Theory of direct frequency output vibrating gyroscopes

Vibrating gyroscopes are instruments for measuring the angular velocity of a system with respect to an inertial reference frame. Most currently available vibrating gyroscopes are based on the excitation of a reference vibration in the plane of a vibrating structure, and the amplitude detection of the vibration normal to the plane induced by the Coriolis effect, which is proportional to the angular velocity of the applied rotation. This paper describes a new vibrating gyroscope based on the simultaneous driving of the two modes of vibration (in plane and out of plane) and the detection of resonance frequencies. It is shown, in this paper, that the resonance frequencies of the two modes vary with the applied angular velocity, and that the difference between them is approximately proportional to the applied angular velocity. It is demonstrated that this kind of gyroscopes presents a lock-in effect related to the natural frequencies and the driving electronics. The results obtained are fundamental to the design of this kind of gyroscopes.