考虑接触边界条件的经纬仪主镜面形误差分析

The Surface Error Analysis of Theodolite Primary Mirror Considering Contact Boundary Condition

为了精确分析经纬仪主镜的面形均方根,对主镜支撑连接球绞的仿真方法进行研究.建立了主镜支撑系统的有限元模型,对比了刚性连接、约束节点自由度和接触边界条件三种球绞的仿真方法.采用接触边界条件方法仿真得到的主镜面形均方根值为16.37nm,应用干涉仪检测得到主镜在径向支撑状态下的面形均方根值为17.53nm,仿真结果与实验结果的偏差为6.62%.实验结果显示三种方法中,接触边界条件法能较准确地获得主镜面形均方根值,用此方法对主镜径向支撑结构进行了参数化分析,获得径向支撑位置、长度和宽度对主镜面形的影响规律,可以为主镜面形的精确分析及主镜支撑结构设计提供参考.

In order to obtain the accurate surface error Root Mean Square （RMS） of the theodolite primary mirror, the research on the simulation method of sphere joints in the primary mirror supports was carried out. The detail finite element model of primary mirror supporting structures was established. A comparison was made among three simulation methods of sphere joints. They are the method of rigid connection, the method of restricting the freedom of nodes and the method of contact boundary condition. The surface error RMS of primary mirror tested by interferometer is 17. 53 nm, while the simulated surface error RMS of the primary mirror is 16. 37 ran. The deviation between simulated results and experimental results is 6. 62o/oo. The experimental results show that the method of contact boundary condition can obtain a more accurate surface error RMS of the primary mirror than the other two methods. The parameterized analysis was conducted on the structures of the primary supports by the method mentioned above. The influence of lateral supports＇ location, lateral supportsr length and lateral supports＇ width to the surface error of the primary mirror was obtained. It＇s a good reference to the accurate analysis of the primary mirror surface error and the design of the primary mirror supports that simulating sphere joints using the method of contact boundary condition.