Mechanism of a deterministic compliant figuring process (CFP) in Ni-P surface formation considering the robustness of the tool influence function: modeling and experimental investigation
Authors: Li Yuhao , Li Guo , Xue Jiadai , Ding Fei , Wang Bo 
Published: October 2023

Abstract
Deterministic small-tool polishing is paramount to fabricating ultra-precise aspheric X-ray optical components with the precise dwell time algorithm employed to remove the surface material in this procedure. However, the sub-aperture polishing removal function introduces surface ripple characteristics and degrades optical performance due to its narrower full width at half maximum, reducing the volume removal rate and inducing the surface high-spatial frequency and mid-spatial frequency error. It is urgent to insert flexibility control into deterministic small-tool polishing to enhance the adaptive capacity of tools to curvature variations and to obtain stable Gaussian-like tool influence functions. This paper explored the surface finishing removal mechanism based on a compliant figuring process, which verified the robustness and removal efficiency of the tool influence function for the planar and various curvatures of the Ni-P surface. Initially, a flexible head with in-situ correction of high slurry absorption and retention capacity on a self-developed six-axis ultra-precision figuring machine was selected as the figuring tool. Based on the compliant figuring process removal mechanism with three removal regimes, the relative velocity and contact pressure model were established. Meanwhile, an orthogonal experiment utilizing the compliant tool to figuring the planar specimen surface was carried out on the figuring testing machine, analyzing the impact of the removal function on the surface roughness and the form accuracy, and a pre-experiment was conducted to confirm the validity of the model. Furthermore, the orthogonal analysis of the variance approach was implemented to analyze the weight of the influencing factors of the compliant figuring process and to obtain the optimal process parameters for a stable Gaussian-like distribution removal function. As a result, the material removal kernel was sensitive to the offset accounting for 40%, and the error was 8% in the predicted value of the volume removal rate under the optimal parameter conditions. The magnitude trend of the mid-frequency error was suppressed, and the frequency error was converted to facilitate the subsequent processing in the curve of 1-power spectral density. Finally, the stability of figuring variable curvature large optics was delved into, the effect on the form accuracy and the optical performance with the variation of the residence time distribution, including the matching relationship between the full-width at the half of the maximum and spatial wavelength. From the perspective of optical performance, the mid-frequency ripple of the optics element is effectively enhanced from 2.4nm PV to 1.8nm PV following the second iteration and the half-power diameter of the multilayer film optics is promoted from 54.26 arcsec to 41.77 arcsec via the star-point approach and the visible light observation approach.