Effect of geometrical electrode defects on the bias and sensitivity of tuning fork angular rate sensor

In a perfect vibrating beam gyrometer the sensing mode of vibration is only excited by the Coriolis effect and it is assumed that the sensing electrodes do not respond to the primary mode of vibration. This is the case if the shape of the vibrating beam and of the electrodes don't exhibit geometric defects. In this paper we consider, in a practical point of view, the effect of geometrical defects, like misalignment, of electrodes. These defects can induce a non zero output signal (called the bias) when the gyrometer doesn't rotate and, in a less part, an alteration of the scale factor. We restrict our attention to small defects, which induce only a small dissymmetry of electrodes with respect to the symmetric axis of the beam. The method used to compute the amplitude of vibration, as well as the output current, needs to determine the static electric field in the cross section of the sensor. To do that we use an approximated method based on the decomposition of the electric potential in Fourier series. Although we here consider a tuning fork device, all what is presented is obviously valid for a single beam rate sensor.