Optimal Shape Design of Three Dimensional MEMS With Applications to Electrostatic Comb Drives

A methodology for solving inverse problems in Micro-electromechanical (MEM) systems is proposed in this paper. Design of variable shape electrostatic comb drives (shape motors), in order to obtain desired force profiles, is presented as an application of the general methodology. This analysis includes simulation, sensitivity analysis and optimization. A comb drive is one of the most important microactuators in MEM systems. In a standard comb drive, the capacitance varies linearly with displacement, resulting in an electrostatic driving force which is independent of the position of the moving fingers (relative to the fixed ones) except at the ends of the range of travel. It is of interest in some applications to have force profiles such as linear, quadratic or cubic. Such shaped comb drives could be useful, for example, for electrostatic tuning or to get actuators with longer ranges of travel than those of standard comb drives. The present paper addresses the issues of simulation, sensitivity analysis, and then design (inverse problem) of comb drives with variable height profiles. Three-dimensional simulations of the exterior electrostatic field, and the resultant forces on the comb drive, are carried out with the exterior, indirect, boundary element method. Following direct simulation, sensitivity analysis is carried out by the direct differentiation approach. The variable of interest is the driving force while the design variables are parameters that determine the shape of the moving fingers. Next, an inverse problem is posed as follows: determine the height profile of the moving fingers such that the driving force is a desired function of the displacement of the comb drive. Comb drives of appropriate shapes, that produce desired force profiles, are obtained by this approach. Numerical results are given for shape motors that produce linear or cubic force profiles as functions of travel. The optimization code “E04UCF”, from the NAG package, is used for this phase of the work.