Analytical modelling of ultra-thin gas squeeze film

Abstract

In this study, the characteristics of an ultra-thin gas squeeze film are analysed using the modified molecular gas film lubrication (MMGL) equation with coupled roughness and rarefaction effects taken into consideration. A modified squeeze number (Σ) and modified plate aspect ratio (β) are proposed to estimate molecular gas film lubrication characteristics. Using Σ, β and a simple mapping method, the linearized MMGL problem can be reduced to the continuum gas film problem and the MGL characteristics can be exactly estimated if the pressure flow factors (ϕXP,ϕYP) and the rarefaction coefficient (Q̄P(D)) are known. The present models are computationally compact, and thus applicable to simulation of a microelectromechanical system.

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

“…(24b) is exactly the same as the results proposed by Pan et al (1998). In addition, the present results reduce to the results of Li (1999) in the slip flow region under fully diffuse reflection (a 1 = a 2 = 1) with roughness effects considered. As shown in Fig.…”

“…The spring force increases with the tilting frequency, and the damping force increases till the cut-off frequency is reached and decreases thereafter. As presented in (Li 1999), the spring force increases as C 0 increases, c increases, or H S0 decreases. Four combinations of ACs are discussed for the gas rarefaction.…”

“…1, a rectangular mirror with dimension l 0 9 w 0 is tilting about the y-axis. The analysis domain of the squeeze film (mirror size) is À l 0 2 \x 0 \ l 0 2 and À w 0 2 \y 0 \ w 0 2 : The maximum displacement in z-direction occurs at x ¼ AE l 0 2 : Modifying the procedure in the previous publication (Li 1999), the dynamic coefficients of the squeeze gas film between a tilting micromirror and the substrate can be easily obtained. The solution procedure for the present problem is as follows:…”

“…To account for the effects of gas rarefaction and surface roughness on squeeze film, Bhushan and Tonder (1989a, b) use the effective viscosity and pressure flow factors separately in the ARTE. Latter, the coupling effects of gas rarefaction and surface roughness on lubricating film were proposed in the ARTE by Li and Weng (1997), and were applied in squeeze film for arbitrary Knudsen number conditions (Li 1999). In addition, the effects of accommodation coefficients (ACs) and gas rarefaction are considered in the modeling of squeeze film damping (Veijola et al 1997), flow in microchannel (Jang and Wereley 2006), and gas bearing of magnetic head sliders flying on a rotating disk (Huang and Bogy 2000).…”

A Macro Model of Squeeze-Film Air Damping in the Free-Molecule Regime

“…One is based on the modification of continuum theories. Examples in this category include, but are not limited to, the modification of Reynolds' equation by employing the effective viscosity obtained either from a linearized Bhatnagar-Gross-Krook solution of the Poiseuille flow 12,14,23 or from experimental data 24,25 via curve fitting, by using a pressure dependent effective flow rate coefficient 13 and a modified pressure boundary condition with coefficients extracted from the NavierStokes slip-jump simulations and the direct simulation Monte Carlo ͑MC͒ simulations. 15 Most of these methods have demonstrated their accuracy in the slip regime ͑Kn Յ 0.1͒, i.e., the near continuum regime.…”