超大口径弯月镜支撑点布局-刚度-校正力联合优化

Layout-stiffness-correction force joint optimization of support system for ultra-large thin meniscus mirror

在超大口径原位加工与检测中,目前多采用被动式Whiffletree液压支撑系统(原位支撑),而该类支撑单元的轴向刚度存在较大差异性,会显著影响轻薄型反射镜的面形精度。为解决这一问题,研究了主动型原位支撑的支点布局、单元刚度和主动校正力的联合优化方法。首先,针对支撑单元刚度差异,提出了支撑刚度、支点位置的分级布局优化方法,获得了支撑系统的初始优化解;其次,结合模式定标法和最小二乘法,进行了支撑点主动力校正,以获得支撑面形的最终优化解;最后,结合具体案例的数字仿真试验,验证了方法的有效性。结果表明:对于4 m弯月型轻薄反射镜,仅被动支撑下,分级布局优化后,60点方案面形精度RMS值由150.6 nm减少到32.9 nm,78点方案面形精度RMS值由45.2 nm减少到22.6 nm,优化效果显著;进一步经主动校正后,60点方案和78点方案面形精度RMS值分别为14.6 nm和6.9 nm,均满足面形精度RMS值小于λ/40(λ=632.8 nm)的指标要求;最终选取60点轴向支撑方案。通过对支点布局、支撑刚度和校正力进行联合优化,可以大幅增加原位支撑系统的适用性、灵活性,降低实施难度。

Passive hydraulic support units(PHSUs)are frequently used in the in-situ fabrication and testing(in-situ support).However,the difference in PHSUs’stiffness will affect the mirror surface figure,especially for those thin meniscus mirrors.In order to solve this problem,the joint optimization method of layout,stiffness and active correction is studied.Firstly,for the difference of PHUS'stiffness,a hierarchical layout optimization method for support stiffness and support position is proposed to obtain the initial optimization solution of the support system.Then,the mode calibration method and the least square method is used for active correction of support system to obtain the final optimized solution of the mirror surface figure.Finally,the effectiveness of the method is verified by a numerical simulation experiment with specific cases.The results show that,for 4 m thin meniscus mirror,after layout optimization,with the hydraulic passive support system,the root mean square(RMS)of the mirror surface errors of 60 point axial support system is reduced from 150.6 nm to 32.9 nm,and the RMS value of the mirror surface errors of 78 point axial support system is reduced from 45.2 nm to 22.6 nm.The optimization effect is remarkable.After active correction,the RMS value of the mirror surface errors of 60 point axial support system is 14.6 nm,and it is 6.9 nm for 78 point axial support system.The requirement of the RMS value of the mirror surface error is less thanλ/40(λ=632.8 nm).The support systems meet the requirement.Finally,the 60 point axial support system was selected.Through the joint optimization of layout,stiffness and active correction for supporting points,it can greatly increase the applicability,flexibility and reduce the difficulty of implementation for the in-situ support system.