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

利用有限元法建立了压电陀螺的数值模拟器。给出了三维模型的有限元公式，其中包括由于绕任意轴旋转的科里奥利力的影响。各向异性弹性也包括在公式中。为了验证仿真器的准确性和有效性，本文首先以一个正方形薄板的陀螺为例进行了仿真。它被证实，三维分析的数值结果与以前报道的二维分析的结果显示出良好的一致性。可以通过三维分析来进行现实分析。再举一个例子，说明一个方薄板的弯曲振动陀螺。弯曲模式陀螺仪对绕任意轴的旋转具有灵敏度。可以使用弯曲模式的陀螺仪分别检测围绕z轴和x或y轴的旋转角频率。最后，对薄方板陀螺仪样机进行了实验研究。计算结果与实验结果吻合较好。结果表明，所开发的三维仿真器对压电陀螺仪的分析和设计是有用的。

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. For a numerical example, the gyroscope of a thin square plate is first considered to evaluate the accuracy and the validity of the developed simulator. It is confirmed that the numerical results by the three-dimensional analysis show good agreement with the results by the two-dimensional analysis which is previously reported. The realistic analysis can be carried out by the three-dimensional analysis. For another example, the gyroscope of a thin square plate vibrating in flexural mode is next demonstrated. The flexural mode 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 the gyroscope in flexural mode. The experiments are finally carried out for the prototype gyroscope of a thin square plate. It is confirmed that the numerical results show good agreement with the experimental results. It is shown in the above results that the developed three-dimensional simulator is useful to analyze or design of the piezoelectric gyroscopes.