Lumped model of MEMS diaphragm compressors

This article presents a quasi-static lumped model of MEMS circular and square/rectangular diaphragm compressors subjected to a specified peak actuation pressure. In this work equations necessary for determining the pressure rise vs. flow rate relationship for a specific peak actuation pressure are provided. In addition, equations are also presented for determining the temporal variation of chamber pressure and volume. The results of the quasi-static lumped model are found to be in good agreement with that of the results of a transient three-dimensional model studied using COMSOL Multiphysics 4.2a. The independent variables of this model are the geometric, material and operating parameters associated with the MEMS compressor. The geometric parameters are compressor chamber dimensions while the material properties include the diaphragms Young’s modulus and Poisson’s ratio and the ratio of specific heats of the gas. The operating parameters are the operating frequency and peak actuation pressure; actuation pressure is assigned a sinusoidal form. The performance of MEMS compressors improves with increase in peak actuation pressure when all other parameters are held constant. With increase in the depth of the compression chamber the performance characteristics of MEMS compressors degrade provided all parameters are maintained constant. The model also predicts that increase in just the planar dimensions of the diaphragm reduces the maximum achievable pressure ratio. It is found that the performance of the MEMS compressor is inversely related to Young’s Modulus and the thickness of the diaphragm; thus it would be appropriate to make MEMS compressors with materials of low Young’s modulus or thin diaphragms or a combination of both. Based on the model it is observed that the temporal variation of diaphragm deflection significantly varies from that of the actuation pressure for all operating conditions, unlike assumed in literature, except for those operating conditions existing at the extremes of a performance characteristics curve.