A novel specialized material removal rate model considering the synergistic effect of dynamic pressure and shear stress for the permanent-magnet small ball-end magnetorheological polishing

Abstract

Permanent-magnet small ball-end magnetorheological polishing is often used to process small glass workpiece. During polishing, the pressure and shear stress are generated by magnetorheological fluid on the workpiece surface. When conducting fixed-point polishing experiment on fused silica plane workpiece, it was found that the polished pits were mainly distributed on one side of the polishing head's rotation axis. However, the available material removal model considering only a single force cannot explain the cause of polished pit offset phenomenon. It is speculated that the synergistic effect of the two forces on material removal may lead to the offset phenomenon. In order to accurately describe the material removal mechanism of this polishing method, a novel material removal rate model is established in this research. First, a group of actual polished pits are obtained through fixed-point polishing experiment. Then, a novel pressure-shear stress synergistic material removal rate model with unknown coefficients is established. Based on this model, the fixed-point polishing process is simulated by finite element method. The simulated polished pits under different model coefficients are obtained, and the influence rules of model coefficients on the polished pit contour is analyzed. Finally, by seeking the minimal fitting error between the simulated and actual contours, a group of optimal model coefficients are determined, namely, the shear stress coefficient is 1, the dynamic pressure coefficient is 1.2, and the weight coefficient of polishing velocity is 1.9. Through verification, the relative error between the simulated and actual contours can be as low as −9.12 % to 7.13 %. The novel model reveals that the material removal is caused by both shear stress and dynamic pressure. The dynamic pressure is distributed on one side of the polishing head axis and plays a leading role in material removal, which can well explain the cause of offset phenomenon. This research fills the blank of material removal mechanism of this polishing method, and the novel model provides a theoretical basis for process optimization research.