Gao Zhiyong, Wang Shang, Wang Zhi, Ding Xukai
School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study, University of Chinese Academy of Sciences (UCAS), Hangzhou 310012, China.
University of Chinese Academy of Sciences, Beijing 101408, China.
Micromachines (Basel). 2023 Aug 29;14(9):1686. doi: 10.3390/mi14091686.
As an inertial sensor with excellent performance, the hemispherical resonator gyro is widely used in aerospace, weapon navigation and other fields due to its advantages of high precision, high reliability, and long life. Due to the uneven distributions of material properties and mass of the resonator in the circumferential direction, the frequencies of the two 4-antinodes vibration modes (operational mode) of resonator in different directions are different, which is called frequency splitting. Frequency splitting is the main error source affecting the accuracy of the hemispherical resonator gyro and must be suppressed. The frequency splitting is related to the structure of the resonator. For the planar-electrode-type hemispherical resonator gyro, in order to suppress the frequency splitting from the structure, improve the accuracy of the hemispherical resonator gyro, and determine and optimize the equivalent bottom angle parameters of the hemispherical resonator, this paper starts from the thin shell theory, and the 4-antinodes vibration mode and waveform precession model of the hemispherical resonator are researched. The effect of the equivalent bottom angle on the 4-antinodes vibration mode frequency value under different boundary conditions is theoretically analyzed and simulated. The simulation results show that the equivalent bottom angle affects the 4-antinodes vibration mode of the hemispherical resonator through radial constraints. The hemispherical resonator with mid-surface radius R=15 mm and shell thickness h=1 mm is the optimization object, and the stem diameter and fillet radius R1 are experimental factors, with the 4-antinodes vibration mode frequency value and mass sensitivity factor as the response indexes. The central composite design is carried out to optimize the equivalent bottom angle parameters. The optimized structural parameters are: stem diameter D=7 mm, fillet radii R1=1 mm, R2=0.8 mm. The simulation results show that the 4-antinodes vibration mode frequency value is 5441.761 Hz, and the mass sensitivity factor is 3.91 Hz/mg, which meets the working and excitation requirements wonderfully. This research will provide guidance and reference for improving the accuracy of the hemispherical resonator gyro.
半球谐振陀螺作为一种性能优异的惯性传感器，因其具有高精度、高可靠性和长寿命等优点，在航空航天、武器导航等领域得到了广泛应用。由于谐振器材料特性和质量在圆周方向上分布不均匀，谐振器在不同方向上的两种四波腹振动模式（工作模式）的频率不同，这被称为频率分裂。频率分裂是影响半球谐振陀螺精度的主要误差源，必须加以抑制。频率分裂与谐振器的结构有关。对于平面电极式半球谐振陀螺，为了从结构上抑制频率分裂，提高半球谐振陀螺的精度，并确定和优化半球谐振器的等效底角参数，本文从薄壳理论出发，研究了半球谐振器的四波腹振动模式和波形进动模型。理论分析并模拟了等效底角在不同边界条件下对四波腹振动模式频率值的影响。模拟结果表明，等效底角通过径向约束影响半球谐振器的四波腹振动模式。以中面半径R = 15 mm、壳厚h = 1 mm的半球谐振器为优化对象，以杆径和圆角半径R1为实验因素，以四波腹振动模式频率值和质量灵敏度因子为响应指标。采用中心复合设计对等效底角参数进行优化。优化后的结构参数为：杆径D = 7 mm,圆角半径R1 = 1 mm, R2 = 0.8 mm。模拟结果表明，四波腹振动模式频率值为5441.761 Hz，质量灵敏度因子为3.91 Hz/mg，很好地满足了工作和激励要求。本研究将为提高半球谐振陀螺的精度提供指导和参考。
