大型光学望远镜副镜位姿精调机构的优化设计  

Optimal design of pose and position fine tuning apparatus for secondary mirror in large optical telescope

作　　者：徐刚[1] 杨世模[1] 龚雨兵[1] 

机构地区：[1]中国科学院国家天文台

出　　处：《光学精密工程》2008年第7期1181-1189,共9页Optics and Precision Engineering

基　　金：国家自然科学基金资助项目(No.10778628)

摘　　要：分析了大型光学望远镜副镜位姿精调机构的性能要求,提出了基于Gough-Stewart平台机构的副镜位姿精调机构的2个设计准则:运动精度准则和刚度准则。选取Gough-Stewart平台机构的2个角度尺寸参数和3个无量纲化的线性尺寸参数作为设计变量,分析了各设计变量对机构性能的影响规律;提出了与设计准则相对应的2个全条件性指标:运动传递精度指标和刚度指标,按照统一目标法的乘除法构造统一目标函数,建立有约束单目标优化问题数学模型。针对机构性能比较的实际需要,以普适空间替代全条件性指标中的可达工作空间。针对选定的设计变量定义域,以改进的遗传算法计算得到机构参数的Pareto最优解。结果表明,当动定平台的半径比为1.095时,机构性能最优,相对于动定平台的半径比≤1时的最优解,运动传递精度指标提高了0.7%,刚度指标减少了4.0%。本文的优化设计方法及最优解为位姿精调机构的优化设计提供了参考。The performance requirements of pose and position fine tuning apparatus for secondary mirror in large optical telescope were analyzed. Based on Gough-Stewart manipulators, two design criteria for the optimal design of pose and position fine tuning apparatus were brought out, one is transmission precision performance and the other is stiffness performance. Two angular-dimensioned parameters and three nondimensionalized linear-dimensioned parameters as design parameters were selected to analyse the effect of each parameter on performances. Then, two global conditioning indexes were brought out, one is movement precision performance index and the other is stiffness performance index. Based on requirement for pose and position adjustments,a general workspace was adopted to replace the reachable workspace. In the guideline of unified objective method, a unified objective function and a mathematical model were established for solving a constrained single objective optimization problem,and an improved genetic algorithm was used to obtain the Pareto optimal solution within the definite areas selected. Experimental results indicate that the performance is optimal when the ratio of base radius to platform radius is 1. 095. Compared with the optimal performance when the ratio of base radius to platform radius is less than 1, transmission precision performance index increases by 0. 7% and stiffness performance index reduces by 4.0 %.

关 键 词：望远镜副镜 位姿精调机构 Gough-Stewart平台机构 无量纲化参数 遗传算法 优化设计 

分 类 号：TH743[机械工程—光学工程]