Analytical model for an electrostatically actuated miniature diaphragm compressor

Abstract

Abstract. This paper presents a new analytical approach for quasi-static modeling of an electrostatically actuated diaphragm compressor that could be employed in a miniature scale refrigeration system. The compressor consists of a flexible circular diaphragm clamped at its circumference. A conformal chamber encloses the diaphragm completely. The membrane and the chamber surfaces are coated with metallic electrodes. A potential difference applied between the diaphragm and the chamber pulls the diaphragm towards the chamber surface progressively from the outer circumference towards the center. This zipping actuation reduces the volume available to the refrigerant gas, thereby increasing its pressure. A segmentation technique is proposed for analysis of the compressor by which the domain is divided into multiple segments for each of which the forces acting on the diaphragm are estimated. The pull-down voltage to completely zip each individual segment is thus obtained. The required voltage for obtaining a specific pressure rise in the chamber can thus be determined. Predictions from the model compare well with other simulation results from the literature, as well as to experimental measurements of the diaphragm displacement and chamber pressure rise in a custom-built setup.

Dynamic analysis of an electrostatic compressor

“…The chamber-diaphragm system of interest in a diaphragm compressor, however, does not consist of parallel plates due to the non-linear profile of the compressor chamber (Sathe et al, 2008). For estimating the damping coefficient of this non-linear system, the domain is divided into multiple annular flat plate systems, for which an expression for damping coefficient is available in the literature.…”

“…In order to be able to use Equation (7) for the non-linear compressor geometry, this analysis takes advantage of the segmentation method introduced and developed in Sathe et al (2008). For the non-linear geometry of the diaphragm compressor chamber, an arrangement of multiple parallel dampers with different initial gaps (h) is used as shown in Figure 6.…”

“…This leads to a deflection of the diaphragm towards the chamber wall, thereby compressing a refrigerant vapor trapped in the chamber, the flow of which is controlled through inlet manifolds and discharge valves. An analytical model for such a diaphragm compressor was previously developed and experimentally validated by the authors (Sathe et al, 2008). The model was used to conduct a detailed optimization study in which the diaphragm compressor array required for removing heat from electronics was identified for two applications: a desktop computer with 200 W cooling capacity and a laptop computer with 80 W cooling capacity (Sathe et al, 2009).…”

“…In the analytical simulation model, the domain was divided into a number of radial segments and a quasi-static force balance on the diaphragm was carried out for each segment so that the pull-down voltage could be calculated. Details of the principle of operation, analytical modeling and experimental evaluation of the diaphragm compressor are available in Sathe et al (2008), and are not repeated here. The analysis assumed that the deflection of the diaphragm in each segment was a quasi-static process, i.e., the diaphragm deflects in a series of extremely small steps.…”

“…The present work models the damping force in the non-linear (curved) compressor chamber by extending the segmentation modeling approach developed in Sathe et al (2008). The results obtained with the dynamic model are compared to those predicted by the quasi-static model for understanding the influence of the dynamic forces.…”