Compensation strategy and optimization of machining parameters for bonnet nonlinear deformation under polishing path errors

This study develops a nonlinear deformation compensation strategy for bonnet polishing, addressing how creep and stress relaxation under cyclic loading degrade surface accuracy in optical component manufacturing. Continuous polishing cycles (creep) and repeated expansion cycles (stress relaxation) reveal that the tool influence function (TIF) width increases nonlinearly with cycle number, showing a Logarithmic trend. The TIF width grew by 55.46% and 91.38% in the two cases, far exceeding the tolerance for fine sub-aperture polishing. To capture this behavior, a support vector regression (SVR)-based prediction model was established, achieving fitting accuracies of 98.07% and 99.26%. By integrating contact pressure and velocity distribution models, the TIF prediction accuracy reached 97.77% for Gaussian-type TIFs and 78.07% for M-shaped TIFs, reflecting shape transitions when the critical offset depth was exceeded. Furthermore, a mathematical model of polishing center offset was combined with the SVR TIF width model to correct Tangential path deviations caused by bonnet expansion. Verification experiments demonstrated that, without correction, a 4-mm offset produced a central depression with PV = 0.205λ, exceeding specification limits. With the proposed compensation, the PV value was reduced to 0.077λ, meeting the requirements of high-end optical components. The synchronous correction of bonnet-induced deformation and path errors ensures stable mass production of precision optics.