基于NSGA-III的半球谐振陀螺的频率裂解补偿
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山东理工大学机械工程学院淄博255000

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TH721V241.5

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泰山学者青年专家项目(tsqn201909108)、山东省自然基金面上项目(ZR2021MF042)资助


Frequency splitting compensation of hemispherical resonator gyro based on NSGA-III
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College of Mechanical Engineering, Shandong University of Technology, Zibo 255000, China

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    摘要:

    半球谐振陀螺是目前精度最高的一种振动陀螺。对于半球谐振陀螺,在制造过程中难以完全避免的工艺缺陷会导致谐振子的质量、刚度、品质因数、密度、弹性模量、阻尼等参数周向分布不均匀,产生频率裂解现象,使得主、次振动存在误差耦合。传统的频率分裂补偿方法会导致半球谐振陀螺的品质因数降低,且存在补偿成本高、操作复杂等问题。提出了一种电平衡补偿方案,通过对不同的电极施加静电力改变谐振子的刚度,实现对频率裂解的补偿,并结合NSGA-III多目标优化算法对补偿参数进行了优化,首次将静电修调方案对谐振子本身性能的影响、功耗问题以及该方案所能提供的频率裂解补偿值同时进行考虑,以实现针对半球谐振陀螺频率裂解的最优补偿。经过验证,该方法针对不同的谐振子和频率裂解在所选参数下能够给出最优的补偿方案,频率分裂补偿值提高了50.2%,补偿电压的需求分别降低6.3%和56.3%,补偿精度高于0.5 mHz;补偿后谐振子的检测误差降低了一个数量级,固有频率仅降低2.3%。该方案可以有效提高陀螺仪的动态性能,为半球谐振陀螺的频率裂解的最优化补偿提供了一种参考,且该方法同样适用于杯型、环形等哥氏陀螺仪。

    Abstract:

    The hemispherical resonator gyroscope (HRG) is currently the most accurate type of vibrating gyroscope. However, manufacturing defects inevitably cause uneven circumferential distribution of parameters such as mass, stiffness, quality factor, density, elastic modulus, and damping in the resonator, leading to frequency splitting and coupling errors between primary and secondary vibrations. Traditional frequency splitting compensation methods often reduce the quality factor and involve high costs and complex operations. In contrast, an electrostatic balance compensation scheme has been proposed, which applies electrostatic forces to different electrodes to adjust the resonator′s stiffness and compensate for frequency splitting. When combined with the NSGA-III multi-objective optimization algorithm, this approach optimizes the compensation parameters while considering the impact on resonator performance, power consumption, and the achievable frequency splitting compensation values. Validation results demonstrate that this method provides optimal compensation for frequency splitting in various resonators and frequency splits, achieving a 50.2% increase in compensation value. It also reduces required compensation voltages by 6.3% and 56.3%, maintaining an accuracy better than 0.5 mHz. After compensation, measurement errors decreased by an order of magnitude, with only a 2.3% reduction in natural frequency. This approach significantly enhances the dynamic performance of gyroscopes and offers valuable insight for optimal frequency splitting compensation in HRGs. It can also be applied to other types of gyroscopes, such as cup and ring gyroscopes.

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高忠峰,李平华,乔琦,廖嘉洛,庄须叶.基于NSGA-III的半球谐振陀螺的频率裂解补偿[J].仪器仪表学报,2025,46(3):296-306

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  • 在线发布日期: 2025-05-28
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