Equivalent Modeling and Verification of a High-Steepness and Lightweight Elliptical Aluminum Mirror

Abstract

In order to realize the compact layout of aerospace payloads, the design and manufacture of high-steepness lightweight aluminum alloy mirrors is a key technology to be explored. For high-steepness mirrors, the traditional method is to establish the initial thickness that satisfies the bending stiffness through finite element optimization iteration, which cannot achieve fast modeling and performance estimation. In this paper, firstly, the equivalent modeling method of the mirror with high steepness is proposed to achieve the equivalent of the elliptic mirror with a diameter of 410 × 310 mm and F# less than 0.7. Based on the mathematical model, topology shape optimization was used to build a highly lightweight mirror structure that could be quickly assembled, and the equivalent area–mass density of the mirror is less than 34 kg/mm2. Next, the rationality of design feasibility was verified by simulation analysis. Finally, by using single point diamond turning combined with post polishing process, the high-precision manufacturing of conventional aluminum alloy mirror was realized. The results show that the mirror shape accuracy is 1/10 λ (λ = 632.8 nm), and the surface roughness Ra is 3.342 nm. This research provides strong theoretical support and application prospects for the low-cost and rapid manufacturing of high-steepness lightweight aluminum alloy mirrors.