考虑摩擦的圆柱面切向接触刚度分形模型研究*

为了更准确地计算圆柱面切向接触刚度，本文考虑摩擦因素的影响，在圆柱面分形接触模型的基础上，引入存在摩擦时弹塑性变形的临界面积公式，并利用切向接触刚度的基本理论，推导考虑摩擦的圆柱面切向接触刚度分形模型，并通过Matlab对上述模型进行仿真，研究不同参数(摩擦因数、分形维数、粗糙度幅值 、材料的特性参数、曲率半径)以及接触的形式对切向接触刚度的影响。仿真结果表明：切向接触刚度与法向载荷成正比关系，但随分形维数取值范围的变化分别呈现指数与线性规律。摩擦因数与切向接触刚度成反比关系;材料的特性参数对切向刚度的影响，不仅与分形维数有关，还与自身取值关联;分形维数，粗糙度幅值与切向刚度的关系，受分形维数和材料特性参数的影响呈现正比或反比趋势。另外，内接触比外接触时的切向刚度大;随着曲率半径的变大，切向刚度增加。该研究为后续开展高副结合面动力学分析提供理论 基础。

Research on Fractal Model of Tangential Contact Stiffness between Cylindrical Surfaces Considering Friction Factors

In order to precisely calculate tangential contact stiffness (TCS) between cylindrical surfaces, this paper presents the establishment of fractal model for TCS calculation between cylinders considering friction factors. This model is obtained by introducing the equation of critical contact area of elastoplastic deformation with friction and employing the basic theory of TCS, based on the fractal contact model of two cylinders’ surfaces, and by employing the Matlab to simulate the model, the changing law of TCS affected by different parameters (such as: friction coefficient, fractal dimension, roughness amplitude, material propertied parameters and curvature radius of cylinders) and contact type is investigated. The numerical results are as follows: the relationship between TCS and normal load is direct ratio, which appears exponential and linear rule respectively with variation of fractal dimension. TCS is inverse proportional to friction coefficient. Effect of material propertied parameters on TCS changes with size of fractal dimension as well as the value itself. The correlations between fractal dimension and TCS, roughness amplitude and TCS are direct or inverse proportion depending on the value of fractal dimension and material propertied parameters. Furthermore, TCS of inner contact is bigger than that of outer contact; TCS increases with curvature radius of cylinders. The theory here helps to analyze the dynamic characteristics between high-pair’s joint surfaces in the future.