针对某空间相机超轻和高热稳定性的要求,设计一体化的背板结构,使得支撑背板既是整机主承力板,又是主反射镜支撑背板;采用具有高比刚度、高热稳定性的SiC作为背板材料,通过施加最小尺寸约束的变密度拓扑优化,确定支撑板背部筋的布置;建立以第二代非支配排序遗传算法为优化算法的多目标优化模型,集成反射镜面形误差和背板质量,完成背板的尺寸优化设计,背板质量仅为0.591 kg,筋厚的最小值为2.1 mm;最后利用有限元分析对优化结果进行动、静力学性能分析。结果表明:在5 ℃温升载荷下,反射镜组件镜面面形方均根为0.158 nm,具有良好的热稳定性;在X向重力载荷作用下(与光轴垂直方向/面形检测方向),镜面面形的方均根为1.169 nm,峰谷值为5.403 nm;反射镜组件的一阶固有频率为397 Hz,镜面边缘随机振动响应(RMS)小于16g ,满足空间应用。

According to the requirements of ultra-light and high thermal stability of a space camera, an integrated backplate structure is designed so that the supporting backplate is not only the backplate of the main mirror, but also the main bearing plate of the space camera. The SiC with high specific stiffness and high thermal stability is used as the backplate material. The layout of back ribs is determined by the variable density topology optimization with the addition of a minimum size constraint. The size optimization design is completed by a multi-objective optimization model with Non-dominated Sorting Genetic Algorithm II (NSGA-II), integrating the mirror surface shape and the mass of the backplate. The mass of the backplate is only 0.591 kg and the minimum rib thickness is 2.1 mm. The dynamic and static performances of the optimization results are finally analyzed by the finite element analysis. The results show that the root-mean-square value of the mirror shape in the mirror assembly is 0.158 nm under a temperature rising load of 5 °C, which means good thermal stability. The root-mean-square value of the mirror shape is 1.169 nm and the peak to valley value is 5.403 nm under the X-direction gravity load (the direction perpendicular to the optical axis/the direction of detecting surface shape). The first-order intrinsic frequency of the mirror assembly is 397 Hz and the random vibration response value of the sampling point of the mirror edge is less than 16g. These mean the requirements for space application are satisfied.