3.1.8在Abaqus-tandard中使用自适应网格的胎面磨损模拟

1、3.1.8TreadwearsimulationusingadaptivemeshinginAbaqus/Standard3.1.8在Abaqus/Standard中使用自适应网格的胎面磨损模拟Product:Abaqus/StandardThisexampleillustratestheuseofadaptivemeshinginAbaqus/Standardaspartofatechniquetomodeltreadwearinasteadyrollingtire.Theanalysisfollowscloselythetechniquesusedin“Steady-staterollin

2、ganalysisofatire,”Section3.1.2,toestablishfirstthefootprintandthenthestateofthesteadyrollingtire.Thesestepsarethenfollowedbyasteady-statetransportstepinwhichawearrateiscalculatedandextrapolatedoverthedurationofthestep,providinganapproximateconsiderationofthetransientprocessofwearinthissteady-statepr

3、ocedure.本示例说明了在Abaqus/Standard中使用自适应网格划分作为用于对稳定滚动轮胎中的胎面磨损进行建模的技术的一部分。该分析紧接着使用在“轮胎的稳态滚动分析”第3.1.2节中使用的技术，以首先建立轮胎的足迹，然后建立稳定滚动轮胎的状态。然后，这些步骤之后是稳态传输步骤，其中在该步骤的持续时间内计算和外推磨损率，提供对该稳态过程中的磨损的瞬态过程的近似考虑。Problemdescriptionandmodeldefinition问题描述和模型定义Withsomeexceptions,notedhere,thedescriptionofthetireandfiniteeleme

4、ntmodelisthesameasthatgivenin“Importofasteady-staterollingtire,”Section3.1.6.Sincethefocusofthisanalysisistreadwear,thetreadismodeledinmoredetail.Inaddition,alinearelasticmaterialmodelisusedinthetreadregiontoavoiddifficultiesadvectingthehyperelasticmaterialstateduringtheadaptivemeshingprocedure.除了一些

5、例外，在此指出，轮胎和有限元模型的描述与“进口稳态滚动轮胎”第3.1.6节中给出的相同。由于本分析的焦点是胎面磨损，所以胎面被更详细地建模。此外，在胎面区域中使用线性弹性材料模型以避免在自适应啮合过程期间平流超弹性材料状态的困难。Theaxisymmetrichalf-modelofthe175SR14tireisshowninFigure3.1.81.TherubbermatrixismodeledwithCGAX4andCGAX3elements.ThereinforcementismodeledwithSFMGAX1elementsthatcarryrebarlayers.Anembed

6、dedelementconstraintisusedtoembedthereinforcementlayersintherubbermatrix.Thetreadismodeledwithanelasticmaterialofelasticmodulus6MPaandPoissonsratio0.49.Therestofthetireismodeledwiththehyperelasticmaterialmodel.ThepolynomialstrainenergypotentialisusedwithcoefficientsC10=106,C01=O.O,andD1=2x10-8.There

7、barlayersusedtomodelthecarcassfibersareorientedat0totheradialdirectionandhaveanelasticmodulusof9.87GPa.Themodulusincompressionissetto1/100thofthemodulusintension.TheMarlowhyperelasticmodelisusedtospecifythenominalstress-nominalstraindataforsuchamaterialdefinition.Theelasticmodulusintensionofthemater

8、ialofthebeltfibersis172.2GPa.Themodulusincompressionissetto1/100thofthemodulusintension.Thefibersinthebeltsareorientedat+20and-20withrespecttothehoop(circumferential)direction.175SR14轮胎的轴对称半模型如图3.1.8-1所示。橡胶基体用CGAX4和CGAX3元素建模。加强件用携带钢筋层的SFMGAX1元件建模。嵌入元件约束用于将加强层嵌入橡胶基质中。胎面用弹性模量6MPa和泊松比0.49的弹性材料建模。轮胎的其余部

9、分用超弹性材料模型建模。多项式应变能量势用于系数C10=106,C01=0.0和D1=2X10-8。用于模制胎体纤维的钢筋层取向为相对于径向方向为0，并且具有9.87GPa的弹性模量。压缩模量设定为拉伸模量的1/100。Marlow超弹性模型用于指定这种材料定义的标称应力-名义应变数据。带状纤维的材料的弹性拉伸模量为172.2GPa。压缩模量设定为拉伸模量的1/100。带中的纤维相对于环向(圆周)方向定向在+20和-20。Thethree-dimensionalmodeliscreatedbyfirstrevolvingtheaxisymmetrichalf-model,usingsymmet

10、ricmodelgeneration,by360togeneratethepartialthree-dimensionalmodelshowninFigure3.1.8-2.Afocusedmeshisappliedatthefootprintregion.Thepartialthree-dimensionalmodelisthenreflectedaboutalinetogeneratethefullthree-dimensionalmodel.Theresultsarethentransferredfromtheendofthefootprintsimulationforthepartia

11、lthree-dimensionalmodel(seeFigure3.1.8-2).通过首先使用对称模型生成来旋转轴对称半模型360以产生如图3.1.8-2所示的部分三维模型来创建三维模型。在足迹区域应用聚焦网格。然后，部分三维模型关于线反射以生成完整三维模型。然后将结果从部分三维模型的印迹模拟结束转移（参见图3.1.8-2）。Adaptivemeshinglimitationsintirewearcalculations轮胎磨损计算中的自适应啮合限制Theuseofadaptivemeshingnecessarilyplacesthefollowingrestrictionsonthetir

12、emodelusedforthisexample: Cylindricalelementsarecurrentlynotsupportedwithadaptivemeshingandarenotusedinthismodel. Adaptivemeshinggenerallyperformspoorlywithhyperelasticmaterialmodels,duetotheinaccurateadvectionofdeformationgradientstatevariables.Thetread,therefore,ismodeledwithanelasticmaterialdefin

13、ition. Embeddedelementsincludingrebarlayerscannotbeusedwithintheadaptivemeshdomain. Adaptivemeshsmoothingonfreesurfacesoccursindirectionsdeterminedbyfeaturesoftheelementgeometry,whichmaynotalwaysbeconsistentwithoreasilyenabledescriptionofweardirections.Asaresult,asdiscussedbelow,youwillgenerallyhave

14、todoadditionalworktoexplicitlydescribethedirectionofwear.使用自适应网格划分必须对用于该示例的轮胎模型施加以下限制： 圆柱形元素当前不支持自适应网格划分，不在此模型中使用。由于变形梯度状态变量的不准确平流，自适应网格通常对超弹性材料模型表现不佳。因此，胎面用弹性材料定义建模。包括钢筋层的嵌入元件不能在自适应网格域内使用。自由表面上的自适应网格平滑发生在由元素几何形状的特征所确定的方向上，其可能不总是与磨损方向一致或者容易地描述磨损方向。因此，如下所述，您通常需要做额外的工作来明确描述磨损的方向。Loading载荷Theanalysisis

15、conductedinfivestages,beginningwithanaxisymmetricmodelandendingwithafullthree-dimensionalmodelcreatedusingsymmetricmodelgeneration.Thefirstfourstepsfollowcloselythoseusedin“Steady-staterollinganalysisofatire,”Section3.1.2.该分析以五个阶段进行，从轴对称模型开始，并以使用对称模型生成创建的完整三维模型结束。前四个步骤紧跟在“轮胎的稳态滚动分析”中使用的那些，第3.1.2节。1.

16、 Axisymmetricinflation:Aninflationpressureof200kPaisappliedtotheinteriorofthetire,whilesymmetryconditionsareimposedatthemidplane轴对称充气：对轮胎内部施加200kPa的充气压力，而在中平面上施加对称条件。2. Three-dimensionalfootprintanalysisofthepartialmodel:Theaxisymmetrichalf-modelisrevolvedaroundtheaxleaxis部分模型的三维足迹分析：轴对称半模型围绕车轴轴旋转。3

17、. Three-dimensionalfootprintanalysisofthewholemodel:Thepartialthree-dimensionalmodelisreflectedaboutalinetogeneratethefullthree-dimensionalmodel整个模型的三维足迹分析：部分三维模型反映一条线以生成完整的三维模型。4. Steady-statetransport:Thegeneratedfullmodelisthensubjectedtoasteady-statetransportanalysisat30km/h.Anangularvelocityof2

18、5rad/sisspecifiedforthetire.Theseconditionscorrespondtoastateofbraking.Inertiaeffectsandviscoelasticityaretakenintoaccountduringthisstep稳态运输：然后将所产生的全模型以30km/h进行稳态运输分析。为轮胎规定了25rad/s的角速度。这些条件对应于制动的状态。在该步骤期间考虑惯性效应和粘弹性。5. Treadwearsimulation:Thetreadwearsimulationisconductedinthefinalstep,inwhichthevelo

19、cityofthetireisheldconstantandtheweariscomputedfromthefrictionalenergydissipatedandappliedaroundtheperipheryofthetire.Inertiaeffectsandviscoelasticityaretakenintoaccountduringthissimulationaswell.Thisstepisrunforadurationof3.6x106s,simulating30,000kilometersoftravelofthetireat30km/h.胎面磨损模拟：胎面磨损模拟在最终

20、步骤中进行，其中轮胎的速度保持恒定，并且由在轮胎的周边周围消散和施加的摩擦能量计算磨损。在该模拟期间也考虑惯性效应和粘弹性。该步骤运行持续时间为3.6X106秒，模拟轮胎以30km/h行驶30,000千米的行程。Thefinalstepusesawearmodel,whichpredictsawear,orsurfaceablation,ratebasedonthesteadyrollingofthetire.Weareinterestedinpredictingtireconfigurationchangesasaresultofthiswearrate;hence,wemustintrod

21、ucesomemodelingassumptionsthatenablemodelingofatransienteffectinasteady-stateprocedure.最后一步使用磨损模型，其基于轮胎的稳定滚动预测磨损或表面消融速率。我们有兴趣预测由于这种磨损率导致的轮胎配置变化;因此，我们必须引入一些建模假设，使稳态过程中的瞬态效应建模。Thebasicassumptionmadeisthatthesteady-statetransportsteptimecanbeinterpretedasareal-timedurationofrollingatthecurrentangularve

22、locity.Weconsiderthattheconfigurationchangesduetowearhaveonlyaminoreffectontherollingtiresolutionatanytime;hence,theresultsremainvalidinasteady-statesenseateachtimethroughthestep.Withthisassumptionwecansimultaneouslyconsidereffectsattwodisparatetimescales:theshortertirerevolutiontimescaleandthelonge

23、rtirelifetimescale.所做的基本假设是稳态传输步长时间可以解释为在当前角速度下的滚动的实时持续时间。我们认为由于磨损引起的构型变化在任何时候对滚动轮胎溶液只具有很小的影响;因此，在每次通过该步骤时，结果在稳态意义上保持有效。使用这个假设，我们可以同时考虑两个不同时间尺度的效应：较短的轮胎转速时间尺度和较长的轮胎寿命时间尺度。Wearmodel磨损模型Toillustratethewearprocess,asimplewearmodelisemployedbasedontheassumptionthatthewearrateisalinearfunctionofthelocalc

24、ontactpressureandsliprate.Althoughwecancalculatethesequantitieslocally,duetotheEulerianformulationusedinsteady-statetransporttheymustbeappliedovertreadstreamlinestomodelthewearoftheentiretireperimeter.为了说明磨损过程，基于磨损率是局部接触压力和滑移率的线性函数的假设，采用简单的磨损模型。虽然我们可以本地计算这些量，由于在稳态运输中使用的欧拉公式，它们必须在胎面流线上应用以模拟整个轮胎周长的磨损。

25、Wearratecalculation磨损率计算ThewearconstitutivemodelemployedforthissimulationisaformoftheArchardmodel,whereis2訂炸thevolumetricmaterialloss,orwear,rate;kisanondimensionalwearcoefficient;Histhematerialhardness;Pistheinterfacenormalpressure;Aistheinterfacearea;andistheinterfacesliprate.Herewecanseethatthete

26、rms厂-describeafrictionalenergydissipationrate.Fortirerubberweassumeawearcoefficientk=1.11x10-4andamaterialhardnessH=2GPa.用于该模拟的磨损本构模型是Archard模型的形式，其中是体积材料损失或磨损，速率;k是无量纲磨损系数；H是材料硬度；P为界面法向压力;A是接口面积;并且是界面滑移率。这里我们可以看到这些术语描述了摩擦能量耗散率。对于轮胎橡胶，我们假设磨损系数k=1.11X10-4,材料硬度H=2GPa。Thegoalofthefollowingdevelopmentis

27、anexpressionforamaterialrecession,orablation,rate,whichcanbeappliedtoanodetosimulatewear.First,consideraribbonaroundthetire,wherethecenterlineofthisribbonisdefinedbyasequenceofnodescomprisingoneofthesurfacestreamlinesonthetirestread.Thiscenterlineisthenboundedoneithersidebythetributaryregionofthesur

28、faceassociatedwitheachnode.Thecombinationofallsuch“streamribbons”thencomprisesthetotalsurfaceofthetireinvolvedintire-to-roadcontactinteractions.Weexpecttheweartooccuruniformlyoverthisstreamribbon;hence,weexpressawearratefortheentireribbon,以下开发的目标是材料衰退或消融速率的表达，其可以应用于节点以模拟磨损。首先，考虑轮胎周围的带，其中该带的中心线由包括轮胎胎

29、面上的表面流线之一的节点序列限定。然后，该中心线在任一侧被与每个节点相关联的表面的支路区域限界。所有这种“流束带”的组合然后包括涉及轮胎-道路接触相互作用的轮胎的总表面。我们期望在这条流带上均匀地发生磨损;因此，我们表示整个色带的磨损率，=备P（x我）Y仗卫ell,H/ribbonwheretisthetimeand.*isthecurrentconfigurationposition.SinceweareusingtheEuleriansteady-statetransportprocedure,wecannowrewritethisexpressioninatime-independent

30、form,其中t是时间，是当前配置位置。由于我们使用欧拉稳态传输程序，我们现在可以以时间无关的形式重写这个表达式，/p何勺何T（s）ds,wheresisapositionalongthestreamlineand:1isthewidthofthestreamribbonatpositions.Wecanalsoexpressyasafunctionofthelocalmaterialrecessionrate,其中s是沿流线的位置，并且是位于位置s处的流束带的宽度。我们还可以表示为当地物质衰退率的函数，Equatingthesetwoexpressionsinadiscreteformres

31、ultsinthefollowingexpression,summedoverastreamline:将这两个表达式以离散形式相等，得到以下表达式，在流线上求和：whereisanodalablationvelocityand；isthenodalcontactarea.Thisequationimpliesthatisgenerallynotuniformalongthestreamline,whichfollowsasaconsequenceofthestreamribbonwidthvaryingasitentersandleavesthetirefootprint.Since,howe

32、ver,weareablatingnodesawayfromthefootprintregionsolelytomaintainareasonablegeneralshapeoftheworntireconfiguration,wewillaccepttheassumptionofauniformnodalablationvelocity.Thisenablesthefollowingexpressionfor/.:其中是节点消融速度并且是节点接触面积。该方程意味着沿着流线通常不是均匀的，这是流线带宽度随着其进入和离开轮胎印迹而变化的结果。然而，由于我们仅仅为了维持磨损轮胎构型的合理大致形状而

33、将足迹区域烧蚀掉节点，所以我们将接受均匀节点消融速度的假设。这启用以下表达式：Usingagaintheassumptionthatthevariationinstreamribbonwidthcanbeneglected,:,andrecognizingthatthenodalcontactareaenablesasimplerexpressionthatdoesnotrequiretheuseofcontactareas:再次使用流带宽度的变化可以忽略的假设，并且认识到节点接触区域能够实现不需要使用接触区域的更简单的表达：h=吃二iR2EWearprocessimplementation磨

34、损过程实现Withthisexpressionforwearrateintheformofasurfaceablationvelocity,thewearcannowbeappliedinasteady-statetransportanalysis.UsersubroutineUMESHMOTIONisusedtospecifytheablationvelocityvectorsatthenodesthatareontheexteriorsurfaceofthetire.UMESHMOTIONdefinesadaptivemeshconstraintvelocitiesandisusedinc

35、onjunctionwithadaptivemeshing,ameshsmoothingtechniqueappliedattheendofeachconvergedincrement.Theablationvelocitiesspecifiedthroughtheusersubroutineareappliedatthetreadsurfacenodes,andadaptivemeshsmoothingadjustsnodesintheinteriortreadregiontomaintainawell-shapedmesh对于以表面消融速度的形式的磨损速率的表达式，磨损现在可以在稳态传输分

36、析中应用。用户子程序UMESHMOTION用于指定在轮胎外表面上的节点处的消融速度矢量。UMESHMOTION定义自适应网格约束速度，并与自适应网格划分结合使用，自适应网格划分是在每个收敛增量结束时应用的网格平滑技术。通过用户子程序指定的消融速度被应用在胎面表面节点处，并且自适应网格平滑调整内部胎面区域中的节点以保持良好形状的网格。Toaccumulatewearquantitiesaroundeachtreadstreamline,thenodalnumberingschemealongthestreamlinesmustberecordedintheusersubroutine.Thisr

37、ecordismadeinasetofcommonblockvariables.ThecommonblockrecordsnodesthatbelongtonodesetNADAPT(Figure3.1.8-4)andthatlieattherefereneecross-section(0)ofthefullmodel.Thecommonblockvariablesalsoincludethenodenumberingoffsetsspecifiedforsymmetricmodelgeneration,which,togetherwiththereferencecross-sectionde

38、finitions,completelydescribethetreadsurfacenodenumbering.Thefollowingvariablesneedtobedefinedintheexternalcommonblock:为了在每个胎面流线周围累积磨损量，沿着流线的节点编号方案必须记录在用户子程序中。该记录在一组公共块变量中进行。公共块记录属于节点集合NADAPT(图3.1.8-4)且位于完整模型的参考横截面(0)的节点。公共块变量还包括指定用于对称模型生成的节点编号偏移，其与参考横截面定义一起完全描述了胎面表面节点编号。以下变量需要在外部公共块中定义： nStreamlines

39、:Thenumberofnodesattherefereneesection(fullmodel)atwhichwearisapplied.nStreamlines:应用磨损的参考节(完整模型)处的节点数。 nGenElem:Thenumberofsectorsorelementdivisionsalongthestreamlineinthemodel.nGenElem：模型中沿流线的扇区数或元素分割数。 nRevOffset:Thenodeoffsetspecifiedaspartofthedefinitionofarevolvedsymmetricmodel.nRevOffset:作为旋转

40、对称模型定义的一部分指定的节点偏移。 nReflOffset:Thenodeoffsetspecifiedaspartofthedefinitionofareflectedsymmetricmodel.(Setthisparameterequaltozeroifthemodelisnotreflected).nReflOffse：t作为反射对称模型定义的一部分指定的节点偏移。(如果模型未反映，请将此参数设置为零。 jslnodes:Thearraythatcontainstherequirednodalinformationforallnodespotentiallyundergoingwea

41、ratthereferencesection.Thisisanarrayofsize(2,nStreamlines).Foreachstreamlinethefirstcomponentisthenodenumberofthe“rootnode”(nodeainthefollowingdiscussion),whichisthenodeonthatparticularstreamlineatthereferencesection.Thesecondcomponentisthenodethatprovidestheweardirection(nodebinthefollowingdiscussi

42、on).Thissecondcomponentisnecessaryonlyforthetreadcornernodes.Setitequaltothenumberofthenodeatthereferencesectionthatdefinestheweardirection.Fornodesthatarenotlocatedattreadcorners,setthesecondarraycomponentequaltozero.Thewearwillbeappliedoppositetothelocal3-directionforthesenodeslocatedawayfromtread

43、corners.jslnodes包含在弓I用节可能发生磨损的所有节点的所需节点信息的数组。这是一个大小为(2,nStreamlines)的数组。对于每个流线，第一分量是“根节点”(在以下讨论中的节点a)的节点编号，其是在参考节段处的特定流线上的节点。第二分量是提供磨损方向的节点(以下讨论中的节点b)。该第二分量仅对于胎面角节点是必要的。将其设置为等于定义磨损方向的参考节处的节点编号。对于不位于胎面拐角的节点，将第二个数组分量设置为零。对于远离胎面拐角的这些节点，磨损将被施加在与局部3方向相反的方向上。Thevariablesintheexpressionforwearareaccessedfr

44、omtheanalysisdatabaseusingtheutilityroutinesGETVRNandGETVRMAVGATNODE.PisaccessedfromoutputvariableCSTRESS;一fromvariableCDISP;andthearedeterminedfromstreamlinenodalcoordinates,accessedfromvariableCOORD.使用实用程序GETVRN和GETVRMAVGATNODE从分析数据库访问磨损表达式中的变量。P从输出变量CSTRESS访问;从变量CDISP;并且从流线型节点坐标确定，从变量COORD访问。Wear

45、motiondirections磨损运动方向Thewearrate，isthenappliedasthecomponentsofthemeshconstraintvectorvariableULOCAL.ThisvariableispassedintotheusersubroutinewithdefaultmeshsmoothingmotionsdefinedinalocalcoordinatesystemALOCAL,whichreflectsameasureofthesurfacenormalatthecurrentnode.The3-directionisdefinedasthedire

46、ctionoftheoutwardnormalandisbasedonanaverageofelementfacetnormalsnearthenode.Undermostcircumstancesitissufficienttodescribewearasresultinginablation,ornodalrecession,oppositetothisdirection.Atthetreadcorners,however,thisaveragenormaldoesnotprovideanaccurateweardirection.Theappropriatenormalisshownin

47、Figure3.1.8-5andiscomputedasfollows:Supposeaisacornernodeonthetread.Itispossibletoidentifyanodebthatliesalongtheedgeofthetread.Inthiscasetheweardirectionisgivenbythevectorab.Byknowingthecoordinatesofaandb,thewearcanbecalculatedintheglobalcoordinatesystemandrotatedintothelocalcoordinatesystem(ALOCAL)

48、directions.然后将磨损速率应用为网格约束向量变量ULOCAL的分量。该变量被传递到具有在局部坐标系统ALOCAL中定义的默认网格平滑运动的用户子程序，其反映当前节点处的表面法线的测量。3方向被定义为外向法线的方向，并且基于节点附近的元素面法线的平均值。在大多数情况下，足以描述磨损导致与该方向相反的消融或节点衰退。然而，在胎面角处，该平均法线不提供精确的磨损方向。适当的法线如图3.1.8-5所示，计算如下：假设a是胎面上的角节点。可以识别沿着胎面的边缘的节点b。在这种情况下，磨损方向由矢量ab给出。通过知道a和b的坐标，磨损可以在全局坐标系中计算并旋转到局部坐标系(ALOCAL)方向。

49、Resultsanddiscussion结果讨论Thetiremodelisrunforadurationof3.6x106s,or1000hours,theequivalentof30,000kilometersofoperationat30km/h.Figure3.1.8-6showstheresultingtreadprofileincludingtheeffectsofwear.Figure3.1.8-7showsthefootprintdistributionsofthecontactpressureandthecontactpressureerrorindicatorforanewtireandoneintheas-wornconfiguration.轮胎模型运行持续时间