为了获得轴向支撑结构对经纬仪大口径主镜面形的影响规律, 对主镜轴向支撑结构进行了结构拓扑优化设计及参数化分析。首先, 采用接触边界条件方法建立了详细的主镜支撑系统有限元模型, 对主镜初始支撑结构下的面形误差进行仿真分析, 获得主镜初始支撑结构下光轴水平及光轴竖直状态下主镜的面形RMS值。然后, 应用4D干涉仪对主镜径向支撑状态下的面形RMS进行了检测, 有限元仿真得到的主镜面形RMS值与实验结果的偏差为13.2%, 证明了仿真方法的准确性。最后, 对主镜轴向支撑结构进行了结构拓扑优化, 并根据拓扑优化结果建立新的主镜轴向支撑结构模型, 对其重要尺寸进行了参数化分析。优化的主镜支撑结构的主镜面形误差明显优于初始结构: 轴向支撑状态下主镜面形误差的RMS值由11.49 nm提升至8.38 nm。该研究可以为主镜支撑结构的设计提供重要参考。

In order to obtain the effect of supporting structures on the surface error of theodolite primary mirror, the topology optimization and parameter analysis of axial supporting structures of primary mirror were performed. First, contact boundary condition was used to establish the detail finite element model of primary mirror supporting structures. The surface error of original supporting structures was analyzed and the surface error RMS was obtained under both horizontal optical axis condition and vertical optical axis condition. Then, a 4D interferometer was used to measure the surface error RMS under lateral supporting condition. Results show that the deviation of surface error RMS of numerical results and experimental results is 13.2%, which verify the accuracy of simulation method. At last, the topology optimization of the primary axial supporting structures was carried out. The new axial supporting structures were made according to the topological configuration. After that, the parameter analysis was carried out on some important dimensions of axial supporting structures. Results show that the primary mirror surface error RMS of optimized supporting structures is obviously better than the original one. The original surface error RMS of axial supporting is 11.49 nm, while the optimized one is 8.38 nm. The research is an important reference to the design of primary mirror supporting structures.