作为一种性能优良的惯性传感器,半球形谐振陀螺广泛应用于航空航天,武器导航等领域由于其高精度的优势,高可靠性,和长寿。由于谐振器的材料特性和质量在圆周方向上的不均匀分布,谐振器在不同方向的两个4波腹振动模式(工作模式)的频率是不同的,这叫做频率分裂。频率分裂是影响半球形谐振陀螺精度的主要误差源,必须加以抑制。频率分离与谐振器的结构有关。对于平面电极型半球形谐振陀螺,为了抑制结构的频率分裂,提高半球形谐振陀螺的精度,并确定和优化半球形谐振器的等效底角参数,本文从薄壳理论出发,研究了半球形谐振器的4波腹振动模式和波形进动模型。理论分析和模拟了不同边界条件下等效底角对4波腹振型频率值的影响。仿真结果表明,等效底角通过径向约束影响半球形谐振器的4波腹振动模式。以中间表面半径R=15mm,壳体厚度h=1mm的半球形谐振器为优化对象,茎直径D和圆角半径R1是实验因素,以4波腹振型频率值和质量敏感因子为响应指标。进行中心复合设计以优化等效底角参数。优化后的结构参数为:阀杆直径D=7mm,圆角半径R1=1mm,R2=0.8mm。仿真结果表明,4波腹振动模式频率值为5441.761Hz,质量灵敏度系数为3.91Hz/mg,这符合工作和励磁的要求。该研究将为提高半球谐振陀螺的精度提供指导和参考。
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 D 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.