Levitation Force Investigation of Bulk HTSC Above Halbach PMG with Different Cross-Section Physical Dimensions by 3D-Modeling Numerical Method

The levitation force of a bulk high temperature superconductor (HTSC) over Halbach permanent magnet guideways (PMG) with different cross-section configuration is studied by numerical method. The Halbach PMG is composed of three host permanent magnets (HPMs) and two slave permanent magnets (SPMs). One cylindrical bulk HTSC with a diameter of 30 mm and height of 15 mm is used. The 3D-modeling is formulated by the H-method. The numerical resolving codes are practiced using finite element method (FEM). The E-J power law is used to describe the electric current nonlinear characteristics of bulk HTSC. By the method, the influence of the cross-section physical dimensions of Halbach PMG on the levitation forces of bulk HTSC levitated above the PMG is studied. The simulation results show that increasing the width of SPM ( \(W_\mathrm{SPM})\) can enhance the bulk HTSC levitation performance immediately under the condition of keeping the ratio of \(W_\mathrm{HPM}\) ( \(W_\mathrm{HPM}\) : the width of HPM) to \(W_\mathrm{SPM}\) between 1.6 and 1.8, the ratio of td (the height of the PMG) to \(W_\mathrm{HPM }\) between 1.2 and 1.4. By the method, the bulk HTSC better levitation performance can be expected.     

3D-Modeling Numerical Solutions of Electromagnetic Behavior of HTSC Bulk above Permanent Magnetic Guideway

This paper presents a 3D-modeling numerical method using finite element method (FEM) to simulate the electromagnetic behavior of high-temperature superconductors (HTSC). The models are formulated by the magnetic field vector method (H-method). The resolving code was written by FROTRAN language. The electromagnetic properties of HTSC are described though Kim critical-state model. The magnetic fields and current distribution in the bulk HTSC in the applied non-uniform external magnetic fields generated by the permanent magnetic guideway (PMG) are obtained using the proposed method. The magnetic levitation forces by the interaction between the bulk HTSC and the PMG are calculated. In order to validate the method, measurement of the vertical force between a bulk YBaCuO(YBCO) and a PMG is obtained. The measurement and simulation results show good matching. This method could be used in the HTSC magnetic levitation transportation system optimization design.      

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.     

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.     

Levitation Force Relaxation of HTS Bulk above NdFeB Guideways at Different Approaching Speeds

The zero-field cooling levitation force relaxation of the YBCO bulk above two types of NdFeB guideways, which were used in the high-temperature superconducting maglev vehicle system, was studied experimentally when the bulk moved towards the guideways at different speeds. In this experiment, a sample with the diameter of 50 mm and thickness of 15 mm was used; the time range in the relaxation measurements was from 0 s to 200 s. As a result, a nearly linear logarithmic decay of the levitation forces with time was observed. It was found that the influence of the approaching speeds on the levitation force relaxation is different, and that the levitation force decay is closely related to the guideway structures. Based on the monopole peak PMG, the approaching speeds will influence more the levitation force decay than the multipole Halbach. So the maglev vehicle above mutipole Halbach structure PMG will work more stably than that above the monopole peak PMG.      

The Influence on Levitation Force of the Bulk HTSC Above a Permanent Magnet Guideway Operating Dive-Lift Movement with Different Angles

In practical applications, the operating of accelerating or decelerating inevitably happens in the high temperature superconducting (HTS) Maglev train. For the further research of the Maglev properties of bulk high temperature superconductor (HTSC) above a permanent magnet guideway (PMG), by moving a fixed vertical distance, this paper studies the influence on levitation force of the bulk HTSC operating dive-lift movement with different angles. Results show that with the angle increasing, the maximal levitation force decreases when the levitation gap is about 10?mm and the hysteresis is increasing. The hysteresis reaches the largest at first time of back and forth movement, and with the operating times increasing; the hysteresis is almost the same case in the following times of back and forth movements.     

A Method to Increase the Lateral Reversible Region of Bulk YBCO Above a Permanent Magnet Guideway

Lateral reversible region of the bulk high-T _c superconductor (HTSC) above the permanent magnet guideway (PMG) is a key parameter for the high-T _c superconducting (HTS) maglev system. The lateral stability and guidance force are proportional to the width of the lateral reversible region. When the lateral displacement of the bulk HTSC exceeds the reversible region, the maglev system will return to a new lateral equilibrium position. The method with the use of pre-displacement can successfully increases the lateral reversible region of the bulk HTSC. By the correct choice of the maximum lateral offset and a new starting point, the instability of flux motion can be suppressed. Unsuitable usage of this method will cause the intersection of guidance force and reduce the reversible region. Analyses based on the magnetizing history and pinning metamorphoses well explain the experimental results. Difference between this method and the pre-load method is also discussed in this article.     

Investigation of the Lateral Reversible Region of YBCO Bulk above a Permanent Magnet Guideway

The lateral reversible region of the high-T _c superconductor (HTSC) bulk YBCO above a permanent magnet guideway (PMG) is investigated experimentally in this study. The dependence of the lateral reversible region upon selected parameters, such as Field Cooling Height (FH), Working Height (WH), and magnetic field structure, is studied. Results show that the lateral reversible region of the HTSC bulk is not only proportional to the magnitude of the guidance force or guide-force hysteresis, but closely related to the external applied magnetic field structure, FH, WH, and the size and shape of the HTSC bulk. A conclusion that the lateral reversible region of an HTSC bulk over the single peak symmetrical PMG prior to multipeak Halbach PMG is drawn. The results may be helpful to the design and optimization of maglev systems composed of a permanent magnet guideway and HTSCs.     

Effect on Bulk High-Tc Superconductors from a Permanent Magnet Guideway with a Transverse Slope

The effect on an array of high temperature superconductors (HTSC) by a permanent magnet guideway (PMG) with a transverse slope is studied experimentally. The HTSC array was suspended on top of a PMG capable of changing transverse angles, and the fabrication of the measurement platform to obtain the results is explained. Transverse angles of 0° to 12° degrees were achieved and the levitation force and guidance forces of the HTSC-PMG system were measured. The levitation force and guidance force were found to increase and decrease, respectively, with the increasing of the tilting of the PMG with respect to the HTSC array. The understanding of these results is discussed so design of future HTS maglev vehicles can be achieved.     

Improved Maglev Performance of Bulk High-Temperature Superconductors with?a?Re-magnetization Process After Zero-Field?Cooling

Zero-field cooling (ZFC) and field cooling (FC) are the two most popular activation ways of the bulk high-temperature superconductors (HTSCs). The former can bring a big levitation force but a poor stability, while the latter can bring a good stability but a reduced levitation force due to the trapped flux. Under this rule, it is very difficult to improve the levitation force (load capability) and guidance force (stability) at the same time with the given bulk HTSCs and applied field in practice. In the paper, based on the re-magnetization ability of bulk HTSCs, the maglev performance of bulk HTSCs with a re-magnetization process after ZFC was experimentally investigated above a permanent magnetic guideway (PMG). The bulk HTSCs were firstly cooled down at a far distance above the PMG, but before moving to the working height, an additional process was introduced to descend the bulks to a lower height to magnetize again by the PMG field. Experimental results show that, at certain re-magnetization height above PMG, the levitation force and guidance force could be improved simultaneously compared with the results of normal FC cases, which is different from the present performance improvement with the sacrifice of one important force. This result presents a possible working way for the levitation applications of bulk HTSCs by employing a re-magnetization process after ZFC, and is also useful to optimize the performance of high-temperature superconducting Maglev vehicle systems.     

Influence of the Air Gap between Adjacent Permanent Magnets on the Performance of NdFeB Guideway for HTS Maglev System

For the permanent magnet guideway (PMG) of the high temperature superconducting (HTS) magnetic levitation (Maglev) vehicle system, there should be many air gaps between two adjacent permanent magnets by connecting, which may fluctuate magnetic field in the propulsion direction of the vehicle. A three-dimensional (3D) model of a PMG is built up using FLUX 3D software. The magnetic field density of an NdFeB PMG is measured and simulated by 3D and 2D models. Comparison among their results indicate that the simulation results of the 3D model agree better with the measuring results than that of the 2D model, and thus the 3D model is more suitable to describe the PMG. By the model, the influence of the air gap on the uneven of the magnetic field density in the propulsion direction is studied. It is found that the magnetic field 15 mm above the PMG is roughly even in the propulsion direction, although the magnetic field at 2 mm is not even. Since the working height 15 mm is a sensitivity parameter for the onboard high temperature superconductor (HTSC), the levitation force at working height 15 mm above PMG is measured, which indicates that the influence of the air gap on the levitation force is very small so as to be ignored in the quasi-static state.     

Levitation-Force Investigation of High-Temperature Superconducting Maglev System Under Different Variations of the Vertical Displacement

In the practical application of high-temperature superconducting (HTS) maglev vehicle, the vehicle body ascends and descends in the vertical direction frequently with the passengers on and off boarding, such vertical movement may change the levitation performance but this influence have not been researched. In this article, the influence of the vertical movement on the levitation force in two different types of permanent magnet guideway (PMG) and different movement displacements was experimentally analyzed. We found that the levitation force drastically decays first, and then decays slightly, which is similar to the relaxation phenomena. Meanwhile, the experimental results indicate that the levitation force decay trends to enlargement with the decrease of the working height (WH) and with the increase of the vertical displacements. These phenomena can be ascribed to the magnetic hysteresis loss in the bulk high-temperature superconductor (HTSC).     

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.     

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.     

Magnetic Forces Relaxation Step Change Characteristics of YBCO Bulk with Mechanical Impact Load over a NdFeB Guideway

Magnetic force relaxation of YBCO bulk above the NdFeB permanent magnet guideway (PMG) with impact load has been investigated. An experimental setup has been built using a single YBCO bulk and a symmetrical center NdFeB PMG. There are two experimental methods: the case of magnetic levitation force relaxation measuring perturbed with impact load in zero-field-cooling (ZFC); and the case of magnetic levitation and guidance force relaxation measuring synchronously perturbed with impact load in field-cooling (FC). The results show that there is magnetic levitation and guidance forces relaxation step change at the time of the impact load. Two times impact loads are applied for each method. The first step change range is much larger than the second one. The Bean critical model and Anderson–Kim theory are used to analyze it.     

Magnetic Brake Considerations for the High-<Emphasis Type="Italic">T</Emphasis><Subscript>c</Subscript> Superconducting Maglev Vehicle System

Levitation, guidance and driving/braking are three indispensable parts for a high temperature superconducting Maglev vehicle system. To maintain the advantage of a passive, non-contact levitation system, a magnetic brake based on a discontinuous permanent magnet guideway (PMG) is introduced. Its feasibility is verified by the experimental investigations on the behavior of a levitated bulk high temperature superconductor (HTSC) moving towards the broken-off PMG. When the bulk moves towards the broken-off PMG, a braking force will be generated to hold back the bulk due to the inhomogeneous field distribution. That is to say, this magnetic braking mechanism can act as a safe-protection function. The magnetic brake just makes use of the existing PMG, which is very simple with no extra components needing to be added. This makes it very economical and practical for the future application of the HTS Maglev vehicle system.     

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.     

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.     

Enhanced Maglev Performance by Field Cooling for HTS Maglev System in Curve Negotiation

In the practical operation of high-temperature superconducting (HTS) maglev system, the problem of curve negotiation cannot be neglected. During the process of going through curve path, the maglev vehicle would laterally deviate from the center of the permanent magnet guideway (PMG) because of centrifugal forces. To explore the performance variation of the maglev system in this process, the electromagnetic forces (levitation force and guidance force) of a HTS bulk levitation unit were experimentally investigated by different eccentric distances (EDs). The ED is emulated by laterally moving the levitation unit relative to the PMG. Experimental result shows that in field-cooling (FC) conditions, the levitation force generally shows a increase tendency with the growing EDs, while it keeps decreasing in zero-field-cooling (ZFC) conditions. And, the levitation force with large EDs in the FC condition is larger than that in the ZFC condition. The guidance force is enhanced in both conditions within ED of 15 mm, and in FC condition, the force is larger than the case of ZFC. Comparing the above two important magnetic force results, the FC condition is recommended for the safe operation of the HTSn system in curve negotiation.     

Numerical Study of the Curve Route Levitation Performance of the HTS Bulk over NdFeB Guideway

The passive levitation has a self-adjust characteristic to adapt to environmental changes. Levitation Height (LH) or Lateral Displacements (LD) of the high-temperature superconducting (HTS) Maglev vehicle, running over Permanent Guideway (PMG), will change respectively or synchronously due to some external reasons, which caused the vehicle move a certain distance in vertical direction (Y direction) or horizontal direction (X direction) according to a line space route curve along Y or X direction, or random route lying in a XY plane which is perpendicular to the vehicle running direction (Z direction) corresponding to a complicated space route curve. In these cases, how are the levitation performances of the HTS bulk? From a simplest space line route, this paper studied computationally the curve route levitation performance of the HTS bulk which is subject to a PMG applied field. Results show that the change of the levitation and guidance force is different when the HTS bulk moved along line space route. This provides important scientific theories for the numerical simulation of HTS Maglev vehicle.