Although magnetorheological finishing (MRF) is being widely utilized to achieve ultra-smooth optical surfaces, the mechanisms for obtaining such extremely low roughness after the MRF process are not fully understood, especially the impact of finishing stresses. Herein we carefully investigated the relationship between the stresses and surface roughness. Normal stress shows stronger impacts on the surface roughness of fused silica (FS) when compared with the shear stress. In addition, normal stress in the polishing zone was found to be sensitive to the immersion depth of the magnetorheological (MR) fluid. Based on the above, a fine tuning of surface roughness (RMS: 0.22 nm) was obtained. This work fills gaps in understanding about the stresses that influence surface roughness during MRF.

The dwell time algorithm is one of the key technologies that determines the accuracy of a workpiece in the field of ultra-precision computer-controlled optical surfacing. Existing algorithms mainly consider meticulous mathematics theory and high convergence rates, making the computation process more uneven, and the flatness cannot be further improved. In this paper, a reasonable elementary approximation algorithm of dwell time is proposed on the basis of the theoretical requirement of a removal function in the subaperture polishing and single-peak rotational symmetry character of its practical distribution. Then, the algorithm is well discussed with theoretical analysis and numerical simulation in cases of one-dimension and two-dimensions. In contrast to conventional dwell time algorithms, this proposed algorithm transforms superposition and coupling features of the deconvolution problem into an elementary approximation issue of function value. Compared with the conventional methods, it has obvious advantages for improving calculation efficiency and flatness, and is of great significance for the efficient computation of large-aperture optical polishing. The flatness of φ150 mm and φ100 mm workpieces have achieved PVr₁₅₀ = 0.028 λ and PVcr₁₀₀ = 0.014 λ respectively.