The influence of vertical deflection of the supports in modeling squeeze film damping in torsional micromirrors

The objective of this work is to create an analytical framework to study the problem of squeezed film damping in micromirrors considering the bending of the supporting torsion microbeams. Using mathematical and physical justifications, nonlinear Reynolds equation governing the behavior of the squeezed gas underneath the mirror is linearized. The resulting linearized equation is then nondimensionalized and analytically solved for two cases of the infinitesimal and finite tilting angle of the mirror. The obtained pressure distribution from the solution of the Reynolds equation is then utilized for finding the squeezed film damping force and torque applied to the mirror. The results show that in the case of the infinitesimal tilting angle, the squeezed film damping can be modeled with a linear viscous damping in both torsional and lateral directions. It is also shown that when the mirror's rotation angle is small, with increasing the length of the mirror, the damping force and damping torque are increased. For the case of the finite tilting angle it was observed that the applied damping torque highly depends on the tilting angle of the mirror as well as the ratio of its vertical to angular velocity and as a result the effect of the vertical velocity of the mirror on the squeezed film damping force and torque applied to the mirror cannot be simply neglected. It is expected that the qualitative and quantitative knowledge resulting from this effort will ultimately allow the analysis, optimization, and synthesis of micromirrors for improved dynamic performance.

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