静电拉伸薄膜反射镜的多电极成形控制

Surface shape control of electrostatic stretching membrane mirror by multi-electrodes

针对现有薄膜反射镜成形控制方法存在求解复杂,工程实用性差等问题,提出了基于反演求解的半解析成形控制方法。首先,基于Karman方程和静电场理论推导了所要拉伸的抛物面面形与施加压强分布的关系及实验所需的离散电极环电压值;其次,利用有限元软件建模和分析,验证所推导的压强分布;最后,在口径为300mm的三环电极的静电拉伸反射镜实验平台上进行了验证实验。实验显示,拉伸面形最大变形量与理论值基本吻合,面形误差与传统均匀压强下的相比有所减少,最好的实验结果得到的PV值和RMS值较均匀压强下的值分别减少了9.76%和15.38%。仿真及实验结果表明:所描述的方法可以控制面形并提高面形精度,与传统的成形控制方法相比较具有简单实用等优点。

For the complex control and unpractical calculation of the surface shape control method for an electrostatic stretching membrane mirror in engineering,a semi-analytical method of surface shape control based on an inverse approach was proposed.Firstly,the relation between required pressure distribution and voltages and the desired parabolic shape were derived based on the Karman equation and electrostatic field theory.Then,the finite element analysis was used to establish a model to validate the pressure distribution and a verified test was performed on a Ф300 mm three concentric annular electrode membrane mirror.The experimental results show that the measured values of max displacement are consistent with the theoretical ones basically.The surface shape error has been reduced as compared with that of traditional method and the best RMS and PV values of shape surfaces have reduced by 9.76% and 15.38% respectively under a uniform pressure.In conclusion,the method described can control surface shape and can improve the surface accuracy.Compared with other methods,the method is simpler and more practical.