基于泛形理论的机械结合面接触刚度的力学表征

The joint surface is known as the most important factor during the mechanical manufacturing and equipment manufacturing process due to its wide applications and the significant influence. However, the contact stiffness of the joint surface is easy to be influenced by many different factors, which may have a great impact on the machine accuracy. This research will focus on the following influence factors, such as micro-roughness, surface damage and residual stress of the joint surface. The main works are as follows. First of all, based on the ubiquitiform theory, the author presents the mathematics representation of the micro-roughness of the joint surface induced by surface defects, corrosion and so on, and then provides a ubiquitiform model to describe the influence of changes of microstructure on the macroscopic parameters. Secondly, the author also investigates the microscopic mechanism of surface cracks and surface layer damage caused by the cyclic loading, and finds the mechanical characterization of surface damage based on the ubiquitiform method, where the investigation results show the evolution law that the surface damage will reduce the stiffness of the joint surface according to the ubiquitiform theory. Thirdly, after the study on the influence of the residual stress on the contact stiffness of the joint surface, its mathematical expression is provided. Finally, a meshless method is used in the simulation of the stiffness of the joint surface, and a comprehensive method referring to all of the influence factors above is proposed to investigate contact stiffness of the joint surface, providing a theoretical foundation for the further study on the properties of the joint surface. Besides, as a comprehensive research subject referring to multidisciplinary fields, such as machinery, mechanics, and materials and so on, this research solves the fundamental problems in the design of the machine tool, and has a great theoretical significance on the study of overall performance of the machine tool.

结合面是机械装备制造领域应用最广、影响最大、最重要的要素，其接触刚度受多种因素影响，对整机精度有至关重要的影响。本研究将针对接触表面的微观不平整性、表面损伤和残余应力等因素对结合面刚度影响的本质特征开展研究工作，主要有：采用泛形几何研究结合面表面缺陷、腐蚀等因素引起的微观不平整度的数学表征，建立微观形貌变化对宏观参量影响的泛形模型；探究循环载荷引起的表面裂纹和表层损伤的微观机理，以泛形方法给出表面层损伤的力学表征，得到基于泛形理论的损伤层刚度下降的变化规律；研究残余应力的存在对结合面接触刚度影响，给出其数学表达；建立无网格方法应用于结合面刚度分析的计算模型，提出综合考虑以上因素的结合面接触刚度计算方法，为结合面特性的深入研究奠定良好的理论基础。本项目是涉及机械、力学和材料等多学科交叉的综合课题，解决的是机床设计中重要的基础性问题，对机床整机特性的研究具有重要的理论意义。

该项目主要采用泛形理论精确表征材料表面不平整度，进而分析机械结合面的刚度变化，以期为机械结构接触面的精准分析奠定理论基础，从而提高机械设备的加工精度，是针对我国装备制造业自主创新设计开发中迫切需要解决的基础性研究工作。研究工作基于泛形理论，给出了考虑裂纹泛形特征的断裂参量，包括：泛形临界应力、泛形应力强度因子、泛形裂纹扩展力和泛形断裂能，实验结果表明，采用泛形理论，可以得到更加准确的分析计算结果；提出了采用泛形理论进行断裂韧度GIC测量的新方法；考虑材料的非均匀特性，假设材料参数服从Weibull统计分布，模拟I型裂纹的扩展路径，得到了与实验基本一致的结果，分析表明不同的非均匀参数将得到不同的裂纹扩展形貌；以广义泛形Sierpinski地毯构造粗糙表面微凸体的分布模型，进行了泛形理论下的粗糙表面模拟；建立了泛形理论下粗糙表面弹性接触法向刚度的理论关系，得到了接触表面粗糙度的泛形表征，研究了法向载荷、粗糙表面和泛形复杂度等对法向和切向接触刚度的影响；分析了表面损伤层的形成机理，提出了非线性疲劳累积损伤演化模型，推导了考虑损伤临界状态有效弹性模量不为零的疲劳损伤演化方程，研究了对含有单边损伤层与双边梯度损伤层梁的刚度变化；分析了疲劳裂纹萌生和疲劳裂纹扩展的破坏机理，提出了采用塑性应变能密度作为疲劳破坏的判定指标，给出了疲劳寿命的计算公式；通过数值模拟得到了加工和工作过程形成的残余应力分布规律，研究了存在残余应力时机床导轨材料参数的变化规律，建立了残余应力影响下的结构变形的分析模型；将无网格方法成功地应用于结合面接触刚度的分析，推导了相关的接触公式，建立了结合面的无网格分析模型；研究了功能梯度材料结构中多种表面波传播的频散和衰减特性，分析了不同梯度参数对频散及衰减的影响规律，为采用超声检测方法得到材料表面缺陷的测试奠定了理论基础。本研究解决了机床设计中的基本问题，对研究机床的整体性能具有重要的理论意义。