针对某离轴三反光学系统中的大长宽比长条形SiC反射镜镜面边缘随机振动加速度响应均方根值过大的特点, 提出一种采用“基结构法”的反射镜结构拓扑优化方法, 以随机振动加速度响应均方根值最小化为优化目标.首先对某初始反射镜结构进行有限元分析, 发现反射镜镜面边缘点Z向加速度响应均方根值过大.其次, 应用连续体结构拓扑优化思想, 以反射镜镜面边缘点的随机振动加速度响应均方根值作为优化目标, 以镜面峰谷值、镜体一阶约束频率作为约束条件, 以反射镜筋板式基结构作为优化空间, 对反射镜镜体结构进行拓扑优化设计, 得到了一种各项力学性能指标及面形精度均满足指标要求的反射镜轻量化结构.最后, 通过有限元分析与振动试验, 验证了本文设计的反射镜结构拥有良好的力学性能, 其中反射镜镜体质量相比优化前降低了13%, 镜面边缘点的Z向随机振动加速度响应均方根值降低了58%, 证明了本文优化方法的有效性.

According to the characteristics of too large root mean-square value acceleration response of random vibration at edges of rectangular space mirror with large aspect ratio, this paper propose a topological optimization based on ground structure method to design the structure of rectangular space mirror, with the goal for minimizing the acceleration root-mean-square values of random vibration. Firstly, after the finite element method analysis to the initial rectangular space mirror structure, the author find that the acceleration root-mean-square values of random vibration at the edge of mirror is too large to meet the requirements of design. Based on continuum structural topology optimization thought, by using the acceleration root-mean-square values of random vibration at rectangular space mirror's edge as an optimization object, the optical aberration PV and the primary frequency of mirror as the design restraint, the rib plate type ground structure of mirror as the design variable, a topology optimization function is established. Futhermore, the new mirror based on the structure obtained by topology optimization was designed. Finally, by the finite element analysis and vibration test, the new structure of mirror is proved with a good dynamic performance and lightweight rate. Especially, mirror mass has reduced 13%, and the acceleration root-mean-square values of random vibration at mirror’s edge in Z direction reduced by 58%. The results demonstrate the validity of proposed approach properly.