Tool influence function(TIF) adaptation to figure error in magnetorheological finishing of complex surfaces

Complex optical surfaces are integral to advanced optical systems, and magnetorheological finishing (MRF) serves as their primary fabrication method. A single constant tool influence function (TIF), however, cannot readily reconcile processing precision with processing efficiency. The resulting throughput limitation cannot meet the great demand for complex optical surfaces, thereby constraining the development of optical systems. To address this trade-off, this paper proposes a polishing method in which the TIF adapts to the figure error. First, a dwell time model incorporating the adaptation of the TIF to the figure error was established. Particle swarm optimization was then employed to select the adaptive processing scheme. The stability and effectiveness of the model were then verified through simulation, followed by experimental validation of its correctness and effectiveness. Compared with a high-precision single-TIF process (TIF #3, d = 0.20 mm), the adaptive method yielded a 32.4% larger residual RMS error but reduced the processing time by 72.7%. Compared with a fast single-TIF process (TIF #12, d = 0.40 mm), the adaptive method reduced the residual RMS by 33 nm (32.9% relative reduction) and cut the processing time by 9.4 min. These results demonstrate that TIF adaptation to figure error in MRF effectively balances processing efficiency and precision for complex surface optics. The method provides theoretical and technical support for efficient MRF based fabrication of complex curved optical elements and carries substantial practical value.