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The superconducting rotor magnetic levitation device can be used to make an angular velocity sensor, and the high-speed rotating superconducting rotor is the basis for achieving high-precision measurement of the superconducting rotor magnetic levitation device. The heat loss and radial mass eccentricity of the superconducting rotor can cause thermal quenching and resonance in the driving process, which is unfavorable to the driving process of the superconducting rotor. Therefore, it is necessary to maintain a certain quantity of helium gas in the superconducting cavity in the driving process, to transfer the heat generated by the driving process and avoid its resonance. But helium gas also has a drag torque on the rotating superconducting rotor, affecting the driving process of the superconducting rotor. Based on this, the drag torque of the helium on the rotating superconducting rotor is studied. Firstly, the Van der Waals equation is introduced to analyze the properties of low-temperature helium, and a method of studying the drag effect of low-temperature helium on the rotating superconducting rotor is proposed based on Reynolds law and Stoke’s first problem. Then, an experiment on superconducting rotor speed attenuation is conducted to verify the proposed analysis method. Based on the finite element method, the driving electromagnetic structure and driving torque of the superconducting rotor are analyzed. Finally, the influence of helium on the driving process of the superconducting rotor is investigated, including critical driving speed, acceleration time of the superconducting rotor, and frictional heat of the helium on the superconducting rotor. The research results further enrich the study of the drag torque of low-temperature gases on rotating superconductors, providing a reference for further optimizing the driving process of superconducting rotors.
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Keywords:
- superconducting magnetic levitation /
- superconducting rotor /
- helium drag torque /
- electromagnetic drive
[1] 胡新宁, 王厚生, 王晖, 王秋良 2010 光学精密工程 18 169
Hu X N, Wang H S, Wang H, Wang Q L 2010 Opt. Precis. Eng. 18 169
[2] 江磊, 钟智勇, 仪德英, 张怀武 2008 仪器仪表学报 29 1115
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Jiang L, Zhong Z Y, Yi D Y, Zhang H W 2008 Chin. J. Sci. Instrum. 29 1115
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[3] 崔春艳, 胡新宁, 程军胜, 王晖, 王秋良 2015 物理学报 64 018403
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Cui C Y, Hu X N, Chen J S, Wang H, Wang Q L 2015 Acta Phys. Sin. 64 018403
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[5] 张源, 胡新宁, 崔春艳, 崔旭, 牛飞飞, 黄兴, 王路忠, 王秋良 2023 物理学报 72 128401
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Zhang Y, Hu X N, Cui C Y, Cui X, Niu F F, Huang X, Wang L Z, Wang Q L 2023 Acta Phys. Sin. 72 128401
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Tang J Q 2005 Ph. D. Dissertation ( Harbin: Harbin Engineering University
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[8] Stephenson W B, Whitfield D L 1971 IEEE Trans. Aerosp. Electron. Syst. AES-7, 1131
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[10] Dorfman J R, Sengers J V 1986 Phys. A. Stat. Theor. Phys. 134 283
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Google Scholar
[12] Hu X N, Wang Q L, Gao F, Lei Y Z, Cui C Y, Li L K, Yan L G 2014 IEEE Trans. Instrum. Meas. 63 859
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[13] Simon I 1953 J. Appl. Phys. 24 19
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[14] 沈青 2003 稀薄气体动力学 (北京: 国防工业出版社)第7—14页
Shen Q 2003 Rarefied Gas Dynamics(1st edn). (Beijing: National Defense Industry Press) pp7–14
[15] 陈伟芳, 赵文文, 江中正, 刘华林 2016 气体物理 1 9
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Chen W F, Zhao W W, Jiang Z Z, Liu H L 2016 Phys. Gas 1 9
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[16] 尹钊, 陈雪亮 2003 聊城大学学报 16 98
Yin Z, Chen X L 2003 J. Liaochen 16 98
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[18] 李椿, 章立源, 钱尚武 2015 热学 (北京: 高等教育出版社) 第22—24页
Li C, Zhang L Y, Qian S W 2015 Thermal (3rd Ed.) (Beijing: Higher Education Press) pp22–24
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He L M, Zhao G, Cheng B Q 2009 Gas Dynamics(1st edn. ) (Beijing: National Defense Industry Press) pp3–13, 199–201
[21] 邹高万, 贺征, 顾璇 2013 黏性流体力学 (北京: 国防出版社)第219—223页
Zou G W, He Z, Gu X 2013 Viscous Fluid Mechanics (1st edn. ) (Beijing: National Defense Industry Press) pp219–223
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Wang H, Wang Q L, Hu X N, Cui C Y, Su H J, He Z M 2018 Cyro. Supercond. 46 1
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Zhao B, Zhang H L 2013 Application of Ansoft 12 in Engineering Electromagnetic Fields (Beijing: China Water Power Press) pp47–59
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图 1 超导转子磁悬浮结构示意图
Figure 1. Magnetic suspension structure diagram of the superconducting rotor.
图 2 超导转子结构模型
Figure 2. Model of the superconducting rotor.
图 3 力矩器结构模型 (a)超导转子定中结构; (b)力矩器产生磁场分布
Figure 3. Structural model of torquer: (a) Superconducting rotor’s polar axis alignment structure; (b) distribution of magnetic field generated by the torque.
图 4 悬浮线圈产生的磁场分布图
Figure 4. Distribution of magnetic field generated by suspension coils.
图 5 超导转子转速衰减实验示意图
Figure 5. Schematic diagram of superconducting rotor speed attenuation experiment.
图 6 超导转子转速衰减实验
Figure 6. Experimental data on speed attenuation of superconducting rotor.
图 7 系数α和β的拟合曲线
Figure 7. Fitting curve of coefficients α and β.
图 8 非稀薄气体中转速衰减实验数据与理论计算数据的比较 (a) 40000 Pa; (b) 4000 Pa; (c) 1000 Pa; (d) 200 Pa; (e) 20 Pa; (f) 3.27 Pa
Figure 8. Comparison between experimental data and theoretical calculations for non rarefied gases: (a) 40000 Pa; (b) 4000 Pa; (c) 1000 Pa; (d) 200 Pa; (e) 20 Pa; (f) 3.27 Pa.
图 9 稀薄气体中转速衰减实验数据与理论计算数据的比较 (a) 0.221 Pa; (b) 0.016 Pa
Figure 9. Comparison of experimental and theoretical data of speed attenuation in rarefied gas: (a) 0.221 Pa; (b) 0.016 Pa.
图 10 超导转子驱动结构
Figure 10. Superconducting rotor drive structure.
图 11 超导转子内孔磁场分布图
Figure 11. Distribution of magnetic field in the inner hole of the superconducting rotor.
图 12 超导转子驱动力矩分布 (a)单路定子通电; (b)两路定子线圈通电
Figure 12. Distribution of driving torque for superconducting rotor: (a) Single stator energized; (b) two stator coils energized.
图 13 超导转子临界驱动转速分析
Figure 13. Analysis of critical driving speed of the superconducting rotor.
图 14 超导转子的驱动过程
Figure 14. Driving process of superconducting rotor.
图 15 不同压强加速到200 Hz的时间
Figure 15. Time for different pressures to accelerate to 200 Hz.
图 16 超导转子的氦气摩擦功率
Figure 16. Helium friction power of the superconducting rotor.
表 1 超导球腔压强对应的克努森数
Table 1. Knudsen number corresponding to pressure in superconducting sphere cavity.
压强/Pa 克努森数Kn 气体领域 P > 38.4 Kn < 0.01 非稀薄气体 38.4 > P > 3.84 0.01 < Kn < 0.1 滑流 3.84 > P > 0.0384 0.1 < Kn < 10 过渡领域 0.0384 > P 10 < Kn 自由分子流 
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表 2 实验数据与理论计算误差对比
Table 2. Comparison of experimental data and theoretical calculation errors.
氦气压强/Pa 平均误差(衰减1 h)/% 最大误差(衰减1 h)/% 40000 1.5 3 4000 1.46 2.05 1000 2.14 4.18 200 –1 –2 20 1.6 3.6 3.27 1 2 0.221 –10.34 –20.07 0.016 –13.08 –27.6
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[1] 胡新宁, 王厚生, 王晖, 王秋良 2010 光学精密工程 18 169
Hu X N, Wang H S, Wang H, Wang Q L 2010 Opt. Precis. Eng. 18 169
[2] 江磊, 钟智勇, 仪德英, 张怀武 2008 仪器仪表学报 29 1115
Google Scholar
Jiang L, Zhong Z Y, Yi D Y, Zhang H W 2008 Chin. J. Sci. Instrum. 29 1115
Google Scholar
[3] 崔春艳, 胡新宁, 程军胜, 王晖, 王秋良 2015 物理学报 64 018403
Google Scholar
Cui C Y, Hu X N, Chen J S, Wang H, Wang Q L 2015 Acta Phys. Sin. 64 018403
Google Scholar
[4] Schoch K F, Darrel B 1967 Proceedings of the 1966 Cryogenic Engineering Conference Colorado, America, June 13–15, 1967 p657
[5] 张源, 胡新宁, 崔春艳, 崔旭, 牛飞飞, 黄兴, 王路忠, 王秋良 2023 物理学报 72 128401
Google Scholar
Zhang Y, Hu X N, Cui C Y, Cui X, Niu F F, Huang X, Wang L Z, Wang Q L 2023 Acta Phys. Sin. 72 128401
Google Scholar
[6] 汤继强 2005 博士学位论文 (哈尔滨: 哈尔滨工程大学)
Tang J Q 2005 Ph. D. Dissertation ( Harbin: Harbin Engineering University
[7] Wang H, Hu X N, Cui C Y, Wang L, Wang Q L 2018 IEEE Trans. Appl. Supercond. 28 5207905
Google Scholar
[8] Stephenson W B, Whitfield D L 1971 IEEE Trans. Aerosp. Electron. Syst. AES-7, 1131
[9] Beams J W, Young J L, Moore J W 1946 Appl. Phys. 17 886
Google Scholar
[10] Dorfman J R, Sengers J V 1986 Phys. A. Stat. Theor. Phys. 134 283
Google Scholar
[11] Wang H, Hu X N, Cui C Y, Wang H, Liu J H, Wang L 2017 IEEE Trans. Appl. Supercond. 27 3601305
Google Scholar
[12] Hu X N, Wang Q L, Gao F, Lei Y Z, Cui C Y, Li L K, Yan L G 2014 IEEE Trans. Instrum. Meas. 63 859
Google Scholar
[13] Simon I 1953 J. Appl. Phys. 24 19
Google Scholar
[14] 沈青 2003 稀薄气体动力学 (北京: 国防工业出版社)第7—14页
Shen Q 2003 Rarefied Gas Dynamics(1st edn). (Beijing: National Defense Industry Press) pp7–14
[15] 陈伟芳, 赵文文, 江中正, 刘华林 2016 气体物理 1 9
Google Scholar
Chen W F, Zhao W W, Jiang Z Z, Liu H L 2016 Phys. Gas 1 9
Google Scholar
[16] 尹钊, 陈雪亮 2003 聊城大学学报 16 98
Yin Z, Chen X L 2003 J. Liaochen 16 98
[17] 石荣彦 2014 物理通报 9 32
Google Scholar
Shi R Y 2014 Phys. Bull. 9 32
Google Scholar
[18] 李椿, 章立源, 钱尚武 2015 热学 (北京: 高等教育出版社) 第22—24页
Li C, Zhang L Y, Qian S W 2015 Thermal (3rd Ed.) (Beijing: Higher Education Press) pp22–24
[19] Hu X N, Wang Q L, Cui C Y 2010 IEEE Trans. Appl. Supercond. 20 892
Google Scholar
[20] 何立明, 赵罡, 程邦勤 2009 气体动力学(北京: 国防出版社)第3—13, 199—201页
He L M, Zhao G, Cheng B Q 2009 Gas Dynamics(1st edn. ) (Beijing: National Defense Industry Press) pp3–13, 199–201
[21] 邹高万, 贺征, 顾璇 2013 黏性流体力学 (北京: 国防出版社)第219—223页
Zou G W, He Z, Gu X 2013 Viscous Fluid Mechanics (1st edn. ) (Beijing: National Defense Industry Press) pp219–223
[22] 韩红彪, 高善群, 李济顺, 张永振 2015 机械科学与技术 34 1621
Google Scholar
Han H B, Gao S Q, Li J S, Zhang Y Z 2015 Mechanical Science and Technology for Aerospace Engineering 34 1621
Google Scholar
[23] Hu X N, Wang Q L, Cui C Y, Gao F, Wang H, Li Y, Wang H S, Cheng J S, Dai Y M, Yan L G 2014 IEEE Trans. Instrum. Meas. 63 2789
[24] 赵尚武, 胡新宁, 崔春燕, 王秋良 2008 稀有金属材料与工程 37 217
Google Scholar
Zhao S W, Hu X N, Cui C Y, Wang Q L 2008 Rare Metal Mater. Eng. 37 217
Google Scholar
[25] 王浩, 王秋良, 胡新宁, 崔春燕, 苏华俊, 何忠名 2018 低温与超导 46 1
Google Scholar
Wang H, Wang Q L, Hu X N, Cui C Y, Su H J, He Z M 2018 Cyro. Supercond. 46 1
Google Scholar
[26] 应纯同1990 气体输运理论及应用 (北京: 清华大学出版社) 第21—25页
Ying C T 1990 Gas Transport Theory and Applications(1st Ed.) (Beijing: Tsinghua University Press) pp21–25
[27] Vanitterbeek A, Keesom W H 1938 Physica 5 257
Google Scholar
[28] 赵博, 张洪亮 2013 Ansoft 12在工程电磁场中的应用(北京: 中国水利水电出版社出版社)第47—59页
Zhao B, Zhang H L 2013 Application of Ansoft 12 in Engineering Electromagnetic Fields (Beijing: China Water Power Press) pp47–59
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