Fractal geometry model for wear prediction

Fractal characterization of surface topography is applied to the study of contact mechanics and wear processes. The structure function method is used to find the fractal dimension D and the topothesy L. We develop a fractal geometry model, which predicts the wear rate in terms of these two fractal parameters for wear prediction. Using this model we show that the wear rate V_r and the true contact area A_r have the relationship V_rαA_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 (i.e. the lowest wear rate) fractal dimension 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 wear testing show good agreement with the predictions based on the model.