【作者】 刘天祥；

【导师】 刘更；

【作者基本信息】 西北工业大学 ， 机械设计及理论， 2006， 博士

【摘要】 作为摩擦学研究的重要分支之一的接触力学研究是分析摩擦磨损和润滑问题的基础。本文运用近年来发展的在计算区域划分及结点排布上较为灵活的无网格方法(Meshless Methods或Meshfree Methods)，通过采用较有效的表面形貌的描述方法，研究了表面粗糙度、弹塑性变形、摩擦热和表面效应等因素影响下的宏观—微观接触机理，建立了一套较有效解决以上问题的数值计算方法。为工程机械接触力学特性的预测，指导相关产品的设计奠定了较好的基础。本文介绍了无网格伽辽金(Element-Free Galerkin，EFG)方法的具体数学描述。研究了无网格伽辽金—有限元(Element-Free Galerkin-Finite Element，EFG-FE)耦合方法的基本原理和计算流程。通过算例讨论了EFG方法中拉格朗日乘子和权函数影响域半径对计算精度的影响，并验证了EFG-FE耦合方法的有效性。运用EFG-FE耦合方法求解真实粗糙表面弹塑性接触问题。在对无网格区域相关参数研究的基础上，指出了用EFG-FE耦合方法求解接触问题时的合理参数范围。结果表明，无网格方法相比于有限元方法更能合理地反映材料在接触过程的塑性变形行为。提出了一种基于自适应粗糙表面描述的弹塑性接触模型。去除了对采用等间距结点描述的粗糙表面轮廓影响较小的结点。分析了不同阈值对自适应表面弹塑性接触力学特性的影响，在保证计算精度的同时大大节省了运算时间和计算机资源。建立了可考虑屈服应力温度相关的粗糙表面热弹塑性接触模型。研究了摩擦力和不同热输入情况下圆柱体与弹塑性平面的接触力学特性。研究表明，在考虑剪切摩擦力作用后，弹塑性接触压力分布不再关于接触区域中轴线对称而出现了“塌陷”现象。通过无网格方法解与有限元方法解比较发现不恰当的有限元网格划分会造成接触压力的数值震荡，而无网格方法可避免这一现象的发生。发现忽略温度相关效应将高估最大接触压力而低估相应外载荷下产生的接触面积。求解了考虑屈服应力温度相关的粗糙表面热弹塑性接触问题，探讨了摩擦热效应对表面温升、接触压力和接触体应力分布的影响。利用EFG-FE耦合方法研究了微观粘着接触问题，提出求解弹性粘着接触问题的数值计算模型。通过对弹性微圆柱体与半无限大刚性平面的粘着接触问题的计算论证了该方法的可行性。分析了铝、铜、铁三种材料圆柱体在不同Tabor数下的粘着接触外载荷与接触半带宽的关系、接触压力分布和应力分布等。最后，总结了全文，指出解决现代接触力学问题未来可能的发展方向和趋势。更多还原

【Abstract】 Analyzing the contact performance between two surfaces plays a key role in studyingriction, wear, and lubrication in tribological system. The goal of this dissertation is to(?)evelop macro-micro numerical models for understanding contact mechanics characteristicsvith some complicated factors such as surface topography of real rough surfaces,elasto-plastic behaviors, frictional heating, surface effects on micro-scale, etc., with the(?)ssistance of the newly developed numerical methods, called meshfree methods or meshlessnethods, which are regarded to be a potential, flexible and versatile numerical technique in(?)ecent years. It is anticipated that the research results will develop a better understanding andnew methods for macro-micro scale contact mechanics, and advance the state-of-the-art ofmechanical design of engineering systems.Main procedures of meshfree methods are reviewed and discussed. The element-freeGalerkin (EFG) method which is based on the moving least-square approximation is studied.Some numerical examples are carried out by using the EFG method to investigate theimposition of essential boundary conditions by Lagrange multipliers and the influences ofchanging data of weight functions. An element-free Garlerkin-finite element (EFG-FE)coupling method is then presented and implemented.The EFG-FE coupling method, combined with the linear mathematical programmingtechnique, is used to solve two-dimensional elasto-plastic contact problems of rough surfaces.The effects of a few key factors of the meshfree methods, such as the number of Gaussintegration points and parameters that determine the weight function, on the precision ofcontact solutions are investigated. The results indicate that the meshfree methods can moreeasily follow plastic deformations than the finite element method and are more suitable forexpressing plastic flows in the elasto-plastic contact simulations.An adaptive-surface elasto-plaStic asperity contact model is presented in this paper. Sucha model is developed in order to reduce the computing time by removing the surface nodesthat have little influence on the contact behavior of rough surfaces. The effects of differentthresholds on the contact pressure distributions, real contact areas, and the elasto-plastic stress fields in the contacting bodies are investigated and discussed.A thermal elasto-plastic contact model which can consider the effects of temperature-dependent yield strength is developed to investigate the influences of the steady-statefrictional heating on the contact performance of surface asperities and subsurface stress fieldsbetween two contacting bodies. The model is verified through the contact analysis of a rigid,isolated cylinder with a thermal elasto-plastic plane. The results show that the contactpressures of elasto-plastic contact with considering the frictional tractions are no longersymmetric. By comparing the results obtained from the EFG-FE coupling method with thatfrom FEM, it reveals that the contact pressures solved by FEM would be oscillatory if the FEmeshs are produced unsuitably, while this phenomenon will be avoided by using the meshfi’eemethods. Furthermore, the thermal effects on the contact pressure, real area of contact, andaverage gap of real rough surface with different frictional heat inputs under the thermalelasto-plastic contact conditions are studied.A microscale adhesive contact model based on the EFG-FE coupling method is presented.The model is first validated through comparison with theoretical solutions. A numericalsimulation of the adhesive contact between a micro elastic cylinder and a rigid half-space isthen conducted. The adhesive contact characteristics of three metals (Al, Cu and Fe) arestudied at different Tabor parameters. The relationships of the applied load and contact halfwidth of the adhesive contacts are analyzed. Contact pressures, stress contours and deformedprofiles of different cylinder sizes and applied loads are illustrated and discussed. The resultsare compared with published solutions, and good agreements are observed.Finally, some conclusions and observations are given and recent development tendenciesof advanced contact mechanics are discussed and outlined.更多还原