Modelling squeeze film effects in a MEMS accelerometer with a levitated proof mass

A triaxial accelerometer is presented which employs as its proof mass a mechanically free micromachined disc that is electrostatically levitated. Air damping plays a critical role in the operation of the accelerometer, providing stability to an inherently unstable system. Systems that operate beyond the cut-off frequency, however, suffer reduced gain due to the spring component of the squeeze film damping, resulting in decreased sensitivity. A finite-element model for extracting squeeze film damping coefficients for transverse and rotational motion of the disc, via an analogy to heat transfer theory, is presented. The use of the analogy enables a reduction of the problem from a complex three-dimensional computational fluid dynamics domain to a two-dimensional heat transfer domain. The model is used to evaluate the effect of including damping holes in the proof mass. The high-frequency oscillation and physical size of the proof mass dictate that the accelerometer is operated well beyond its cut-off frequency and so the inclusion of damping holes in the proof mass can result in an increase rather than decrease in the damping coefficient. The resulting system-level model, implemented in Matlab/Simulink, is then used to evaluate the effect of the squeeze film damping on the device performance.