Deflection and Pull-In of a Misaligned Comb Drive Finger in an Electrostatic Field

Abstract

The elastic deflection of a comb drive finger in an electrostatic field is considered. The finger can be symmetrically located between two rigid fingers of the matching comb, in which case the problem reduces to a pure bifurcation problem for which the critical voltage can be determined. Alternatively, due to the nonlinear motion of an approximate straight-line guidance mechanism, the base of the finger can have a lateral and angular displacement, which results in a smooth curve of equilibria with a limit point, after which pull-in occurs. An analytic model is derived, which is validated by 2-D and 3-D finite-element analyses and experiments. For the analytic model, an assumed deflection shape and a series expansion of the electrostatic capacity yield the deflection curves. This shows that the pull-in occurs at a voltage that is reduced by an amount that is about proportional to the two-third power of the relative base displacement. The theoretical results for the case of a lateral base displacement have been experimentally tested. The results show a qualitative agreement with the analytic model, but the experimental deflections are larger and the pull-in voltages are lower. The finite-element analyses show that these differences can be explained from neglected fringe fields and deviations from the nominal shape.