A generalized energy transfer model for squeeze-film air damping in the free molecular regime

A generalized energy transfer model (EIM) 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 EIM proposed by Bao et al by using the weighted average of square traveling distance l(2) (l is the molecular traveling distance in the gap) to replace the plain average of l(2), (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 EIM 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 EIM can find practical applications in MEMS.