中文摘要：

基于Hertz弹性理论及分形几何学理论,以粗糙表面突峰变形特征、表面突峰承受法向接触载荷的光滑性和连续性为基础以及严格区分弹性变形和塑性变形,构架微动结合面的一种法向接触校对分形模型。导出表面突峰法向弹性接触载荷和表面突峰法向变形量之间的幂函数方程,提出微动结合面2个突峰之间互相作用的法向接触刚度的求导函数而非偏导函数求解准则。数值仿真曲线揭示：对于给定的法向接触载荷,随着分形维数的增加,实际接触面积首先增加然后降低;增加法向接触载荷或降低表面粗糙度都将增大实际接触面积;微动结合面法向接触刚度随着实际接触面积、法向接触载荷、相关因子或材料性能参数的增大而增大,而随着分形粗糙度的加大而降低;分形维数在较小范围内,微动结合面法向接触刚度随着分形维数从1变大而增强;但分形维数在较大范围内,微动结合面法向接触刚度时常随着分形维数的加大接近于2而降低。微动结合面法向接触校对分形模型的构思,能深入研究微动两粗糙表面之间的实际接触状态。

英文摘要：

On the basis of Hertz elastic theory and fractal geometry theory, one normal contact modification fractal model of fretting joint interface, following the character of the harsh surface bulge＇s deflection, smoothness and continuity of normal contact load exerting surface asperity as well as differentiating severely elastic deformation and plastic deflection, is proposed. The power function equation between surface summit＇s normal elastic contact load and its normal deformation is presented. Furthermore, the solving rule of differential function not partial differential function to attain fretting joint interface two bulges＇ interacting normal contact stiffness is addressed. The digital simulation curves reveal that real contact area firstly increases and afterwards decreases with the augment of fractal dimension at the given normal contact load. Real contact area may outright add by increasing normal contact load or reducing surface roughness. Fretting joint interface normal contact stiffness enhances as the increase of real contact area, normal contact load, relating factor or material property parameter, yet an increase in fractal roughness causes a decrease in fretting joint interface normal contact stiffness. Fretting joint interface normal contact stiffness increases when fractal dimension increases from 1 in the smaller range of fractal dimension; nevertheless, fretting joint interface normal contact stiffness sometimes shrinks when fractal dimension increases close to 2 in the larger range of fractal dimension. Conceiving normal contact amendment fractal model of fretting joint interface investigates deeply the practicable contact states between fretting two coarse surfaces.