On the modeling of a capacitive angular speed measurement sensor

• A capacitive novel sensor for measurement of a rotating shaft angular speed was introduced.
• A mathematical model for modeling of the sensor was given.
• The effects of the sensor’s design parameters on its stability and sensibility were investigated.

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.