Modeling a Pull-In Instability in Micro-Machined Hybrid Contactless Suspension

A micro-machined hybrid contactless suspension, in which a conductive proof mass is inductively levitated within an electrostatic field, is studied. This hybrid suspension has the unique capability to control the stiffness, in particular along the vertical direction, over a wide range, which is limited by a pull-in instability. A prototype of the suspension was micro-fabricated, and the decrease of the vertical component of the stiffness by a factor of 25% was successfully demonstrated. In order to study the pull-in phenomenon of this suspension, an analytical model was developed. Assuming quasi-static behavior of the levitated proof mass, the static and dynamic pull-in of the suspension was comprehensively studied, also yielding a definition for the pull-in parameters of the hybrid suspension.