Levitation Force Characteristics and Parameter Optimization of Permanent Magnet Tracks

doi:10.3969/j.issn.1004-132X.2023.19.012

Abstract

Abstract: Facing on the high temperature superconducting flux pinned maglev trains， a method of optimizing permanent magnet tracks was proposed by Taguchi orthogonal method. The influences of Halbach double peak permanent magnet tracks size on magnetic field was studied by finite element method， and the influencing factors were optimized in order to obtain the comprehensive magnetic field performance. A method of equivalent treatment of high-temperature superconductors(abbreviation for equivalent treatment method) was proposed based on frozen image mode， and the correctness of the equivalent treatment method was verified by experimental data. The results show that the influences of the height of the permanent magnet tracks on the average magnetic flux intensity and the average magnetic flux intensity per unit mass are far greater than that of the sectional width， and the pure iron thickness is a non-significant factor. Based on the equivalent treatment method， it is found that the suspension forces increase as the suspension gaps decrease. The suspension forces provided by the optimized permanent magnet railway are of 1.5 times that provided by the experimental permanent magnet tracks， the suspension stiffness increases rapidly as the number of rows of high temperature superconductors increase.

Key words: high temperature superconducting flux pinned maglev train, permanent magnet tracks, Taguchi method, parameter optimization, levitation force

摘要： 面向高温超导钉扎磁悬浮列车，提出了一种利用田口正交方法优化永磁轨道参数的方法，通过有限元法研究了Halbach型双峰永磁轨道的尺寸对磁场的影响，以综合磁场性能最佳为目标对影响因素进行了优化。基于冻结镜像模型提出了等效处理高温超导体的方法（简称等效处理方法），并通过实验数据验证了该方法的正确性。研究结果表明，永磁轨道截面高度对平均磁感应强度和单位质量平均磁感应强度的影响远超截面宽度对它们的影响，纯铁厚度为非显著影响因素；基于等效处理方法得到的悬浮力随悬浮间隙的减小而增大；优化永磁轨道提供的悬浮力为实验永磁轨道提供悬浮力的1.5倍，悬浮刚度随高温超导体行数的增大迅速增大。

关键词: 高温超导钉扎磁悬浮列车, 永磁轨道, 田口法, 参数优化, 悬浮力

CLC Number:

U237

ZHANG Mingliang, YANG Dawei, LI Mingyuan, YANG Xinmeng, LIU Liru, ZHANG Lianpeng. Levitation Force Characteristics and Parameter Optimization of Permanent Magnet Tracks[J]. China Mechanical Engineering, 2023, 34(19): 2370-2380.

张明亮, 杨大伟, 李明远, 杨新梦, 刘丽茹, 张连朋. 永磁轨道参数优化和悬浮力特性研究[J]. 中国机械工程, 2023, 34(19): 2370-2380.

References

［1］张文跃，赵正伟，佟来生，等. 高温超导高速磁浮交通系统悬浮导向与牵引方案研究［J］. 低温物理学报， 2020， 42（3）：158-167.
ZHANG Wenyue， ZHAO Zhengwei， TONG Laisheng， et al. Study on Suspension Guidance and Traction Scheme of High Temperature Superconducting High Speed Maglev Traffic System［J］. Cryophysics， 2020， 42（3）：158-167.
［2］邓自刚，刘宗鑫，李海涛，等. 磁悬浮列车发展现状与展望［J］. 西南交通大学学报， 2022， 57（3）：455-474.
DENG Zigang， LIU Zongxin， LI Haitao， et al. The Development Status and Prospect of Maglev Train［J］. Journal of Southwest Jiaotong University， 2022， 57（3）：455-474.
［3］刘文旭，李文龙，方进. 高温超导磁悬浮技术研究论述［J］. 低温与超导， 2020， 48（2）：44-49.
LIU Wenxu， LI Wenlong， FANG Jin. Research on HTS Maglev Technology［J］. Low Temperature and Superconductivity， 2020， 48（2）：44-49.
［4］ZHANG Mingliang， SUN Guoxiang， LIU Pengfei， et al. Research on Force Characteristics and Running Performance of Novel Type High-temperature Superconductor Magnetic Levitation Vehicle［J］. Journal of Superconductivity and Novel Magnetism， 2022， 35（3）：635-646.
［5］伊建辉，孟范鹏，姜衍猛，等. 高温超导磁悬浮列车静态悬浮特性研究［J］. 低温工程， 2019（6）：56-61.
YI Jianhui， MENG Fanpeng， JIANG Yanmeng， et al. Study on the Static Suspension Characteristics of HTS Superconducting Maglev Train［J］. Low Temperature Engineering， 2019（6）：56-61.
［6］王家素，王素玉. 高温超导磁悬浮列车研究综述［J］. 电气工程学报， 2015， 10（11）：1-10.
WANG Jiasu， WANG Suyu. Summary of High-temperature Superconducting Maglev Train Research Report［J］. Journal of Electrical Engineering， 2015， 10（11）：1-10.
［7］刘晓宁，柯志昊，邓自刚. 高温超导磁悬浮准静态力弛豫特性研究［J］. 西南交通大学报， 2023， 58（4）：845-852.
LIU Xiaoning， KE Zhihao， DENG Zhigang. Study on Quasi-static Force Relaxation Properties［J］. Journal of Southwest Jiaotong University， 2023， 58（4）：845-852.
［8］熊嘉阳，邓自刚. 高速磁悬浮轨道交通研究进展［J］. 交通运输工程学报， 2021， 21（1）：177-198.
XIONG Jiayang， DENG Zigang. Research Progress in High-speed Maglev Rail Transit［J］. Journal of Transportation Engineering， 2021， 21（1）：177-198.
［9］徐飞，罗世辉，邓自刚. 磁悬浮轨道交通关键技术及全速度域应用研究［J］. 铁道学报， 2019， 41（3）：40-49.
XU Fei， LUO Shihui， DENG Zigang. Research on Key Technology and Full Speed Domain Application［J］. Journal of Railways， 2019， 41（3）：40-49.
［10］张明亮，李明远，刘鹏飞，等. 面向高温超导钉扎磁悬浮列车悬浮特性研究［J］. 中国机械工程2022， 33（22）：2764-2771.
ZHANG Mingliang， LI Mingyuan， LIU Pengfei， et al. Research on Suspension Characteristics of HTS Pinned Maglev Train［J］. China Mechanical Engineering， 2022， 33（22）：2764-2771.
［11］LI Haitao， DENG Zigang， HUANG Huan， et al. Experiments and Simulations of the Secondary Suspension System to Improve the Dynamic Characteristics of HTS Maglev［J］. IEEE Transactions on Applied Superconductivity， 2021， 31（6）：3602508.
［12］张明亮. 面向航天器对接接口的高温超导磁通钉扎连接技术研究［D］. 哈尔滨：哈尔滨工业大学， 2016.
ZHANG Mingliang. Research on High Temperature Superconducting Magnetic Flux Ligation Technology［D］. Harbin：Harbin Institute of Technology， 2016.
［13］陈绍琰，郑挺，刘郊，等. 永磁轨道外磁场横向不对称分布特性［J］. 低温与超导， 2020， 48（5）：34-40.
CHEN Shaoyan， ZHENG Ting， LIU Jiao， et al. Characteristics of the Transverse Asymmetric Distribution of the Magnetic Field Outside the Permanent Magnet Railway［J］. Low Temperature and Superconductivity， 2020， 48（5）：34-40.
［14］WEN Yuyan， YING Xin， HONG Wei， et al. Comparative Study between Electromagnet and Permanent Magnet Rails for HTS Maglev［J］. Superconductor Science and Technology， 2020， 33（3）：035011.
［15］WANG B， ZHENG J， CHE T， et al. Dynamic Response Characteristics of High Temperature Superconducting Maglev Systems：Comparison between Halbach-type and Normal Permanent Magnet Guideways［J］. Physica C：Superconductivity and Its Applications， 2015， 519：147-152.
［16］DENG Z， WANG J， ZHENG J， et al. High-efficiency and Low-cost Permanent Magnet Guideway Consideration for High-Tc Superconducting Maglev Vehicle Practical Application［J］. Superconductor Science and Technology， 2008， 21（11）：115018.
［17］JING H， WANG S， LIU W， et al. A High-Tc Super-conducting Maglev System Using T-shaped Permanent Magnet Single-guideway［J］. IEEE Transactions on Applied Superconductivity， 2008， 18（2）：795-798.
［18］SOTELO G G， DE OLIVEIRA R A H， COSTA F S， et al. A Full Scale Superconducting Magnetic Levitation（MagLev）Vehicle Operational Line［J］. IEEE Transactions on Applied Superconductivity， 2015， 25（3）：1-5.
［19］HEKMATI A， MAFI H. Impact of Magnetization Angles in Permanent Magnet Guideways on High-temperature Huperconductors' Levitation［J］. IEEE Transactions on Magnetics， 2016， 52（9）：1-9.
［20］梁星，赵立峰，付志方. 基于Ansoft的永磁轨道排布方式的仿真优化［J］. 低温与超导， 2013， 41（3）：49-52.
LIANG Xing， ZHAO Lifeng， FU Zhifang. Simulation Optimization of the Permanent Magnet Orbit Arrangement Mode Based on Ansoft［J］. Low Temperature and Superconductivity， 2013， 41（3）：49-52.
［21］王妙，杨旭，王凡，等. 永磁轨道不同组合方式的磁场分布研究［J］. 西安航空学院学报， 2018， 36（1）：66-71.
WANG Miao， YANG Xu， WANG Fan， et al. Study of Different Combinations of Permanent Magnet Orbits［J］. Journal of Xi'an Aviation University， 2018， 36（1）：66-71.
［22］SUN Ruixue， ZHENG Jun， ZHENG Botian， et al. New Magnetic Rails with Double-layer Halbach Structure by Employing NdFeB and Ferrite Magnets for HTS Maglev［J］. Journal of Magnetism and Magnetic Materials， 2018， 445， 44-48.
［23］廖兴林，郑珺，刘璐，等. 不同重叠排列方式的双层高温超导块材在永磁轨道上方的悬浮特性［J］. 低温与超导， 2010， 38（10）：18-22.
LIAO Xinglin， ZHENG Jun， LIU Lu， et al. Suspension Characteristics of Double-layer High-temperature Superconducting Blocks above the Permanent Magnet Orbit in Different Overlapping Arrangements［J］. Low Temperature and Superconductivity， 2010， 38（10）：18-22.
［24］任仲友， Oliver de Hass，王晓融，等. 永磁导轨上组合与单块YBCO的悬浮力关系研究［J］. 低温物理学报， 2003（增刊1）：182-186.
REN Zhongyou， de HASS O， WANG Xiaorong， et al. Study on Combination and YBCO［J］. Journal of Cryogenic Physics， 2003（S1）：182-186.
［25］任仲友，王家素，王素玉，等. 高温超导磁悬浮车导向力测试装置［J］. 电工电能新技术， 2003（1）：77-80.
REN Zhongyou， WANG Jiasu， WANG Suyu， et al. High Temperature Superconducting Maglev Vehicle Guide Force Test Device［J］. Electrical Power New Technology， 2003（1）：77-80.
［26］申政，方进，李云贤，等. 高温超导飞轮储能系统磁悬浮力的仿真计算与实验分析［J］. 低温与超导， 2013， 41（1）：8-12.
SHEN Zheng， FANG Jin， LI Yunxian， et al. Simulation Calculation and Experimental Analysis of Magnetic Levitation in High Temperature Superconducting Flywheel Energy Storage System［J］. Low Temperature and Superconductivity， 2013， 41（1）：8-12.
［27］吴爽，方进. 永磁体尺寸对高温超导磁悬浮力的影响分析［J］. 低温与超导， 2018， 46（7）：38-42.
WU Shuang， FANG Jin. Analysis of the Influence of Permanent Magnet Size on High-temperature Superconducting Magnetic Suspension Force［J］. Low Temperature and Superconductivity， 2018， 46（7）：38-42.
［28］KE Zhihao， LIU Xiaoning， CHEN Yining， et al. Prediction Models Establishment and Comparison for Guiding Force of High-temperature Superconducting Maglev Based on Deep Learning Algorithms［J］. Superconductor Science and Technology， 2022， 35（2）：024005.
［29］胡尊祥，邓自刚，刘珍，等. 垂向磁场变化量对高温超导块材悬浮力特性的影响［J］. 低温物理学报， 2020， 42（6）：266-272.
HU Zunxiang， DENG Zigang， LIU Zhen， et al. Effect of Vertical Magnetic Field Variation on the Suspension Force Characteristics of High-temperature Superconducting Blocks［J］. Journal of Cryogenic Physics， 2020， 42（6）：266-272.
［30］史景文，朱理铭，周大进，等. 悬浮杜瓦通过永磁轨道开断处的纵向力研究［J］. 低温物理学报， 2021， 43（5）：311-318.
SHI Jingwen， ZHU Liming， ZHOU Dajin， et al. Longitudinal Force Study at Permanent Magnet Railway［J］. Journal of Cryogenic Physics， 2021， 43（5）：311-318.
［31］WU Xingda， XU Kexi， YUE Cao， et al. Modeling of Hysteretic Behavior of the Levitation Force between Superconductor and Permanent Magnet［J］. Physica C：Superconductivity and Its Applications， 2013， 486：17-22.
［32］ZHANG Mingliang， HAN Yanjun， GUO Xing， et al. The Connection Characteristics of Flux Pinned Docking Interface［J］. Journal of Applied Physics， 2017， 121：113907.
［33］陈志贤，池茂儒，吴兴文，等. 高温超导磁悬浮车辆曲线通过动态特性分析［J］. 机车电传动， 2020（4）：70-75.
CHEN Zhixian， CHI Maoru， WU Xingwen， et al. High Temperature Superconducting Maglev Vehicle Curve through Dynamic Characteristic Analysis［J］. Electric Transmission of Locomotive， 2020（4）：70-75.
［34］陈楠，陈洋，孙睿雪，等. 高温超导-永磁混合悬浮车基本系统的理论模型与实验［J］. 科学通报， 2020， 65（9）：847-855.
CHEN Nan， CHEN Yang， SUN Ruixue， et al. Theoretical Model and Experiment of the Basic System of High-temperature Superconducting Permanent Magnet Hybrid Suspension Vehicle［J］. Scientific Bulletin， 2020， 65（9）：847-855.
［35］刘博，张东，杨本康，等. 高速磁浮车用高温超导直线电动机的研究综述［J］. 低温与超导， 2021， 49（4）：31-35.
LIU Bo， ZHANG Dong， YANG Benkang， et al. Review of High Temperature Superconducting Linear Motor for High Speed Maglev Vehicle［J］. Low Temperature and Superconductivity， 2021， 49（4）：31-35.
［36］宋文娟，方进，丘明，等. 外加磁场强度对高温超导磁悬浮力影响的分析［J］. 低温与超导， 2014， 42（5）：32-36.
SONG Wenjuan， FANG Jin， QIU Ming， et al. Analysis of the Influence of Applied Magnetic FieldStrength on High-temperature Superconducting Magnetic Suspension Force［J］. Low Temperature and Superconductivity， 2014， 42（5）：32-36.
［37］任仲友，王家素，王素玉，等. 提高YBCO块材在外磁场中悬浮力［J］. 低温物理学报， 2003， 25（3）：202-208.
REN Zhongyou， WANG Jiasu， WANG Suyu， et al. Improve the Suspension Force of YBCO Block in the External Magnetic Field［J］. Journal of Cryogenic Physics， 2003， 25（3）：202-208.

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