Analytical behavior of rectangular electrostatic torsion actuators with nonlinear spring bending

In this paper, we study the pull-in effect for rectangular electrostatic torsion actuators by using analytical calculations that include the higher order effects of nonlinear spring bending. The calculation approach speeds the design of such systems. The method is found to be suitable for actuators with single long beam springs where the ratio of the resonant frequencies for the torsion and bending modes is up to at least 3.5, in the region where bending dominates torsion. After fitting the theory in this paper to Coventor simulation results with three nonphysical coefficients, the fractional differences between Coventor simulation and analytical calculation results are smaller than 6%. The method is also suitable for at least one class of folded spring designs, with greatly decreased bending mode displacement. The main results are also verified by comparing them with published experimental results.