Experimental Validation of a Modified Halbach Array for Improved Electrodynamic Suspension Efficiency

Electrodynamic suspension (EDS) system based on moving Halbach Array over a conducting plate has been verified to be poor in stability, but it is not clear whether the load could impact on it. This paper focuses on the effect of the load on the stability of the EDS system based on the Halbach array moving over a plate. Generalized energy was introduced by quantifying the Hamiltonian function. By Padé approximation, formulas to obtain both the amplitude and frequency were given. Load varied from 50kg to 64kg, keeping the generalized energy fixed to study the stability. Results show that the stability of electrodynamic suspension system could be improved by lager load, yet the oscillation frequency drifts.

The Halbach array permanent magnet (PM) spherical motor (PMSM) consists of a spherical rotor and a spherical-shell stator. The magnetic field distribution surrounding the rotor PMs is closely related to the spherical structure of the Halbach array PMSM. The Halbach array PM configuration characteristics lead to the end leakage magnetic field in the latitudinal direction of the spherical structure, which is end effect. Establishment of an accurate 3-D magnetic field analytical model containing the end leakage magnetic field of the Halbach array PMSM is the foundation of magnetic field distortion research with its influence on eddy-current loss. The magnetic field distribution of the Halbach array PMs in the air gap is calculated using the scalar magnetic potential. Laplace and Poisson equations of the scalar magnetic potential in the spherical coordinate system are derived. To analyze the end leakage magnetic field of the Halbach array PMSM in the latitudinal direction, concept of mechanical pseudo-cycle in the motor latitudinal direction is proposed, and the cycle of Fourier series is redefined. A completed 3-D analytical expression of the Halbach array PMSM magnetic field distribution is derived by the new Fourier series and spatial integral technology, in which the end leakage magnetic field is contained. The results obtained by the proposed analytical method are compared with the numerical results, i.e., the results obtained by the finite-element method, which verify the effectiveness of the analytical method. Magnetic field distribution containing the end leakage magnetic field in different magnetization methods is compared and analyzed, which shows that the Halbach array magnetization has a larger main air-gap magnetic field and a smaller end leakage magnetic field. The effect of motor structure parameters on the end leakage magnetic field is analyzed, and the effect of end leakage magnetic field on eddy-current loss is preliminarily discussed, which shows that eddy-current loss caused by end effect almost accounts for half of the total eddy-current loss. The research on end effect and the effect of motor parameters on end effect are of great significance. In the end, the leakage magnetic field results obtained by the proposed analytical method are verified by the experimental results.

This paper introduces an innovative hybrid array consisting of both permanent and electro magnets. It will enable us to develop an active control mechanism for underdamped electro-dynamic suspension (EDS) Maglev systems. The proposed scheme is based on the Halbach array configuration which takes the major technical advantage from the original Halbach characteristics: a strongly concentrated magnetic field on one side of the array and a cancelled field on the opposite side. In addition, the unique feature of the proposed concept only differs from the Halbach array with permanent magnets. The total magnetic field of the array can be actively controlled through the current of the electro-magnet’s coils. As a result, the magnetic force produced by the proposed hybrid array can also be controlled actively. This study focuses on the magnetic characteristics and capability of the proposed array as compared to the basic Halbach concept. The results show that the proposed array is capable of producing not only an equivalent suspension force of the basic Halbach permanent magnet array but also a controlled mode. Consequently, the effectiveness of the proposed array confirms that this study can be used as a technical framework to develop an active control mechanism for an EDS Maglev system.

The vertical stability of permanent magnet (PM) electrodynamic suspension (EDS) system with a passive damping plate is studied because of the well‐known under‐damped nature of the EDS suspension system. The passive damping plate is installed under the Halbach permanent magnet array. When the vehicle‐mounted Halbach array and passive damping plate move to cut the track conductive plate, the 2D eddy current force is derived by establishing equations of magnetic vector potentials and using the Maxwell stress tensor method. And a 2D finite‐element model (FEM) is built to validate the accuracy of the derived levitation force equation. Based on the derived levitation force equation, the vertical stability of the PM EDS system with a passive damping plate and the effects of the main parameters on the damping ratio are analysed.

In high-speed magnetic railways, it is necessary to create the forces that lift the train. This effect is achieved by using active (EMS) or passive (EDS) magnetic systems. In a passive system, suspension systems with permanent magnets arranged in a Halbach array can be used. In this paper, an original Halbach array with various alternately arranged horizontally and vertically magnetized magnets is proposed. Correctly selected geometry allows us to obtain higher values of levitation forces and lower braking forces in relation to a system with identical horizontally and vertically magnetized elements. The effect of such a shape of the magnetic arrangement is the reduction of instantaneous power consumption while traveling due to the occurrence of lower braking forces. In order to perform a comparative analysis of the various geometries of the Halbach array, a simulation model was developed in the ANSYS Maxwell program. The performed calculations made it possible to determine the optimal dimensions of horizontally and vertically magnetized elements. The results of calculations of instantaneous power savings for various cruising speeds are also included.

A novel permanent magnetic rail for HTS levitation propulsion system

In this paper, a permanent magnet (PM) electrodynamic suspension (EDS) system with a novel Halbach array is presented, to overcome the uncontrol of the levitation force in the PM EDS system. The novel Halbach array consists by winding normal conductor coils on permanent magnets surface. The 2-D analytical expression of the space static magnetic field is calculated using Biot-savart law and surface current method. When the vehicle-mounted novel Halbach array moves to cut the conductive plate, the space magnetic field equations are obtained by establishing equations of magnetic vector potentials using complex Fourier transform of space static magnetic field. The levitation force and drag force are derived using Maxwell stress tensor method. And a 2-D finite-element model is built to validate the accuracy of this proposed analytical model. Furthermore, the effects of the main characteristic parameters on the levitation force are analysed.

Electrodynamic suspension with a permanent magnet Halbach array is suitable for ultrahigh-speed vacuum pipeline transportation. The optimization of a Halbach array is helpful to save cost and increase carrying capacity. Intricate analytical expressions of electromagnetic forces or time-consuming numerical simulation show inherent defects in the structural optimization. To solve the abovementioned problem, this article develops an analytical optimization by two stages. First, a brief approximate analytical expression of electromagnetic forces is established by omitting high-order harmonic components for both the scalar magnetic potential and vector magnetic potential. Second, the lift-to-weight ratio is taken as the optimization index, and the optimal wavelength-to-gap ratio and thickness-to-gap ratios are put forward by seeking extreme values. The numerical simulation is conducted to verify the validation of the analytical optimization, and the result shows that the optimal structural parameters are highly reliable. An experimental rotatory device for electrodynamic suspension with optimal sizes for a Halbach array is built to verify the validation of the analytical expressions of electromagnetic forces.

The ultra-high-speed rocket sled plays an important role in the ground test by simulating altitude flight. Rocket sleds can only be lifted for a short time with thermally uninsulated superconductors moving among an eddy-current-induced copper array. For the purpose of durable lifting, an electrodynamic suspension (EDS) with a permanent magnet (PM) Halbach array moving over a conductor plate can be adopted to upgrade the rocket sled. The earlier study built a two-dimensional (2D) model for the PM EDS system. Yet, 2D modelling in our earlier research ignored the magnetic field variation along both widths of the Halbach array and conductor plate. This resulted in a more than 50% error between the analytical electromagnetic forces with both the three-dimensional (3D) simulated and experimental results. To reduce the error, this paper puts forward more accurate analytical electromagnetic force formulas by a 3D modelling method encompassing both widths of the Halbach array and conductor plate. The 3D model was built by periodically extending the PM EDS system along both directions of the width and length. Then, by double Fourier series expansion and omitting high-order components, the electromagnetic forces can be approximated by brief formulas. Moreover, lift-to-weight and lift-to-drag optimization are discussed. Finally, the correctness of the 3D electromagnetic force formulas was verified by both the numerical simulation and experiment.

To improve the uniformity of magnetic flux and increase the stroke of the magnetic levitation system, this paper designs a novel 6-DOF magnetic levitation system and proposes an improved novel Halbach array. First, a repulsive passive magnetic bearing is utilized to provide levitation force, leading to a noticeable reduction in levitation power consumption. Then, a magnetic circuit model for the magnetic levitation system is established, and the improved novel Halbach array is optimized based on this model. Next, the stable levitation model and measurement model for the system are established, and the magnetic field distribution and magnetic bearing stiffness are analyzed. Results indicated an increase of 0.1[Formula: see text]T in the maximum magnetic flux density, accompanied by an improvement in the uniformity of magnetic flux. Additionally, there is an enhancement of 10% in magnetic bearing stiffness. Finally, a prototype of the system is constructed, and the stable levitation simulation and experiment of the actuator are conducted with this system. The maximum levitation absolute displacement error obtained by simulation is about 655[Formula: see text]nm, and the experimental results exhibited a maximum levitation absolute displacement error of approximately 750 nm for the system, confirming the effectiveness of the proposed modeling method.

This paper aims to study the maglev force and vibration attenuation characteristics of quasi-zero stiffness cruciform maglev isolators (CMIs). The maglev force and stiffness of CMIs were analytically computed based on equivalent charge theory, and the transfer function of the system was conducted. The effects of magnet geometry parameters and air gap on the maglev force, stiffness, and vibration transmission characteristics of the CMI system were revealed through parametric analyses. With the increase in magnet length and width, the maximum value of maglev force increases, but the displacement range of near-zero stiffness, amplitude, and phase of the system gradually decrease. With the increase in magnet height, the displacement range of near-zero stiffness increases, while the variation in the amplitude and phase of the system has minimal impact. Meanwhile, in the Halbach array, the height variation of the magnet at different positions has different impacts on the magnetic force. As the air gap increases, the maximum value of maglev force decreases, but the amplitude and phase gradually increase, and the displacement range of near-zero stiffness first rises and then decreases. Finally, an experimental study was carried out to test the vibration attenuation characteristics of CMIs, in which sinusoidal excitation, hammer strike excitation, and random excitation were applied.

Electrodynamic suspension (EDS) with a linear permanent magnet Halbach array, which can be used in ultrahigh-speed maglev systems, has gained increasing attention in recent years. However, inefficient calculation methods of electromagnetic forces restrict the stability research of EDS systems. Hence, an efficient 3D analytical model of the electromagnetic force is established in the paper based on an improved analytical model of the source magnetic field excited by the Halbach array, and then the application conditions of the model are studied. Finally, the analytical results are compared with the experimental results, which are provided by the experiments carried out on a high-speed rotating experiment platform with a flywheel. The results show that the proposed model can shorten the computation time of electromagnetic force to less than 10 ms and the relative errors of analytical results are around 5% under the conditions ①wp/τ≥2.5, wd/wp≥1.5 or ②wp/τ≥4, wd/wp≥1 (τ is the pole pitch of the Halbach array, wp is the width of the permanent magnet, wd is the width of the conducting plate). The analytical model meets the engineering requirements and can provide a reference for further stability research and experiments on EDS systems.

For the electrodynamic suspension (EDS) system in the high-speed magnetic levitation (Maglev) train, high-temperature superconducting (HTS) coils made of ReBCO-coated conductors can be used as levitation magnets. In this paper, a three-dimensional (3-D) model of the HTS EDS system is built for the design of the suspension system of a full-scale high-speed Maglev train. Subsequently, the levitation and drag forces are analyzed using finite-element method (FEM), and the force performances of different operating currents, reaction board thicknesses, and air gap lengths are investigated. And the distribution of the eddy current on the reaction board induced by the moving HTS magnets is obtained. Moreover, according to the eddy current distribution and force analysis results, a mirror image method is proposed to simplify the calculation and accelerate the estimation of the saturated levitation force of an HTS EDS system. The calculation results of the model are verified by the FEM model with an error less than 8%. Finally, the model is expanded to a full-scale HTS EDS system, which validates the feasibility of applying to the high-speed Maglev train.

This paper illustrates the working principle of an electrodynamic bearing and investigates the effect of variation of rotational speed, magnet width, its orientation and air gap on the bearing forces. In a case study, the radial force has also been checked using finite element methods for the permanent magnets arranged in Halbach array. The focus of the investigation is to compare the two models and show how the resultant bearing force responds to a change in rotational speed for a particular off-centre displacement and the corresponding changes observed in the Halbach array model from the permanent magnet counterpart. Analysis results show that the magnetic forces are depended on rotational speeds, air gap and magnet width as well as its arrangement.

This work is the study of a passively stable null-flux suspension system for maglev vehicles. The electrodynamic suspension is based on eddy currents that arise in a conductive material exposed to a variable magnetic field, establishing repulsive forces. The figure-eight-shaped coils, responsible for the train's levitation and orientation functions, provide a high levitation-drag ratio and establish a passively stable suspension system at high speeds. It is currently utilized by the JR-Maglev, Japanese levitation train proposal. However, unlike this, aiming at simplifying the structure, the source of the magnetic field is composed of permanent magnets arranged in Halbach arrays. First, the system is modeled by the theory of dynamic circuits. The emphasis is on the direct calculation of forces through the variation of energy in the coils. Then, simulations using the 3D-dimensional finite element method are used to check results. The forces acting on the magnets are characterized as a function of the magnet's position and speed, seeking to optimize the Halbach matrix's dimensions.