationtime,onlyaquarterofworkro11 wassimulated.

    Twobasichypotheseswereadoptedbeforesim

    ulation.

    (1)Planehypothesis

    Forthesymmetryofrollgeometricalshapeand theperiodicityofboundarycondition,workrollwas

    dividedintomanymoreplanes,whichshowedthe sameheatbehaviorandonlytimewasdifferent.For example,theheatbehaviorofthellthplaneisequal tothatofthekkthplaneafterrotatingadegreeof0 (Fig.3).

    (2)Eveninitializationcondition

    Tosavethecalculationtime,theinitialization conditionofplane(Fig.1)wastakenastheeven va1ueinthesection.

    ?/,/////////

    ?//

    i

    i,

    /

    ///

    /~/

    ///

    ,/,///////////

    ........一一一L.'_-'..:....

    0I

    I

    I

    Fig.3Schematicplaneofbasichypotheses Fromtheabovebasichypothesis,instantheat behaviorsofrollweredescribedbyheatbehaviorac

    cumulationofaplaneinthewholerollingtime,and thecomplex3Dtransienttemperaturefieldissimpli

    fledintoasimple2Dtransienttemperaturefield.At thesametime,muchmorecalculationtimewas saved.

3FEMMathematicModel

    FEMmodelwasestablishedbycoupledelement (PLANE13)anddividedunequally(shownin Fig.4).Theelementgridsinrollsurfaceandstrip contactzoneweredividedmoreminutelyforthe temperatureinthesezonesvariedgreaterthanthatin Fig.4Aquarterofworkrollfiniteelementmodel anyotherzonesofro11.Therewere10layersonro11 surface,andtheelementthicknessofeach1ayerwas 0.5mm.Thereare651nodesand600elementsto

    tally.

    Theheatbalanceequationof2Dtransientroll temperaturefieldwasdescribedasfollows:

No.6AnalysisofTemperatureFieldandThermalCrownofRollDuringHotRollingbySimpli

    fiedFEM.29.

    =++1?IDfv===I十十I(1)

    Heatflowdensitywasdescribedasafunctionof temperaturegradient:

    q(z,)=?忌(2)

    Theinitialtemperaturefieldwasdescribedas follows:

    (z,r,)J.=(z,r)(3)

    Accordingtotheanalysisofrollboundarycon

    ditions,theheatflowdensityofdifferentnodesat differenttimeweregivenasfollows:

    q(z,r,?)(T8)

    r;R,z~W/2,m×丁N???m×TN+挈丁N

    q(z,r,?)=J}l(TT)

    rR,z~W/2,m×T+TN??m×T+ TN,.rmXTN+TN??mXTN+TN 7r7r

    q(z,r,?)J}l(r)

    :R,z~W/2,m×丁N+T???mXT+ T,.m×丁N+拿重丁N???m×7r/7r

    T+

    q(z,r,t)=J}1()

    TN???m×丁N+弩丁,or R,z>W/2,m×

    mXTN

    mXTN

    +T???m×丁N+,o7r7r +???m×T+T

    7r

    :,z>w/2,mXT+T???mXT+ TN,ormXTN+T?m×

    7r7

    T

    q(z

    q(z

    q(z

    where

    rollte

    r

    r

    r

    ?)0

    ?)=0

    ?)0

zL/2,to??<..

    r=0,t0??<o.

    z0,t0??<..

    Pisdensityofroll;

    mperature}tistime,

    cvisspecificheat}Tis

    isheatconductivityco

    efficientliS~:oll'radiusofrandomlocation;isco

    ordinateinaxialdirection;aiscontactconduction coefficientofstripandroll;hisheatradiationcoef

    ficient;hisairconvectionheatexchangecoeffi

    cient;hwiscoolingwaterheatexchangecoefficient; iscoolingwatertemperature;isrollsurface temperature;isairtemperature;Tisstriptern

    perature;Risworkrollradius;Lisbarrellengthof workroll;Wisstripwidth;EAisradianofarcBA: BAX(X=J,G,F,E,D,C)isradianofarcBAX (X=J,G,F,E,D,C)(Fig.1);TNisrollrota

    tioncycle;misrollrotationnumber.

    Thetemperatureofdifferentnodeswasde

    scribedasfollows:

    T(zl,rj,.)=Tzi~rj+(1l--kk)](4)

    where0isplanenumberofworkroll;T(,rj,0z, t0)istemperatureofnodeT(,rj,0z)attimet0; andTf,rj,,+(zz一忌屉)1istemperature.f

    node(,rj,)attime?.+IN(1lkk)

    .

    Thermalcrown,(R)wasobtainedaftercalcu

    lationofrolltemperaturefieldbythefollowingequa tion;

(R)--(TTro)rdr=(1+v)fiATR

    (5)

    where?isevenascendingtemperatureofroll crosssection,?}isrolllinearexpansioncoeffi

    cient,m/?;visPoissonratio.

    4ResultsandDiscussion

    The7thstandinhotrollingwastakenasanex

    ampleforcalculation.Theparametersadoptedinthe analysisaregiveninTable1.

    Thetemperaturevariationatkeypointsofroll surfacelayerinthefirstroundisshowninFig.5. Thesurfacenodetemperatureinthecontactarea roseto240?quicklywiththecontactwithhot

    strip.thendecreasedtoabout8O?becauseofthe

    roleofcoolingwater.Themaximumtemperatureof nodesunderrollsurfacedecreasedwithdepth.The temperatureofnodesonrollsurfacetemperature variedintensively,whereasthetemperatureofinner nodesvariedgradually,forexample,thetempera

    tureofnode.whichis5mmawayfromrol1surface, changedgradually.Thisisthereasonwhyitalways tookabout2hforrolltoshowheatbalance. Thetemperaturefieldandthermalcrownofroll at9460sareshowninFig.6.Itcanbeseenthat themaximaltemperatureandthethermalcrownat rollsurfacecenterreaches161.667?and128pm

    respectivelyat9460s.

?3O?JournalofIronandSteelResearch,InternationalVol_13

    Table1Parametersusedforanalysisof7thstand

Rollrotationdegree/(.)

    110

    90

    70

    2Ooo400060008ooO10000

    Rollingtlme/s Fig.5TemperaturechangeatkeypointsinrollsurfacelayerFig.7Thermalcrownvariationofr

    ollsurfacecenter =883舶?

    t04ll拍?

    MX

    :54804?

    ll20566?

    C=71.244?

    G=137006?

    D=87685?

    =l63446?

    Affi554m

    Effi71um

    B=21.9pm

    Fffi87.3um

    Cffi382pm

    G=104pm

    |D=.6um

    H=120um

    ANSYS0

    NODALSOL1]TION ?ME=9480

    TILMP(AVG)

    RSYS=0

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