An inversely designed model for calculating pull-in limit and position of electrostatic fixed-fixed beam actuators

Abstract

This study presents an inverse approach to obtain a relation between applied voltage and displacement of the midpoint of fixed-fixed beam actuator. The approach has two main sections. The first one is the inverse design of a model to replace real action of upper beam under electrostatic force. The formula obtained from the first section does not comprise the residual stress and gives very small errors when there is no residual stress on the upper electrode. So, the second part was carried out to add this important system variable into the formula. Likewise, inverse solution was again applied in the later section. The final formula demonstrates that pull-in limit of clamped-clamped actuator is to be at around 40% of original spacing that is in agreement with simulation and previous experimental results. Its percentage errors are within 2% when compared with simulations that are based on finite element method (FEM). The results are comparable to numerical solutions received from diverse distributed models which require more calculation power in electrostatic and structural domains. On top of that, our formula is valid for all displacements from original position up to pull-in limit.