考虑摩擦的球面切向接触刚度分形模型研究

为准确且方便地计算两球面的切向接触刚度（TCS），在前期对两球面接触分形模型研究的基础上，通过引入考虑摩擦因素的弹塑性变形临界面积计算公式，并基于接触面切向刚度基本理论，建立了考虑摩擦因素的两球面切向接触刚度的分形模型。对模型进行了仿真分析，结果表明：切向接触刚度与法向载荷成正比关系;摩擦因数与切向接触刚度的关系因分形维数的变化而呈现出不同的规律;受到分形维数变化的影响，切向接触刚度随接触面材料特性参数和分形粗糙度幅值的增大而增大;在一定工况下，切向接触刚度在分形维数取1.5时达到最大，且当分形维数在1.5左右时，其值增大最快;球面内接触比外接触时的切向刚度大;随着曲率半径的增大，切向刚度增大。研究结果为后续开展高副结合面（如轴承等）润滑及动力学分析提供了理论基础。

Research on Fractal Model of TCS between Spherical Surfaces Considering Friction Factors

In order to precisely calculate TCS between spherical surfaces, this paper presented the establishment of fractal model for TCS calculations between spheres considering friction factors. This model was obtained by introducing the equation of critical contact area of elasto-plastic deformation with friction and employing the basic theory of TCS, and based on the fractal contact model of two spherical surfaces. The numerical results show that: the TCS increases with normal loads; the relationship between TCS and friction coefficient is vary as the fractal dimension changes. It is efficient to improve the TCS by adding material propertied parameters and fractal roughness amplitude. The maximum value appears in TCS when the fractal dimension is 1.5 and the TCS increases significantly when the fractal dimension is about 1.5. Furthermore, TCS of inner contact is bigger than that of outer contact; TCS increases with curvature radius of cylinders. The theory herein helps to analyze the lubrication and dynamic characteristics between high-pair's joint surfaces(like bearings) in the future.