High-accuracy process based on the corrective calibration of removal function in the magnetorheological finishing

The corrective calibration of the removal function plays an important role in the magnetorheological finishing (MRF) high-accuracy process. This paper mainly investigates the asymmetrical characteristic of the MRF removal function shape and further analyzes its influence on the surface residual error by means of an iteration algorithm and simulations. By comparing the ripple errors and convergence ratios based on the ideal MRF tool function and the deflected tool function, the mathematical models for calibrating the deviation of horizontal and flowing directions are presented. Meanwhile, revised mathematical models for the coordinate transformation of an MRF machine is also established. Furthermore, a Ø140-mm fused silica plane and a Ø196 mm, f/1∶1, fused silica concave sphere samples are taken as the experiments. After two runs, the plane mirror final surface error reaches PV 17.7 nm, RMS 1.75 nm, and the polishing time is 16 min in total; after three runs, the sphere mirror final surfer error reaches RMS 2.7 nm and the polishing time is 70 min in total. The convergence ratios are 96.2% and 93.5%, respectively. The spherical simulation error and the polishing result are almost consistent, which fully validate the efficiency and feasibility of the calibration method of MRF removal function error using for the high-accuracy subaperture optical manufacturing.