在廣義卡氏座標下分析石英半球殼振子的瑕疵與控制器

Abstract

半圓球殼振動陀螺儀在加工過程中，會造成幾何、材料的不均而產生質量-勁度瑕疵，當半圓球殼具有質量-勁度與阻尼瑕疵時，其自然頻率會產生分歧，對於陀螺儀的使用造成影響，故本研究建立一個修正方法以避免瑕疵的存在造成陀螺儀使用上的問題。 瑕疵半圓球殼實務上是以雷射束去材料的方式進行質量-勁度修正，修正的位置於低頻質量-勁度主軸，因此本文利用強迫振動的方式來找出質量-勁度主軸方向。另外，阻尼瑕疵可於阻尼主軸方向施加外力來消除，而當半圓球殼沒有質量-勁度度瑕疵時，可利用自由振動找出阻尼主軸的方向。 本研究也建立一個在卡氏座標上對半圓球殼振幅的控制器，於球殼上鍍電極，外圍配置驅動電極片，給予適當的電壓會產生靜電吸引力，利用此力來進行比例控制，使振幅達到理想的大小。

Mass-stiffness imperfections will be produced by geometric and material errors which would arise from the manufacturing process of hemispherical resonator gyroscope (HRG). When there exists mass-stiffness and damping imperfections in hemispherical shell, it would make the natural frequency divergent and would have effect on the operation of gyroscope. In consequence, this study establishes a modified method to avoid the existence of imperfections. In practice, the mass-stiffness of the defective hemispherical shell would be corrected by a laser beams method, which is aimed at reducing materials, and the correction-needed place is in the low-frequency mass-stiffness principal axis. Hence, the article uses the forced vibration method to find the direction of the mass-stiffness principal axis. In addition, damping imperfections can be eliminated by exerting the external force in the direction of the damping principal axis. When there is no mass-stiffness imperfection in the hemispherical shell, the direction of the damping principal axis can be found by free vibration. In the study, we also design a controller to adjust the amplitude of the hemispherical shell in the generalized Cartesian coordinates. We coat the electrode sheets on the shell, configure drive electrode in the periphery and apply the appropriate voltage to bring about electrostatic attraction. Further, we make use of the electrostatic attraction to conduct proportional control to achieve the satisfactory amplitude.