On the Periodic Symmetric Electrostatic Forcing of a Microcantilever

Constant-gap electrostatic actuators exhibit the side pull-in instability, which may occur with respect to translational, rotational, or deformational degrees of freedom. Previous analytical and simulation studies show that a mathematical model of translational side pull-in can be stabilized using open-loop oscillatory excitation. This paper shows how the translational stabilization method may be adapted to deformational side pull-in. A single comb drive finger is modeled as a clamped-free cantilever beam, which is then mapped to an equivalent one-degree-of-freedom translating rigid body. Comparing the analytical stability map for the translational motion to a stability map obtained by multi-physics finite-element analysis of the cantilever suggests that the linear stability map captures the deformational behavior behavior of the cantilever reasonably well. The use of a stabilizing drive signal promises to double the maximum stroke or force density of electrostatic comb drives.