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

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.