Resonant frequency characterization of a novel MEMS based membrane engine

Robert Michael Gifford

This thesis provides information regarding the characterization and control of the resonant frequency of the Washington State University P3 Micro Engine. It is essential to establish means to measure and control engine resonant frequency, since resonant operation is vital to the P3 engine operation. In order to measure the resonant frequency of the engine, a forced-vibration method and a free-vibration method were developed. Using the forced-vibration method, an engine assembled with a 3 mm generator, 75 µm cavity depth, and a 500 mm bubble diameter resulted in a resonant frequency of 10,100 Hz. The same engine was also tested using the free vibration method where a beating frequency was observed in the “after ringing” response. A Fourier transform of the response yielded a resonant mode matching the forced vibration experiment. In order to eliminate the beating frequency an alternate membrane was used. Using the free-vibration method, an engine assembled with a 4 mm silicon membrane, 75 µm cavity depth, and a 1170 um bubble diameter resulted in a resonant frequency of 2037 Hz with an experimental repeatability of +/- 8.6%. A parametric study was conducted to determine the effects of membrane size, bubble diameter, and cavity thickness on resonant frequency. Results showed that membrane size had a very large effect on resonant frequency. Engines assembled with the same cavity depth but differing silicon membrane side lengths of 3 mm, 4 mm, 6 mm, and 8 mm had average resonant frequencies of 2550 Hz, 1615 Hz, 742 Hz, and 416 Hz, respectively. Bubble diameter had very little effect on resonant frequency, providing only a +/- 8.2% change for bubble diameters ranging from 400 µm to 1500 µm. Three engine cavity depths were tested: 75 µm, 150 µm, and 225 µm for engines assembled with 4 mm silicon membranes and varying bubble diameter. An increase in resonant frequency was seen as the cavity depth was increased. The mean resonant frequencies with 95% confidence for the 75 µm, 150 µm, and 225 µm cavity depths were 1206 ± 206 Hz, 1615 ± 154 Hz, and 2081 ± 291 Hz, respectively. Therefore, membrane size and cavity depth have very good potential to control system resonant frequency. Finally, a model was developed to serve as a design tool for controlling engine resonant frequency based on system parameters. The model operates under the principles of an added virtual mass factor, relating the resonant frequency of the engine to the theoretical resonant frequency of the upper membrane of the engine in a vacuum. The model was shown to fit the experimental data well. The model was further extrapolated to provide the necessary engine dimensions required to achieve a resonant frequency of 500 Hz.

Resonant frequency characterization of a novel MEMS based membrane engine

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