分形粗糙表面接触变形分段计算模型

A Piecewise Calculation Model for Fractal Rough Surface Contact Deformation

针对现有分形理论描述粗糙表面接触变形过程存在的问题,以与波长对应的系数作为尺度划分依据,提出了一种考虑分形细节和微凸体接触变形过程的分段计算模型.通过数学推导和分析论述粗糙表面的接触变形过程,得出了与现有分形理论不同的结论,并论述了其不同的原因.基于此考虑了各尺度之间等效模型的连续性,导出了真实接触面积与载荷之间的隐函数关系,并进行了数值模拟分析.结果表明:粗糙表面的接触变形过程是从塑性变形到弹性变形的转变,在转变过渡区域会出现弹性变形和塑性变形交替的过程;某一确定尺度下微凸体变形前的顶端曲率半径是一个不随变形量变化的定值;当分形维度接近1时,粗糙表面以塑性变形为主,此时表面接触性质仅受到材料的影响;分形维度存在一个最佳值,此时粗糙表面接触性质最好.

To address the existing problems of fractal theory,apiecewise calculation model was proposed.This new model was calculated by different functions with the corresponding parameters set by the wavelength.The fractal detail and deformation process of asperity were considered in this model.The contact deformation process of rough surface was studied and the relationship between real contact area and load was given.The analysis results showed that contact deformation process of rough surface is a transition from plastic to elastic contact model,where elastic deformation and plastic deformation model alternately take place.The top radius of curvature of the asperity is a fixed value which is independent of the deformation under a certain scale.When the fractal dimension is close to 1,the rough surface is dominated by the plastic deformation,and the surface contact property is only affected by the material.An optimal value of fractal dimension is existed when the rough surface contact property is the best.