Influence of the Trapped Field on the Levitation Performance of the Magnetized Bulk High-<Emphasis Type="Italic">T</Emphasis><Subscript><Emphasis Type="Italic">c</Emphasis></Subscript> Superconductor

A magnetized bulk high-T _c superconductor (HTSC) magnet is a good candidate to improve the levitation performance of the high-T _c superconducting (HTS) maglev system. Compared with the unmagnetized bulk HTSC, the magnetized bulk HTSC magnet can supply stronger levitation or guidance force above a permanent magnet guideway (PMG). Different from the permanent magnet, the magnetic field of a magnetized bulk HTSC magnet is sustained by the induced superconducting current produced during the magnetizing process. Given that the induced superconducting current within the magnetized bulk HTSC magnet is very sensitive to the magnetic field, the levitation performance of the magnetized bulk HTSC magnet is directly related to its own trapped field and the magnetic field of the PMG. This article discusses the influence of trapped and external magnetic fields on the levitation performance of a magnetized bulk HTSC magnet by experiments, and the Critical State Model is used to analyze the test results. The analyses and conclusions of this article are useful for the application of magnetized bulk HTSC magnet in practical HTS maglev systems.     

Characteristic of the Guidance Force in the High-T c Superconducting Levitation System with Pre-Load Process

The stable levitation above permanent magnet is an important characteristic of the bulk high-T _c superconductor (HTS). When an external force pushes the bulk HTS up, down or sideways, or tries to tilt it, a restoring force can return it to its initial position. The HTS Maglev relied on this characteristic can overcome the external force from wind or pass the curve lines successfully. The change of guidance force (GF) during many times lateral movement is studied. Experiments show that GF increases during the lateral movement, no matter what kind of PMG or HTS is used, and the change of the GF slows down after 5 times lateral movement. The pre-load method can reduce the levitation force decay during lateral movement. So the influence of GF by the pre-load method is needed to be studied. It is found that the pre-load method can increase GF and reduce the change of the GF during lateral movement. The Halbach permanent magnetic guideway (PMG) can offer much more GF but the change is larger just as the levitation force decays. The GF of cylindrical bulk HTS increases more than of the rectangular bulk HTS in the pre-load case. The characteristics of the GF during the lateral movement are explained. These results are important for further HTS Maglev vehicle system designs.     

Permanent Magnet Enhancement of Fully Superconducting MgB2-YBa2Cu3O7−x Bearing

This paper reports the experimental verification and improved concept of the previously reported fully superconducting magnetic bearing using bulks on both the rotor and the stator in a cylindrical geometry. Experimental measurements on pulsed magnetisation and levitation force between a magnetised 25.5 mm diameter YBCO bulk inside an MgB₂ hollow cylinder are reported proving the concept of a bulk–bulk bearing. The maximum force achieved after field cooling of the MgB₂ bulk in the field of a 1.68 T magnetised YBCO bulk was 501 N. The improved concept relies on additional ring shaped permanent magnets placed on the bottom of the MgB₂ cylinder. These rings create additional axial force in the bearing system. Permanent magnet rings can boost the force for the existing bearing design by enhancing the field trapped in the MgB₂ tube and providing a ‘cushion’ of magnetic field for the bottom YBCO bulk by exploiting zero field cooling. In particular the enhancement of the force is largely due to the favourable distortion of the trapped field in the MgB₂ cylinder and is much greater than the direct repulsive force between a magnetised YBCO bulk and permanent magnet only. Various permanent magnet configurations are evaluated by modelling of levitation force using the perfectly trapped flux model. The high force densities of bulk–bulk bearings allow them to support large loads useful for application such as flywheel energy storage.     

Flux Concentrator Optimization of PMG for High-Temperature Superconducting Maglev Vehicle System

The permanent magnetic guideway (PMG) composed of permanent magnet (PM) and steel is developed under flux concentration principle, which is the crucial component of high-temperature superconducting (HTS) maglev vehicle system. Optimum PMG design is an effective way to increase levitation force and associated stiffness for improving the load capability of HTS maglev vehicle. In order to realize higher vertical field component B _z in upper surface, three PMG demonstrators with three different forms of flux concentrator are fabricated with same volume of magnet. The levitation performances of onboard HTS bulks array over them are studied. The experimental results indicate that the PMG with a permanent magnet as the flux concentrator would produce biggest levitation force, levitation stiffness and trapped flux when interacting with HTS superconductor.     

Calculation of Levitation Force between Small Superconducting Cylinder and Magnetic Ring in the Critical State

Levitation force between a small superconducting cylinder in the mixed state and a magnetic ring was calculated using the critical state model. The dependence of the levitation force on the size of the superconductor as well as the magnet was investigated. The finite size effect of the superconductor is included by demagnetizing factor approximation. The stiffness for the levitating system was calculated. The position of the maximum levitation force depends on the size of the superconductor and the magnet. Trend of the calculated force is in agreement with the experimental results.      

磁流体浸没物磁场力分析及磁浮特性

物体浸没于磁流体中表现出磁浮特性，对其受力状态分析是准确描述其悬浮状态的前提和基础。基于非线性磁流体应力张量模型和稳态Bernoulli方程，建立磁流体中浸没物受力模型。借助非磁性体受力模型的简化计算方法以及磁性体与磁流体之间的多场效应关系，分别对非磁性体、磁性体两类浸没物在磁流体中所受磁浮力进行分析，结果表明非磁性浸没物在磁流体中仅受到外加磁场贡献的一次磁浮力，而磁性浸没物除受到一次磁浮力外，还受到其自身激发磁场贡献的二次磁浮力．永磁体在磁流体中位置决定的磁浮力满足一定条件时，永磁体能够自悬浮于磁流体中。     

Magnetic levitation above the superconducting YBa2Cu3O7−x /polymer 0-3 and 2-2 composites

Superconducting YBa₂Cu₃O_7–x /polyurethane 0-3 composites have been fabricated with several volume fraction fillers. Magnetic forces between a small permanent magnet and the composites have been measured at 77 K and show hysteretic behaviour as a function of their separation distances. Such behaviour indicates multiple equilibrium heights of the magnet levitating above the composites. It is shown that the levitation height increases with increasing volume fraction of superconductor filler. The parallel YBa₂Cu₃O_7–x /polyurethane and series YBa₂Cu₃O_7–x /polypropylene 2-2 composites were also prepared and only tested for magnetic levitation.     

The Influence of Excitation Frequency on Magnetic Levitation Systems with a High-T c Superconductor

In this paper we present a numerical analysis of dynamic features of the levitation system generated by an interaction between a levitated permanent magnet (PM) and a high-T _c superconductor (HTSC) excited by an oscillatory external source. The obtained results show that the value of the frequency (f _free) of the PM displacement in the case of the levitation system generated by an interaction between a levitated PM and a fixed HTSC is equal at the resonance frequency (f _re) of the levitation system generated by an interaction between a levitated PM and HTS excited by an oscillatory external source and the resonance frequency (f _re) is mainly dependent upon the cooling position (Z ₀) and the mass of the PM. The numerical problem in this paper is solved by using the control volume method (CVM).     

Superconducting bulk magnet for maglev vehicle: Stable levitation performance above permanent magnet guideway

High-temperature superconducting (HTS) maglev vehicle is well known as one of the most potential applications of bulk high-temperature superconductors (HTSCs) in transported levitation system. Many efforts have promoted the practice of the HTS maglev vehicle in people's life by enhancing the load capability and stability. Besides improving the material performance of bulk HTSC and optimizing permanent magnet guideway (PMG), magnetization method of bulk HTSC is also very effective for more stable levitation. Up to now, applied onboard bulk HTSCs are directly magnetized by field cooling above the PMG for the present HTS maglev test vehicles or prototypes in China, Germany, Russia, Brazil, and Japan. By the direct-field-cooling-magnetization (DFCM) over PMG, maglev performances of the bulk HTSCs are mainly depended on the PMG's magnetic field. However, introducing HTS bulk magnet into the HTS maglev system breaks this dependence, which is magnetized by other non-PMG magnetic field. The feasibility of this HTS bulk magnet for maglev vehicle is investigated in the paper. The HTS bulk magnet is field-cooling magnetized by a Field Control Electromagnets Workbench (FCEW), which produces a constant magnetic field up to 1 T. The levitation and guidance forces of the HTS bulk magnet over PMG with different trapped flux at 15 mm working height (WH) were measured and compared with that by DFCM in the same applied PMG magnetic field at optimal field-cooling height (FCH) 30 mm, WH 15 mm. It is found that HTS bulk magnet can also realize a stable levitation above PMG. The trapped flux of HTS bulk magnet is easily controllable by the charging current of FCEW, which implies the maglev performances of HTS bulk magnet above PMG will be adjustable according to the practical requirement. The more trapped flux HTS bulk magnet will lead to bigger guidance force and smaller repulsion levitation force above PMG. In the case of saturated trapped flux for experimental HTS bulk magnet, it is not effective to improve its maglev performances by increasing of charging magnetic field, when the guidance force at WH 15 mm is 5.7 times larger than that by DFCM of FCH 30 mm. So introducing HTS bulk magnet into the present maglev system is feasible and more controllable to realize stable levitation above applied PMG, which is an important alternative for the present HTS maglev vehicle.     

Correlations Between Magnetic Flux and Levitation Force of HTS Bulk Above a Permanent Magnet Guideway

In order to clarify the correlations between magnetic flux and levitation force of the high-temperature superconducting (HTS) bulk, we measured the magnetic flux density on bottom and top surfaces of a bulk superconductor while vertically moving above a permanent magnet guideway (PMG). The levitation force of the bulk superconductor was measured simultaneously. In this study, the HTS bulk was moved down and up for three times between field-cooling position and working position above the PMG, followed by a relaxation measurement of 300 s at the minimum height position. During the whole processes, the magnetic flux density and levitation force of the bulk superconductor were recorded and collected by a multipoint magnetic field measurement platform and a self-developed maglev measurement system, respectively. The magnetic flux density on the bottom surface reflected the induced field in the superconductor bulk, while on the top, it reveals the penetrated magnetic flux. The results show that the magnetic flux density and levitation force of the bulk superconductor are in direct correlation from the viewpoint of inner supercurrent. In general, this work is instructive for understanding the connection of the magnetic flux density, the inner current density and the levitation behavior of HTS bulk employed in a maglev system. Meanwhile, this magnetic flux density measurement method has enriched present experimental evaluation methods of maglev system.     

The Stable Magnetic Levitation of a Cylindrical Ferromagnetic Object

This paper introduces a control method using a ring magnet for the stable levitation of a cylindrical ferromagnetic object. The levitation has a strong stability with anti-disturbance abilities, and weight can be placed on the floating magnet. The magnetic field created by the ring magnet provides stabilities in 3 degrees of freedom of the floating magnet, and a feedback control in the horizontal plane is introduced to the control system. Analytical calculation and experiments have been done to prove the feasibility of this control method.     

Influence of an applied magnetic field on shielding current paths in a high TC superconductor

The influence of an applied magnetic field on shielding current paths in a bulk high T_c superconductor was investigated. This issue is very important for the quantitative analysis of levitation force, since the distortion and localization of the current paths have been found to be a major source of discrepancy between computed and experimental results. Furthermore, it has been speculated that the current paths vary, depending on the applied magnetic field. The magnetic field due to superconducting currents was measured by a Hall sensor when a permanent magnet was positioned at different gaps from a superconductor. The current paths were then reconstructed from the measured field data by an inverse analysis. A genetic algorithm, which is a robust probabilistic optimizing method, was used for the inverse analysis. It was found that the current paths merged into larger loops as the permanent magnet was retreating from the superconductor. It implies that a stronger applied magnetic field locally degrades the current density (J_c) and the shielding current paths are localized by these low-J_c areas which act as insulating boundaries.     

Magnetic Levitation With High-Tc Superconducting Thin Films

The levitation force between a permanent magnet and a superconducting thin film was investigated experimentally. The configuration consisted of a cylindrical NdFeB permanent magnet placed above a circular YBa₂Cu₃O_7– disk with common cylinder axis. Precise measurements were made of the vertical force F _z and the magnetic stiffness _z as a function of the magnet–superconductor separation at 77 K. Several features contrasting the levitation force produced using bulk superconductors were observed. Thin films produced very high values for F _z and _z per unit volume of superconducting material. The hysteretic behavior of F _z during decreasing and increasing separation resulted in loops of nearly symmetrical shape, which also contain a peak in the repulsive force branch. The observations are analyzed and explained with good quantitative agreement using recent theories for flux penetration in thin superconductors in transverse magnetic fields.     

Size Effects on Levitation Force Between a Magnet and a Superconducting Thin Film in the Meissner State

The levitation force between a permanent magnetic disk and a thin superconducting disk in the Meissner state is calculated using the dipole–dipole interactions model. The levitation force as a function of the magnet and superconductor radii, the levitation height, and the superconductor thickness is studied under the assumption that the radius of the magnet is much smaller than the radius of the superconductor. Results showed an increase in the levitation force as a function of the radius of the superconducting disk. However, the levitation force decreases as the radius of the permanent magnetic disk increases. Demagnetizing effects are taken into account by considering the appropriate demagnetizing factor for the suggested system.     

Numerical Studies of Axial and Radial Magnetic Forces Between High Temperature Superconductors and a Magnetic Rotor

The magnetic bearing is considered as one of the most prospective applications of high temperature superconductors (HTSs) which can realize stable levitation in a magnetic field generated by permanent magnet devices or coils. The exploration of this kind of HTS bearing through numerical investigation is usually made by assuming the induced current circulates only within the ab-plane and thus simplifying the actual three-dimensional problem to a two-dimensional one. In this paper, on the basis of the three-dimensional model of the HTS bulk established before, we further introduce the developed finite-element software to calculate the magnetic field generated by a magnetic rotor which is composed of permanent magnet (PM) rings and ferromagnet (FM) shims, and in this way, we can investigate the magnetic forces (radial force and axial force) of a simplified HTS bearing model, i.e., two symmetric HTS bulks and a magnetic rotor, at a three-dimensional level. The investigations performed in this paper lead to the observations: the favorable configuration to construct the HTS bearing is that the axial height of each HTS element should be equivalent to the axial heights of PM ring plus FM shim; the increase of the radial thickness of PM ring will improve both the radial force and the axial force considerably, but its margin decreases; the enhancement of critical current density of HTSs due to the decrease of operating temperature can result in a higher increase of both the radial and axial force with a lower nominal gap between the HTSs and the magnetic rotor.     

Effect of reciprocating motions around working points on levitation force of superconductor-magnet system

In order to simulate vibration around working points in practical operation of superconducting levitation system, magnet in a simple superconductor-magnet system are conducted reciprocating motions around static height in this study. Two YBCO cylindrical samples with different grain orientations are used to investigate the effect of reciprocating motions of magnet on superconducting magnetic force. The c-axis of sample S1 is perpendicular to the top surface while sample S2 is parallel to the top surface. The initial cooling processes for the superconductors include zero-field-cooled (ZFC) and filed-cooled (FC). Compared to the levitation force before reciprocating motions, the ZFC levitation force at static height becomes smaller after reciprocating while the FC force presents opposite phenomenon. It is found that levitation force at static height tends to be stable after several times of reciprocating under ZFC and FC conditions and its time-decay phenomenon is suppressed in some extent, which is meaningful for the practical application of superconducting levitation system. Based on vortex dynamic, some physical discussions are presented to the experimental results.     

Dynamic Simulation of High Temperature Superconductors Above a Spinning Circular Permanent Magnetic Guideway

Before a high temperature superconducting (HTS) magnetic levitation (Maglev) vehicle system can be fully applied and operational, the study of its dynamic characteristics is necessary. With the developed HTS Maglev dynamic measurement system (SCML-03), with a circular permanent magnet guideway (PMG) of 1.5 m in diameter, the vehicle’s translational motion above a PMG can be effectively simulated with the PMG allowed to rotate freely. Levitation force measurements of a high temperature superconductor (HTSC) array of seven YBa₂Cu₃O_7−x bulks were carried out above regular (linear) and a simulated (circular) PMG. The levitation force above a linear PMG segment and a circular PMG segment in the static state is found to be in good agreement with each other. The levitation force in the dynamic state is found to slowly attenuate since the presence of a rotating circular PMG below the HTS array is found to be analogous to the application of an AC external magnetic field.     

Magnetic Levitation With High-T c Superconducting Thin Films

The levitation force between a permanent magnet and a superconducting thin film was investigated experimentally. The configuration consisted of a cylindrical NdFeB permanent magnet placed above a circular YBa₂Cu₃O_7?δ disk with common cylinder axis. Precise measurements were made of the vertical force F _z and the magnetic stiffness κ _z as a function of the magnet–superconductor separation at 77 K. Several features contrasting the levitation force produced using bulk superconductors were observed. Thin films produced very high values for F _z and κ _z per unit volume of superconducting material. The hysteretic behavior of F _z during decreasing and increasing separation resulted in loops of nearly symmetrical shape, which also contain a peak in the repulsive force branch. The observations are analyzed and explained with good quantitative agreement using recent theories for flux penetration in thin superconductors in transverse magnetic fields.     

Influence of Re-magnetized HTS Bulk Samples on the Levitation Performances of a Maglev System

High-T _c superconducting (HTS) bulk samples used for a maglev system can be re-magnetized after being subjected to another applied magnetic field which may influence the levitation performance of a HTS bulk over the permanent magnetic guideway (PMG). In order to clarify the relationship between the HTS bulk’s re-magnetization and its levitation performance, a YBCO bulk was re-magnetized at different values and its levitation performance studied experimentally above a permanent guideway (PMG) system. The results show that the increase of trapped magnetic flux inside the HTS bulk is closely related to the magnitude and direction of the applied field during the re-magnetization process. Furthermore, the levitation force changes on the HTS-PMG system affected by the re-magnetized HTS bulk are discussed allowing for optimization improvements to the maglev system load capabilities.     

‘Electromaglev’-magnetic levitation of a superconducting disc with a DC field generated by electromagnets: Part 1. Theoretical and experimental results on operating modes, lift-to-weight ratio, and suspension stiffness

We present results of a comprehensive study, both theoretical and experimental, of an ‘electromaglev’ system, in which a high-temperature superconducting bulk sample, e.g. YBa₂Cu₃O_7−δ (YBCO), is levitated stably in a DC magnetic field generated by electromagnets placed underneath the floating object. Results of the zeroth-order theory agree quite well with experimental results on lift-to-weight ratio and suspension stiffness for three bulk samples: (1) a solid YBCO disc; (2) a YBCO annulus; and (3) a YBCO annulus with a neodymium-iron-boron (Nd-Fe-B) permanent magnet disc (PMD) filling the centre. The experiment has also verified the need to satisfy two requirements to achieve stable levitation with a DC magnetic field only: (1) the spatial flow of the supercurrent in the sample must have at least two degrees of freedom; and (2) the electromagnets must generate a magnetic field profile that satisfies spatial requirements for lateral and pitch stability. A permanent magnet disc has only one degree of freedom for its Amperian current, thus it cannot be levitated stably in this system; the experiment has also demonstrated that an HTS solenoid (wound with silver-sheathed BSCCO-2223 tape) cannot be levitated stably, because the solenoid supercurrent flow is also restricted to the azimuthal direction only. The zeroth-order theory together with the Bean model shows that the supercurrent induced in a YBCO sample is independent of the critical current density, J_c, of the material but is directly proportional to the axial component of the field and that the lift of the sample is directly proportional to the product of the axial and radial components of the magnetic field generated by the electromagnets.