Multiscale functional analysis of wear: A fractal model of the grinding process

In this paper, we propose to create a fractal function defined by an infinite series to model worn surfaces obtained by a grinding process. In this series, each elementary term characterizes a wear process at a given scale. This series is only defined by two parameters: an amplitude parameter and the fractal dimension. This model is tested on worn profiles obtained by using different grinding paper grades and roughness is assessed by tactile profilometry. Then an inverse method is developed to obtain simulated profiles that present the same morphology as the experimental ones. The results from this study prove that our method allows simulation of profiles with elementary functions that characterize the wear process.