依据各向异性分形几何理论的固定结合部法向接触力学模型

Normal Contact Mechanics Model of Fixed Joint Interface Adopting Anisotropic Fractal Geometrical Theory

基于各向异性分形几何理论,考虑微凸体变形特点、表面微凸体承受法向载荷的连续性和光滑性原理,以及区分微凸体分别处于弹性、塑性变形时的一个微凸体实际微接触面积,建立固定结合部法向接触力学模型。采用二变量Weierstrass-Mandelbrot函数模拟各向异性三维分形轮廓表面。推导出划分弹塑性区域的临界弹性变形微接触截面积、结合部量纲一法向载荷、结合部量纲一法向接触刚度的数学表达式。数值仿真结果表明:当表面形貌的分形维数、分形粗糙度一定时,真实接触面积随着结合部法向载荷的增大而增大;结合部法向接触刚度随着真实接触面积、结合部法向载荷、相关因子或材料特性参数的增大而变大;当分形维数由1变大时,结合部法向接触刚度随着分形维数的变大而增大;当分形维数增加到趋近于2时,结合部法向接触刚度有时却会随着分形维数的增加而降低。结合部法向接触力学模型的构建,有助于分析固定接触表面间的真实接触情况。

With anisotropic fractal geometrical theory, the fixed joint interface normal contact mechanics model, considering the feature of the asperity＇s deformation, the continuous and smooth principle of normal load exerting surface asperity as well as distinguishing an asperity real micro contact area when the asperity is in elastic or plastic deformation, is established. The anisotropic three-dimensional fractal profile surface is simulated using Weierstrass-Mandelbrot function with two unknown variables. The mathematical expressions of critical elastic deformation micro contact truncated area demarcating the elastic and plastic regimes, joint interface dimensionless normal load, and joint interface dimensionless normal contact stiffness are deduced. The digital simulation results make clear that real contact area increases with the increases of the joint interface normal load when fractal dimension and fractal roughness about surface topography are constant. Joint interface normal contact stiffness adds with increasing real contact area, joint interface normal load, relating factor or material property parameter. Joint interface normal contact stiffness enhances as the increase of fractal dimension from 1. However, joint interface normal contact stiffness sometimes diminishes as the augment of fractal dimension close to 2. Establishing normal contact mechanics model helps to analyze the real contact conditions between fixed contact surfaces.