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Research Papers

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

[+] Author and Article Information
M. J. Simon

V. M. Bright, Y. C. Lee

 Department of Mechanical Engineering, University of Colorado, 427 UCB, Boulder, CO 80309-0427

R. Radebaugh

 National Institute of Standards and Technology, 325 Broadway, Boulder, CO 80305-3337

J. Mech. Des 134(1), 011006 (Jan 04, 2012) (12 pages) doi:10.1115/1.4005329 History: Received January 17, 2011; Revised September 29, 2011; Published January 04, 2012; Online January 04, 2012

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.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 2

Side-view free-body diagram of the microcompressor analytical model incorporating assembly variation errors through adjustment of θ2 –θ7 to obtain a net offset rb (or in angular terms θrb ) of the linkage to membrane attachment point parallel to the plane of the membrane. The diagram is not to scale for clarity

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Figure 3

Affine mapping from the symmetrical annular loading case to the asymmetrical

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Figure 1

Microcompressor prototype (a) and (b) depression in the metalized polyimide diaphragm was created by the generated pressure during operation

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Figure 4

(a) General PZT ΔH as a function of F and (b) manufacturer specified and calculated actuator performance curves

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Figure 5

(a) Simplified numerical model geometry and (b) free-body diagram

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Figure 6

The common geometry for the adjustable and fixed microcompressor configurations

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Figure 7

High nonlinearity exists once significant P accumulates within the chamber. A small negative change in δ results in a marked increase in P.

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Figure 8

The analytically computed CRDFA and CRDFF compared to the numerically computed CRDFA and CRDFF using the primary model and the simulation results for scales 1–3

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