不平衡质量引起的半球谐振陀螺锚固损失理论分析  

Theoretical analysis for anchoring loss of hemispherical resonant gyro caused by unbalanced mass

作　　者：刘奎 于鑫海 段杰 苏定宁 李绍良 赵万良 LIU Kui;YU Xinhai;DUAN Jie;SU Dingning;LI Shaoliang;ZHAO Wanliang(Shanghai Aerospace Control Technology Institute,Shanghai 201109,China;Shanghai Engineering Research Center of Inertia,Shanghai 201109,China)

机构地区：[1]上海航天控制技术研究所,上海201109 [2]上海惯性工程技术研究中心,上海201109

出　　处：《中国惯性技术学报》2023年第7期683-687,共5页Journal of Chinese Inertial Technology

基　　金：国家自然科学基金面上项目(62171420);上海市人才发展资金(2021007)。

摘　　要：半球谐振陀螺(HRG)是一种高精度的陀螺仪。其核心部件为做四波腹振动的半球谐振子,由于半球谐振子不可避免地会产生加工误差,因此会导致谐振子在做四波腹振动时产生较大的锚固损失。为了对锚固损失进行定量计算,首先从谐振子的不平衡质量出发,计算谐振子在做四波腹振动时的不平衡力。然后根据欧拉-伯努利梁假设计算支撑杆的横向振动与轴向振动,并基于半无限体假设计算谐振子的锚固损失,推导出基于弹性力学假设的半球谐振陀螺锚固损失理论计算公式。最后通过数值仿真验证了一至三阶不平衡质量导致的Q值衰减周期分别为π、π/2、π/3。该结论可以用于指导半球谐振陀螺锚固损失的修调。Hemispheric resonant gyroscope(HRG)is a kind of high-precision gyroscope.The core component is the hemispherical harmonic oscillator which is used for four-wave abdominal vibration.Due to the error in the machining process of hemispherical harmonic oscillator,the large anchorage loss of the harmonic oscillator will be caused when the four-wave abdominal vibration is carried out.In order to calculate the anchoring loss quantitatively,firstly,the unbalance force of resonator is calculated according to the unbalance mass of resonator during the four-wave abdominal vibration.Then the transverse vibration and axial vibration of the support rod are calculated according to Euler-Bernoulli beam hypothesis,the anchor loss of resonator is calculated based on the semi-infinite body hypothesis,and the theoretical formula for anchoring loss of HRG based on the elastic hypothesis is obtained.Finally,it is verified by numerical simulation that the attenuation period of Q value caused by the first to third order unbalanced mass is π,π/2,π/3 respectively.The conclusion can provide guidance for the adjustment of anchoring loss of HRG.

关 键 词：半球谐振陀螺 谐振子 不平衡质量 不平衡力 锚固损失 

分 类 号：U666.1[交通运输工程—船舶及航道工程]