Loading-unloading contact model between three-dimensional fractal rough surfaces

Abstract

Based on fractal theory, a loading-unloading contact model between three-dimensional rough surfaces has been developed. The critical contact areas of a single asperity are scale dependent. The expressions between contact area and contact load for a single asperity in loading and unloading processes are obtained. The truncated asperity size distribution functions of different frequency indexes in loading and unloading processes are deduced. The dimensionless relation between the total contact load and the total real contact area is obtained in loading and unloading processes. When 3D fractal rough surface is in elastic deformation, the dimensionless load-area relations of loading and unloading processes are identical. When 3D fractal rough surface is in inelastic deformation, the dimensionless total real area in unloading process is greater than the dimensionless total real area in loading process for a given contact load. For a given load, the differences in total real contact area between loading and unloading processes decrease with an increase in fractal dimension.

Modeling of the Loading–Unloading Contact of Two Cylindrical Rough Surfaces with Friction

“…The corresponding unloading contact model varies with the final deformation stage of the loading process. Asperities on the surface still satisfy the fractal characteristic at the end of the unloading process [39,44]. The size distribution in contact of two cylindrical surfaces in the unloading process can be written as:…”

“…Because Equations (15) and (32) are regressed by the results of finite element method(FEM), some errors are involved in Equation (39). The load correction factor K u is introduced to minimize these errors [39,44] and Equation (39) can be rewritten as:…”

“…where K ucep1 is the load correction factor of the first elastoplastic stage. By substituting Equations (26) and (40) into Equation (39), K ucep1 can be given as:…”

“…The classical KE model [7] and the Yuan model [39] are the available models for loading and unloading contact process and limited to planar surfaces.…”

“…Yuan [38] proposed a revised MB model, and deduced the transition from elastic, elastoplastic to full plastic deformation for a single asperity whose contact area and load is related to asperity level. Further, Yuan [39] extended this model to develop a loading-unloading contact model between three-dimensional rough plane surfaces based on fractal theory, and the relation between the total contact load and the total real contact area was obtained in the loading and unloading processes. Xu [40] developed the revised size distribution functions for the two-dimensional and three-dimensional fractal rough surfaces respectively, and the validity of the model was verified by comparing with the experimental data.…”