Deterministic polishing is critical to the fabrication of ultra-precision aspheric optics, where precise dwell time algorithms are used to remove surface material. However, the sub-aperture polish removal function introduces surface ripple characteristics and degrades optical performance due to its narrow full width at half maximum and mismatched spatial wavelengths, reducing volume removal rate and introducing high and medium spatial frequency errors on the surface. Therefore, there is an urgent need to introduce pre-processing and post-processing to improve flexibility control in deterministic small tool polishing, enhance the adaptability of the tool to the workpiece surface with changing curvature, and obtain a stable Gaussian-like tool influence function. This paper explores the surface finishing removal mechanism based on the compliant figuring process and verifies the robustness and machining accuracy of the tool influence function for plane and variable curvature Nickel-phosphorous alloy machined surfaces. Firstly, based on the removal mechanism of the figuring process, the relative velocity and contact pressure models were established. Secondly, the influence of the radius of curvature and the amount of offset on the removal function is discussed. Finally, the high frequency band and middle frequency band of the one-dimensional power spectral density curve are analyzed in detail, and the reliability and modification ability of the compliant figuring process are verified according to the amplitude spectrum image.
The removal function in machining is not an ideal impulse function, and the material removal at any point on the workpiece is a superposition of the removal at that point from the distribution of removal at surrounding points. When the residence time suddenly jumped to zero at the edge, the removal function and the residence time convolution results will gradually decrease at the edge, the removal matrix at the edge of the formation of the "collapse", after many convolution iterations, the edge of the face shape of the error convergence rate is lower than the other positions, resulting in edge effects. This paper firstly put forward an iterative algorithm based on the residence time of the cylindrical projection, and then analyze the edge effect in the iterative algorithm, and put forward two methods to suppress the edge effect, and select different removal functions and the form error on the algorithm to carry on the simulation calculation. Finally, the results of machining of mold #54 verifies the effective suppression of edge effect error by the method in this paper.
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