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。作为一个数值例子，首先考虑了薄方平板陀螺仪，以评估所开发的模拟器的精度和有效性。经验证，三维分析的数值结果与文献报道的二维分析结果吻合较好。可以通过三维分析进行逼真的分析。再举一个例子，说明了薄方形板在弯曲模式下振动的陀螺仪。挠曲模式陀螺仪对绕任意轴旋转具有一定的灵敏度。可以在弯曲模式下使用陀螺仪分别检测绕z轴和x轴或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。数值计算结果与实验结果吻合较好。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. 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.