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超导转子凭借其独特的物理性质, 在精密测量领域具有巨大的应用潜力. 超导转子磁悬浮装置可制作高精度角速度传感器, 在外界干扰力矩作用下, 极轴偏移初始位置是引起超导转子极轴漂移误差的原因, 其中球面误差和地球自转属于主要误差源, 对超导转子球面误差引起的极轴研究结果为提升转子漂移精度、进行误差补偿提供了一定参考. 速度进行补偿是实现超导转子磁悬浮装置高精度的关键步骤. 基于此, 开展了完整球形超导转子球面误差和地球自转对超导转子极轴偏移特性的影响因素研究. 首先, 本文基于矢量磁势方程对超导转子磁支承结构进行建模, 分析了理想状态下(即悬浮于球腔中心位置)超导转子表面的磁场强度分布, 研究了磁支承力特性. 然后分析了球面误差引起的超导转子的磁支承干扰力矩, 并基于超导转子动力学方程, 建立了超导转子动力学模型, 给出了不同转子结构参数下超导转子极轴漂移误差的分布规律. 最后, 探讨了地球自转对超导转子漂移测试的影响. 研究结果为后续提升转子漂移精度、优化转子结构设计和漂移测试方法的完善提供了参考.Superconducting rotor has great potential applications in the field of precision measurement due to its unique physical properties. The superconducting rotor magnetic levitation device can be used to fabricate high-precision angular velocity sensors. Under the action of external interference torque, the pole-axis deviation from the initial position is the cause of the superconducting rotor pole-axis drift error, in which the spherical surface error and the earth’s rotation belong to the main sources of error, and compensating for the pole-axis drift speed caused by the spherical surface error of the superconducting rotor is a key step in realizing the high-precision superconducting rotor magnetic levitation device. Based on this, the factors affecting the spherical surface error of a complete spherical superconducting rotor and the rotation of the earth on the pole-axis offset characteristics of a superconducting rotor are investigated. First, the magnetic support structure of the superconducting rotor is modeled based on the vector magnetic potential equation, the magnetic field strength distribution on the surface of the superconducting rotor in the ideal state (i.e. suspended in the center of the spherical cavity) is analyzed, and the magnetic support force characteristics are investigated. Then the magnetic support interference moment of the superconducting rotor caused by the spherical surface error is analyzed, and a superconducting rotor dynamics model is established based on the superconducting rotor dynamics equations, and the distribution law of the superconducting rotor pole-axis drift error under different rotor structural parameters is given. Finally, the influence of the earth’s rotation on the superconducting rotor drift test is investigated. The results provide a reference for subsequently improving rotor drift accuracy, optimizing rotor structure design and improving drift test methods.
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Keywords:
- Complete spherical superconducting rotor /
- spherical error /
- polar axis offset characteristics /
- earth’s rotation
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图 2 (a) 悬浮线圈产生的磁场分布图; (b) 悬浮于中心位置时, 超导转子狭窄缝隙内磁感应强度分布图
Fig. 2. (a) Distribution of magnetic field generated by suspension coils; (b) distribution map of magnetic induction intensity in the narrow gap of the superconducting rotor when suspended at the center position.
图 3 上下线圈同时通电2.7—3.0 A时超导磁悬浮系统磁密分布图
Fig. 3. Magnetic density distribution diagram of superconducting maglev system when the lower coil is energized at 2.7—3.0 A simultaneously.
图 5 超导球形转子欧拉角示意图
Fig. 5. Schematic diagram of Euler angle of superconducting spherical rotor.
图 6 超导转子磁感应强度计算模型
Fig. 6. Calculation model for magnetic induction intensity of superconducting rotor.
图 7 (a)超导转子产生的磁支承干扰力矩; (b)磁支承力矩产生的漂移速度
Fig. 7. (a) Magnetic support interference torque generated by superconducting rotor; (b) drift velocity generated by magnetic support torque.
图 8 (a) a2 = 100 μm, a3 = 1 μm, 超导转子产生的磁支承干扰力矩; (b) a2 = 1 μm, a3 = 100 μm, 超导转子产生的磁支承干扰力矩; (c) a2 = 100 μm, a3 = 1 μm, 超导转子磁支承干扰力矩产生的漂移速度; (d) a2 = 1 μm, a3 = 100 μm, 超导转子磁支承干扰力矩产生的漂移速度
Fig. 8. (a) When a2 = 100 μm, a3 = 1 μm, the superconducting rotor generates magnetic support interference torque; (b) when a2 = 1 μm, a3 = 100 μm, the superconducting rotor generates magnetic support interference torque; (c) a2 = 100 μm, a3 = 1 μm, drift velocity generated by the interference torque of the superconducting rotor magnetic support; (d) a2 = 1 μm, a3 = 100 μm, drift velocity generated by the interference torque of the superconducting rotor magnetic support.
图 9 a2和a3连续变化时, 磁力矩变化情况
Fig. 9. Changes in magnetic torque during a2 and a3 continuous variation.
图 10 (a)中心位置向下偏移0.1 mm时, 产生的磁支承干扰力矩; (b)中心位置向上偏移0.1 mm时, 产生的磁支承干扰力矩; (c)中心位置向下偏移0.1 mm时, 超导转子磁支承干扰力矩产生的漂移速度; (d)中心位置向上偏移0.1 mm时, 超导转子磁支承干扰力矩产生的漂移速度
Fig. 10. (a) When the center position is shifted downwards by 0.1 mm, the magnetic support interference torque generated by the superconducting rotor; (b) when the center position is shifted upwards by 0.1 mm, the magnetic support interference torque generated by the superconducting rotor; (c) drift velocity caused by magnetic support interference torque of superconducting rotor when the center position is shifted downwards by 0.1 mm; (d) drift velocity generated by the interference torque of the superconducting rotor magnetic support when the center position is shifted upwards by 0.1 mm.
图 11 悬浮在不同位置时, 狭窄缝隙内的磁感应强度大小分布
Fig. 11. Distribution of magnetic induction intensity in narrow gaps when suspended at different positions.
图 13 由于地球自转, 转子极轴绕罐体轴旋转的轨迹在$xoy$面的投影
Fig. 13. Due to the rotation of the Earth, the trajectory of the rotor’s polar axis rotating around the axis of the tank is projected onto the $xoy$ plane.
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