Dependence of Ultimate Operating Speed of a Solid-state Wave Gyroscope that does not Degrade the Measurement Accuracy on the Parameters of Its Resonator

Abstract

The article analyzes the ring resonator motion equation of a wave solid-state gyroscope (WSG). Bending oscillations making the ring resonator alternately take the shape of a circle or an ellipse are considered. The analysis uses an ellipse corresponding to the amplitude values of the ring particle radial movements. The ellipse equation is written in a coordinate system where the coordinate axes pass through the nodes of a standing wave excited in a ring resonator. The transition into the ellipse equation from rectangular coordinates to polar ones allows calculation the radial displacement derivatives of the resonator particles with respect to the angle. When differentiating according to time, it is assumed that the radial movements of the ring resonator particles follow a cosine law, i.e., oscillate harmonically. As a result, the time derivatives of the resonator particle radial displacements and their angle derivatives were calculated. The maximum values of the radial displacements of the ring resonator particles with respect to angle, time, and mixed derivatives with respect to angle and time were found using expressions for their derivatives. The values obtained allowed evaluation the maximum values of the terms included in the WSG ring resonator motion equation. All values are obtained in the form of expressions containing the amplitude of ring resonator oscillations in the standing wave nodes, the circular oscillation frequency, and the ring resonator radius. Due to significant smallness of the terms containing the square of the angular velocity and the angular acceleration, compared to other terms in the motion equation of the WSG ring resonator, the conditions for the angular velocity and the angular acceleration were obtained. If the obtained conditions are met the ring resonator motion equation, with excluded terms containing the squared angular velocity and the angular acceleration, can be considered as an adequate model of the WSG. Otherwise, another mathematical model should be applied.