Fractal characterisation and modeling in fracture mode grinding of optical glass

In the fabrication process of ophthalmic lenses, the surface texture achieved by the fine grinding operation of the glass moulds has a very important influence on the duration of the subsequent polishing operation and on the conformance of the final product to the specifications. In the literature some models suitable to the characterization of the polishing phase are already available. Therefore, a virtual environment aimed at the simulation of the surface texture induced by the grinding operation should be envisaged in order to identify the optimal operating conditions of the glass moulds manufacturing process. In the present paper, the modified Weistrass-Mandelbrot function (W-M) has been investigated to assess its effectiveness in the characterization of the surface texture and in the simulation of the roughness profiles of ground glass moulds for lenses. The analysis has been performed by comparing the Ra roughness parameter computed from profiles measured by a profilometer and profiles simulated using the W-M function for bi-fractal surfaces. Emphasis has been given to the identification of “n” and “G” parameters of the W-M functions, usually overlooked in the literature. An Rf parameter has been defined that summarizes the fractal parameters used in the definition of the W-M function. A correlation between the roughness parameters and the Rf parameter has been proposed. The correspondence between simulated and measured profiles is fair, both by visual inspection and by comparing the considered roughness parameters. Moreover, a linear relationship between the actual Ra and Rf and between the Ra computed on the simulated profile (defined Raf) and Rf has been identified.