Mid-spatial frequency error characteristics induced by tool influence function in bonnet polishing

Bonnet polishing, a cost-effective and high-precision polishing technique with remarkable adaptability, is widely utilized in the precision machining of complex curved surfaces. However, mid-spatial frequency (MSF) error residuals significantly constrain its convergence efficiency in form error correction and ultimate machining accuracy. This paper investigates the influence of tool removal function characteristics on MSF errors during bonnet polishing. Initially, the theoretical removal functions under varying tool and process conditions were derived through finite element simulations, with the computational framework grounded in Preston's law, Hertzian contact mechanics, and kinematic analysis. Subsequently, a spectral-domain simulation model was developed to quantify MSF error residuals on optically finished surfaces based on the characterized removal functions. The simulation results indicate that under conditions of larger curvature bonnets and lower air pressure, the MSF error residuals are smaller. Finally, experiments were conducted on a high-precision flat fused silica element with a diameter of 100 mm to validate the MSF prediction model, and the experimental results showed good consistency with the simulation results. The findings of this study provide critical guidance for suppressing MSF errors in high-precision bonnet polishing applications.