机床结合面三维形貌的数字化仿真和微观接触刚度的建模与计算研究

It is particularly important to calculate and analyze the joint contact stiffness with the machine tool developing to high precision digitization. Existed theory of contact stiffness calculation is mainly two-dimensional rough surface contact under certain assumptions. The calculation error is bigger.This project is researched on key problems of the joint 3D surface topography and the normal and tangential contact stiffness basis of the previous research achievements. Based on wavelet theory and fractal theory，the machined 3D surface topography are analysis evaluation，wavelet decomposition and reconstruction，fractal function simulation. The digital analysis and calculation method of surface morphology is put forwarded. Based on the combination of contact mechanics and fractal theory，the single asperity contact characteristics modeling and calculation are put forwarded for the positive and lateral contact in the deformations of elastic，elastic-plastic and plastic. The 3D rough surface normal and tangential contact stiffness relationships with contact load，contact deformation，the contact area are analyzed. Through two rough surface normal and tangential contact stiffness of modeling and theoretical calculation，the relationships and laws of the normal and tangential contact stiffness between the material，processing technology，the load are revealed. The calculated results are verified with experiments and engineering. This project is pay equal attention to theory，method and applied，and it has important academic significance and engineering application value.

随着机床向精密化、数字化方向发展，结合面接触刚度的计算与分析显得尤为重要。现有对结合面接触刚度理论计算主要建立在一定假设下的二维粗糙表面接触上，计算结果不够准确。本项目拟在前期研究的基础上，针对机床结合面三维形貌的法向与切向接触刚度的关键问题开展研究。基于小波理论和分形理论相结合，分析、模拟和评定一定条件下的机械加工表面微观形貌，构建三维数字化微观表面形貌模型；将接触力学和分形理论结合起来，通过单对微凸体在正接触和侧接触时弹性塑性接触，构建法向和切向接触刚度的理论计算模型，分析法向和切向接触刚度与面压、变形、面积等参数之间的关系，揭示它们之间的非线性特性，并进一步构建两个三维微观粗糙表面接触刚度的理论计算模型，揭示结合面的微观接触机理；通过结合面法向和切向刚度实验分析与材料、加工、载荷等参数之间的关系，探索结合面法向和切向接触刚度的影响规律，为机床的设计与计算奠定一定的理论。

装备制造业作为国民经济发展和国防建设提供技术装备的基础性产业，加强制造过程数值模拟与仿真等先进制造技术的研究与应用将推动机械工业制造能力提升。项目主要从机械结合面接触刚度实验平台升级、表面三维形貌测量和表征、微观接触刚度建模和分析、机床主轴与床身的静动态有限元建模和振动测试、接触刚度的预测等进行了系列研究。（1）通过实际加工粗糙表面的三维形貌测量与分析表明，机械加工粗糙表面具有分形特性，粗糙表面轮廓高度分布服从正态分布。（2）基于分形几何和接触力学理论，围绕考虑微凸体间发生相互作用时的法向和切向结合面接触刚度问题展开研究，建立了微凸体相互作用接触刚度、接触载荷等参数之间的函数关系，分析在不同塑性指数下微凸体相互作用对接触载荷与法向和切向接触刚度间关系产生的影响关系，研究了结合面接触刚度机理。（3）通过有限元、数值计算方法，建立了微凸体在侧向接触时的结合面法向和切向接触刚度模型，仿真分析了结合面法向和切向接触刚度与法向载荷的影响规律，研究结果与实验结果一致。（4）将研究成果应用到天水星火机床有限责任公司生产的CK61125数控机床的设计与建模中，通过机床关键零部件的建模与分析、振动特性测量与分析，获得机床关键部件的静动态特性参数，为机床的进一步结构优化设计提供了科学参数和实验基础数据。（5）针对机械结合面接触特性参数与其影响因素之间存在复杂的非线性映射关系，基于ESN回声状态网络理论对结合面法向接触刚度进行仿生学预测建模，研究结果表明，该算法的预测精度可达0.0016%以上。