An Analytical Model for a Piezoelectric Axially Driven Membrane Microcompressor for Optimum Scaled Down Design

Abstract

A new and comprehensive analytical model for membrane microcompressors driven axially by a single lead zirconium titanate (PZT) stack actuator that incorporates assembly variation errors is presented. The model can be used as a future design aid, to predict dynamic device performance as a function of error severity and as microcompressor dimensions are scaled down from the macro to micro scale. The major conclusion of this work is that since micro compressors can be made adjustable to achieve maximum compression ratio another factor besides assembly variation error reduces the achievable compression ratio. An analytical method to predict the maximum pressure to within ∼5% of that experimentally measured is developed. Also, a numerical method to predict the maximum pressure to within ∼0.6% of that experimentally measured is defined. Moreover, an analytical method to predict the compression ratio degradation factor as a function of assembly variation error for adjustable and fixed devices is presented. It is shown that compression ratio is a function of this single net error parameter, and that this function is scale invariant. The model also outputs membrane moments, vertical shear forces, and stresses throughout actuation cycles.