为了使大孔径长条形空间反射镜支撑结构同时满足高刚度、高强度和良好的热尺寸稳定性要求, 建立了反射镜支撑系统的模态解析数学模型, 并对该模型所描述的反射镜沿各轴向的平动和转动模态特性进行了研究。根据模态解析解得出3个支撑点确保质量分布相对均匀时, 系统的动-静态刚度最大的结论, 并结合有限元分析技术确定了反射镜的支撑位置。此外, 在支撑结构中设置了柔性环节, 改善了反射镜在各工况下所受的应力环境以确保其光学性能。通过优化柔性铰链最薄处的厚度和圆弧半径两个参数来调节反射镜的面形精度, 使面形精度满足设计要求。分析及试验结果表明: 柔性铰链最薄处厚度为4 mm, 圆弧半径为2 mm时, 反射镜在重力和4℃均匀温升工况下的面形精度RMS值均优于12.3 nm; 组件实际一阶固有频率为146 Hz, 与有限元分析结果的误差小于5%; 柔性支撑结构动态应力响应远小于材料的屈服极限, 完全满足反射镜结构系统的设计要求。

To design a large aperture rectangular mirror with high stiffness, high strength and good thermal dimensional stability precisely, an analytical mathematical model of the mirror supporting system was established and its modal characteristics were investigated. Firstly, the support location of the mirror was determined according to the conclusion obtained by modal analytical solution that the dynamic and static stiffness is the highest when the three supports keep the mass distribution relatively homogenous. Then, the support structure was analyzed in detail by Finite Element Method(FEM) and a new type of flexible support was presented. By adjusting two parameters, the thinnest thickness and the arc radius of a flexible hinge, the surface figure accuracy of the mirror was modified. Finally, the modal analysis of mirror component was performed. Analytical and experimental results indicate that the surface figure accuracy of the mirror can reach RMS 12.3 nm under the load case of gravity and 4℃ uniform temperature rise, respectively, when the thickness of the flexible hinge is 4 mm and its circular radius is 2 mm. Moreover, its first order natural frequency is 146 Hz, which shows an error under 5% compared to FEA results. Research demonstrates that the mirror structure satisfies all design indexes.