Dynamic Circuit Theory Research Articles

Equivalent Simulation and Measurement for the Electrodynamic Suspension System Based on the Dynamic Circuit Theory

Equivalent Simulation and Measurement for the Electrodynamic Suspension System Based on the Dynamic Circuit Theory

Electrical Circuits Simulator in Null-Flux Electrodynamic Suspension Analysis

This paper employed an electrical circuit simulator to investigate an electrodynamic suspension system (EDS) for passenger rail transport applications. Focusing on a null-flux suspension system utilizing figure-eight-shaped coils (8-shaped coils), the aim was to characterize the three primary electromagnetic forces generated in an EDS and to compare the findings with existing literatures. The dynamic circuit theory (DCT) approach was utilized to model the system as an electrical circuit with lumped parameters, and mutual inductance values between the superconducting (SC) coil and the upper and lower loops of the 8-shaped coil were calculated and inputted into the simulator. The results were compared with experimental data obtained from the Yamanashi test track. The comparison demonstrated close alignment between the theoretical expectations and the obtained experimental curves, validating the accuracy of the proposed model. The study highlights the advantages of this new approach, including faster computation times and efficient implementation of modifications. Overall, this work contributes to the ongoing development and optimization of null-flux suspension Maglev systems.

Study on Beat Vibration of a High Temperature Superconducting EDS Maglev Vehicle at Low Speed

Vertical displacement acceleration and the pitch angle record produce the phenomenon of beat vibration when testing a 200 m electro-dynamic suspension (EDS) magnetic levitation (maglev) test vehicle with high-temperature superconducting (HTS) at the CRRC Changchun Railway Vehicles Co., Ltd., where the vehicle is clamped and in planar motion. First, to examine this phenomenon, this paper establishes dynamic equations of the vehicle with three degrees of freedom (DOF), and the levitation force on each superconducting magnet (SCM) is calculated by dynamic circuit theory. Second, the theory vertical equilibrium point is obtained from the average of the levitation force for a different velocity and the magneto-motive force (MMF) of the SCM. Third, this paper decouples SCM levitation forces from each other using MATLAB/SIMULINK, and a multi-body dynamic model with six DOF is developed in SIMPACK. All vertical displacements and acceleration responses, as well as the pitch angle and acceleration response from the simulation, appear to show the phenomenon of beat vibration since there are two closing natural frequencies of approximately 2 Hz and 2.4 Hz. Finally, based on the traversing method considering the influence of the velocity, initial vertical displacement, and the MMF of the SCM, the multi-body dynamic model is frequently utilized to study the response of the mean and amplitude of vertical displacement and that of the pitch angle. The results show that increasing the MMF or velocity could decrease the vertical displacement and pitch angle; the mean vertical displacement is a little larger than the theory equilibrium point; and the amplitude of vertical displacement is small when the initial vertical displacement is near the theory equilibrium point. Both the numerical and experimental results verify the validity of the dynamic circuit model and mechanical model in this paper.

Vehicle-track coupled dynamics model for superconducting electrodynamic suspension train

In the previous studies of superconducting EDS train, the magneto-electric coupling between superconducting magnets (SCMs) and null-flux coils (NFCs), was equivalent to a vibration system with constant stiffness. This premise has decoupled the magnetic/track interaction and is not able to study the dynamics issues in an accurate and comprehensive level. Therefore, the vehicle-track coupled dynamics model of superconducting EDS train, with magneto-electric-force coupling fully considered, was established to explore the vehicle-track interaction relationship in this paper. A mathematical model based on Newton’s laws and 3-D dynamic co-simulation model were built respectively by Simulink and MATLAB-SIMPACK to compare the operating performances with the time/frequency domain. Meanwhile, the dynamic electromagnetic forces were calculated by dynamic circuit theory rather than merely assuming the constant stiffness. The dynamic responses of suspension vehicle show that, the vibration of carbody and frame are mainly concentrated about 1 Hz and 5 Hz respectively. The use of equivalent model in the previous studies has overestimated the negotiation capacity of superconducting EDS train. Furthermore, the vertical vibration accelerations of frame in the coupled model are relatively larger, whereas the lateral vibration is comparatively smaller. Therefore, the electromagnetic calculation of superconducting EDS train with constant stiffness overestimates/underestimates the dynamic performances.

A new suppression strategy of pitching vibration based on the magnetic-electric-mechanical coupling dynamic model for superconducting EDS transport system

The superconducting electrodynamic suspension (EDS) train is suitable for high-speed maglev rail transit because of its low drag force, strong levitation force, large suspension gap, and so on. However, the electromagnetic forces of four pairs of superconducting coils on one bogie are dynamically unequal in practical operation. This causes the bogie to vibrate in the pitching axis, which affects the train system's safety, stability, and comfort. Therefore, proposing an appropriate strategy to suppress the bogie pitching vibration is significant. First, based on the dynamic circuit theory, energy method and rigid body dynamics, the magnetic-electric-mechanical coupling dynamic model of eight superconducting high-field coils in the bogie and ground null-flux coils was established to explore the characteristics of fluctuating and unequal electromagnetic forces. The synchronous current and motion responses were further calculated using the Runge-Kutta algorithm. Second, the bogie's vibration characteristics were analyzed and the reasons for the vertical and pitching vibration were discussed. And the accuracy of the model was verified by comparing the levitation force with the experiment data. Third, a non-uniform exciting currents supply strategy for the superconducting coils was proposed under the comprehensive evaluation of the suppressing effect on the pitching vibrations. Finally, several cases were given to prove the effectiveness of the strategy. The results show that the total electromotive force increased by 0.005% after adopting the proposed non-uniform exciting currents supply strategy. But the minimum and maximum amplitude of pitching vibration and the growth rate of pitching vibration decreased by 97.00%, 95.76%, and 81.45%, respectively. This new strategy can effectively suppress the pitching vibration of the bogie without changing the already-designed mechanical structure. This established magnetic-electric-mechanical coupling dynamic model and the suppression strategy provide reference and a new idea for the superconducting EDS system's safety, stability, and comfort.

Analytical Modeling of the Closed-Loop Operation and Quench Behavior for Superconducting Electrodynamic Suspension Train

Superconducting electrodynamic suspension (EDS) as one of the most promising ultrahigh-speed transportations has been widely followed with great interest in the past decades, and service safety under high-speed operation is always the focus of academic attention. Thereinto, an evaluation method of quench behavior can effectively reduce and even avoid the risky accident in advance for the EDS train, possessing in a more realistic sense. In this article, we established an analytical model for the superconducting EDS with cross-connection, fully considering the arbitrary attitudes of the bogie and closed-loop operation of onboard superconducting magnets (SCMs), on the basis of spatial coordinate transformation and dynamic circuit theory. Meanwhile, the data of the finite-element model and experiment, regarded as references, validate the availability of the proposed analytical model. Afterward, we systematically analyzed and revealed the end effect caused by the SCMs and characteristics of 3-D electromagnetic interactions from the perspective of normal operation and quench conditions, respectively. The results show that the quench behaviors of SCMs have a significant influence on the operating characteristics of trains and are dependent upon the installation position of the disabled SCMs, providing an invaluable tool for the studies of the train dynamics under quench conditions.

Equivalent inductance model for the design analysis of electrodynamic suspension coils for hyperloop

Hyperloop is a new concept of ground transportation. In Hyperloop, travelling occurs in near-vacuum tubes under 0.001 atm at a subsonic speed of up to 1200 km/h. During acceleration to and driving at a subsonic speed, magnetic levitation is employed. Thus far, various levitation technologies in existing high-speed maglev trains have been considered. Among those technologies, superconducting (SC) electrodynamic suspension (EDS) is a highly effective levitation system for Hyperloop owing to its advantages of a large levitation gap, levitation stability, and control being unnecessary. However, analyzing an EDS system requires the electromagnetic transient analysis of complex three-dimensional (3D) features, and its computational load generally limits the use of numerical methods, such as the 3D finite element method (FEM) or dynamic circuit theory. In this study, a novel model that can rapidly and accurately calculate the frequency-dependent equivalent inductance was developed. The developed model was then applied to design an EDS system using the decoupled resistance-inductance equations of levitation coils. Next, levitation coils of SC-EDS were designed and analyzed for use in Hyperloop. The obtained results were compared with the FEM results to validate the developed model. In addition, the model was experimentally validated by measuring currents induced by moving pods.

3-D FEM Modeling of the Superconducting EDS Train With Cross-Connected Figure-Eight-Shaped Suspension Coils

Superconducting electrodynamic suspension (EDS) train has become a suitable candidate for the future ultra-high-speed ground transportation because of its unique advantages of self-stability suspension and guidance performances, large suspension gap, and high suspension/drag ratio. It is indispensable to develop an efficient electromagnetic modeling method for the EDS train. An analytical model based on the dynamic-circuit theory and virtual displacement method has been proposed, but it has to know exactly the mutual inductance between the on-board magnet and ground suspension coil before calculating the induced current and electromagnetic force. Thus, this article is to establish an efficient 3-D finite element method (FEM) model for the EDS train, in which the mutual inductance is not required. First, the critical current of the REBCO magnet serving as the on-board magnet of the EDS train is estimated. Second, based on the vector magnetic potential method and circuit principle, the 3-D FEM model of the EDS train is established with the magnetic potential boundary condition employed to avoid the moving mesh of on-board magnet. Third, the 3-D FEM model is validated by comparing the analytical results as well as the published measurement data. Finally, the electromagnetic behaviors of EDS train under the guidance offset and suspension offset conditions are investigated with the validated 3-D FEM model.

Study on the characteristics of superconducting electrodynamic suspension system based on dynamic circuit theory

Purpose The purpose of this paper is to analyze the influence of different parameters on the characteristics of the superconducting electrodynamic suspension (EDS) system. Design/methodology/approach The authors used an analytical model based on the dynamic circuit theory to perform the analysis. The authors proposed an inductance criterion to improve the calculation accuracy. They also proposed a three-dimension finite element method (FEM) to verify the validity of the analytical model. Findings The levitation force and guiding force increase with the superconducting magnet (SCM) speed and show a saturated trend, while the drag force decreases with the SCM speed. The vibration characteristic is the inherent characteristic of the superconducting EDS. The frequency and amplitude are affected by the gap between adjacent null-flux coils. The levitation force first increases and subsequently decreases with the levitation height. The total levitation force of the SCM increases with the superconducting coil (SC) number, while the average levitation force of an SC decreases with the SC number. The total levitation force nonlinearly increases with the SC number. Originality/value The authors introduced an inductance criterion for better understanding and using the analytical model, and they also proposed a 3D FEM method. The 3D FEM method could be extended to simulate the other EDS systems with more complex structures which the numerical model is no longer applicable. The results of the parameter study could deepen people’s understanding of EDS.

3-D Analytical Model of Racetrack HTS Coil Subject to Travelling Magnetic Fields

Magnetic levitation (maglev) train has the unique advantages of no-mechanical contact, high operating speed, and so on. All those advantages indicate the potential of maglev in the future ultra-high-speed ground transit, in which the high-temperature superconducting (HTS) linear synchronous motor (LSM) is essential because of its sample structure and excellent performance. HTS LSM is a typical application of racetrack HTS coil subject to travelling magnetic field. Motivated by an efficient method to promote the application of maglev, a 3-D analytical model combining the dynamic circuit theory and virtual displacement method was proposed for estimating the performances of racetrack HTS coil in LSM. To verify the proposed 3-D analytical model, the calculated open-circuit magnetic field and back electromotive force were compared with the numerical results of a 3-D finite element model in which the actual geometry of HTS LSM and the nonlinear conductivity of HTS tapes were taken into account. Based on the validated 3-D analytical model, the characteristics of HTS LSM was analyzed. The obtained results indicate that the validated 3-D analytical model could be a very efficient tool for the characteristic analysis and optimization of HTS LSM.

Semianalytical Calculation of Superconducting Electrodynamic Suspension Train Using Figure-Eight-Shaped Ground Coil

Superconducting electrodynamic suspension (EDS) train has the unique advantages of excellent levitation and guidance stabilities, large levitation gap, and so on. All of these merits make it a promising candidate for the future ultrahigh-speed transportations. In order to explore the dynamic characteristics of the EDS system with a figure-eight-shaped coil (ground coil), this article transforms the complex electromagnetic field coupling between the superconducting magnets and ground coils into a reduced circuit relationship based on the dynamic circuit theory. Meanwhile, the motion characteristics are introduced to establish the field-circuit-motion-coupled model. In this article, a faster and more convenient semianalytical method was proposed to solve mutual inductance. First, the dynamic circuit model of a single-sided figure-eight-shaped null-flux EDS system was established. The magnetic coupling calculation was carried out between the onboard superconducting magnets and ground coils by a semianalytical method. Furthermore, the time-step iteration method was utilized to solve the induced current governing equation of the ground coil under different operating conditions. The energy method was employed to find the transient solution of the levitation force, guidance force, and drag force. Second, the field-circuit-motion-coupled model was validated by the experimental data of MLX01 on the Japanese Yamanashi testline. To investigate the influence upon the suspension and guidance caused by the different connection types of figure-eight-shaped coil, a cross-connected EDS train dynamic circuit model was built. Finally, based on the field-circuit-motion-coupled model, the essential parameters affecting the stability of the system were explored, and the characteristics of the system when vertical or lateral displacement occurs were calculated and analyzed. The achievements of this article can provide a reference for the design of the EDS train for future even higher speed transportation.

Study of a Null-Flux Coil Electrodynamic Suspension Structure for Evacuated Tube Transportation

This paper focuses on the study of a null-flux coil electrodynamic suspension structure for evacuated tube transportation (ETT). A Maglev system in evacuated tubes is a promising concept for high speed transportation systems, and the design of levitation structure is a critical part among the subsystems. The whole system with functions of levitation, guidance, and propulsion is proposed in this paper, and the utilization of magnetic fields from both sides of magnets makes the system simple. The figure eight shaped null-flux coil suspension structure is adopted to provide a high levitation-drag ratio. The equivalent circuit model of the null-flux coil structure is established by employing the dynamic circuit theory. Based on the determination of the mutual inductance between the null-flux coil and the moving magnet, electromagnetic forces are calculated through an energy method. The validity of the dynamic circuit model is verified by comparing the calculation with the 3D finite element analysis (FEM) results, and the working principle of the null-flux coil structure is described. The effects of vehicle speed and the time constant of the coil on the electromagnetic forces are studied at the bottom level of force impulses in one coil and verified by FEM simulation. The characteristics of electrodynamic forces as functions of the magnet speed, the vertical displacements, and the lateral displacements are investigated based on the dynamic circuit theory, and the levitation-drag ratio is compared with that of plate type structure. The results show that the proposed structure is a promising option for application in ETT, and the following study will focus on the dynamic research of the electrodynamic suspension (EDS) system.

Chaotic characteristics of corona discharges in atmospheric air

A point-plane electrode system in atmospheric air is established to investigate the mechanism of the corona discharge. By using this system, the current pulses of the corona discharges under the 50 Hz ac voltage are measured using partial discharge (PD) measurement instrument and constitute the point-plane voltage-current (V-I) characteristic equation together with the voltage. Then, this paper constructs the nonlinear circuit model and differential equations of the system in an attempt to give the underlying dynamic mechanism based on the nonlinear V-I characteristics of the point-plane corona discharges. The results show that the chaotic phenomenon is found in the corona circuit by the experimental study and nonlinear dynamic analysis. The basic dynamic characteristics, including the Lyapunov exponent, the existence of the strange attractors, and the equilibrium points, are also found and analyzed in the development process of the corona circuit. Moreover, the time series of the corona current pulses obtained in the experiment is used to demonstrate the chaotic characteristics of the corona current based on the nonlinear dynamic circuit theory and the experimental basis. It is pointed out that the corona phenomenon is not a purely stochastic phenomenon but a short term deterministic chaotic activity.

Study on figure-eight-shaped coil electrodynamic suspension magnetic levitation systems without cross-connection

Two figure-eight-shaped coils for electrodynamic suspension (EDS) magnetic levitation (MAGLEV) systems without cross-connection are proposed and analyzed. The guideway coils are positioned under the MAGLEV vehicle; they are parallel to the horizontal plane. The interaction of a magnetic module on the vehicle, composed of three or four superconducting (SC) coils, with a guideway module, composed of two figure-eight coils, is studied by means of the dynamic circuit theory. The currents in the SC coils are supposed to be constant in time while they move as a rigid body, with a constant velocity. Some results are presented and compared with those for a standard side-wall cross-connected system.

Thermal stability of maglev SCMs with vibration-induced disturbances

Abstract In magnetic levitation (Maglev) systems, the interaction between the superconducting magnets (SCMs) and the discrete ground coils causes electromagnetic and mechanical vibrations. These disturbances can limit the performance of the Maglev. We examine how the electromagnetic oscillations are translated into mechanical vibrations and the subsequent effects on thermal stability. Dynamic circuit theory is used to determine the harmonic forces on the SCM. The vibrational response of the SCM to these forces is analyzed via normal mode calculations. The energy dissipation within the conductor due to hysteresis damping is then determined, forming the input to a two-dimensional thermal stability analysis. This paper focuses on the extension of the thermal stability model from one to two dimensions and results obtained from modeling the performance of MLU002. Results of this analysis show how variations in mechanical properties of the conductor affect the stability of MLU002 as a function of velocity. It was found that vibrational resonance occurs at certain combinations of Young's modulus and vehicle velocity, quenching the magnets. The ability to predict the velocity at which resonances occur allows future Maglev designs to avoid such quenches by shifting the critical velocity above that intended for operation.

Forces on a magnet moving past figure-eight coils

The lift, drag, and guidance forces acting on a permanent magnet are measured as different arrays of figure-eight (null-flux) coils pass under the magnet. The experimental results are in good agreement with the predictions of dynamic circuit theory, which can be used to investigate other coil arrays. >

Applications of the dynamic circuit theory to Maglev suspension systems

The applications of dynamic circuit theory to electrodynamic suspension (EDS) systems are discussed. Emphasis is placed on the loop-shaped coil and the figure-eight-shaped null-flux coil suspension systems. Mathematical models, including very general force expressions that can be used for the development of computer codes, are provided for each of these suspension systems. The general applications and advantages of the dynamic circuit model are summarized. The transient and dynamic analysis and computer simulation of Maglev systems are emphasized. The method can be applied to many EDS Maglev design concepts. It is also suited for the computation of the performance of Maglev propulsion systems. Numerical examples are presented to demonstrate the capability of the model. >

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.

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.

Moments and force densities of the electrodynamic levitation system

Theoretical predictions of the moments and the force density distributions on the superconducting magnet and on the conducting sheet guideway are given for the reference levitation system design proposed for the Canadian Maglev vehicle. The theoretical method is based on the Lorentz force, \tilde{J} \times \tilde{B} and the solution follows from a combination of the dynamic circuit theory and the EM field theory already developed. Very good correlations are found with the moments measurements already published. The data from the predictions are important for vehicular mechanics analysis and for mechanical structural design of fastenings and bracings.