PPLATE,k,area,gap,volt,rper,sel
Electrostatic parallel plate actuator for normal motion

k           spring constant of the beam in N/m
area      overlapping area of the electrodes in µm2
gap       distance between the two plates in µm
volt       applied voltage in Volt
rper       relative permittivity of the medium, it is approximately 1 for air
sel         number denoting the selected result.
Use 1 for pull-in voltage, 2 for actuation force and 3 for balanced displacement of the electrode

Notes

A parallel plate actuator consists of a plate or mass forming the movable electrode suspended from beams over another fixed flat plate forming the fixed electrode. The movable electrode is free to move normal or perpendicular to its surface. When a voltage is applied between the electrodes, the electrostatic force would pull the movable electrode towards the fixed one. This displacement will continue till the elastic force balances out the electrostatic force. This position is described as stable balanced displacement. The force generated at this balanced position is given as actuation force. There is a limiting voltage that can be applied to the actuator beyond which the movable plate will continue to move towards the fixed plate due to ever increasing electrostatic force and finally would fall in contact with the fixed plate. This limiting voltage is called the pull-in voltage. The maximum displacement at that state would be 1/3rd the gap distance. The maximum elastic or electrostatic force exerted by the actuator corresponds to the pull-in voltage and maximum displacement.

Use this form to estimate the pull-in voltage, actuation force and stable balanced displacement of a parallel plate actuator. One set of parallel plates are assumed. If n such pairs are used, the total actuation force will be n times the estimated actuation force.

The plot shows the electrostatic and elastic force dependency on displacement. The nonlinear nature of elastic force creates two balanced positions, one is stable and other unstable. A smaller displacement is the stable one. If the displacement of the electrode is increased beyond the unstable position due to some reason like an external acceleration load, it will go into a pulled in state. At the pull-in voltage there will be only one solution to the stable position and that corresponds to the maximum displacement. When the applied voltage is higher than the pull-in voltage, there is no balance of forces and the actuator will become unstable and the electrodes will come into contact. Use the cross hair tool to locate the balanced displacement and the corresponding force.

Assumptions

-The pull-in voltage can be increased by inserting a serial capacitor. This capacitor is not included in this circuit.
-The spring constant of the beam is known. If unknown, this can be calculated under Mechanics > Structures > Beams.
-The medium between the electrodes is air by default with a relative permittivity of 1.
-The gap between the electrodes is uniform.
-The parasitic capacitance is not considered.
-The estimated force is normal to the plate surface. Tangential force is not calculated.
-Damping is not considered.
-The displacement in the absence of electrostatic force is considered to be zero.
-Constant driving voltage is assumed.
-There is no overshooting caused by electrostatic force.