摘要
针对望远镜发射系统承载空间与承载质量的限制与大口径、高分辨率反射镜使用需求之间的矛盾,开展了轻质柔性薄膜反射镜地基试验研究,实现了静电拉伸式薄膜反射镜的精确成形控制。针对口径为300 mm的同心环分布式电极静电拉伸聚酰亚胺镀铝薄膜反射镜,基于泊松方程的薄膜小变形近似求解,并通过确定每环电极对面形的影响函数来确定分布式电极对反射镜薄膜成形的控制矩阵,进而利用最小二乘法求得了分布式电极对面形精确控制所需的分布电压。用ANSYS有限元分析法对比结果,分析相关误差并总结控制方法。结果显示,在薄膜中心变形量超过2.5 mm以后,基于泊松方程的理论求解和ANSYS有限元分析结果相差很大,计算面形与理想面形偏差也很大;认为只有综合运用数值计算和有限元分析,通过确定分布式电极对面形的控制矩阵,运用最小二乘法求解分布式电压,才能准确地实现薄膜小变形面形的预知和控制。
To reduce the contradiction between the system space and the load-carrying capacity of a launching system and with the demand of reflectors with large apertures and high resolutions,a lightweight and flexible membrane reflector was developed and the precise control of the electrostatic stretched membrane reflector was realized. For a Ф300 mm electrostatic stretched polyimide membrane reflector coated with aluminium controlled by concentric annular electrodes, the control matrix for the reflector shape was determined by deducing the influence function of each electrode and the needed voltages on the distributed electrodes for the shape precise control were acquired by the leastsquare fitting on the basis of the approximate solution of the Poisson equation. The result by proposed method was compared with that obtained by ANSYS. It is shown that when the membrane center deflection is higher than 2.5 mm, the result is very different from that obtained by ANSYS, and the computed deflection deviates from an ideal deflection greatly. It cames to the conclusions that predicting and controlling the membrane shape of the small deflection exactly must use synthetically numerical computations and the least-square fitting, and also must find the membrane control matrix of the distributed electrode to solve the distributed voltages.
出处
《光学精密工程》
EI
CAS
CSCD
北大核心
2009年第4期732-737,共6页
Optics and Precision Engineering
基金
国家863高技术研究发展计划资助项目(No.2007AA12Z113)
关键词
静电拉伸
薄膜反射镜
分布式电极
控制矩阵
最小二乘法
electrostatic stretching
membrane reflector
distributed electrode
control matrix
leastsquare fitting method
