Aerodynamic damping in MEMS

Compact Model of Squeeze-Film Damping Based on Rarefied Flow Simulations

Graduate Students: Xiaohui Guo, Sruti Chigullapalli

A new compact model of squeeze-film damping is developed based on the numerical solution of Boltzmann kinetic equation [1-2]. The schematic is shown in figure 1. The pressure contour and streamlines for cases with Knudsen numbers being 50 and 0.05 are presented in figure 2.

The new model provides a simple expression for the damping coefficient and the quality factor valid through the slip, transitional and free-molecular regimes. In this work, we have applied statistical analysis to the current model using chi-squared test [2]. The damping predictions are compared with three different models based on the Reynolds equation [3-4], as shown in figure 3. At high Knudsen numbers, the structural damping dominates the gas squeeze-film damping [5]. When the structural damping is subtracted from the measured total damping force, good agreement is found between the model predictions and the experimental data [6], as shown in figure 4.

Figure 1. Schematic of SFD for microcantilevers [2].

Figure 2. Pressure field and streamlines at Kn = 50.0(Left) and 0.05(Right) [2].

Figure 3. Comparisons of Quality factors for Mode-3 [2-4].

Figure 4. Comparisons of predictions by the ESBGK-based correlation and experimental data in reference [2, 6], L = 300 micron, g = 2.0, 6.3 micron.

References:

[1] X. Guo and A. Alexeenko, Simulations of Aerodynamic Damping for MEMS Resonators, 39th AIAA Fluid Dynamics Conference, San Antonio, Texas, USA, Jun. 22-25, 2009.

[2] X. Guo and A. Alexeenko, "Compact Model of Squeeze-Film Damping based on Rarefied Flow Simulations", Journal of Micromechanics and Microengineering, Vol. 19, No. 4, April 2009, 045026.

[3] T. Veijola, Compact models for squeezed-film dampers with inertial and rarefied gas effects. Journal of Micromechanics and Microengineering, 2004. 14(7): p. 1109-1118.

[4] M. A. Gallis and J. R. Torczynski, An improved Reynolds-equation model for gas damping of microbeam motion. Journal of Microelectromechanical Systems, 2004. 13(4): p. 653-659.

[5] H. Sumali, Squeeze-film damping in the free molecular regime: model validation and measurement on a MEMS. Journal of Micromechanics and Microengineering, 2007. 17(11): p. 2231-2240.

[6] O. B. Ozdoganlar, B. D. Hanshce, and T. G. Carne, Experimental modal analysis for micro-electro-mechanical systems. Society for Experimental Mechanics, 2005. 45 (6).