Driving force profile design in comb drive electrostatic actuators using a level set-based shape optimization method

Electrostatic actuators, actuators actuated by electrostatic forces, are now widely used as sensors and switches, especially in Micro-Electro-Mechanical Systems (MEMS). Among different kinds of electrostatic actuators, the comb drive type is one of the most popular because it has a relatively large range of displacement. In design problems for electrostatic actuators, the driving force profile is of primary engineering importance. In this paper, we develop a structural optimization method for comb drive electrostatic actuators that achieves prescribed driving force profiles, based on a level set-based shape optimization method that provides optimal configurations with clear boundaries, solutions that are valid in an engineering sense. Accurate calculation of the electrostatic forces that occur on the structural boundaries during optimization is important for developing actuators that operate with prescribed driving forces. In the conventional level set-based shape optimization methods, inaccuracies in the calculation of these electrostatic forces occur because the structural boundaries are seldom aligned with the finite element method (FEM) nodes. To precisely calculate the electrostatic forces, we developed a mesh adaptation scheme by which the finite element nodes are brought into alignment with the structural boundaries at every iteration of the optimization procedure. In the following, we explain the details of the proposed level set-based shape optimization method, in which a multi-objective optimization problem is formulated to achieve a prescribed driving force profile. The sensitivity is derived using the adjoint variable method. Four numerical examples are provided, to examine the suitability of the proposed optimization method.