Squeeze film effects on dynamic performance of MEMS μ-mirrors-consideration of gas rarefaction and surface roughness

Abstract

The squeeze film behavior of MEMS torsion mirrors is modeled, analyzed and discussed. Effects of gas rarefaction (first-order slip-flow model with non-symmetric accommodation coefficients, ACs) and surface roughness are considered simultaneously by using the average Reynolds type equation (ARTE). Based on the operating conditions with small variations in film thickness and pressure, the ARTE is linearized. A coordinate transformation, by stretching or contracting the axes by referring to the roughness flow factors, is proposed to transform the linearized ARTE into a diffusion type modal equation. The dynamic coefficients (stiffness and damping coefficients) are then derived and expressed in analytical form. The results show that the tilting frequency (or C 0 squeeze number), roughness parameters (c Peklenik numbers, r standard deviation of composite roughness) and gas rarefaction parameters (D inverse Knudsen number, a 1 ; a 2 : ACs) are all important parameters on analyzing the dynamic performance of MEMS torsion mirrors.

Stability Analysis and Transient Response of Electrostatically Actuated Microbeam Interacting With Bounded Compressible Fluids

“…On the other hand, besides the electrostatic force and geometrical and material specifications, the ambient temperature variations [12][13][14] and squeeze film effects of surrounding gas [15][16][17] could also affect the free vibration and transient responses and instability conditions. When the microstructure is located in a gas medium, the added damping of the gas comes into view in low frequency ranges, while in the high frequency range, the stiffness effects of the surrounding medium become more important [18].…”

Investigation on Effect of Surface Roughness Pattern to Dynamic Performance of Mems Resonators in Various Types of Gases and Gas Rarefaction

“…Fukui and Kaneko [5] derived the modified Reynolds equation with Poiseuille flow rate (Q P ) to model the effect of gas rarefaction. Also, the surface roughness effect can be solved by (1) mixed average film thickness functions [6], (2) average flow factors [3,[7][8][9][10] for all surface roughness pattern directions, and (3) using the fractal model [11] to generate functions for random surface roughness. To consider the surface roughness patterns, Patir and Cheng [12] first proposed the modified Reynolds equation using flow factors.…”

Probabilistic Sensitivity Analysis of Wear Property for MEMS Gas Bearing

“…Lee Y-B et al [14] compared the bearing load capacity between the continuous flow model and the rarefied model, and the conclusion indicated that the bearing capacity considering the rarefaction effect was only 90% of that without considering the rarefaction effect. Li WL [15] used the first-order slip-flow model with non-symmetric accommodation coefficients to simulate the rarefaction effect and coupled the surface roughness model with the dynamic analysis of the bearing. His research showed that the decrease of the Kn number enhanced the rarefaction effect.…”