Correction of the Preston equation for low speeds

According to Preston [J. Soc. Glass Technol. 11, 214 (1927)], the wear on a glass point in the polishing process is proportional to the work given by frictional force between glass and tool. He supposed that the frictional coefficient is a constant value. To verify this hypothesis, we measured the dragging forces applied to a tool as a function of the relative speed between a rotating glass and the tool center. To reproduce these experimental results, it was necessary to propose a new model, for which the frictional coefficient has a Gaussian dependence with relative speed. Therefore the wearing Preston equation has to be modified in order to include the frictional coefficient as a function of the relative speed.