大口径透镜混合柔性支撑结构优化设计

针对大口径透镜，提出了一种新型混合柔性支撑结构，能够使透镜同时满足面形精度及位置精度要求。首先利用卡氏第二定理对各柔性铰链进行分析，建立支撑组件整体柔度模型。然后以柔性支撑组件的总变形能为目标函数，以位置精度及实际使用空间要求为约束，建立结构优化设计模型。之后确定径向柔性支撑结构对组件整体柔度的敏感度最大并对其刚度进行验证。最后对优化后的透镜组件整体结构进行有限元分析，同时利用曲面拟合方法计算镜面面形精度。仿真结果表明，在该新型混合柔性支撑结构的作用下，透镜在各要求工况下的面形精度均优于λ/20 (λ=632.8 nm)。所设计的新型混合柔性支撑结构及其理论分析过程可为高精度大口径透镜的支撑技术提供参考。

Optimization design of large-aperture lens mixed flexible support structure

A novel mixed flexible support structure was proposed to satisfy the requirements of surface and position accuracy of a large-aperture lens. First, Castigliano’s second theorem was used to analyze the various flexible hinges and the whole flexibility model of the support component was established. Then, the objective function of the total deformation energy of the flexible support assembly was used to establish the constraint equation based on the position accuracy and the actual space requirements, and a structural optimization design model was established. It was determined that the radially flexible support structure was the most sensitive to the flexibility of the flexible support assembly, and its stiffness was verified. Finally, the finite element analysis of the optimized whole structure of the lens assembly was carried out, and the surface accuracy was obtained by using the geometric fitting method. The simulation results show that the surface shape accuracy of the new hybrid flexible support structure is better than λ/20 (λ=632.8 nm) under various conditions. The novel mixed flexible support structure and its theoretical analysis process can provide a reference for the supporting technology of high precision large-aperture lens.