Fractal geometry modeling with applications in surface characterisation and wear prediction

Manufactured surfaces such as those produced by electrical discharge machining, waterjet cutting and ion-nitriding coating can be characterized by fractal geometry. A modified Gaussian random fractal model coupled with structure functions is used to relate surface topography with fractal geometry via fractal geometry via fractal dimension (D) and topothesy (L). This fractal characterization of surface topography complements and improves conventional statistical and random process methods of surface characterization, Our fractal model for surface topography is shown to predict a primary relationship between D and the bearing area curve, while L affects this curve to a smaller degree. A fractal geometry model for wear prediction is proposed, which predicts the wear rate in terms of these two fractal parameters. Using this model we show that the wear rate V_r and the true contact area A_r have the relationship V_rα (A_r)^m(D), where m(D) is a function of D and has a value between 0.5 and 1. We next study the optimum (ie the lowest wear rate) fractal diemsnsion in a wear process. It is found that the optimum fractal dimension is affected by the contact area, material properties, and scale amplitude. Experimental results of bearing area curves and wear testing show good agreement with the two models.