Near-Contact Gas Damping and Dynamic Response of High-g MEMS Accelerometer Beams

Abstract

This paper introduces and experimentally validates a new model for near-contact gas damping of microbeams. The model is formulated based on numerical simulations of rarefied gas dynamics using the Boltzmann Ellipsoidal Statistical Bhatnagar-Gross-Krook (ES-BGK) equation. The result is compared with existing models by simulating the motion of beams under high-g acceleration. To experimentally validate the damping models, single crystal silicon MEMS g-switches with cantilever microbeams of various lengths were utilized. The experimental measurements of beam dynamics under peak accelerations of approximately 50,000 g and acceleration ramp rates from 600 to 3,000 g/μs are compared with simulations. Additionally, the damping coefficients are extracted from existing vibrational mode data, and the resulting values are compared to the various models. The new near-contact model was found to predict contact and release times within a root-mean-square deviation from experiment below 9 and 7 for contact and release events, respectively. The damping values for the vibrational modes away from contact were predicted within 33% error, showing a more consistent predictive capability than provided by earlier models.