SQUEEZE FILM DAMPING EFFECT ON THE DYNAMIC-RESPONSE OF A MEMS TORSIONMIRROR

This paper presents analytical solutions for the effect of squeeze fil m damping on a MEMS torsion mirror. Both the Fourier series solution a nd the double sine series solution are derived for the linearized Reyn old equation which is obtained under the assumption of small displacem ents. Analytical formulae for the squeeze film pressure variation and the squeeze film damping torque on the torsion mirror are derived. The y are functions of the rotation angle and the angular velocity of the mirror. On the other hand, to verify the analytical modeling, the impl icit finite difference method is applied to solve the nonlinear isothe rmal Reynold equation, and thus numerically determine the squeeze film damping torque on the mirror. The damping torques based on both the a nalytical modeling and the numerical modeling are then used in the equ ation of motion of the torsion mirror which is solved by the Runge-Kut ta numerical method. We find that the dynamic angular response of the mirror based on the analytical damping model matches very well with th at based on the numerical damping model. We also perform experimental measurements and obtain results which are consistent with those obtain ed from the analytical and numerical damping models. Although the anal ytical damping model is derived under the assumption of harmonic respo nse of the torsion mirror, it is shown that with the air spring effect neglected, this damping model is still valid for the case of nonharmo nic response. The dependence of the damping torque on the ambient pres sure is also considered and found to be insignificant in a certain reg ime of the ambient pressure. Finally, the convergence of the series so lutions is discussed, and an approximate one term formula is presented for the squeeze film damping torque on the torsion mirror.