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

利用有限元方法，研制了压电式陀螺仪的数值模拟器。给出了三维模型的有限元公式，其中包括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。以方形薄板陀螺仪为算例，对所开发的模拟器的精度和有效性进行了评价。结果表明，三维分析的数值结果与已有的二维分析结果吻合较好。现实分析可以通过三维分析来进行。又举例说明了在弯曲模式下振动的方形薄板陀螺仪。弯曲模陀螺仪对绕任意轴的旋转具有灵敏度。在弯曲模式下使用陀螺仪可以分别检测绕z轴和x或y轴的旋转角频率。最后在薄方板陀螺仪样机上进行了实验。数值计算结果与实验结果吻合较好。上述结果表明，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.