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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。
Based on the fractal geometry theory of anisotropy, taking into account the deformation characteristics of asperities, the continuity and smoothness of the surface asperities under normal load and the actual micro-asperities Contact area, the establishment of a fixed joint normal contact mechanics model. A two-variable Weierstrass-Mandelbrot function is used to simulate anisotropic three-dimensional fractal profile surfaces. The mathematical expressions of the normal contact stiffness of the joint dimension and the normality of the joint are derived by deducing the critical elastic deformation micro-contact cross-sectional area, the joint normal dimension and the normal joint load. The numerical simulation results show that the real contact area increases with the increase of the normal load of the junction when the fractal dimension and the fractal roughness of the surface are constant. The normal contact stiffness of the junction increases with the real contact area When the fractal dimension increases from 1, the normal contact stiffness increases with the increase of the fractal dimension. When the fractal dimension increases from 1, Increasing to approaching 2, the junction normal stiffness sometimes decreases as the fractal dimension increases. The construction of the normal contact mechanics model of the joint helps to analyze the real contact between fixed contact surfaces.