Abstract
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.
Highlights
With the rapid increasing requirements for the fabrication of high-precision optical elements in modern optical systems, several advanced deterministic optical surfacing technologies have been developed over the past decades, such as ultra-precision computer controlled optical surfacing (CCOS), magnetorheological finishing (MRF), ion-beam figuring (IBF), bonnet polishing (BP) [1,2]
It is generally assumed that deterministic optical surfacing technology is a linear shift-invariant system, and the mathematical model of the convolution of the dwell time and removal functions being equal to the distribution of the removal amount is generally adopted, and this is given in Equation (1) [6]:
To validate effectiveness of the algorithm, repetitious experimental studies on flatness figuring was carried outproposed based on the self-developed ion-beam figuring studies on flatness flatness figuring was wassetup carried out based based onthe the15
Summary
With the rapid increasing requirements for the fabrication of high-precision optical elements in modern optical systems, several advanced deterministic optical surfacing technologies have been developed over the past decades, such as ultra-precision computer controlled optical surfacing (CCOS), magnetorheological finishing (MRF), ion-beam figuring (IBF), bonnet polishing (BP) [1,2]. Han et al [19,20] proposed a Gaussian mixture model to model experimental removal functions and provided the dwell time algorithm according to the dynamic characteristics of the machine tool These methods are mainly based on matrix equations, and the computational efficiency might be much lower especially for large-aperture optical elements, so the solution might not be smooth enough. The existing dwell time algorithms are conducted mainly based on a meticulous mathematical theory and designed to pursue high convergence rate Those methods do not adequately consider the distribution characteristics of the removal function and rarely incorporate the speed-smoothing issues that are closely related to convergence efficiency and machine tool motion implementation. The results showed that it performs well in the profile for smoothness and convergence efficiency
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