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1、基于半解析法的接触问题研究 (申请清华大学工学博士学位论文) 培 养 单 位 ： 精密仪器与机械学系 学科 ： 机械工程 研究生 ： 王 战 江 指 导 教 师 ： 胡 元 中 教 授二一年四月 Studies on Contact Mechanics Based on Semi-analytical Method Dissertation Submitted to Tsinghua University in partial fulfillment of the requirement for the degree of Doctor of Engineering by Wang Zhanj
2、iang (Mechanical Engineering ) Dissertation Supervisor: Professor Hu Yuanzhong April, 2010 关于学位论文使用授权的说明 本人完全了解清华大学有关保留、 使用学位论文的规定， 即： 清华大学拥有在著作权法规定范围内学位论文的使用权，其中包括： （1）已获学位的研究生必须按学校规定提交学位论文，学校可以采用影印、缩印或其他复制手段保存研究生上交的学位论文； （2）为教学和科研目的，学校可以将公开的学位论文作为资料在图书馆、资料室等场所供校内师生阅读，或在校园网上供校内师生浏览部分内容； （3）根据中华人民共和
3、国学位条例暂行实施办法 ，向国家图书馆报送可以公开的学位论文。 本人保证遵守上述规定。 （保密的论文在解密后遵守此规定）（保密的论文在解密后遵守此规定） 作者签名： 导师签名： 日 期： 日 期： 摘 要 I 摘 要 本论文使用半解析法求解接触问题。干接触求解基于最小余能方程，接触压力和切向应力使用共轭梯度法求解，通过解析法得到影响系数，由此计算表面变形或位移，并采用快速傅里叶变换加速表面变形计算。半解析法与Reynolds方程结合即可求解润滑接触问题。论文主要研究了弹塑性接触，微滑接触，层状材料接触和球面润滑接触问题。 利用特征应变分析和径向返回算法计算表面残余位移，可将上述接触模型拓展到弹
4、塑性接触，进而建立三维粗糙表面的弹塑性接触模型。由于粗糙度的影响，最大von Mises应力和塑性区域出现在表面附近。对比弹性接触，塑性接触使原先较高的压力降低，较低的压力升高，而处在中间值的压力变化很小。塑性流动使粗糙表面变得平坦。进一步，将塑性变形引起的残余位移叠加到表面建立了弹塑性流体动力润滑模型。在弹塑性流体动力润滑中，从入口区到出口区，膜厚呈现波浪状。在同样工况下，弹塑性流体动力润滑的最小膜厚和中心膜厚较弹性流体动力润滑的最小膜厚和中心膜厚小。 改进了微滑接触求解算法，并将算法扩展到微动接触求解。由于粗糙度的影响，粘着区域存在于多个不连通的区域。单个粗糙峰上切向应力分布呈现和光滑表面
5、接触类似的形状。随着切向力的增加，压力分布沿切向力的相反方向倾斜，粘着区域沿切向力的相反方向移动并逐步减小。 由Papkovich-Neuber势函数得到影响系数，由此分析弹性层状材料接触，并进而推广到层状材料的微滑接触分析，结果显示，在相同载荷工况和摩擦系数下，硬涂层的接触区，粘着区，粘着比，较软涂层小。随着涂层弹性模量增加，最大von Mises应力的位置出现在表面。然后，基于Archard磨损模型，进行了滑动接触磨损的数值研究和实验研究。进一步，研究了层状材料的弹性流体动力润滑问题。硬涂层增加接触中心的压力值，二次压力峰值以及最小膜厚和中心膜厚。随着涂层厚度增加，最大界面剪应力先增加后减
6、小。 将直角坐标点接触的混合润滑模型扩展到球坐标面接触。结果表明，当接触球面间隙较小，载荷较重时，接触压力与Hertz压力分布有明显不同。 关键词: 弹塑性接触；微滑和微动接触；层状材料接触；润滑接触；球面润滑Abstract II Abstract In this dissertation, a semi-analytical method (SAM) is used to solve the contact problems. In the dry contact model, the solutions are obtained on the basis of minimization
7、of complementary energy. Contact pressure and shear tractions are solved by a numerical procedure based on Conjugate Gradient Method (CGM), surface displacements are calculated using the influence coefficients (ICs) derived from the analytical solutions, and the Fast Fourier Transform (FFT) techniqu
8、e to promote the calculation of deformation. Furthermore, the lubricated contact problems by incorporating the Reynolds equation with the SAM can be solved. Elastic-plastic contacts, partial slip contacts, layered or coated materials contacts and spherical lubricated contacts are investigated. The a
9、bove-mentioned model can be extended to the elastic-plastic contacts by superposing the resistant surface deformation calculated via Eigenstrain analysis and J2 radical returning algorithm. As a result, a three-dimensional elastic-plastic contact model is established for the rough contacts analysis.
10、 Due to roughness effect, the maximum von Mises stress and plastic region are found at the locations closer to the surface. In elastic-plastic contacts the pressure distributions are quite different if compared to the results from purely elastic model, i.e., the peak pressure decreases but the valle
11、y pressure increases. Moreover, plastic flow makes the rough surface flatten or less fluctuating. Furthermore, the elastic-plastic hydrodynamic lubrication (EPHL) model is established by incorporating the contact model with the solution of lubrication. Under the conditions of EPHL, from the inlet of
12、 lubricant to the outlet of lubricant, the film thickness exhibits a wave shapes. In the same operating conditions, values of the minimum film thickness and central film thickness are lower than those in elastohydrodynamic lubrication (EHL). The numerical method currently used to solve the partial s
13、lip contacts has been improved by the author and the calculation is extended to the fretting contacts. The good agreement with the results from Cattaneo-Mindlins solution validates the Abstract III numerical method. Then, sinusoidal wave contact is studied. Results show the stick regions appear in s
14、everal disconnected areas due to the roughness effects. Shear tractions exhibit a distribution similarity independent of the size of contact that the shape of shear traction in a single asperity is similar to the results of smooth contact. With the tangential force increasing, the pressure distribut
15、ion skews to the opposite direction of tangential force and the stick zones move to the same direction while shrinking. For the three-dimensional layered or coated materials contact problems, the response functions for calculating the displacements and stresses are determined in the frequency domain
16、 by using the Papkovich-Neuber potentials. The model is used to analyze partial slip contact of layered materials, and results show that the contact area, stick regions and the stick ratio are smaller on stiffer coatings, in comparison with compliant ones under the same contact conditions. For stiffer coatings, the positions of maximum von Mises stress move up to the surface. In addition, the wear behavior of coated materials
