Modeling and Performance Investigation of a Piezoelectric Vibrating Gyroscope

摘要

An improved mathematical model of a piezoelectric vibrating gyroscope is constructed with the effects of electromechanical coupling and rotary inertia taken into account. The gyroscope consists of a cantilever beam with tip mass attached to its free end. The piezoelectric materials are adhered to the four surfaces of the rectangular beam. By using two Euler angles and extended Hamilton's principle, the electromechanical coupled partial differential equations governing the flexural-flexural motions of the piezoelectric gyroscope are obtained. The accuracy and effectiveness of the comprehensive mathematical model are validated by the existing models in literature. The necessity of taking rotary inertia into account is discussed. The natural frequencies of the rotating piezoelectric beam in both drive and sense directions have been investigated by considering the effects of the tip mass, angular speed, and external impedance. The dynamic behaviors of the piezoelectric gyroscope with different parameters, such as the tip mass, the lengths of piezoelectric materials and beam, and the external impedance, have been studied. In particular, the optimal combination of the external excitation frequency and the external impedance for the best calibration curve of the piezoelectric gyroscope is identified. Finally, the dynamic performance of the piezoelectric gyroscope under varying boundary conditions has been investigated for the potential practical applications.