三维弹性接触问题的数值模拟技术及其应用研究

【作者】 李爱民；

【导师】 孙广标；

【作者基本信息】 西北工业大学 ， 机械制造及其自动化， 2004， 硕士

【摘要】 接触问题是工程实践中一类常见、复杂、典型的非线性问题。经典的数学方法和力学方法对大多数接触问题都难以解决，因此需要使用数值计算方法进行求解。有限元数值计算方法的发展，尤其以有限单元法为核心的现代CAE技术的快速发展使有限元数值模拟技术得到了广泛的应用。本文着重采用计算机数值模拟和经验解析解分析对比的方法，对汽车后桥传动用B7517E圆锥滚子轴承进行三维数值模拟研究。汽车后桥传动系统主要以圆锥滚子轴承作为支承，而且为了提高整个系统的支承刚度，在装配时就使锥轴承具有一定的预紧度。 本文在对接触问题的研究和发展现状及接触问题的基本理论进行介绍的基础上，对汽车后桥传动锥轴承弹性接触问题的有限元数值求解方法进行了理论分析。通过对锥轴承的特征参数、接触应力和变形及负荷分布特性的综合分析，得出了圆锥滚子轴承的经典解析解存在局限性的结论。而采用数值模拟技术则可以相对避免解析方法的不足。 本文针对汽车后桥传动锥轴承的接触弹性变形特点、接触应力及负荷分布规律，采用三维实体单元及三维接触单元对圆锥滚子轴承实体模型进行特殊的有限元网格划分，将接触单元按柔体一柔体处理，采用面一面接触分析模式，建立了符合实际的有限元模型。在此基础上，应用商用软件ANSYS对汽车后桥传动锥轴承进行三维有限元模拟与研究，获得了汽车后桥传动锥轴承在两种不同情况下的求解结果。 根据有限元数值模拟结果对经典解析解中接触弹性变形量与作用负荷的关系进行了修正，利用修正过的接触弹性变形公式对汽车后桥传动锥轴承的接触应力和变形及负荷分布规律在无游隙及负游隙两种情况下进行研究，并将结果与经典解析解进行了对比分析。本文的研究结果及研究方法对汽车后桥锥轴承的工程应用、可靠性分析、优化设计等具有重要参考，对研究开发新型锥轴承具有一定的应用价值。更多还原

【Abstract】 Contact problems belong to typical non-linear problems, familiar and specially complicated problems in engineering. It is helpless for classical mathematics and mechanics method to solve contact problems; Resorting numerical compute method is necessary. Due to the development of finite element method and CAE(Computer Aided Engineering) technology based on finite element method, finite element numerical simulation technology has been applied widely. The paper puts emphasis on three-dimensional numerical simulation research for the B7517E conical roller bearing in automotive transmission by comparing computer numerical simulation with classical result. Conical roller bearings are the most important supporting parts in automotive rear bridge, interfered initially.After introducing research & development and basic theory of contact problems, theoretical analysis of finite element numerical solution method is made for contact problems of conical roller bearings in automotive rear bridges. According to synthetical analysis on the feature of parameters, contact pressure & formation and load distribution of conical roller bearings, the limitation is discovered, based on classical solution. Contrarily, numerical simulation & analysis is able to overcome these problems.Special grids is adopted for solid model of conical roller bearings by applying for three-dimensional solid and contact elements, aiming at its characteristic, stress and load distribution of elastic contact problems. Finite element model built in the paper is fit for objective practice, with flexible-flexible contact bodies and surfaces -surfaces contact mode. In term of that, the solution result in two different condition is achieved by ANSYS software.Deep research and comparing analysis between the classical solution and the finite element result is made on contact stress & formation and load distribution of conical roller bearings by revised classical formula of elastic contact problems, according to finite element solution in two different interfering conditions. Thefinial studied outcome and method adopted will bring important effect on engineering application, reliable analysis, optimization design etc. of conical roller bearings, at the same time, certain application value for developing new type of bearings.更多还原