Angular Dependence of Lateral and Levitation Forces in Asymmetric Small Magnet/Superconducting Systems

The dipole-dipole interaction model is used to calculate the angular dependence of lateral and levitation forces on a small permanent magnet and a cylindrical superconductor in the Meissner state lying laterally off the symmetric axis of the cylinder. Under the assumption that the lateral displacement of the magnet is small compared with the physical dimensions of the system, we obtain analytical expressions for the lateral and levitation forces as functions of geometrical parameters of the superconductor as well as the height, the lateral displacement and the orientation of magnetic moment of the magnet. The effect of thickness and radius of the superconductor on the levitation force is similar to that for a symmetric magnet/superconducting cylinder system, but within the range of lateral displacement. The splitting in the levitation force increases with the increasing angle of orientation of the magnetic moment of the magnet. For a given lateral displacement of the magnet, the lateral force vanishes when the magnetic moment is perpendicular to the surface of the superconductor and has a maximum value when the moment is parallel to the surface. For a given orientation of the magnetic moment, the lateral force has a linear relationship with the lateral displacement. The stability of the magnet above the superconducting cylinder is discussed in detail.     

Vibrations in Magnet/Superconductor Levitation Systems

The problem of a small magnet levitating above a very thin superconducting disc in the Meissner state is analysed. The dipole-dipole interaction model is employed to derive analytical expressions for the interaction energy, levitation force, magnetic stiffness and frequency of small vibrations about the equilibrium position in two different configurations, i.e. with the magnetic moment parallel and perpendicular to the superconductor. The results show that the frequency of small vibrations decreases with the increasing levitation height for a particular radius of the superconducting disc, which is in good agreement with the experimental results. However, the frequency increases monotonically up to saturation by increasing the radius of the disc for a particular height of the magnet. In addition, the frequency of vibrations is higher when the system is in the vertical configuration than that when the system is in the horizontal configuration.     

Effective method to control the levitation force and levitation height in a superconducting maglev system

The influence of the width of the middle magnet in the permanent magnet guideways(PMGs) on the levitation force and the levitation height of single-domain yttrium barium copper oxide(YBCO) bulks has been investigated at 77 K under the zero field cooled(ZFC) state. It is found that the largest levitation force can be obtained in the system with the width of the middle magnet of the PMG equal to the size of the YBCO bulk when the gap between the YBCO bulk and PMG is small.Both larger levitation force and higher levitation height can be obtained in the system with the width of the middle magnet of the PMG larger than the size of the YBCO bulk. The stiffness of the levitation force between the PMG and the YBCO bulk is higher in the system with a smaller width of the middle magnet in the PMG. These results provide an effective way to control the levitation force and the levitation height for the superconducting maglev design and applications.     

一种超导重力仪磁悬浮力的等效计算

为实现超导重力仪磁悬浮力的精确计算,以GWR型超导重力仪为模型基础,采用有限元的思想,将超导球表面电流理想化为多个等高共轴电流环,计算出各个电流环与超导线圈的作用力,求和得到线圈与超导球间的磁悬浮力。利用MATLAB完成计算程序实现,通过改变下线圈电流和上、下线圈电流比,获得满足一定条件的磁悬浮力及其梯度。选取合适的模型参数,计算出线圈对质量为m=4.069 g超导球的磁悬浮力大小为:Ftotal=3.988×10^-2N,磁悬浮力梯度为:-9.699×10^-3N/m,此时悬浮力梯度合适,满足系统稳定性和灵敏度的要求。     

Mechanics of a magnet and a Meissner superconducting ring at arbitrary position and orientation

The force and torque exerted by a magnetic dipole on a superconducting ring (or hollow cylinder) in the Meissner state at arbitrary position and orientation are calculated using a Maxwell-London model previously proposed by the authors. The center of the ring is an unstable equilibrium point for the magnet. At this point the ring tends to align the magnet but tends to expel it for any small axial deviation from the center. There is also a non-monotonic and oscillatory dependence of the forces and torques on the position caused by the finiteness of the ring and a torque arises when the magnet is displaced both radially and axially from the center of the cylinder which corresponds to the experimental data. Therefore, the use of a magnet in a Meissner superconducting ring as a self aligning bearing requires a centered position and that the axial unstability to be compensated by additional mechanical means.     

辅助永磁体厚度对单畴GdBCO超导体捕获磁场分布及其磁悬浮力的影响

研究了两种磁悬浮系统组态中圆台形辅助永磁体厚度对高温超导体捕获磁场和超导磁悬浮力的影响。结果表明,圆台形辅助永磁体的下表面和GdBCO超导体上表面同处在一个水平面上,磁化用圆台形辅助永磁体的厚度H从5 mm增加到45 mm时,超导体捕获磁场和磁悬浮力与圆台形辅助永磁体的厚度直接相关。（1）当圆台形辅助永磁体的北极垂直向上且用液氮冷却后移除辅助永磁体时,最大磁悬浮力从21.8 N增大到26.5 N,再减小到22.9 N;（2）当圆台形辅助永磁体的北极垂直向下且用液氮冷却后移除辅助永磁体时,最大磁悬浮力从20.5 N减小到11.9 N ,再增加到20.4 N;（3）两种磁悬浮系统组态中最大磁悬浮力不一致,与零场冷情况下的最大磁悬浮力14.6 N也不同。在超导磁悬浮应用系统设计中,只有科学选择辅助永磁体形状和尺寸,合理设计组合方式,才能获得较强的磁场强度,提高超导磁悬浮力特性,该结果对促进高温超导体的实际应用具有重要的指导作用。     

Effect of the characteristics of a superconductor on the levitation properties of the magnet-superconductor system

The results of the experimental and theoretical investigations of the magnetic levitation force appearing at the interaction of the multilayer superconducting block of the YBa₂Cu₃O_7?x melted textured ceramic and a permanent magnet are presented. The maximum repulsive force and maximum attractive force are determined as functions of the thickness of the superconducting block in the superconductor cooling regime in both zero and nonzero magnetic fields. The dependence of the levitation force on the geometric parameters and critical current of the superconductor is found.     

Influences of cooling height and lateral moving speed on the levitation characteristics of YBaCuO bulks

Using an updated high-temperature superconductor (HTS) maglev measurement system, electromagnetic forces between a YBaCuO bulk superconductor and a permanent magnet (PM) have been measured under different cooling height (CH) and different lateral moving speed of the PM. It is found that the influence of the moving speed on both the levitation and lateral force is substantial and as such the results shown in this work are a benefit to the understanding of levitation systems.     

Lateral magnetic stiffness under different parameters in a high-temperature superconductor levitation system

Magnetic stiffness determines the stability of a high-temperature superconductor(HTS) magnetic levitation system.The quantitative properties of the physical and geometrical parameters that affect the stiffness of HTS levitation systems should be identified for improving the stiffness by some effective methods. The magnetic stiffness is directly related to the first-order derivative of the magnetic force with respect to the corresponding displacement, which indicates that the effects of the parameters on the stiffness should be different from the relationships between the forces and the same parameters.In this paper, we study the influences of some physical and geometrical parameters, including the strength of the external magnetic field(B0) produced by a rectangular permanent magnet(PM), critical current density(Jc), the PM-to-HTS area ratio(α), and thickness ratio(β), on the lateral stiffness by using a numerical approach under zero-field cooling(ZFC)and field cooling(FC) conditions. In the first and second passes of the PM, the lateral stiffness at most of lateral positions essentially increases with B0 increasing and decreases with β increasing in ZFC and FC. The largest lateral stiffness at every lateral position is almost produced by the minimum value of Jc, which is obviously different from the lateral force–Jc relation. The α-dependent lateral stiffness changes with some parameters, which include the cooling conditions of the bulk HTS, lateral displacement, and movement history of the PM. These findings can provide some suggestions for improving the lateral stiffness of the HTS levitation system.     

临界电流密度对场冷超导磁悬浮力的影响研究

基于Kim临界态模型,通过考虑超导块材内部屏蔽电流的穿透历史过程,讨论了场冷条件下临界电流密度对高温超导悬浮系统磁悬浮排斥力和吸引力的影响.结果显示:最大超导磁悬浮排斥力和吸引力均随临界电流密度的增加呈指数关系增加,并趋于饱和;场冷条件下的磁悬浮力回滞能量损耗远高于零场冷情况;存在一个磁悬浮力比率κ,κ值对于评价大电流...     

空间高频交变磁场对超导块材悬浮力影响研究

高温超导磁悬浮装置,如磁悬浮列车和磁悬浮轴承在高速运行时,空间磁场交变及不均匀性扰动会引发超导块材内部损耗并影响性能,传统均匀时变磁场实验研究及仿真模拟无法满足实际工程应用情况.本文通过设计不同永磁阵列得到不同波形,在高速系统驱动下得到不同交变频率下超导块材损耗特性,发现全波型损耗较半波型损耗高,并研究了不同磁场构型悬浮力衰减特性,可为高速超导磁浮应用提供实验依据.     

On levitation of diamagnetic bodies in a magnetic field

Various methods for calculating the force characteristics of a suspension ensuring levitation of diamagnetic bodies of various origin and shape are considered. The method of calculation is based on the computation of the energy of interaction of a body upon its displacement from the center of suspension for an arbitrary configuration of the suspending field. The method of quasi-homogeneous approximation is considered and compared with the method for calculating the force characteristics based on the general formula for the magnetic energy. The necessary and sufficient conditions for conservative stability of the equilibrium state are formulated, and the stability domain is determined. It is shown that the stability domain depends on the size of the body. Calculations of force characteristics are performed specifically for the suspension of a diamagnetic sphere. The dependences of forces and stiffnesses on the magnetic field strength are obtained, which makes it possible to analyze the stability of confinement of the diamagnetic sphere in the field of the system of circular currents.     

辅助永磁体的引入方式对单畴GdBCO超导块材磁场分布及其磁悬浮力的影响

通过对永磁体辅助下单畴GdBCO超导体和方形永磁体在液氮温度、 零场冷、 轴对称情况下磁悬浮力的测量, 研究了三种不同组态中辅助永磁体的引入方式对单畴GdBCO超导块材磁场分布及其磁悬浮力的影响. 实验结果表明, 如果处在超导体上方的测量用方形永磁体N极向下, 则在轴对称情况下, 当方形辅助永磁体N极向上与超导体下表面贴在一起时, 超导体的最大磁悬浮力从没有引入辅助永磁体磁化的14.3 N增加到31.8 N, 提高到222%; 当方形辅助永磁体放置在超导体上表面、 N极垂直向上且场冷后去掉辅助永磁体时, 超导体的最大磁悬浮力从没有引入辅助永磁体磁化的14.3 N增加到21.6 N, 增加到151%; 当方形辅助永磁体放置在超导体上表面、 N极垂直向下且场冷后去掉方形辅助永磁体时, 超导体的最大磁悬浮力从没有引入辅助永磁体磁化的14.3 N减小到8.6 N, 减小为无辅助永磁体时的60%.这些结果说明, 只有通过科学合理地设计超导体和永磁体的组合方式, 才能获得较高的磁场强度, 有效地提高超导体的磁悬浮力特性, 该结果对促进超导体的应用具有重要的指导意义.     

永磁体辅助下单畴GdBCO超导体和永磁体之间的磁悬浮力研究

通过对永磁体辅助下单畴GdBCO超导体和圆柱形永磁体在液氮温度、零场冷、轴对称情况下磁悬浮力的测量,研究了两种不同组态下辅助永磁体对超导体磁悬浮力特性的影响.实验结果表明,当长方体辅助永磁体水平磁化、且磁极N指向超导体时,超导体的最大磁悬浮力从没有引入辅助永磁体的29.8 N增加到61.5 N,增加为没有引入辅助永磁体时的206%.当长方体辅助永磁体的N极与圆柱形永磁体的N极反平行时,超导体的最大磁悬浮力从没有引入辅助永磁体的29.8 N减小到19.6 N,减小为无辅助永磁体时的65.8%.这些研究结果说明,通过科学合理地设计超导体和永磁体的组合方式,能有效地提高超导体的磁悬浮力.该研究结果对促进超导体的应用具有重要的指导意义. 关键词： 单畴GdBCO 永磁体 磁悬浮力     

空心圆柱形永磁体内径对单畴GdBCO超导块材磁悬浮力的影响

通过对空心圆柱形永磁体与单畴GdBCO超导体磁悬浮力的实验测量,研究了空心圆柱形永磁体内径(d)的变化对超导体磁悬浮力的影响.结果发现,当空心圆柱形永磁体内径从0 mm增加到26 mm时,超导磁悬浮力大小与空心圆柱形永磁体内径有着密切关系(最小测量间距Z=2 mm),所有超导磁悬浮力曲线都存在磁滞现象.随着空心圆柱形永磁体内径的增大,最小间距处超导磁悬浮力逐渐减小,从d=0 mm时的14.8 N减小为d=26 mm时的-0.1 N,d≥20 mm时,最小间距处超导磁悬浮力出现负值;当0 mm≤d5 mm时,超导体最大磁悬浮力出现在最小间距处,d≥5 mm时,超导磁悬浮力先增大后减小,最大超导磁悬浮力产生的位置随着内径的增大而变大.研究表明:只有科学合理地设计永磁体结构参数,才能获得较大的磁场强度,提高超导磁悬浮力特性.该结果对设计并优化磁悬浮轴承系统、环形轨道和超导体的实际应用具有一定的指导意义.     

提高YBCO块材在外磁场中悬浮力

本给出了三种提高YBCO块材在外磁场中悬浮力的方法．第一种方法是增强外磁场，对于此方法，本研究了一块直径为30mm的圆柱状YBCO块材分别在圆柱状NdFeB永磁体和NdFeB永磁导轨上的悬浮力．测量结果表明在77K温度下YBCO块在圆柱状NdFeB永磁体上的最大悬浮力为50N，在NdFeB永磁导轨上的最大悬浮力为103．ON．第二种方法是提高YBCO块材自身的性能，包括临界电流密度、俘获磁通和块材尺寸，对于此方法，本仅研究了块材尺寸对悬浮力的影响．三块直径分别为30mm、35mm、40mm的圆柱状YBC0块材在NdFeB永磁导轨上的悬浮力被测量，77K温度下5mm悬浮间距时的悬浮力分别为103．ON、134．5N、175．ON．第三方法是将YBCO块材变成准永久磁体，此种情况下，直径为40mm的圆柱状YBCO块材在77K温度下5mm悬浮间距时的悬浮力高达218．3N．     

基于ANSYS的高温超导混合磁轴承悬浮力分析

基于商用电磁场有限元软件ANSYS以及Bean临界态模型,对由圆柱形高温超导块材、永磁体和超导线圈组成的新型高温超导混合磁轴承的电磁场分布及悬浮力进行了仿真分析,研究了超导线圈对高温超导混合磁轴承悬浮力的影响,同时还通过实验测试了悬浮力。结果表明:仿真与实验具有较好的一致性,使用软件仿真方便可行,其结果较为准确可靠,可为高温超导混合磁轴承的设计和优化提供理论依据。     

高温超导飞轮储能系统磁悬浮力的仿真计算与实验分析

超导磁悬浮飞轮储能装置储能密度大、储能效率高,具有很好的发展前景。阐述了超导磁悬浮飞轮储能装置的基本原理。主要研究了超导块与永磁体之间的间隙、两者的半径和永磁体厚度等尺寸参数对磁悬浮力的影响。运用有限元分析软件ANSYS对磁悬浮的基本模型进行仿真计算,得到模型的磁力线分布,进一步总结各个参数和磁悬浮力之间的关系,并进行实验验证得到的结论。     

超导开关研究和应用综述

超导开关是实现超导磁体闭环运行的关键部件,也称为持续电流开关(PCS),使超导磁体具有极高的磁场稳定度,广泛应用于核磁共振成像(MRI)、核磁共振谱仪(NMR)、磁浮列车、超导储能系统等技术领域. 文中介绍了超导开关的工作原理和结构组成,综述了用于超导磁体的三类主要超导开关的研究发展现状,比较分析了各自的特点和优势,为...     

Near-oscillatory relaxation behavior of levitation force in infiltration and growth processed bulk YBCO/Ag superconducting composites

Time relaxation behavior of levitation force has been studied in IGP bulk YBCO/Ag superconductor using levitation force measurements as these measurements throw light on the magnetic relaxation in superconductors and the underlying vortex dynamics, pinning mechanisms and the nature of pinning forces. The measurements have revealed a hitherto unknown near-oscillatory relaxation of the levitation force with varying magnetic field. This kind of behavior is found to be more pronounced at smaller gap distances between the permanent magnet and the superconductor. A switch-type polarity bistable equilibrium model for the supercurrent structure has been proposed based on the understanding that even the permanent magnet gets magnetized in the presence of the superconductor, which has also been verified and reported here. This model satisfactorily explains the observed oscillatory behavior of relaxation rates.