Modeling damping in dual axis torsion micro-actuators considering the bending of the support beams

Dual axis torsion micro-actuators find variety of applications such as optical switches, biomedical imaging and adaptive optics. Squeezed film air damping is one of the most important energy loss mechanisms in these devices. This damping, is a key factor in determination of the dynamic performance of the micro-electro-mechanical systems. So they have been widely considered by the researchers. The objective of this paper is to suggest a model for the squeezed film damping of dual axis torsional micro-actuators by considering the bending of the supporting torsion beams. To achieve so, the Reynolds equation governing the pressure of the trapped gas between the actuator plate and the underneath electrodes is considered and simplified for the case in which the inertial effects are negligible compared to the viscous effects. The dimensionless form of this equation is then solved using the extended Kantorovich method and the pressure distribution under the actuator is obtained. This pressure distribution is then employed to calculate the resulting force and force of the squeezed film air damping. The effects of the design parameters of the actuator on the dimensionless damping torques, dimensional damping torques and dimensional damping force are studied. The presented results in this paper can be effectively utilized for an accurate dynamic modeling and control of such structures.