Image processing–based material removal rate analysis of morphable polishing tools with labyrinth and dimple textures

Morphable polishing tools are capable of finishing diamond turned surfaces with roughness in the nanometre range. The material removal rate of morphable tools polishing is challenging to calculate due to the labyrinth and dimple textures. This paper introduces a multi-scale theoretical model for predicting the material removal rate of morphable polishing tools. The model includes the polishing velocity, polishing pressure, material removal by an abrasive, and number of effective abrasives. First, polishing velocity is obtained by tool kinematics analysis. Second, polishing pressure is obtained based on image processing. Theoretical polishing pressure is calculated by polishing pressure equations. Morphable tool texture images are binarized and conducted with Boolean product of the theoretical polishing pressure images to get the morphable tool polishing pressure. The morphable tool polishing pressure and 12-image averaged pressure are conducted with Boolean product of the polishing velocity to obtain the instant and average material removal rate. Then, the polishing pressure and material removal rate model are validated through pressure measurement and polishing tests, respectively. It is found that the polishing spot is ellipse shape with long axis (10.6 mm) and short axis (9.6 mm). The material removal rate for smooth tools along the short axis is almost constant while it steadily increased along the negative long axis. For labyrinth tools, the material removal rate along the short axis and the long axis is a trapezoidal shape and scalene triangular shape. For dimple tools, the material removal rate along the long axis and the short axis are similar to isosceles triangular shape. The model results agree well with the experimental data and quantify how morphable tool texture influences the polishing pressure component and influences the material removal rate, which makes the polishing process more predictive. The image processing–based method can be further applied to obtain polishing pressure and material removal rate of different complicated polishing tools.