Modeling surface roughness in the stone polishing process

In this paper, a new method for modeling and predicting the surface roughness of the workpiece in the stone polishing process is developed. This method is based on the random distribution of the stone grain protrusion heights and the force balance by contact grains. To do so, first, the topography of a polishing stone is generated based on a Gaussian distribution with the mean value and standard deviation determined from a given stone grit number. Second, the plasticity theory is applied to determine the micro depth of cut of a single grain for a given workpiece hardness (Brinell number). Third, a search method is developed to determine the number of the contact grains and the micro depth of cut, based on the force balance principle between the force applied on the stone and the forces transmitted to the grains that are in contact with the workpiece. Fourth, a method is presented for predicting the surface roughness based on the micro depth of cut and contact grains. A good agreement of the prediction results with the experimental data proves the effectiveness of the proposed method.