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.     

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.     

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.     

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 forces in single-sided linear induction motors for high-speed ground transport

The levitation force and thrust in a current-controlled single-sided linear induction motor which propels electrodynamically-levitated vehicles are discussed. It has been shown theoretically that the single-sided linear induction motor (SLIM) can operate satisfactorily over suitably large clearance gap compared with the effective height of electrodynamic suspension. The levitation force in SLIM can be used practically as an alternative levitation force in the low-speed region by supplying a primary current several times the rated current within the very short acceleration times. In high-speed Maglev vehicle system with electrodynamic suspension and SLIM propulsion, the aluminum plate for levitation can be saved for the distance to accelerate the vehicle to speeds sufficient for electrodynamic levitation by the cryogenic magnets.     

Optimization of levitation and guidance forces in a superconducting Maglev system

Optimization of the levitation for superconducting Maglev systems requires effective use of vertical and guidance forces during the operation. In this respect the levitation and guidance forces in terms of various permanent magnet array configurations are analyzed. The arrangements of permanent magnet arrays interacting with the superconductor are configured for the purpose of increasing the magnetic flux density. According to configurations, modeling the interaction forces between the permanent magnet and the superconductor are established in terms of the frozen image model. The model is complemented with the analytical calculations and provides a reasonable agreement with the experiments. The agreement of the analytical calculation associated with the frozen image model indicates a strong case to establish an optimization, in which provides preliminary analysis before constructing more complex Maglev system.     

Vertical unstable stability of electrodynamic suspension of high-speed ground transport

The problem considered is the vertical oscillation of a superconducting solenoid moving over a conducting sheet in connection with the electrodynamic suspension of high-speed ground transport. The oscillation is considered to be unstable at a sufficiently high speed. The current oscillation in the superconducting solenoid caused by its mechanical oscillation is also investigated. The superconducting properties of a solenoid are found to have a pronounced effect on stability. Both the theory and numerical results are presented. Methods of oscillation damping are also discussed.     

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.     

Analyses of mechanical characteristics of vacuum circuit breaker during the closing process taking electrodynamic force into account

A dynamic model for the closing process of a medium-voltage vacuum circuit breaker (MWCB) is constructed, and the automatic dynamic analysis of mechanical system software is applied to construct the model by taking electrodynamic force into account. After the electrodynamic force is worked out, the model is employed to investigate the mechanical characteristics during the closing process of a MWCB under the influence of electrodynamic force. The characteristics are also investigated through experiment. Moreover, the simulation and experimental results are in close agreement. The results show that the electrodynamic force not only reduces the moving speed of the main axle's angle to a certain degree but also influences the four parameters used to describe the performance of mechanical characteristics. The simulation and experimental results presented here can be used to highlight the design criteria on the optimal operation and condition monitoring of MWCBs.     

冲击载荷下永磁式电涡流减振器设计及动态特性分析

为研究轮式车辆的电涡流减振器在行进间冲击载荷下的动态特性,结合电涡流理论设计了一种永磁式电涡流减振器,并基于等效磁路模型和麦克斯韦方程分析了其导体筒表面空气间隙处磁感应强度与阻尼力之间的关系;同时,利用有限元法对永磁式电涡流减振器的静、动态磁场分布进行了研究,并分析了不同结构参数对其阻尼特性的影响及不同运动速度下的示功特性曲线。通过建立1/4车辆悬架动力学模型和基于高斯滤波白噪声的随机路面激励模型,对车辆行进间冲击载荷下永磁式电涡流减振器的动态特性进行了分析。结果表明：永磁式电涡流减振器的磁场在动态条件下会发生退磁以及磁感线趋速聚集现象,各结构参数对其阻尼特性的影响较大;永磁式电涡流减振器的响应速度快,压缩、复原阻尼力恒定且平稳,可以高效、快速地消除轮式车辆越野时受到的路面激励和车载武器射击时的冲击载荷,能够有效抑制车体振动。研究结果对提高轮式车辆的越野机动性以及车载武器的射击精度具有重要意义。     

Basic design and characteristics study of a double-axial superconducting magnetic bearing system

Under the background of upgrading energy crisis, a double-axial superconducting magnetic bearing (SMB) system was designed and fabricated for a flywheel energy storage system (FESS) model to demonstrate high temperature superconducting (HTS) energy-saving technologies. In order to levitate and stabilize the shaft sufficiently, the static levitation force and lateral force between high temperature superconductor (HTSC) stator and permanent magnet (PM) rotors in two different sizes were checked. Based on the stable levitation, the dynamic characteristics of the SMB system were also investigated by the excitation experiments. The running experiments show that in the case of a driving motor the shaft can stably rotate along the central axis without any contact, while intensified vibration is also observed near two resonance rotational speeds. These results have been applied to construct and operate the FESS model using the SMB system.     

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.     

Force Analysis of a Permanent Magnet and a Superconducting Hollow Cylinder

The interaction between a cylindrical magnet and a superconducting hollow cylinder in the Meissner state was analyzed using a dipole?Cdipole model. Analytical expression of the levitation force was derived as a function of the magnetic moment, radius of the magnet, radius, and thickness of the superconductor sample. The effect of the magnet??s dimensions on the levitation force was studied. The obtained results show that there is strong dependence of the levitation force on the magnetic dipole orientation at a small magnet?Csuperconductor distance.     

Effects of the relative speed of a magnet moving to and from a single-domain YBCO bulks on their interaction force

Two single-domain YBCO bulks with different grain orientations were used to investigate the effect of relative moving speed between the magnet and YBCO bulk, on their interaction force at LN₂ temperature under zero field cooling (ZFC) state. It is found that the levitation force of the sample S1 with c-axis perpendicular to the top surface is higher than that of the sample S2 with c-axis parallel to the top surface; the maximum levitation force (F_ML) is increasing with the increase of relative moving speed (V_RMS) between the magnet and the samples at first and reaches a peak value for sample S1 and a peak zone values for sample S2, then the F_ML decreases with the increase of V_RMS; the stiffness between the samples and the magnet is decreasing with the increase of the V_RMS. This result is useful for the application of superconducting levitation.     

可变磁路式永磁悬浮系统刚度特性分析及变刚度控制

针对可变磁路式永磁悬浮系统的悬浮力非线性变化的特点,分析系统的刚度特性,提出变刚度控制方法减小系统对外扰作用的敏感度。基于系统力学模型分析了系统结构和控制参数对悬浮刚度的影响,提出了基于悬浮物位移的变刚度控制方法;根据预设的载荷能力和位移变化量,设计参数的变化范围,使系统刚度按设定控制规律发生变化;进行了系统起浮稳定性与系统对外扰敏感度的仿真与实验分析,并与传统PID控制方法进行对比,仿真与实验结果表明:变刚度控制方法能够保证系统稳定起浮,并使外载荷作用时悬浮物的位移变化量减小50%,极大降低了系统对外扰的敏感度,相对于传统PID控制方法其控制特性有较大幅度提高。     

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.      

Analysis of a high Tc superconducting levitation systemwith vibration isolation control

This paper presents a method for controlling vibrations of a levitated high Tc superconducting body subjected to base disturbances. To have the control forces, an actuator consisting of a permanent magnet with an electromagnet was presented. The analytical solution for calculating levitation forces due to the permanent magnet and the control currents in the electromagnet was obtained. The levitation forces obtained coincide with the previously published results. The equation of motion of the levitated body subjected to base disturbances under the control was presented. Nonlinear vibrations of the body were first discussed; then the method of vibration isolation control using the direct disturbance cancellation combining the velocity feedback control was investigated. Numerical calculations were carried out for the levitation forces, with respect to the levitated body subjected to harmonic or pulse base excitations. It was clarified that the present method Is valid for controlling nonlinear systems like the magnetically levitated superconducting body     

Influence of Off-Centre Operation on the Performance of HTS Maglev

Owing to instinctive self-stable levitation characteristics, high-temperature superconducting (HTS) maglev using bulk high-temperature superconductors attracts more and more attention from scientists and engineers around the world. In this paper, the levitation force relaxation and guidance force characteristics of a Y–Ba–Cu–O levitation unit with different eccentric distances (EDs) off the center of the permanent magnet guideway were experimentally investigated under field-cooling (FC) conditions. Experimental results indicate that the levitation force slightly increases at small EDs firstly, but degrades with further increasing of EDs. However, the maximum guidance force and its stiffness exhibit enhancement in moderate ED range. The results demonstrate that a properly designed initial FC eccentric distance is important for the practical applications of HTS maglev according to specific requirements like running in curve lines.     

Theory of superconducting magnet suspension: main results survey

The paper is a survey of theoretical achievements on electro-dynamic suspension of high speed ground vehicles with superconducting magnets. The most essential problems connected with the subject in question are discussed, namely: calculation of lift and drag forces acting on a superconducting magnet, the latter moving above a guideway structure which may be of two different types (either conducting sheet or a series of discrete loops); influence of irregularities of the guideway structure; vertical and longitudinal stability of suspension.     

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.