Reexamineof the Fractal Contact Theory

This project investigates the basic assumption of fractal contact theory. In 1990s, Majumdar and Bhushan (MB) proposed a fractal contact theory based on the Weierstrass-Mandelbrot function (WM function). In this theory, the asperity curvature and the asperity distribution function are assumed by the fractal theory. Recently, Professor Jen-Fin Lin and his students proposed a modified fractal contact by using the chain rule. They found that the fractal dimension of the asperity distribution function and the topothesy of the fractal profile are not constant. Another approach in fractal contact theory is to simulate fractal surfaces by WM function. Then, compute the contact force between such fractal surfaces and a flat surfaces. However, there are problems in all the fractal contact theories. In the MB’s and Professor Lin’s theories, the assumption about the asperity curvature and the asperity distribution function is questionable. Meanwhile, the chain rule used by Professor Lin is also questionable in mathematics. On the other hand, whether WM function can represent real surfaces is need to be investigated. In this project, both numerical analysis and experiment will be employed. In numerical analysis, the WM function will be investigated. The asperity curvature and asperity distribution function of the WM function will be found. The results will be compared with the current theories. In experiment, fractal surfaces will be machined. The properties of fractal surfaces will be compared with the WM function. The result will find the limit of the current fractal contact theories and provide a guide for the development of fractal contact theory. 表

Project ID:PB9709-1102
External Project ID:NSC97-2221-E182-021