磁悬浮敏感陀螺动力学建模与关键误差源分析

基于转子动力学构建了针对一种新型双球形包络面转子磁悬浮敏感陀螺（MSSG）动力学模型，并对陀螺关键误差源进行了理论分析。描述了磁悬浮敏感陀螺的结构特点与角速率测量原理，并分别建立了磁悬浮转子所受电磁力与电磁力矩数学模型，分析了转子微小平移与偏转对转子力学状态的影响机理，利用ANSYS软件得出的有限元仿真结果与模型计算结果基本吻合。在此基础上，从理论上对转子非球形误差和洛伦兹力磁轴承误差2种主要误差源进行了初步分析，给出了干扰力矩解析表达式。计算表明:转子非球形和洛伦兹力磁轴承中磁场分布不均是导致测量误差产生的主要因素。模型的构建可为磁悬浮敏感陀螺的优化设计与分析提供有效理论依据。 

Dynamic modeling and key error sources analysis of magnetically suspended sensitive gyroscopes

The mathematical model of a new magnetically suspended sensitive gyroscope (MSSG) with rotor of double spherical envelope surfaces is established based on rotor dynamics, and the key error sources of the gyro in sensing angular rate are analyzed theoretically. First, structural features and sensing principles of the MSSG are described. Second, the theoretical models of electromagnetic forces and moments acting on the rotor are built respectively. The influencing mechanisms of rotor translation and titling on its mechanical state are analyzed. Simulation results by finite-element method software ANSYS are basically in agreement with the calculated results. Finally, two key error sources of rotor asphericity and Lorentz force magnetic bearing process errors are analyzed, and the analytical expression of the disturbing torques has been constructed. Calculation results show that the rotor aspheric factors and the inhomogeneous magnetic field in Lorentz force magnetic bearing are the major factors inducing disturbance torques. The model provides a valuable theoretical basis for further research on optimization design and analysis of the MSSG.