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

利用有限元方法开发了一种压电式陀螺数值模拟器。给出了考虑绕任意轴旋转的科里奥利力影响的三维模型的有限元列式。各向异性弹性也包含在公式中。对旋转轴的振动模式和方向没有限制。作为数值例子，分别演示了由X切割石英晶体制成的音叉式陀螺仪和L形陀螺仪。利用与振子相关联的模式，即面内模式和面外模式，振子通过设置在振子表面上的电极对来激励和检测。在这些陀螺仪中，激励模式(面内振动)和检测模式(面外振动)的固有频率是不同的，因此通过优化振子的形状来人为地退化这两种模式。结果表明，陀螺仪可以采用由两种不同模式组成的简并模式来工作。研究还表明，陀螺仪对绕任意轴的旋转具有一定的灵敏度。使用这些陀螺仪可以分别检测绕z轴和x或y轴的旋转角频率。结果表明，所开发的三维模拟器对压电式陀螺仪的分析和设计具有一定的参考价值。

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.