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编号： 毕业设计(论文)外文翻译（译文）院 （系）： 机电工程学院 专 业： 机械设计制造及其自动化 学生姓名： 伍荣展 学 号： 1000110131 指导教师单位： 桂林电子科技大学 姓 名： 高成 职 称： 助理研究员 2014 年 05 月 26 日桂林电子科技大学后桥壳疲劳失效的有限元分析预测M.M. Topac, H. Gunal, N.S. Kuralay. Fatigue failure prediction of a rear axle housing prototype by using finite element analysisJ. Engineering Failure Analysis，摘 要对与在试验中，当施加循环垂直应力在后桥壳上，产生了过早的疲劳变形的现象 进行了研究。发现在这些试验中，裂缝主要出现在样品的同一区域。为了确定破坏的原因，建立了完整的后桥壳CAD模型。同时，桥壳的机械性能取决于其材料的拉伸性能。利用这些数据，运用有限元原理进行了应力及疲劳分析。确定了疲劳应变的发生位置以及不发生疲劳应变的最小循环垂直应力。将有限元分析的结果与实验的结果进行对比。设计提出了增强桥壳疲劳寿命的解决方案。关键字：后桥壳；应力集中；失效；有限元分析1 概述由于具有较高的承载能力，固体车桥通常用于重型商用车辆上1。固体车桥的结构见图1。在车辆的使用中，车桥是主要承载部件，由路面不平产生的动态应力进而产生的动态压力导致了车桥产生疲劳破坏。因此，最重要的是进行桥壳抵抗疲劳破坏的寿命预测。在大规模生产前，有必要对桥壳模型在动态垂直应力作用下进行如图2所示的装载能力及疲劳寿命的有限元分析。在这些测试中，由液压机构提供的循环垂直载荷施加在样品上，直到样品出现疲劳破坏。根据承载标 准，桥壳必须能承载N=5X105循环应力而不出现疲劳破坏。在对如图3所示不对称的桥壳模型进行垂直疲劳测试时，在应力达到极限前就有疲劳破坏出现在模型上。因此发现，不出现疲劳破坏的最小循环应力大约为3.7X105。在这些测试中， 裂纹出现在班卓过渡区E1和E2。图4所示为一早期破坏的例子。为了找出早期失效的原因，运用CATIA V5R15商业软件建立了一个详细的桥壳三维模型。利用该模型，建立有限元模型。运用ANSYS V11.0商业有限元分析软件工作平台进行应力和疲劳分析。通过拉伸测试的有限元分析获得了桥壳的材料性能，运用RecurDyn商业CAE软件进行车辆动力学模拟，获得了桥壳最大载荷。通过这些分析，找到应力集中部位。为了实现疲劳分析，引入疲劳强度修正系数建立了桥壳材料的估计S-N曲线。将分析获得的结果与垂直疲劳测试实验的结果进行比较。为了阻止早期破坏并获得增大的疲劳寿命，提出了一些解决方案。 图1 商用车后桥壳总成 图2 桥壳模型乘直疲劳测试图3 桥壳几何形状图4 测试样品底部的疲劳开裂图5 桥壳的完整CAD模型2 有限元模型2.1 CAD和有限元模型分析用全尺寸车桥CAD模型如上图5所示。桥壳本质上由两个相同的薄壁壳组成，薄壁壳的厚度为9.5mm并沿着后桥壳的中性轴焊接。在前端面，一个用螺栓固定了差动齿轮装载器的曾环被焊接在桥壳上用来增强刚度。出于密封性的考虑，将一个圆盖焊接在后端面上。这里，元素A和B为下垂壁卡钳联接。支撑C和D代表轮与地面的接触。车桥支撑联接点之间的距离与后轴轮轨之间的距离相等。运用 CATIA V5R15建立桥壳三维模型。将桥壳的完整CAD模型导入ANSYS V11.0工作平台前置处理界面，建立分析所需的有限元模型。有限元模型用于图6所示的压力及疲劳分析。为了建立有限元模型，桥壳按照SOLID187进行网格划分。S0LID187具有二次位移的三维实体单元并且适用于进行不规则网格划分。桥壳被定义为拥有10个节点，且每个节点拥有3个自由度。运用CONTA174和TARGE170元素建立桥壳各部件之间的联系。焊接表面的联接关系选择为完整的可靠联接。有限元模型由779,305个元素和1,287,354个节点组成。 图6桥壳有限元模型表1 S450N的化学特性（Wt%）表2 抗拉测试结果2. 2 桥壳材料车桥壳是由9.5mm厚的微金属合金管壁经冲压焊接制成的，该管壁的材料为热成型标准钢铁S460N （材料编号1.8901，等同于ISO标准3中E460）。该材料的化学成分是从供应商获得的，具体见表1 4。未加工的S460N的机械性能见参考文献5。然而，桥壳材料在制造过程中需经过若干道工序，包括退火至800C和750C热冲压。为了将工序对机械性能的影响引入有限元分析并确定加工后材料的精确机械性能，从后桥壳模型中抽取5个样本并进行拉伸试验。所有的试验均在室温下进行。从后桥壳模型中抽取的5个样本均在热影响区之外。表2给出的结果均为5个样本的最低值，并将这些结果引入有限元模型。将材料定义为显性各向同向性材料。2. 3 负荷条件有限元分析中的负荷条件是根据垂直疲劳测试中出现早期失效处的支撑区域确定的。测试是在如图7所示的可提供80吨载荷的装置上进行的。该装置是由两个具有承载单元的电动液压执行机构和伺服阀组成的，伺服阀安装在连接A，B的卡钳处。TS表示两个卡钳间的距离，T因表示支撑C，D间的距离即真实后桥壳的轮距。车桥的模型是根据如图8所示的由两个空气弹簧支撑的真实桥壳设计的。因 为载荷施加在牵引臂的偏心轮上，所以弹簧的弹力也产生了弯曲应力，该应力在桥壳上产生了一个额外的弯曲AM。测试样品中的额外弯曲影响由图7所示的液压驱动装置的偏距c提供。每个弹簧的最大设计载荷为F = 2850kg。应力垂直的施加在弹簧底座的点。这导致了在卡钳A, B处产生了静态反应力P=4550kg。因为路面不平使车身的集中质量产生的垂直加速度导致在每个卡钳处的最大动态载荷大约为P的两倍。由ReoirDyn商业CAE软件进行的计算机路面模拟所得的载 荷变化范围为182-9I00kg。垂直疲劳测试所得的载荷特性曲线如图9所示。有限元分析也考虑到了最大动载荷9100kg沿额外弯曲变形M所产生的影响。如图10所示的车桥垂直应力模型是根据参考文献6设计的。图7垂直疲劳测试原理图图8 纵臂的偏心载荷 3 有限元分析及结果有限元分析用于预测应力集中及疲劳寿命较低区域的准确位置。P和M施加在图10所示的卡钳连接处。运用装配1.86GHz因特尔至强四核处理器的HPx因8400工作站借助ANSYS V11.0工作平台进行压力分析。图11所示为有限元分析所得的等应力分布图。分析结果显示应力集中区域F1、F2分布在桥壳承载区域底部的过渡区。从图12中可以看出疲劳失效区域与临界区域在同一位置。计算得出的最大分布应力为 max=388.7Mpa；是材料屈服应力点的78. 1%。这说明桥壳在承受最大静载荷时符合安全条件。图9疲劳测试中的执行机构负荷特性曲线图10桥壳的外加负荷及弯矩图图11 下壳体上的工作应力分布图12测试与分析结果比较4.疲劳寿命预测由于在使用中后桥壳承受动应力，也需要进行疲劳分析。压力寿命的疲劳极限估计值se为se=0.504Sut （1）钢材的强度极限小于1400MPa7，8。这意味着疲劳强度的周期为106或更多。为了预测在105 - 106周期范围内的疲劳寿命，使用参考文献9中使用简单抗拉测试获得所需数据的方法作出桥壳材料的S-N曲线。se代表理想实验样品的压力疲劳寿命。为了预测机械零件的真实疲劳强度se， 需要乘上代表各种设计，制造和环境对疲劳强度影响的修正因子10。Se为 Se=kakbkckdkese （2）式中ka为根据下式得出的表面抛亮度得到的表面因数ka=aSutb （3）由于桥壳表面的粗糙度与经过热冲压工艺的热轧钢板相似，所以推荐的标准为 a=57.7和b=-0.7187.经计算得出ka=0. 564, Sut=629.9MPa。另外，喷丸工艺作为一种常见的爪于减少零件材料表面残留应力的方法，也用于增加热冲压后的桥壳表面的疲劳寿命。文献9中给出这种方法可增加70%的疲劳寿命。因此，在有限元分析中ka的取值为0.959。因为桥壳为非圆形截面，根据横截面深度h远大于50mm假定尺寸因数kb为0.75。由于环境温度T=0-250C，所以弯曲和环境因数 kd=1，进而确定负荷系数kc=1。通过静态有限元分析，可得出应力集中区分布在班卓及横臂过渡区域。所以，除了上述修正因数外，疲劳强度修正因数ke必须引入分析，ke可通过与应力集中系数kf有关的应力集中系数kt得到。因此ke的计算式为ke=1/kf （4）出于安全考虑，kf假设与kt相等7。由于桥壳的大小及形状的复杂性，kt无法从标准文献中查出。另一方面，kt被定义为Kt=peak/nominal （ 5 ）式中peak为凹口处得峰值应力，nominal不出现应力集中时的常应力p9, 12，peak的使用数值可从max=388. 7MPa时的静有限元分析中得出。为了计算nominal将后桥壳简化为一简支梁，其沿纵轴Y的危险横截面X1X1都为矩形并适用于纯弯曲理论6。 nominal按图10所给出的模型的计算公式为nominal=M/Z （6）式中M为弯曲力矩，Z为危险横截面的断面系数。M的取值为41.9xl06Nmm。断面系数Z取值为127507mm3。因此计算得出nominal为329MPa。发现ktkf=1.181，ke=0.846。运用ANSYS V11.0工作平台定义S-N曲线中标绘的修正因数。通过压力寿命决定桥壳材料的疲劳寿命。全部的疲劳分析都是以无限寿命进行的（N=106）。用有限元分析得到的压力分布图进行疲劳寿命计算。由于载荷具有正弦波动特性（平均应力m0），修正方法如下9aSe+mut=1n （7）式中，n表示安全系数。振幅a为a=maxmin2 （8）（8）平均应力am可表示为m=max+min2 （9）式中，通过有限元分析得到max为最大值9100kg，min匹配的最小值为182kg。壳体底部的分配系数n如图13所示。根据疲劳分析结果，估计在周期为ca3.6X105时，桥壳表面F1区域会发生裂纹开裂，该数值低于预测值为5x105周期的最小疲劳寿命。此处n的最小值为0. 93。在桥壳的内表面，最大应力集中发生处F2区域的n值最小，计算结果为0.767。这意味着，在垂直应力测试中区域F1和F2会在载荷周期5X105 前发生疲劳幵裂。5.结构及讨论有限元分析显示在垂直疲劳测试中出现疲劳破坏的区域存在应力集中，该应力集中会导致在最小预测周期5X105前出现过早破坏。此结果与垂直疲劳试验中的结构相同。增大桥壳的疲劳寿命需减小应力集中。减小应力集中，增大疲劳寿命的最简单的方法是金属壁的厚度。然而，在F1F2区域外桥壳符合无限寿命周期条件。增加金属笔厚度导致了不必要的重量增加。例如，增加厚度0.5mm，使得桥壳材料在临界区域的疲劳极限提高到了超过5. 85X105周期，此极限超过了设计的疲劳极限。另一方面，这也意味着提高了汽车非簧载质量5%的重量。所以这并不是实用的解决方法。作为另一种解决方法，可从新设计过渡区域的几何形状。平整的过渡区几何形状可提高疲劳痔命而不增加重量。此外，加固环的形状也对应力集中产生影响。在所研究的该桥壳设计中，加固环的厚度为20mm。为了预测加固环的影响，在没有加固环的情况下又进行了一次有限元分析。在临界区域F2处的最大分布应力为428MPa。这意味着，实用加固环大约减少了10%的应力集中。通过增加此部分的厚度，可能会增加硬度。在此设计中，由于动力系统外形的限制，增加的厚度为5mm。根据此加固环的外形变化 进行静态疲劳分析。然而，分析显示疲劳强度的增加均为其自身的，因此桥壳的疲劳寿命不会增加到超过设计最小载荷周期5X105倍的程度。因此，増加加固环的厚度可与从新设计过渡区几何形状同时使用。 图13下壳体安全系数分布6.总结运用有限元分析方法对卡车后桥壳模型的早期疲劳失效进行分析。在分析中，通过模拟垂直疲劳试验过程，预测应力集中区在班卓过渡区域。发生疲劳开裂的区域与分析所得结果相吻合。通过有限元分析可预测破坏发生的位置。通过稳态和循环张应力确定临界区域。裂缝导致破坏发生在桥壳的应力集中区域。尽管桥壳模型负荷最大垂直载荷静态忍耐条件，分析显示，如果为循环载荷，疲劳破坏可能在预测的最小周期5X105前发生。有限元分析同样可用于估计疲劳失效开始前的周期数。为了解决该问题，増加金属管壁的厚度因为会增加桥壳的重量，所以并不是实用的方法。重新设计班卓过渡区和增加加固环的厚度，这种符合最小设计准则的途径，也许是增强疲劳寿命的好方法。 感谢这篇论文在土耳其伊兹密尔市的Ege Endustri ve Ticaret A.S.的帮助下完成。作者同时也对来自Dokuz Eylul大学的E. Cmar Yeni博士和Pamukkale大学的Cemal Meran博士的批评与建议表示感谢。译文原文出处：M.M. Topac, H. Gunal, N.S. Kuralay. Fatigue failure prediction of a rear axle housing prototype by using finite element analysisJ. Engineering Failure Analysis，(16)2009,:1474-1482.第10页 共10页桂林电子科技大学编号： 毕业设计(论文)外文翻译（译文）院 （系）： 机电工程学院 专 业： 机械设计制造及其自动化 学生姓名： 伍荣展 学 号： 1000110131 指导教师单位： 桂林电子科技大学 姓 名： 高成 职 称： 助理研究员 2014 年 05 月 26 日2利用重型载货汽车的有限元应力分析的初步数据预测其疲劳寿命Roslan Abd Rahman, Mohd Nasir Tamin, Ojo Kurdi马来西亚工程大学机械工程系81310 UTM, Skudai,Johor Bahru摘 要本文对一重型货车底盘做了应力分析。应力分析能够确定零件的最大受力点，是分析零部件疲劳研究和寿命预测的重要手段。前人已有用商用有限元软件ABAQUS软件对底盘模型进行分析的。本次研究的底盘长12.35米，宽2.45米，材料是ASTM低合金钢710（3级），屈服极限552MPa，抗拉强度620MPa。分析结果显示，最大应力点出现在底盘与螺栓连接的空缺处，最大应力为386.9MPa，底盘的疲劳破坏将会从最大应力点开始向车架各部位蔓延。关键字：应力分析；疲劳寿命预测；货车底盘1 简介在马来西亚，很多货车的车架寿命都有20多年，20多年架就会有使用安全的问题。因此，为了确保底盘在工作期间的安全性能，就有必要对底盘作疲劳研究和寿命预测。利用有限元法作应力分析能够确定受最大应力的关键点，这个关键点是导致底盘疲劳损伤的因素之一。应力的大小能够预测底盘的寿命，所以可以根据应力分析的结果精确地预测底盘的寿命，应力分析越精确，底盘寿命预测的越合理。本文是用商用有限元软件ABAQUS软件完成底盘应力分析的。汽车工业（汽车总成及各部件）在马来西亚的工业中占据非常重要的地位。随着东盟自由贸易区的贸易自由化发展，当地的汽车制造商和供应商应该顺应汽车及其零部件的世界级标准要求，比如噪声和振动就有相应的标准。马来西亚的汽车工业主要是依赖于国外的技术，而底盘是实现汽车轻量化的关键结构，所以底盘大多从国外进口。为了改变这种趋势，有必要建立发展马来西亚自己的底盘设计产业，这是对底盘进行研究的目标。底盘车架是汽车的装配基体和承载基体，支承着汽车的各个总成及零部件，如车轴，悬架系统，传动系，驾驶室及拖挂部件等，并将它们整合成一部完整的汽车。货车的底盘经常受到静载荷，动载荷以及周期性载荷。静载荷主要是车厢质量、货物及乘客，底盘的动载荷是由于货车的运动产生的，而发动机的振动和路面的不平整将会产生周期载荷。现有的底盘设计通常是基于静载荷的分析，设计的重点是底盘的强度结构设计，以支承施加在底盘上的载荷。然而货车底盘的受力复杂，包括静载、动载和疲劳破坏方面。据估计，85%到90%的货车底盘的结构破坏是由疲劳破坏引起的1。因此，货车底盘的动态和疲劳分析是很重要的。为了获得底盘的动态和疲劳工况的情况，就要确定各个零部件，如发动机、悬架、变速器等的支承点，并对其优化。许多研究人员都曾研究过货车底盘。Karaoglu and Kuralay曾用铆接的连接方式对底盘所有限元应力分析2。研究数据表明，局部增大纵梁的厚度可以减小边梁的应力，如果不能增大变量的厚度，增加接触面的面积也可以减小应力。Fermer et al用高级疲劳分析软件MSC/Fatigue软件对沃尔沃双燃料车S10做了疲劳寿命分析3，Conle and Chu对复杂的底盘结构的疲劳分析和局部的应力应变分布做了研究4，Ferreira et al研究了汽车零部件耐久性的结构优化问题5，Fermr and Svensson研究了工业上焊接的汽车结构的铁基寿命预测问题6。Filho et.al.考虑到小规模生产的经济可行性，结合适当的动载荷和结构特性对一越野车底盘做了设计分析和优化设计7。研究表明，增大底盘的抗扭刚度，维持车架重心位置不变可以用来优化越野车结构，这样，底盘车架结构的总质量得到优化，结构也跟简单，生产成本也少了。Cosme et al利用计算机辅助设计和工程软件代码Pro/E,ADAMS and ANSYS模拟了改变设计对货车车架的影响8。Chiewanichakorn et al用试验得到的有限元模型，将已破坏的混凝土桥面替换为FRP钢板，分析了桁架桥9。结果数据表明，修复过后，桥的疲劳寿命是修复前钢筋混凝土桥面的两倍，在货车交通研究数据的基础上，桥面载荷及ERP钢板系统的应力范围在无限疲劳寿命范围中，即在其使用期间不会有桁架和地板系统的疲劳破坏现象。Ye 和Moan已经用有限元分析法分析了铝制框加强筋的车架静态和疲劳特性10，改变车架切割形状和相应的焊接过程，同时得到足够的疲劳强度，这样就能够减小制造成本，并且解决连接问题。利用铁的疲劳可以确定可能产生疲劳裂纹的关键点，并能预测门铰链系统的寿命11。本次研究中，对重型载货汽车施加静载荷，对其做应力分析，确定产生疲劳裂纹的危险点位置，以此作为该车架的疲劳寿命预测的备用数据。2 货车车架的有限元分析2.1 有限元法基本概念有限元分析法是一种计算机辅助技术，用来获得工程中边值问题的近似解。简言之，边值问题是一个数学问题，其中一个或是多个应变量必须要满足一个自变量范围已知的微分方程，还要满足特定的边界条件12。有限元法的通俗解释是将一个结构离散成无数个单元（结构碎片），用简单的方法描述每个单元，然后用节点加各个单元重新连接起来，就像这些点是针脚或者点滴粘贴在一起形成各个单元（如图1所示）。这样就会产生一系列的同步代数方程。在分析应力时，这些方程式是节点的平衡方程，这样就会有数百甚至数千个这种方程，那么电脑的硬件要求就较高13。图1 二维轮齿的网格，所有的节点和单元都在纸平面内2.2 有限元法一般步骤有限元法可以分析一些物理问题，包括结构分析、流体分析、热传递和其他问题，分析这些问题有些通用的步骤，这些步骤通常包括一些商用有限元分析软件。主要有三大步骤，即前处理模块、求解模块和后处理模块。前处理模块要建立模型，这是必要的，如果发生了错误，就不会有完美的计算机有限元求解结果。这一步骤包括：定义问题的几何域，所需的单元类型，单元的材料属性，单元的几何性质（长度、面积等等），单元的连通性（网格划分），物理约束（边界条件）和加载。接下来就是求解，在这一步骤中，以矩阵方式列出的控制代数方程和未知的主变量是合成的，用计算结果回带求得其他派生变量，如反应力，单元应力和热流量。这一步骤要进行矩阵计算，数值积分，方程求解，这些都是由软件自动解决的。最后是后处理模块，对结果进行分析和评估。在这一部中，可以完成的操作包括按单元应力的大小分类，检查平衡，计算安全因素，绘制结构的变形形状，以动画的形式显示模型，以不同的颜色显示温度的分布。大型软件都会有一个前处理模块和后处理模块来完成分析，这两个模块都可以和其他的软件相同。前期处理和后期处理根据不同的项目会有各自的程序。2.3 货车的定义和分类货车是一种重型机动车辆，是用来承载货物的。货车的另一种定义是用来牵引的激动车辆。对货车的其他定义将根据货车的类型变化，例如自动倾卸卡车的货物可以作清空处理，车前端的平台末端就可以有空气作用被升起，此时载荷通过重力施加。房车或拖车有两种分类，一种是根据重量分类，由美国政府定的从1级到8级，如表1和表2所示；第二种是更为广泛的分类：轻型载重汽车；中型载重汽车和重型载重汽车。表1 货车分类及等级重量等级最小总质量额定值/磅最大总质量额定值/磅VIUS分类一般分类1级6000轻型轻型2级600110000轻型轻型3级1000114000中型轻型4级1400116000中型中型5级1600119500中型中型6级1950126000轻型-重型中型7级2600133000重型-重型重型8级33001重型-重型重型表2 制造商的货车分类分类等级总质量额定值参考车型轻型10-27kN（0-6000磅）卡车，救护车，运钞车227-45 kN（6001-10000磅）345-62 kN（10001-14000磅）中型462-71 kN（14001-16000磅）市运货车，饮料运货车，拖吊车，校车571-87 kN（16001-19500磅）687-116 kN（19501-26000磅）7116-147 kN（26001-33000磅）重型8147 kN及以上（33000磅及以上）卡车拖拉机，水泥搅拌车，自动倾卸卡车，消防车，城市公交客车注：总质量额定值：制造商指定的质量作为一辆车的最大装载质量（货车加货物）。2.4 货车车架模型该模型如图2所示。模型长12.35m，宽2,45m，材料为ASTM低合金钢710（3级），屈服极限552MPa，抗拉强度620MPa。车架的其他属性见表3。表3 货车车架的材料属性弹性模量E(Pa)密度（kg/m3）泊松比屈服极限（MPa）抗拉强度（MPa）20710978000.3550620图2 货车底盘模型2.5 加载货车模型承受来自车身和货物的静载荷，该车的最大装载质量为36000kg，假设由最大载质量求得一个总的压力，将这个压力平均的分配到货物和底盘上表面的接触面上，具体的加载如图3所示，底盘上表面的压强为67564.6N/m2 。图3 静载荷（压强为67564.6N/m2）2.6边界条件本模型有3个边界条件。第一个施加在底盘前端，第二和第三个边界条件在底盘的后端，如图4所示。第一个边界条件是固定的（约束有轴的平移自由度，释放所有轴的旋转自由度），底盘与驾驶室的接触条件如图5（a）所示。车架与车轴间由弹簧连接，将货物和底盘的重量传递到车轴上，所以第二个边界条件施加在底盘与弹簧上端连接的地方。第二个边界条件如图5所示，平移自由度只约束在轴2上，所有轴的旋转自由度都释放。第三个边界条件施加在底盘孔的内表面和螺栓的外表面的接触面处，在ABAQUS软件中，这种接触是相互作用的，本文中的相互作用是面与面之间的摩擦作用。此时，螺栓所在的轴的平移自由度和旋转自由度都为零，称为固定约束。假定螺栓都是刚性元件，故螺栓选用杨氏模量很高的材料。图4 模型的约束图5 实物的约束注：a第一个边界条件，b、c第二个边界条件，d第三个边界条件3 分析结果及讨论在等效应力云图中，最大应力点在底盘开孔的地方，即与螺栓接触的地方，如图6所示，最大应力为386.9MPa，最大应力点在86104单元和16045节点上。底盘开孔处的内表面与非常坚硬的螺栓接触。第三个边界条件也是固定约束，因此会产生一个很大的应力。基于静态安全系数理论，取安全系数为1.43，由安全系数公式得：安全系数=极限应力/许用应力 （1）图6 等效应力云图及最大应力点Vidosic建议根据结构的载荷和材料选取一些安全系数，对于一些常用的材料，当载荷很容易确定时，安全系数可以取1.5到2。基于分析结果，为了得到底盘精确的安全系数值，有必要减小最大应力值，因此对底盘结构进行修改以提高安全系数，尤其是在临界点区。底盘的位移和最大位移点如图7所示，最大位移为4.995mm，位于底盘中部，最大的偏转在第一个边界条件和第二个边界条件的中部。为了验证分析结果，最大应力发生在第一个边界条件和第二个边界条件之间，这一部分可以近似的简化为一维的简支梁结构，在其中点施加集中力载荷，用施加在中点的集中力代替均匀分布在梁上的压力，这一力的大小等于压强的大小乘以受到压力的所有面的面积，求得结果与分析结果近似。计算求得的结果表明，这个简支梁的应变点在梁的中部，大小为： (2)图7 应变分布云图及最大应变点位置模拟结果的最大应变值为4.99mm，比数值分析计算结果大11.2%。4 结论从数值分析可以看出，应力关键点出现在与螺栓连接的底盘孔处，最大应力值是很重要的，因为安全系数低于推荐值。由于疲劳破坏是从最大应力点开始的，可以断定，这一关键点是一些破坏的起源。因此，要注意减少这一点上的应力值，这是很重要的。分析得到的最大挠度的位置与受均布载荷的简支梁的最大变形位置一致。参考文献1 MSC. Fatigue, 2003. Encyclopedia. Los Angeles (CA, USA): MacNeal,Schwendler Corporation.2 Karaoglu, C. and Kuralay, N.S., 2000. Stress Analysis of a Truck Chassis with Riveted Joints, Elsevier Science Publishers B.V. Amsterdam, the Netherlands,Vol. 38, 1115-1130.3 Fermer, M., McInally, G. and Sandin, G., 1999. Fatigue Life Analysis of Volvo S80 Bi-Fuel using MSC/Fatigue, Worldwide MSC Automotive Conference, Germany.4 Conle, F.A. and Chu, C.C., 1997. Fatigue Analysis and the Local Stress-strain Approach in Complex Vehicular Structures, International Journal of Fatigue.5 Ferreira, W.G., Martins, F., Kameoka, S., Salloum, A.S. and Kaeya, J.T.,2003. Structural Optimization of Automotive Components Applied to Durability Problems, SAE Technical Papers. 6 Fermr, M. and Svensson, H., 2001. Industrial Experiences of FE-based Fatigue Life Predictions of Welded Automotive Structures, Fatigue & Fracture of Engineering Materials and Structures 24 (7), 2001, 489-500.7 Filho, R.R.P., Rezende, J.C.C., Leal, M. de F., Borges, J.A.F., 2003. Automotive Frame Optimization, 12th International Mobility8 Cosme, C., Ghasemi, A. and Gandevia, J., 1999. Application of Computer Aided Engineering in the Design of HeavyDuty Truck Frames, International Truck & Bus Meeting & Exposition, Detroit, Michigan, November 15 17.9 Chiewanichakorn, M., Aref, A.J., Allampalli, S., 2007. Dynamic and Fatigue Response of a Truss Bridge with Fiber Reinforced Polymer Deck, International Journal of Fatigue, 29, 14751489. 10 Ye, N. and Moan, T., 2007. Static and Fatigue Analysis of Three Types of Aluminium Box-Stiffener/Web Frame Connections, International Journal of Fatigue, 29, 14261433. 11 Bekah, S., 2004. Fatigue Life Prediction in a Door Hinge System Under Uni- Axial and Multiaxial Loading Condition, Master Thesis, Ryerson University, Toronto, Ontario, Canada.12 Hutton, David, V., 2004. Fundamental of Finite Element Analysis, Mc Graw Hill, New York.13 Cook, Robert, D., 1995. Finite Element Modeling for Stress Analysis, John Willey & Sons, Inc, New York. 14 Juvinall, R.C. and Marshek, K.M., 2006. Fundamental Machine Component Design, John Willey & Son, Inc., USA.15 Vidosic, J.P., 1957. Machine Design Project, Ronald Press, New York.第9页 共9页 Jurnal Mekanikal December 2008, No. 26, 76 - 85 76 STRESS ANALYSIS OF HEAVY DUTY TRUCK CHASSIS AS A PRELIMINARY DATA FOR ITS FATIGUE LIFE PREDICTION USING FEM Roslan Abd Rahman, Mohd Nasir Tamin, Ojo Kurdi* Faculty of Mechanical Engineering, Universiti Teknologi Malaysia, 81310 UTM, Skudai, Johor Bahru ABSTRACT This paper presents the stress analysis of heavy duty truck chassis. The stress analysis is important in fatigue study and life prediction of components to determine the critical point which has the highest stress. The analysis was done for a truck model by utilizing a commercial finite element packaged ABAQUS. The model has a length of 12.35 m and width of 2.45 m. The material of chassis is ASTM Low Alloy Steel A 710 C (Class 3) with 552 MPa of yield strength and 620 MPa of tensile strength. The result shows that the critical point of stress occurred at the opening of chassis which is in contact with the bolt. The stress magnitude of critical point is 386.9 MPa. This critical point is an initial to probable failure since fatigue failure started from the highest stress point. Keyword: Stress analysis, fatigue life prediction, truck chassis 1.0 INTRODUCTION The age of many truck chassis in Malaysia are of more than 20 years and there is always a question arising whether the chassis is still safe to use. Thus, fatigue study and life prediction on the chassis is necessary in order to verify the safety of this chassis during its operation. Stress analysis using Finite Element Method (FEM) can be used to locate the critical point which has the highest stress. This critical point is one of the factors that may cause the fatigue failure. The magnitude of the stress can be used to predict the life span of the truck chassis. The accuracy of prediction life of truck chassis is depending on the result of its stress analysis. The more accurate result of stress analysis the more valid the predicted life of object. In this study, the stress analysis is accomplished by the commercial finite element packaged ABAQUS. The automotive industry (vehicles and components) represents a strategic and important business sector in Malaysia. With the eventual trade liberalization of ASEAN Free Trade Area (AFTA), local automotive manufacturers and vendors shall require cars and components of world class standard. Noise and vibration are * Corresponding author: E-mail: ojokurdi Jurnal Mekanikal, December 2008 77 key elements in such standard. The automotive industry in Malaysia is much relying on foreign technology. Truck chassis, which is important structure of lightweight commercial vehicle, is mostly designed and imported from foreign country. In order to change this trend, it is necessary to develop and built Malaysian own chassis design. Study and research on truck chassis is thus required to achieve this goal. The chassis of trucks is the backbone of vehicles and integrates the main truck component systems such as the axles, suspension, power train, cab and trailer. The truck chassis is usually loaded by static, dynamic and also cyclic loading. Static loading comes from the weight of cabin, its content and passengers. The movement of truck affects a dynamic loading to the chassis. The vibration of engines and the roughness of road give a cyclic loading. The existing truck chassis design is normally designed based on static analysis. The emphasis of design is on the strength of structure to support the loading placed upon it. However, the truck chassis has been loaded by complex type of loads, including static, dynamics and fatigue aspects. It is estimated that fatigue is responsible for 85% to 90% of all structural failures 1. The knowledge of dynamic and fatigue behavior of truck chassis in such environment is thus important so that the mounting point of the components like engine, suspension, transmission and more can be determined and optimized. Many researchers carried out study on truck chassis. Karaoglu and Kuralay 2 investigated stress analysis of a truck chassis with riveted joints using FEM. Numerical results showed that stresses on the side member can be reduced by increasing the side member thickness locally. If the thickness change is not possible, increasing the connection plate length may be a good alternative. Fermer et al 3 investigated the fatigue life of Volvo S80 Bi-Fuel using MSC/Fatigue. Conle and Chu 4 did research about fatigue analysis and the local stress-strain approach in complex vehicular structures. Structural optimization of automotive components applied to durability problems has been investigated by Ferreira et al 5. Fermr and Svensson 6 studied on industrial experiences of FE-based fatigue life predictions of welded automotive structures. Filho et. al. 7 have investigated and optimized a chassis design for an off road vehicle with the appropriate dynamic and structural behavior, taking into account the aspects relative to the economical viability of an initial small scale production. The design of an off-road vehicle chassis is optimized by increasing the torsional stiffness, maintenance of center of gravity, total weight of structure and simpler geometry for reduction of production cost. The integration of computer aided design and engineering software codes (Pro/Engineer, ADAMS, and ANSYS) to simulate the effect of design changes to the truck frame has been studied by Cosme et al 8. Chiewanichakorn et al 9 investigated the behavior of a truss bridge, where an FRP deck replaced an old deteriorated concrete deck, using experimentally validated finite element (FE) models. Numerical results show that the fatigue life of the bridge after rehabilitation would be doubled compared to pre-rehabilitated reinforced concrete deck system. Based on the estimated truck traffic that the bridge carries, stress ranges of the FRP deck system lie in an infinite fatigue life Jurnal Mekanikal, December 2008 78 regime, which implies that no fatigue failure of trusses and floor system would be expected anytime during its service life. Ye and Moan 10 have investigated the static and fatigue behavior of aluminium box-stiffener/web frame connections using Finite Element Analysis (FEA) to provide a connection solution that can reduce the fabrication costs by changing the cutting shapes on the web frame and correspondingly the weld process meanwhile sufficient fatigue strength can be achieved. FE based fatigue was used to locate the critical point of probable crack initiation and to predict the life in a door hinge system 11. In this study, stress analysis of heavy duty truck chassis loaded by static force will be investigated to determine the location of critical point of crack initiation as a preliminary data for fatigue life prediction of this truck chassis. 2.0 FINITE ELEMENT ANALYSIS OF TRUCK CHASSIS 2.1 Basic Concept of FEM The finite element method (FEM) is a computational technique used to obtain approximate solutions of boundary value problems in engineering. Simply stated, a boundary value problem is a mathematical problem in which one or more dependent variables must satisfy a differential equation everywhere within a known domain of independent variables and satisfy specific conditions on the boundary of the domain 12. An unsophisticated description of the FE method is that it involves cutting a structure into several elements (pieces of structure), describing the behavior of each element in a simple way, then reconnecting elements at nodes as if nodes were pins or drops of glue that hold elements together (Figure 1). This process results in a set of simultaneous algebraic equations. In stress analysis these equation are equilibrium equations of the nodes. There may be several hundred or several thousand such equations, which mean that computer implementation is mandatory 13. Figure 1: A coarse mesh, two-dimensional model of gear tooth. All nodes and elements lie in plane of the paper 13 Jurnal Mekanikal, December 2008 79 2.2 A General Procedure for FEA There are certain common steps in formulating a finite element analysis of a physical problem, whether structural, fluid flow, heat transfer and some others problem. These steps are usually embodied in commercial finite element software packages. There are three main steps, namely: preprocessing, solution and postprocessing. The preprocessing (model definition) step is critical. A perfectly computed finite element solution is of absolutely no value if it corresponds to the wrong problem. This step includes: define the geometric domain of the problem, the element type(s) to be used, the material properties of the elements, the geometric properties of the elements (length, area, and the like), the element connectivity (mesh the model), the physical constraints (boundary conditions) and the loadings 12. The next step is solution, in this step the governing algebraic equations in matrix form and computes the unknown values of the primary field variable(s) are assembled. The computed results are then used by back substitution to determine additional, derived variables, such as reaction forces, element stresses and heat flow. Actually the features in this step such as matrix manipulation, numerical integration and equation solving are carried out automatically by commercial software 13. The final step is postprocessing, the analysis and evaluation of the result is conducted in this step. Examples of operations that can be accomplished include sort element stresses in order of magnitude, check equilibrium, calculate factors of safety, plot deformed structural shape, animate dynamic model behavior and produce color-coded temperature plots. The large software has a preprocessor and postprocessor to accompany the analysis portion and the both processor can communicate with the other large programs. Specific procedures of pre and post are different dependent upon the program 12. 2.3 Truck definition and classification Generally, truck is any of various heavy motor vehicles designed for carrying or pulling loads. Other definition of the truck is an automotive vehicle suitable for hauling. Some other definition are varied depending on the type of truck, such as Dump Truck is a truck whose contents can be emptied without handling; the front end of the platform can be pneumatically raised so that the load is discharged by gravity. There are two classifications most applicable to Recreational Vehicle tow trucks. The first one is the weight classes, as defined by the US government, ranging from Class 1 to Class 8 as listed in Table 1 and Table 2. The second is classified into a broader category: Light Duty Truck Medium Duty Truck Heavy Duty Truck Jurnal Mekanikal, December 2008 80 Table 1: Classification and classes of truck Weight Class Minimum GVWR (lbs) Maximum GVWR (lbs) VIUS * Category Common Category Class 1 6,000 Light-duty Light Duty Class 2 6,001 10,000 Light-duty Light Duty Class 3 10,001 14,000 Medium-duty Light Duty Class 4 14,001 16,000 Medium-duty Medium Duty Class 5 16,001 19,500 Medium-duty Medium Duty Class 6 19,501 26,000 Light-heavy Medium Duty Class 7 26,001 33,000 Heavy-heavy Heavy Duty Class 8 33,001 Heavy-heavy Heavy Duty Table 2: Vehicle manufacturer truck classification Category Class GVWR1 Representative Vehicles 1 0 - 27 kN (0 - 6,000 lbs.) 2 27 - 45 kN (6,001 - 10,000 lbs.) Light 3 45 - 62 kN (10,001 - 14,000 lbs.)pickup trucks, ambulances, parcel delivery 4 62 - 71 kN (14,001 - 16,000 lbs.)5 71 - 87 kN (16,001 - 19,500 lbs.)6 87 - 116 kN (19,501 - 26,000 lbs.)Medium 7 116 - 147 kN (26,001 to 33,000 lbs.)city cargo van, beverage delivery truck, wrecker, school bus Heavy 8 147 kN and over (33,000 lbs. and over)truck tractor, concrete mixer, dump truck, fire truck, city transit bus Notes: Gross Vehicle Weight Rating (GVWR): weight specifiedby manufacturer as the maximum loaded weight (truck pluscargo) of a single vehicle. 2.4 Model of Truck Chassis The model is depicted in Figure 2. The model has length of 12.35 m and width of 2.45 m. The material of chassis is ASTM Low Alloy Steel A 710 C (Class 3) with 552 MPa of yield strength and 620 MPa of tensile strength. The other properties of chassis material are tabulated in Table 3. Jurnal Mekanikal, December 2008 81 Table 3: Properties of truck chassis material 14 Modulus Elasticity E (Pa) Density (kg/m3)Poisson Ratio Yield Strength (MPa) Tensile Strength (MPa) 207 x 109 7800 0.3 550 620 Figure 2: Model of truck chassis 2.5 Loading The truck chassis model is loaded by static forces from the truck body and cargo. For this model, the maximum loaded weight of truck plus cargo is 36.000 kg. The load is assumed as a uniform pressure obtained from the maximum loaded weight divided by the total contact area between cargo and upper surface of chassis. Detail loading of model is shown in Figure 3. The magnitude of pressure on the upper side of chassis is calculated as 67564.6 N/m2. Figure 3: Static load (pressure = 67564.5 N/m2) 2.6 Boundary Conditions There are 3 boundary conditions (BC) of model; the first BC is applied in front of the chassis, the second and the third BC are applied in rear of chassis. They are shown in Figure 4. The type of BC 1 is pinned (the displacement is not allowed in all axes and the rotation is allowed in all axes) that represent the contact condition Jurnal Mekanikal, December 2008 82 between chassis and cab of truck as shown in Figure 5(a). The BC 2 represents the contact between chassis and upper side of spring that transfer loaded weight of cargo and chassis to axle. The contact condition of BC 2 in the object is shown in Figure 5. In the BC 2, the displacement only occurred in axis 2 and the rotation respect to all axes is zero. In the position where the BC 3 applied, there is a contact between inside surface of opening chassis and outside surface of bolt. In ABAQUS, this contact is called interaction. In this case, the type of the interaction is frictionless surface to surface contact. In the BC3, the displacement and the rotation is zero in all axes on all of bolts body. This condition is called fixed constrain. The bolt in BC 3 was assumed perfectly rigid. This assumption was realized by choosing a very high Youngs Modulus value of the bolt properties. Figure 4: Boundary conditions representation in the model Figure 5: Boundary conditions representation in the object, 4(a) BC 1, 4(b) and 4(c) BC 2, 4(d) BC 3 Jurnal Mekanikal, December 2008 83 3.0 RESULTS AND DISCUSSION The location of maximum Von Misses stress is at opening of chassis which is contacted with bolt as shown in Figure 6. The stress magnitude of critical point is 386.9 MPa. This critical point is located at element 86104 and node 16045. The internal surface of opening of chassis was contacted with the very stiff bolt. The BC 3 is also a fixed constraint, thus it cause a high stress on it. Based on static safety factor theory, the magnitude of safety factor for this structure is 1.43. The formula of Safety Factor (SF) is defined by 11: SF = significant strength of material corresponding significant stress from normal load (1) Figure 6: Von Misses stress distribution and critical point location Vidosic 15 recommends some value of safety factor for various condition of loading and material of structures. He recommends the value of 1.5 to 2 for well known materials under reasonably environmental condition, subjected to loads and stresses that can be determined readily. Based on this result, it is necessary to reduce the stress magnitude of critical point in order to get the satisfy SF value of truck chassis. The truck chassis can be modified to increase the value of SF especially at critical point area. The displacement of chassis and location of maximum displacement is shown in Figure 7. The magnitude of maximum displacement is 4.995 mm and occurs at middle of chassis. Maximum deflection is occurred at the middle of BC 1 and BC 2. For validation purpose, the region between BC 1 and BC 2 of chassis where the highest stress occurred is approximated by one dimensional simple beam loaded by concentrated force at mid point. The uniform distributed pressure on this region is replaced by a single concentrated force at mid point. The magnitude of the single force is obtained by multiplying the magnitude of pressure with the total area where the pressure is applied. The result agrees well with this approximation. Jurnal Mekanikal, December 2008 84 The approximation result shows