Electrodynamic Levitation System Research Articles

Modeling and experimental validation of electrodynamic maglev systems

The pursuit of novel, environmentally friendly solutions for mobility and transportation has been a relevant area of technical and scientific progress in recent years. In this regard, the Hyperloop concept is a novel solution for sustainable transportation of people and goods at high speed. The electrodynamic levitation system in Hyperloop represents a key enabling technology. Nevertheless, its unstable nature is crucial and requires proper analysis and understanding. This paper proposes the experimental stabilization of electrodynamic maglev systems by means of passive components. A downscaled test setup is used to validate the numerical models that govern passive maglev systems. Setups for quasi-static and dynamic testing are proposed. The former experiments lead to model parameter tuning. The latter reproduce unstable behavior and assist in testing a stabilization method. Results in the time and frequency domains are used to analyze the system response and validate the proposed approach.

Passive Multi-Degree-of-Freedom Stabilization of Ultra-High-Speed Maglev Vehicles

Abstract Over the last decades, the search for fast and efficient transportation systems has raised the interest toward maglev technologies. In this scenario, the Hyperloop paradigm is regarded as a breakthrough for future mobility. However, its practical implementation requires the solution of key shortcomings. Among these, the stability of the electrodynamic levitation system remains partially unexplored. The state of the art presents numerous attempts to attain stable behavior. In recent works, the stabilization of maglev vehicles has been addressed only for the vertical dynamics. Nevertheless, stable operation of all degree-of-freedom is required for a successful implementation of these transportation systems. The present paper addresses the full stabilization of a downscaled vehicle where levitation and guidance are provided by electrodynamic means. To this end, a design methodology supported by analytical modeling is proposed, where the degree-of-freedom are stabilized by suitably introducing secondary suspension elements. The design of the secondary suspension and the guidance system is obtained through the optimization of stability and dynamic performance. Then, a multibody model is developed. Both numerical approaches are compared in the frequency domain for validation purposes. Finally, the multibody model is simulated in the time domain to assess system performance in the presence of track irregularities and evaluate coupling effects between the degree-of-freedom.

A Multi-domain Approach to the Stabilization of Electrodynamic Levitation Systems

Abstract The Hyperloop transportation system paradigm has gained increasing attention in the last years due to its potential advantages in technology, territory, and infrastructure. From an engineering point of view, it would lead to fast, safe, efficient transportation of passengers and cargo. The stability of the electrodynamic levitation system represents a key enabling aspect of Hyperloop. In this context, the state of the art presents numerous attempts to stabilize these systems without definitive guidelines on how to attain proper, stable behavior. Furthermore, research has provided extensive literature in the context of electrodynamic bearings, which requires proper interpretation and generalization into the translational domain. In this paper, we address the stabilization of levitation systems by reproducing the strong interaction between the electrodynamic phenomenon and the mechanical domain. A novel lumped-parameter model with a multiple-branch circuit is proposed and tuned through finite-element simulations to replicate the electrodynamic behavior. The multi-domain equations are linearized and the unstable nature of the levitation system is identified and discussed. Then, a suitable method to add damping and optimize stability is studied. Finally, the linearized model is compared with the nonlinear representation to validate the followed approach.

Влияние стыков в путевой структуре на характеристики системы электродинамической левитации

Влияние стыков в путевой структуре на характеристики системы электродинамической левитации

Numerical simulation of a simple low-speed model for an electrodynamic levitation system based on a Halbach magnet array

The design and analysis of a small prototype of a magnetic levitation system at low-speed using a Halbach-type magnet array is presented here. For that purpose, we have arranged a copper rim over a carbon fiber wheel, which is driven by an electric motor in presence of the magnet array, in such a manner that allows performing the experiment readily. The analysis of the system is undertaken under a two-dimensional (2D)-approach which permits computing and extending the study of our model to higher speeds. Our work is completed with a series of experimental measurements of lift and drag forces for different circumstances. Initially, the drag force is significant but after the compensation speed (when both forces balance) it slowly decreases. Conversely, the lift force becomes progressively bigger in such a manner that it attains quickly noteworthy values. We observe that the theoretical compensation speed is always minor than the experimental one and that the measured values for both forces are slightly smaller than the expected, although the main features of the experiment are well matched by our numerical simulation.

Laboratory scale prototype of a low-speed electrodynamic levitation system based on a Halbach magnet array

In this paper we analyse the behaviour of a small-scale model of a magnetic levitation system based on the Inductrack concept. Drag and lift forces acting on our prototype, moving above a continuous copper track, are studied analytically following a simple low-speed approach. The experimental results are in good agreement with the theoretical calculations. 3D-numerical simulations are also used to highlight the significance of the edge effects and to extrapolate the results to higher speeds.

Magnetic Force Calculation Between Thin Coaxial Circular Coils in Air

We present new and fast procedures for calculating magnetic forces between thin coaxial circular coaxial coils in air. The results are expressed in semianalytical form in terms of the complete elliptical integrals of the first and second kind, Heuman's Lambda function, and a term that must be solved numerically. These expressions are accurate and simple to use for several practical applications. We also describe a comparative method based on the filament technique. We discuss the computational cost and the accuracy of two methods and compare them with already published data. Results obtained by our two approaches are in excellent agreement with each other. They can be used in industrial electromagnetic applications such as electrodynamic levitation systems, linear induction launchers, linear actuators, and coil guns.

ABOUT THE POSSIBILITY OF SEMI STABILITY VERTICAL OSCILLATIONS IN A SYSTEM OF ELECTRODYNAMIC LEVITATION

An energy-modeling technique for studying theoretical possibilities of stabilization of electrodynamic levitation systems has been presented. Based on the generally accepted mathematical assumptions, the effect of selfstabilization of vertical oscillations of the on-board magnet has been examined. The authors have demonstrated that dependence of the residual energy on the weight of the magnet allows minimizing the energy with the use of constructive methods. The derived results are of a practical significance.

ABOUT THE IMPACT OF SEPARATION OF MAGNETIC FLUX ON THE FLUCTUATIONS OF THE CREW IN THE SYSTEM OF ELECTRODYNAMIC LEVITATION

The joint vertical and lateral oscillations of a moving superconductive magnet in the electrodynamic levitation system with the discrete track structure have been researched. There has also been studied the effect of magnet flow separation into oscillation processes in the moving magnet. It has been shown that introduction of the extra superconductive coils enables to modify the own frequencies of vertical magnet oscillations.

Development of Linear Generator System Combined with Magnetic Damping Function

One of the most important subjects in the superconducting Maglev system is a method for providing onboard service power. As a solution, a linear generator is being developed that can collect power without contact by utilizing the harmonic magnetic field around the ground coils and generate an electromagnetic force between them and the superconducting magnets by controlling the current in the generator coils. By using this controllable electromagnetic force, it becomes possible to add magnetic damping to the electrodynamic levitation system with a small damping force. This paper describes the results of the running tests of the linear generator using zero-phase current control, combined with the magnetic damping function.

The Development of Linear Generator System Combined with Magnetic Damping Function

In the superconducting Maglev system, a method for providing on-board service power is one of the most important subjects of technological development. As a solution, a linear generator is being developed that can collect power without contact by utilizing the harmonic magnetic field of ground coils. It can also generate electromagnetic force between the superconducting magnets and ground coils by controlling the current in the generator coils. By using this controllable electromagnetic force, it becomes possible to add magnetic damping to the electrodynamic levitation system, which is characterized by an intrinsically very small damping force. This paper describes the results of the vehicle running tests of the linear generator using zero-phase current control, combined with a magnetic damping function.

Experimental Studies of Droplet Evaporation Kinetics: Validation of Models for Binary and Ternary Aqueous Solutions

Abstract Experiments were conducted with an electrodynamic levitation system to study the kinetics of droplet evaporation under chemically rich conditions. Single solution droplets of known composition (HNO3/H2O or H2SO4/HNO3/H2O) were introduced into an environmentally controlled cubic levitation cell. The gaseous environment was set intentionally out of equilibrium with the droplet properties, thus permitting the HNO3 mass accommodation coefficient to be determined. Measurements were performed at room temperature and various pressures (200–1000 hPa). Droplet sizes (initial radii in the range 12–26 μm) were measured versus time to high precision (±0.03 μm) via Mie scattering and compared with sizes computed by different models for mass and heat transfer in the transition regime. The best agreement between the theoretical calculations and experimental results was obtained for an HNO3 mass accommodation coefficient of 0.11 ± 0.03 at atmospheric pressure, 0.17 ± 0.05 at 500 hPa, and 0.33 ± 0.08 at 200 hPa. The determination of the mass accommodation coefficient was not sensitive to the transport model used. The results show that droplet evaporation is strongly limited by HNO3 and occurs in two stages, one characterized by rapid H2O mass transfer and the other by HNO3 mass transfer. The presence of a nonvolatile solute (SO2−4) affects the activities of the volatile components (HNO3 and H2O) and prevents complete evaporation of the solution droplets. These findings validate recent attempts to include the effects of soluble trace gases in cloud models, as long as suitable model parameters are used.

A null-current electro-dynamic levitation system

All electro-dynamic levitation systems (EDS) have peak drag forces and peak and average power consumption to deal with in order to be viable in Maglev applications. Both factors affect the energy cost and the capital cost of the propulsion system. A significant improvement for EDS systems is a so-called null-current configuration. It consists of two Halbach arrays, one above the track and one below the track. The two arrays are oriented with respect to one another so that their horizontal field components add while their vertical field components oppose. In this way, the levitating field component is enhanced while the field component that excites the currents in the ladder-track between the two arrays is weakened. The basic idea is that the lower induced current and the higher levitating field component produce the necessary levitation force. At the same time the drag force is much lower, since it depends on the product of the induced current and the vertical field component.

An Electrodynamic Levitation System for Studying Individual Cloud Particles under Upper-Tropospheric Conditions

Abstract A laboratory system composed of an electrodynamic levitation cell within an environmental control chamber has been designed and built. The system is ideal for studies of individual particles, such as pure water droplets, aqueous solution droplets, solid salt particles, and ice crystals, under mid- and upper-tropospheric conditions. The experimental system has several features that make it particularly useful for studies of cloud physics. The levitation cell has a cubic geometry with transparent electrodes, thus allowing for full, three-axis positioning of a levitated particle, as well as a large range of viewing angles for optical access and light-scattering measurements. Particles in the approximate diameter range of 10 to 100 μm can be suspended indefinitely with minimal wall influences. The levitation cell is housed within an environmental control chamber capable of operating at temperatures (T), pressures (p), vertical velocities (w), and saturation ratios (with respect to ice, Si) in the ran...

The Environmental Control of Individual Aqueous Particles in a Cubic Electrodynamic Levitation System

ABSTRACT The experimental investigation of aerosol particles often requires special apparatus to ensure that the walls of the system interfere minimally with the measurements. Electrodynamic levitation offers an attractive approach because the particle, when suitably charged, is held away from the system walls by time-dependent electric fields. A new electrodynamic levitation system has been developed expressly for investigating aqueous particles in controlled gaseous environments. A cubic cell was used in conjunction with the carefully controlled introduction of gas into the cell to form a wall-less flow reactor that is ideal for thermodynamic and kinetic studies involving reactive reagents. Unlike most previous cell configurations, the cubic geometry permits three-axis position control of the particle and an ability to measure the gravitational and drag forces simultaneously and independently when the gas flow is horizontally aligned. Preliminary results at room temperature of the mass gained by salt and sulfuric acid particles exposed to various humidities show the basic characteristics of the cell. New results with sulfuric acid particles exposed simultaneously to the vapors of water and nitric acid show that nonvolatile and volatile solutes cause aqueous particles to behave in qualitatively different ways. Such results confirm that cloud formation in the atmosphere should be enhanced by the presence of soluble trace gases under suitably low-temperature conditions.

Analysis of superconducting magnet (SCM)-ground coil interactions for EDS Maglev coil configurations

The performance of electrodynamic magnetic levitation systems is dominated primarily by the electromagnetic interactions between the onboard superconducting magnets (SCMs) and the normal levitation and propulsion coils situated on the guideway. Alternative designs are examined for coil configurations in terms of the resulting SCM-ground coil interactions. In particular, the modified null flux configuration and the ladder-on-box-beam approach are compared. Magnetic drag, levitation, and guidance forces are considered on an absolute and per (kg/m) of ground coil basis.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Induced currents and forces for the split-guideway electrodynamic levitation system

A three-dimensional integral equation formulation of the electrodynamic interaction of an array of superconductive magnets moving over a pair of conducting guideway strips is reviewed. The induced current distribution in the split-guideway conductors and the lift, drag, and lateral forces are presented, and the effects of vehicle speed, lateral displacement, and gap between the guideway strips on levitation characteristics are discussed.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Dynamic circuit and Fourier series methods for moment calculation in electrodynamic repulsive magnetic levitation systems

A general theory of moments for electrodynamic magnetic levitation systems has been developed using double Fourier series and dynamic circuit principles. Both employ Parseval's theorem using either wave constant derivatives or the polar waveconstant principle of the Fourier-Bessel/double Fourier series equivalence. A method for calculating angular derivatives of moments and forces is explained, and for all of these methods comparisons are made with experimental results obtained for single and split rail configurations. Extensions of dynamic circuit theory for tilted nonflat and circular magnets are also explained.

Equilibrium dynamics and stability of null-flux, brake-flux, and double-track, normal-flux electrodynamic levitation systems

The three electrodynamic levitation (EDL) schemes most frequently suggested as alternatives to the normal-flux, single-track schemes are theoretically examined. The analysis concentrates on the null-flux design. Comments regarding the brake-flux and double-track, normal-flux schemes are made by analogy only. For the first time the zero-torque equilibrium of a system under the influence of an external driving force is considered. The often-used zero-pitch assumption is herein refuted. Lift, drag, and the lift-to-drag ratio as a function of the dynamic equilibrium suspension positions are calculated. The equilibrium equations of motion are expanded to include small perturbations and the resulting relations are then used to analyze the stability of the equilibrium suspension positions with regard to external disturbances. The new analysis shows that substantial heave mode supression is possible with the alternative systems. Throughout the analysis comparison is made with the normal-flux, single-track model characteristics.

The validity and the limitations of the AC impedance- modeling technique in electrodynamic levitation systems

Because the impedance-modeling technique is such a convenient tool, it is used often (and sometimes incorrectly) for the prediction of forces in electrodynamic levitation systems. In spite of its widespread applications, the technique rests on flimsy theoretical foundations. This paper presents force formulas, derived from the dynamic circuit theory, which establish both the validity and the limitations of the technique. The cases of a holonomic and a nonholonomic guideway are treated. The method of equivalencing frequency to velocity is found to be incorrect algebraically. The extent to which approximate equivalencing of frequency to velocity can be relied on, is demonstrated by numerical examples.