Modeling of material removal in pre-structured magnetorheological elastic polishing based on lame differential equation and its experimental validation

Magnetorheological elastic polishing is a new polishing method for aluminum alloy mirrors due to its high polishing efficiency and low processing damage. However, the traditional polishing pressure model is not applicable to magnetorheological elasticity polishing processing conditions due to the lack of supporting removal theory. As a result, the processing can only rely on experience, often leading to the problem of uneven polishing. In order to achieve the MREP process improvement and enhance the polishing of aluminum alloys, a pre-structured magnetorheological elastic polishing (MREP) removal method is proposed. In this study, the gradient magnetic field excited by permanent magnets was calculated based on the molecular current model. The interaction between magnetized particles in the magnetic chain inside the magnetorheological elastic polishing head was analyzed by using the magnetic dipole model, and the elastic modulus E was constructed as a function of the gradient magnetic field. Using the idea of finite elements, the machining pressure of MREPH was solved according to Hooke's law and lame differential equation. A mathematical model of the material removal function of MREPH was developed by combining Preston's equation. To verify the accuracy of the contact pressure model, the contact pressure was measured by using vision sensors and pressure sensors. The accuracy of the established material removal model was verified by polishing experiments. Fixed-point polishing and single trajectory polishing were experimented. Moreover, the relationships between the polishing effects and the process parameters (Polishing speed, extrusion depth, and polishing magnetic field strength) were investigated. According to the generated material removal map and above impact relationship, process optimization can be carried out. Finally the excellent surface quality was obtained. Sa decreased from 187.368 nm to 20.385 nm (Optimized by 89.1 %). Sz decreased from 1372.539 nm to 164.441 nm (Optimized by 88.0 %). Ra decreased from 245.109 nm to 25.835 nm (Optimized by 89.4 %). PV decreased from 714.921 nm to 85.163 nm (Optimized by 88.1 %).