Modelling of an accelerometer based on 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.