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A generalized energy transfer model (ETM) for squeeze-film air damping of micro plates in the free molecular regime is developed. The development of the model is based on: (1) the modification of the ETM proposed by Bao et al by using the weighted average of square traveling distance (l is the molecular traveling distance in the gap) to replace the plain average of , (2) the incorporation of the Monte Carlo (MC) model by Hutcherson and Ye so that some assumptions in Bao’s model causing the overestimation of quality factor are released, and (3) the use of Sumali’s empirical formula to relate the ETM to MC model quantitatively. The generalized ETM developed in this paper features: (1) a closed form equation for predicting quality factor according to the parameters of the system, (2) without suffering from the abnormal behavior when the aspect ratio of the plate goes high, and (3) good agreement with experimental results. As a result, the ETM can find practical applications in MEMS.

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Based on the energy transfer model (ETM) proposed by Bao et al. and the Monte Carlo (MC) model proposed by Hutcherson and Ye, this paper proposes an efficient molecular model (MC-S) for squeeze-film damping (SQFD) in rarefied air by releasing the assumption of constant molecular velocity in the gap. Compared with the experiment data, the MC-S model is more efficient than the MC model and more accurate than ETM. Besides, by using the MC-S model, the feasibility of the empirical model proposed by Sumali for SQFD of different plate sizes is discussed. It is proved that, for various plate sizes, the accuracy of the empirical model is relatively high. At last, the SQFD of various vibration frequencies is discussed, and it shows that, for low vibration frequency, the MC-S model is reduced to ETM.

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