基于分形理论的滑动摩擦表面接触力学模型

依据分形理论,考虑微凸体变形特征及摩擦作用的影响建立滑动摩擦表面接触力学模型。采用一个三次多项式来表达弹塑性变形微凸体的接触压力与接触面积的关系,从而满足在变形状态转变临界点处的微凸体接触面积与接触压力转化皆是连续和光滑的条件。推导出滑动摩擦表面临界弹性变形微接触面积、临界塑性变形微接触面积、量纲一真实接触面积的数学表达式。理论计算结果表明,表面形貌一定时,真实接触面积随着载荷的增大而增大;载荷一定时,真实接触面积随着特征尺度系数的增大而减小,随着分形维数的增大先增大后减小;当表面较粗糙时,摩擦因数对真实接触面积的影响很小;随着表面光滑程度的增大,摩擦因数对真实接触面积的影响增大,真实接触面积随着摩擦因数的增大而增大,特别是当摩擦因数较大时,真实接触面积增大的幅度也较大。接触力学模型的建立,为研究滑动摩擦表面间的摩擦磨损性能提供了依据。

Sliding Friction Surface Contact Mechanics Model Based on Fractal Theory

According to fractal theory,the sliding friction surface contact mechanics model considering the influences of the asperity’s deformation and friction is established.The relationship of elastic-plastic deforming asperity’s contact pressure and contact area is expressed by a cubic polynomial,by which the continuous and smooth conditions of transformation of asperity contact area and contact pressure at the critical point of transition of distorting state are obtained.The mathematical expressions of critical elastic deformation micro contact area,critical plastic deformation micro contact area,dimension 1 real contact area of sliding friction surface are deduced.Theoretical calculation results show that real contact area increases with the increases of the load when the surface topography is constant.Real contact area decreases with the increases of characteristic length scale,and increases at first and then decreases with the increases of fractal dimension when the load is constant.Friction factor has little influence on real contact area when the surface is coarser.Friction factor has a great influence on real contact area as the increases of smoothness of surface,and real contact area increases with the increases of friction factor,especially,real contact area increases greatly when the friction factor is large.The contact mechanics model provides a foundation for study of the friction and wear performance of sliding friction surfaces.