A novel piezoelectrically actuated flexural/torsional vibrating beam gyroscope

Vibrating beam gyroscopes are fast becoming the most widely used gyroscopes in many commercial applications. This paper deals with a vibrating beam gyroscope consisting of a cantilever beam with rigid mass attached to its end and undergoing coupled flexural–torsional vibrations. The gyroscope can be used to measure the angular velocity of the rotating base of the beam. The primary (flexural) vibrations are produced in the beam using a piezoelectric patch (bender type) actuator. Due to the base rotation, a gyroscopic effect is generated which induces secondary (torsional) vibrations in the beam. First, a detailed mathematical modeling of the system is developed using extended Hamilton's Principle. The system governing equations are solved and simulated using assumed mode model expansion to analyze the gyroscopic coupling produced due to the base rotations. Finally, the effects of secondary base rotation (cross-axis effects) on the performance of the gyroscope are presented. Also, it is shown that the gyroscopic effect increases with increase in base rotation rate, primary excitation amplitude and length of the beam. It is further proven that the secondary base rotations (cross-axis effects) have an adverse effect on the gyroscope performance. Such detailed analysis on the effects of secondary rotation can be utilized to devise elimination strategies in order to improve gyroscopic performance.