针对地基大口径望远镜次镜系统加工精度和装调精度的要求, 提出了基于拓扑优化的次镜系统结构设计方法。该方法利用变密度的拓扑优化思想, 将次镜系统的Spider结构和Serrurier桁架的设计域限定为基结构, 以期望方向的变形最小, 通过材料的去留决定结构的最终形状和尺寸。首先, 以相对密度为设计变量, Spider结构以1阶振型和重力方向变形为设计约束, 桁架以X向和Y向变形为设计约束, 建立各结构的拓扑优化模型; 然后, 以拓扑优化所得构型为基础, 利用Workbench进行优化迭代; 最后, 设置优化参数, 采用有限元法进行动静刚度分析和优化。结果显示4 m望远镜次镜系统的1阶谐振为22.7 Hz, 光轴指向天顶和水平时重力方向偏移分别为-0.173 mm和-0.195 mm, 并且Spider结构和Serrurier桁架的轻量化率超过30%。该结果验证了文中方法的有效性。

Aiming at the precision requirement of machining and assembling for the SM system of the large-aperture grounded telescope, a design method for the structure of SM system based on topology optimization was presented. Based on the variable density idea of topology optimization, the ground structure was restricted to be the Spider and Serrurie trusses, the target was that the deformation along the expected direction was minimized, and the last appearance and dimension were described by whether the material was deleted from the ground structure or not. Firstly, the relative density was taken as design variable, and then by using 1st modal and deformation in gravity direction for the Spider and deformation along the X and Y axis for the truss as a design restraint, a topology optimization model was established. Secondly, on the basis of concept structure obtained by topology optimization, it was iterated and optimized by using Workbench. Finally, the optimized parameter was set, and the static and dynamic stiffness was analyzed and optimized using the finite element method. It shows that the 1st modal in the 4 m telescope SM system is 22.7 Hz, and the deviation in the direction of the gravity is -0.173 mm and -0.195 mm when the optical axis is parallel and vertical to the gravity direction, and the lightweight ratio exceeds 30% for the Spider and Serrurier truss, respectively. The results demonstrate the validity of the proposed approach properly.