Development of Piezoelectric Gyroscopes of Monolithic Configuration for Detection of Three-dimensional Rotation

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A numerical simulator for piezoelectric gyroscopes is developed using the finite element method. The finite element formulation is given for three-dimensional models including the effect of Coriolis force due to rotation around the arbitrary axis. Anisotropic elasticity is also included in the formulation. There is no limitation for the vibrational modes and the direction of the gyratory axis.For numerical examples, a tuning fork gyroscope and a L-shaped gyroscope made of X-cut quartz crystal are respectively demonstrated. The modes associated with the vibrator, in-plane and out-of-plane modes, are utilized for which the vibrator is excited and detected by pairs of the electrodes provided over the vibrator surfaces. In these gyroscopes the natural frequencies of the excitation mode (in-plane vibration) and that of the detection mode (out-of-plane vibration) are inhelently different, so it is made to artificially degenerate both modes by optimizing the shape of the vibrator. It is shown that the gyroscopes can be operated by using the degenerate mode consisting of two different modes. It is also shown that the gyroscopes has a sensitivity to the rotation around the arbitrary axis. It is possible to separately detect the rotational angular frequency around the z axis and x or y axes using these gyroscopes. It is shown in the above results that the developed three-dimensional simulator is useful to analyze or design of the piezoelectric gyroscopes.