Multi-Scale Model of Mid-Frequency Errors in Semi-Rigid Tool Polishing of Diamond-Turned Electroless Nickel Mirror

Semi-rigid tool polishing is widely used in the high-precision manufacturing of electroless nickel surface due to its stable material removal and high efficiency in correcting mid- and high-frequency profile errors. However, predicting mid-frequency errors remains challenging due to the complexity of their underlying sources. In this study, a theoretical model for semi-rigid tool polishing was developed based on multi-scale contact theory, incorporating a bridging model, rough surface contact, and Hertzian contact mechanics. The model accounts for the effects of tool surface roughness, polishing force, and path spacing. A series of experiments on diamond-turned electroless nickel mirrors was conducted to quantitatively evaluate the model’s feasibility and accuracy. The results demonstrate that the model can effectively predict mid-frequency errors, reveal the material removal mechanisms in semi-rigid polishing, and guide the optimization of process parameters. Ultimately, a surface with mid-frequency errors of 0.59 nm Rms (measured over a 1.26 mm × 0.94 mm window) was achieved, closely matching the predicted value of 0.64 nm.