A multibody-based dynamic simulation method for electrostatic actuators

Abstract

A numerical simulation method is developed to analyze the dynamic responses of electrostatic actuators, which are electromechanically-coupled systems. The developed method can be used to determine the dynamic responses of cantilever-type switches, which are an example of typical MEMS (Micro-Electro-Mechanical System) devices driven by an electrostatic force. We propose the approach that adopts a point charge to deal with electric field effects between electrodes. This approach may be considered as a lumped parameter model for the electrostatic interactions. An advantage of this model may be the easy incorporation of the electrostatic effects between electrodes into a multibody dynamics analysis algorithm. The resulting equations contain the variables for position, velocity, and electric charge to describe the motion of the masses and the charges on the electrodes in a system. By solving these equations simultaneously, the dynamic response of an electrostatically-driven system can be correctly simulated. In order to realize this approach, we implement the procedures into RecurDyn, the multibody dynamics software developed by the authors. The developed numerical simulation tool was evaluated by applying it to cantilever-type electrostatic switches in many different driving conditions. The results suggest that the developed tool may be useful for predicting behaviors of electrostatic actuators in testing as well as in design.

Review on the Modeling of Electrostatic MEMS

“…However, due to the interaction between electrostatic force and structural behavior, namely the electromechanical coupling effects due to the coupling of multiple physical fields, such as stress fields and electrical fields, and since the system is nonlinear, instability of the pull-in often results, which leads to failures including stick, wear, dielectric changing, and breakdowns. Many studies have focused on common applications of electrostatic principle in MEMS devices, including: the instability when pull-in phenomenon occurs [ 7 – 37 ]; the deformation characteristic of microstructures subjected to electrostatic loads [ 18 , 38 – 41 ]; shape and position of drive electrodes [ 42 – 45 ]; dynamic response and optimization of electrostatic loads [ 46 – 57 ]; air damping effect [ 58 – 66 ], analysis method of chaos and bifurcation in electrostatic-driven systems [ 67 , 68 ], such as finite element method (FEM), finite difference method (FDM), and finite cloud meshless method (FCM) [ 68 – 73 ]; simulation software and systems of simulated dynamic behaviors, such as ANSYS, ABAQUS, COULOMB, MEMCAD, and macro models [ 69 , 72 , 74 – 78 ]; effects of routing parameters (voltage and temperature) on electrostatic force [ 79 ]; inherent nonlinear stiffness softening effect [ 70 , 80 – 82 ]; device reliability related failure modes and mechanisms; material selection; and reasonable design [ 8 , 32 , 38 , 83 – 92 ]. Without a thorough understanding of the effects of electrostatic force in MEMS systems, many practical phenomena, such as instability, nonlinearity and reliability, would have no scientific explanation.…”