Mechanics reveal of hardness-dependent contact force during magnetorheological finishing based on granular flow-Hertzian hybrid model

Magnetorheological finishing (MRF) has been widely used in the ultra-precision fabrication of optical components with different materials and shapes. As a flexible polishing method, MRF can be applied to the fabrication of ultra-thin brittle mirrors. However, the differences in contact force variations for materials with different hardness have been mainly studied by experimental investigation. There is no quantitative analysis and mechanism research related to the contact force of MRF, which is very important for the application of MRF in the optical manufacture. In this study, the material removal mechanism in MRF is investigated based on the granular flow theory and Hertzian contact theory. The modified quantitative shear force theoretical equation is established through the Preston equation. The relationship between material hardness, penetration depth, carbonyl iron powders (CIPs) concentration, CIPs size, and polishing contact force is analyzed. It is found that when the material hardness is the same, the contact force on the workpiece increases with the increase of penetration depth, CIPs concentration, and CIPs size. When the material hardness varies, the normal force on the workpiece increases, and the shear force decreases as the material hardness increases. Theoretical analysis and experimental results show strong consistency. This research provides what we believe to be new insights into the contact force and material removal mechanism of MRF. The research results are of significant importance for the further application of MRF.