Simple but Accurate Models for Squeeze-film Dampers

Simple but accurate compact models are derived for squeeze-film dampers having rectangular areas and vibrating in translational or in torsion motion. First, shape functions are derived that enable fast and accurate calculation of the low squeeze number damping coefficient for any aspect ratio of the damper surface. Next, a series-form approximation for larger squeeze numbers is derived utilizing these shape functions with additional truncation sections. The accuracy of the approximated impedance is studied as a function of the number of sections. The models are useful in calculating the damping in various kinds of micromechanical sensors, such as accelerometers.