Stability analysis of an electrostatically actuated out of plane MEMS structure

In the present research, stability and static analyses of microelectromechanical systems microstructure were investigated by presenting an out-of-plane structure for a lumped mass. The presented model consists of two stationary electrodes in the same plane along with a flexible electrode above and in the middle of the two electrodes. The nonlinear electrostatic force was valuated via numerical methods implemented in COMSOL software where three-dimensional simulations were performed for different gaps. The obtained numerical results were compared to those of previous research works, indicating a good agreement. Continuing with the research, curves of electrostatic and spring forces were demonstrated for different scenarios, with the intersection points (i.e., equilibrium points) further plotted. Also drawn were plots of deflection versus voltage for different cases and phase and time history curves for different values of applied voltage followed by introducing and explaining pull-in and pull-out snap-through voltages in the system for a specific design. It is worth noting that, at voltages between the pull-in and pull-out snap-through voltages, the system was in bi-stable state. Based on the obtained results, it was observed that the gap between the two electrodes and the applied voltage play significant roles in the number and type of the equilibrium points of the system.

     

On the modeling of a capacitive angular speed measurement sensor

In the present article, a perceptive capacitive sensor for measuring angular speed of a rotating shaft is proposed. The proposed sensor is capable of measuring rotating shaft angular speed, and its changes. The proposed model’s sensing part is a suspended clamped–clamped micro-beam, which is parallel with two fixed substrates from the upper and lower sides through the micro-beam’s width surface. An electric circuit is used to give out capacitance change as a result of angular speed change, in output voltage. The micro-beam undergoes non-linear electro-static pressure that is induced due to the applied bias DC voltage. The suggested sensor has high sensitivity for a large range of working machines rotating parts angular speed measurement. The governing nonlinear partial differential equation of the transversal motion of the beam is derived and solved by step by step linearization (SSLM) and Galerkin weighted residual methods and the stable region of the sensor is determined. The effects of the applied bias voltage and geometrical properties of the micro-beam on the sensitivity and the range of the measurable angular speed of the sensor are discussed.