Uniformity of cluster magnetorheological finishing with dynamic magnetic fields formed by multi-magnetic rotating poles based on the cluster principle

Cluster magnetorheological finishing (MRF) with dynamic magnetic fields formed by synchronous eccentric rotation of multi-magnetic poles is a novel machining method for ultra-smooth and planarized surfaces. It is necessary to optimize the trajectories of abrasives to realize the uniform machining of the workpiece surface. In this study, the influences of the form of motion between the workpieces, the abrasives and the uniform distribution of motion trajectories of abrasives on the surface quality of the workpieces were theoretically investigated. On this basis, a mathematical model for exploring motion trajectories of abrasives during cluster MRF was established. The distribution uniformity of motion trajectories of abrasives was characterized by using the variation coefficient of standard deviation (VCSD) of the number of trajectory points. The influences of deflection mode, deflection amplitude, deflection rate, and distribution of the workpieces on the distribution of motion trajectories were simulated and analyzed. Furthermore, the technological parameters for attaining the optimal uniformity of the machined surface were obtained: polishing a single-crystal silicon substrate with a Y-direction deflection of 20 mm at a deflection rate of 10 mm s−1. By conducting test on two-inch (50.8 mm) single-crystal silicon substrates, surface roughness Ra, material removal rate (MRR), and total thickness variation (TTV) were used to characterize the uniformity of surfaces of the single-crystal silicon substrates. The results show that the test result is consistent with the simulation result obtained through the mathematical model. By polishing the single-crystal silicon substrates for 240 min based on the optimal technological parameters attained through simulation, the TTV of the workpieces decreases from 8.209 to 5.706 μm and the maximum difference of surface roughness Ra decreases from 29.4 to 9.02 nm. Thus, a planarized surface with a surface roughness Ra of 2.69 nm can be obtained.