Topology-optimization-based design method of flexures for mounting the primary mirror of a large-aperture space telescope

Abstract

For the development of a large-aperture space telescope, one of the key techniques is the method for designing the flexures for mounting the primary mirror, as the flexures are the key components. In this paper, a topology-optimization-based method for designing flexures is presented. The structural performances of the mirror system under multiple load conditions, including static gravity and thermal loads, as well as the dynamic vibration, are considered. The mirror surface shape error caused by gravity and the thermal effect is treated as the objective function, and the first-order natural frequency of the mirror structural system is taken as the constraint. The pattern repetition constraint is added, which can ensure symmetrical material distribution. The topology optimization model for flexure design is established. The substructuring method is also used to condense the degrees of freedom (DOF) of all the nodes of the mirror system, except for the nodes that are linked to the mounting flexures, to reduce the computation effort during the optimization iteration process. A potential optimized configuration is achieved by solving the optimization model and post-processing. A detailed shape optimization is subsequently conducted to optimize its dimension parameters. Our optimization method deduces new mounting structures that significantly enhance the optical performance of the mirror system compared to the traditional methods, which only focus on the parameters of existing structures. Design results demonstrate the effectiveness of the proposed optimization method.

Optimization Design of the Spaceborne Connecting Structure for a Lightweight Space Camera

“…Rui et al established a topology optimization model with the mirror shape error caused by gravity and thermal effects as an objective function and the first-order natural frequency of mirror assembly as a constraint condition. The results showed that this optimization method significantly improves the optical performance of the mirror assembly [11]. These studies demonstrated the feasibility of topology optimization in the design of optomechanical structures.…”

Design and Optimization for Mounting Primary Mirror with Reduced Sensitivity to Temperature Change in an Aerial Optoelectronic Sensor

“…A convenient measure to quantify the optical performance of the mirror is RMS (root-mean-square) of the mirror surface shape error. The RMS can be obtained by Zernike polynomial fitting, which is expressed by Equation (1): where N is the number of the nodes of the mirror face, w i is weight of the i -th node, u i is the sag displacement of the i -th node, z 1 , z 2 , z 3 represent the piston, tilt and power term of the deformed surface, respectively [ 12 ].…”

“…According to the simulation result, the configuration of a lightweight mirror for a large-aperture space telescope was obtained. Hu Rui et al [ 12 ] developed a method for designing the flexure for mounting the primary mirror. A topology optimization was firstly adopted to the extraction of conceptual configuration.…”

Lightweight Design of Multi-Objective Topology for a Large-Aperture Space Mirror

“…In order to reach the minimum values of mirror surface shape error caused by lateral gravity, axial gravity, and polishing pressure at the same time, the multi-objective optimization problem is selected for the design method. The practical way to deal with the multi-objective optimization problem is to combine the multiple objectives into a single objective function, which is easy to be solved by assigning weighting factors to the objectives, or choosing the most important one as the objective function and treating the other objectives as the constraint conditions [12].…”