2 m 望远镜K 镜支撑结构优化设计

为了使得某2m望远镜消旋K镜在重力环境温度变化的影响下镜面面形和结构刚度满足要求，设计了一种柔性支撑结构。KM1 支撑方式采用背部三点支撑，通过有限元软件ANSYS 对支撑位置进行优化。并基于伴随变换建立了柔性支撑杆的柔度矩阵，对柔性铰链的厚度、长度和宽度进行优化，使反射镜支撑刚度满足需求，并减轻热应力和装配应力面形的影响。KM2 采用周边三点支撑，间隔120均匀分布，支撑杆结构与KM1 相同。在重力和均匀温降的联合工况下，KM1 和KM2 的有限元仿真结果达到了设计要求，KM1 镜面面形RMS 低于/40，KM2 镜面面形RMS 低于/60，一阶谐振频率均高于100 Hz。

Optimum design of support structure for 2m telescope’s K mirror

A flexible support structure was designed to make the mirror surface figure error and the stiffness of the structure fulfill the requirements of the design of a 2m telescope's K mirror. KM1 was the support at three points on the rear of mirror. The position of support points was optimized by the FEA software ANSYS to minimum the mirror surface's RMS. And the flexibility matrix of the flexible support bar was built by theadjoint transformation. Then based on the flexibility matrix, the thickness, length and the width of the flexure hinge were optimized to reduce the thermal stress and assembly stress and fulfill the requirement of the mirror support's stiffness. KM2 was the support at three points which are uniformly spaced around the circum of mirror. The flexible support bar of KM2 was the same as KM1's. The FEA simulation results of KM1 and KM2 under the work condition of gravity and temperature drop met the design requirements. The RMS of KM1 was less than /40, and the RMS of KM2 was less than/60. Their first order resonant frequency was all over 100 Hz.