Effects of quantities and pole-arrangements of magnets on the magneto-rheological polishing (MRP) performance of sapphire hemisphere

To improve the polishing effectiveness of sapphire hemisphere, the effects of quantities and pole-arrangements of magnets in magnetic field generator on the magneto-rheological polishing (MRP) performance of sapphire hemisphere were investigated through simulation and experiment. After analyzing the distribution of magnetic field on sapphire hemisphere surface and its change with the relative motion between sapphire surface and magnetic field generator during MRP, we developed a material removal rate (MRR) model based on the Preston equation, and the material removal distribution and average removal depth of polished sapphire surface could be predicted. Then according to the calculated material removal distribution, a surface roughness model of polished sapphire was established. Both simulation and experiment results showed that the MRR of polished sapphire increases with the quantity of magnets, while the surface roughness Ra of polished sapphire decreases with the quantity of magnets. As for the effect of pole-arrangement, the cross-stacking arrangement produced a surface of Ra 2.97 nm with MRR of 0.496 μm/h, and the cross-involute arrangement achieved a smoother surface of Ra 0.79 nm with MRR of 0.435 μm/h in MRP. These results showed that the cross-involute and cross-stacking pole-arrangements are favorable for the MRP of sapphire hemisphere. The good agreement between experimental and theoretical results verified the reliability of the established MRR and Ra models.