Modeling of forces and material removal rate in ultrasound assisted magnetorheological polishing (UAMP) of sapphire

In order to fully investigate the polishing performance of the Fe3O4/SiO2 core-shell abrasive for sapphire material, it is necessary to conduct a comprehensive study into polishing forces and establish corresponding mathematical models. In this paper, based on the bonding strength of core-shell abrasive chains and the motion analysis of ultrasonic vibration in UAMP process, the mathematical models of shear force Fτ and normal force FN generated on sapphire surface are established. Experiments were implemented to verify the reliability of the Fτ and FN models under varying parameters, including the volume concentration of core-shell abrasives, excitation gap and working gap. The values and the variation trends of theoretical results are well in agreement with those of experimental results. Then, on the basis of the Fτ and FN models and Preston equation, we proposed a modified material removal rate (MRR) model, in which the contributions of FN and Fτ are all taken into consideration. Through the comparative analysis with the experimental results, the modified MRR model exhibits higher prediction accuracy than those models involving only Fτ or FN. The high-precision MRR model will facilitate the deterministic removal of sapphire surface material in UAMP process.