Research on modeling and self-excited vibration mechanism in magnetic levitation-collision interface coupling system

The modeling and self-excited vibration mechanism in the magnetic levitation-collision interface coupling system are investigated.The effects of the control and interface parameters on the system's stability are analyzed.The frequency range of self-excited vibrations is investigated from the energy point of view.The phenomenon of self-excited vibrations is elaborated with the phase trajectory.The corresponding control strategies are briefly analyzed with respect to the vibration mechanism.The results show that when the levitation objects collide with the mechanical interface,the system's vibration frequency becomes larger with the decrease in the collision gap;when the vibration frequency exceeds the critical frequency,the electromagnetic system continues to provide energy to the system,and the collision interface continuously dissipates energy so that the system enters the self-excited vibration state.

Disturbance rejection tube model predictive levitation control of maglev trains

Magnetic levitation control technology plays a significant role in maglev trains.Designing a controller for the levitation system is challenging due to the strong nonlinearity,open-loop instability,and the need for fast response and security.In this paper,we propose a Disturbance-Observe-based Tube Model Predictive Levitation Control(DO-TMPLC)scheme combined with a feedback linearization strategy for the levitation system.The proposed strategy incorporates state constraints and control input constraints,i.e.,the air gap,the vertical velocity,and the current applied to the coil.A feedback linearization strategy is used to cancel the nonlinearity of the tracking error system.Then,a disturbance observer is implemented to actively compensate for disturbances while a TMPLC controller is employed to alleviate the remaining disturbances.Furthermore,we analyze the recursive feasibility and input-to-state stability of the closed-loop system.The simulation results indicate the efficacy of the proposed control strategy.

Levitation现象研究进展

漂浮(Levitation)现象可以定义为这样一种稳定情况,即在垂直振荡流体中颗粒的重力被完全抵消而仅在某一固定位置附近做振荡运动。作者分析了国内外研究现状,综述了以往学者对该现象进行的实验研究、理论分析以及数值模拟等工作。通过对Levitation现象研究文献的综述,总结了以往学者的一些研究成果,分析了他们所开展的研究之间的共性和分歧,在此基础上提出了目前对Levitation现象研究需解决的问题并对Levitation现象今后研究需要进一步解决的问题做了探讨。

ELECTROMAGNETIC MODEL OF LEVITATION MELTING WITH COLD CRUCIBLE

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Physical Properties of Liquid Terbium Measured by Levitation Techniques

To understand the nature and behavior of rare earth metals in their liquid phases, accurate values of their physical properties are essential. However, to measure their physical properties, the samples should be maintained in liquid phases for prolonged time, and this raises a formidable challenge. This is mainly explained by their high melting temperatures （e.g., 1629 K for Tb）, high vapor pressure, and the risk of melt contamination with a crucible or support. An electrostatic levitation furnace alleviated these difficulties and allowed the determination of density, surface tension, and viscosity of several metals above their melting temperature. Here, first, the levitation furnace facility and the noncontact diagnostic procedures were briefly discussed, followed by the explanation of their thermophysical property measurements over wide temperature ranges. The density was obtained using an ultraviolet-based imaging technique that allowed excellent illumination, even at elevated temperatures. Over the 1615 to 1880 K temperature span, the density measurements could be expressed as p（T） =7.84 × 10^3 -0.47 （T - Tm） （kg · m^-3） with Tm = 1629 K, yielding a volume expansion coefficient a（T） = 6.0 × 10^-5 （K^-1）. In addition, the surface tension and the viscosity could be determined by inducing a drop oscillation to a molten sample. Using this technique, the surface tension data could be expressed as σ（T） = 8.93 × 10^2 - 0.10 （T - Tm）（mN· m^-1） and those for viscosity as η（T） =0.583 exp [4.1 × 10^4/（RT）] （MPa·s） over the 1690 to 1980 K temperature range

THE ELECTROMAGNETIC FIELD CALCULATION AND ANALYSIS OF LEVITATION MELTING WITH COLD CRUCIBLE

In this paper, using the quasi-3D coupled current method, the influences of structure of cold crucible, the power frequency, the electricity property of melt, the coil position and current on the electromagnetic field (EMF) and the levitation characteristics in the melting processes are analyzed. It is shown that in the processes of levitation melting with cold crucible, the power frequency and cold crucible structure are the decisive factors for the ability of magnetic flux penetrating into cold crucible. The magnetic flux density in cold crucible is reduced as the increasing of power frequency, and this tendency becomes stronger when the power frequency is higher than 100kHz. The segmented structure of cold crucible can reduce the induction eddy in itself effectively, and the higher the power frequency is, the better the result is. So, a cold crucible can be segmented into 16-20 sectors for high frequency electromagnetic field and/or 8-12 sectors for lower frequency one. It is also shown that the levitation force of melting charge is related to coil current as a parabolic function.

A practical robust nonlinear controller for maglev levitation system

In order to explore the precise dynamic response of the maglev train and verify the validity of proposed controller,a maglev guideway-electromagnet-air spring-cabin coupled model is developed in the first step.Based on the coupled model,the stresses of the modules are analyzed,and it is pointed out that the inherent nonlinearity,the inner coupling,misalignments between the sensors and actuators,and external disturbances are the main issues that should be considered for the maglev engineering.Furthermore,a feedback linearization controller based on the mathematical model of a maglev module is derived,in which the nonlinearity,coupling and misalignments are taken into account.Then,to attenuate the effect of external disturbances,a disturbance observer is proposed and the dynamics of the estimation error is analyzed using the input-to-state stability theory.It shows that the error is negligible under a low-frequency disturbance.However,at the high-frequency range,the error is unacceptable and the disturbances can not be compensated in time,which lead to over designed fluctuations of levitation gap,even a clash between the upper surface of electromagnet and lower surface of guideway.To solve this problem,a novel nonlinear acceleration feedback is put forward to enhancing the attenuation ability of fast varying disturbances.Finally,numerical comparisons show that the proposed controller outperforms the traditional feedback linearization controller and maintains good robustness under disturbances.

NUMERICAL SIMULATION OF ALTERNATIVE HORIZONTAL LEVITATION ELECTROMAGNETIC CONTINUOUS CASTING（Ⅱ）

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A practical nonlinear controller for levitation system with magnetic flux feedback

This work proposes a practical nonlinear controller for the MIMO levitation system. Firstly, the mathematical model of levitation modules is developed and the advantages of the control scheme with magnetic flux feedback are analyzed when compared with the current feedback. Then, a backstepping controller with magnetic flux feedback based on the mathematical model of levitation module is developed. To obtain magnetic flux signals for full-size maglev system, a physical method with induction coils installed to winding of the electromagnet is developed. Furthermore, to avoid its hardware addition, a novel conception of virtual magnetic flux feedback is proposed. To demonstrate the feasibility of the proposed controller, the nonlinear dynamic model of full-size maglev train with quintessential details is developed. Based on the nonlinear model, the numerical comparisons and related experimental validations are carried out. Finally, results illustrating closed-loop performance are provided.

Vacuum Electromagnetic Levitation Melting and Undercooling of Peritectic Terfenol-D

For the first time, the undercooling of a magnetostrictive material a near peritectic Tb 0.27 Dy 0.73 Fe 1.90 alloy was realized by vacuum electromagnetic levitation melting and 60 K undercooling was obtained. There is one recalescence behavior during solidification of the undercooled melt,which can attribute to the priority precipitation of REFe 2 phase instead of REFe 3 phase, due to preferential nucleation and higher crystal growth rate of REFe 2 phase and the suppression of peritectic reaction. According to the crystal structural characteristics of REFe 2 and REFe 3, REFe 2 is a Laves phase intermetallics with MgCu 2 type structure, which has similar polytetrahedral structure with short range ordered structure in undercooled melt and has lower potential barrier for nucleation than that of REFe 3,which lead to the preferential nucleation of REFe 2 phase directly from the undercooled melt. Also, the similarity of structures between REFe 2 phase and undercooled melt leads to higher crystal growth rate of REFe 2 phase than that of REFe 3.

Levitation mechanism modelling for maglev transportation system

A novel maglev transportation system was proposed for large travel range ultra precision motion.The system consists of a levitation subsystem and a propulsion subsystem.During the propulsion subsystem driving the moving platform along the guideway,the levitation subsystem uses six pairs of electromagnets to steadily suspend the moving platform over the guideway.The model of the levitation system,which is a typical nonlinear multi-input multi-output coupling system and has many inner nonlinear coupling characteristics,was deduced.For testifying the model,the levitation mechanism was firstly controlled by proportional-integral-differential(PID) control,and then a lot of input-output data were collected for model parameter identification.The least-square parameter identification method was used.The identification results prove that the model is feasible and suitable for the real system.

A novel superconducting magnetic levitation method to support the laser fusion capsule by using permanent magnets

A novel magnetic levitation support method is proposed, which can relieve the perturbation caused by traditional support methods andprovide more accurate position control of the capsule. This method can keep the perfect symmetry of the octahedral spherical hohlraum and hasthe characteristics in stability, tunability and simplicity. It is also favorable that all the results, such as supporting forces acting on the super-conducting capsule, are calculated analytically, and numerical simulations are performed to verify these results. A typical realistic design isproposed and discussed in detail. The superconducting coating material is suggested, and the required superconducting properties are listed.Damped oscillation of the floating capsule in thin helium gas is discussed, and the restoring time is estimated.

Structure analysis of levitation chassis of medium-to-low speed maglev vehicles based on left-right decoupling

Levitation chassis, as an extremely important component of maglev vehicles, provides functions of transmitting levitation force and steering force, and directly affects the safety performance of the vehicle. Based on the vertical dynamics model of the levitation chassis, kinetic equations of the model are established, and a simulation program is designed to analyze the structural decoupling function of the chassis, especially under the influence of elastic constraints between the left and right modules, which are exclusively owned by maglev vehicles. A finite element model of the levitation chassis based on left-right decoupling is constructed. Analysis results of the model show that the mechanical properties of the chassis tailored for the vehicle meet the design requirements, and the stiffness and strength is adequate to bear the weight of the whole vehicle.

Levitation force analysis of medium and low speed maglev vehicles

The rule of levitation force variation with different structure and electromagnetic parameters provides a basis for electromagnet design of electromagnetic suspension （EMS） medium and low speed maglev vehicles. In order to acquire accurate calculation results of levitation force, different calculation methods, including analytical method, 2D FEM （finite element method）, and 3D FEM, are applied to investigate the impact of various structural parameters, such as excitation current, air gap, lateral offset, and pole width, on levitation force. The analytical analysis is based on the classic mathematical model of levitation force between electromagnet and rail and performed with MATLAB. In the 2D and 3D FEMs, the numerical calculation of the levitation force is conducted with Ansoft by taking the magnetic saturation into account. In addition, the longitudinal end effect on the levitation force calculation is considered in the 3D FEM. The results show that the 3D FEM is the most accurate among the above three methods for calculating the levitation force, and the analytical method can only work for small current and/or large air gap conditions. A lateral- offset between vehicle and rail will reduce the levitation force; the levitation force descends sharply once the lateral offset exceeds the threshold, i.e., 8% of the pole width for U-shaped electromagnets. The maximum lift-to-weight ratio emerges when the pole width ratio of F type rail to electromagnet is 6：7. This may offer a reference for EMS maglev vehicle design and application.

Computation and Analysis of Propellant and Levitation Forces of a Maglev System Using FEM Coupled to External Circuit Model

This paper studies the propellant and levitation forces of a prototype maglev system where the propellant forces are provided by a linear motor system. For this purpose, the mathematical model and method using finite element method coupled to external circuit model is developed. The details of the propellant and levitation forces for a prototype maglev system under different operating conditions are investigated, and some directions are given for practical engineering applications.

Design and Development of Impeller Synergic Systems of Electromagnetic Type to Levitation/Suspension Flight of Symmetrical Bodies

Using certain models of twistor surfaces for fields of force and the mathematical relationships that lie among fields, lines, surfaces and flows of energy, it has been designed and developed a flight electromagnetic type system based on the synergic study of their electromagnetic field geodesics to generate vehicle levitation, suspension and movement without being in contact with the surface. The idea of such work is to obtain a new flight and impulse patent of an electromagnetic vehicle by principles of super-conduction and some laws of the current like Eddy currents and principles which are very similar to mechanics of sidereal objects like galaxies or stars under models of twistor surfaces. This vehicle will be controlled by one microchip that will be programmed by conscience operators algebra of electromagnetic type that leads to the flow of Eddy currents, the iso-rotations and suspension of the special geometrical characteristics vehicle, generating also on the vehicle structure certain “magnetic conscience” that provokes all movements like succeeding to the sidereal objects in the universe.

Study on Transient Properties of Levitated Object in Near-Field Acoustic Levitation

A new approach to the study on the transient properties of the levitated object in near-field acoustic levitation （NFAL） is presented. In this article, the transient response characteristics, including the levitated height of an object with radius of 24 mm and thickness of 5 mm, the radial velocity and pressure difference of gas at the boundary of clearance between the levitated object and radiating surface （squeeze film）, is calculated according to severa/velocity amplitudes of radiating surface. First, the basic equations in fluid areas on Arbitrary Lagrange--Euler （ALE） form are numericaJly solved by using streamline upwind petrov gaJerkin （SUPG） finite elements method. Second, the formed a/gebraic equations and solid control equations are solved by using synchronous alternating method to gain the transient messages of the levitated object and gas in the squeeze film. Through theoretical and numerical analyses, it is found that there is a oscillation time in the transient process and that the response time does not simply increase with the increasing of velocity amplitudes of radiating surface. More investigations in this paper are helpful for the understanding of the transient properties of levitated object in NFAL, which are in favor of enhancing stabilities and responsiveness of levitated object.

Design and Implementation of Digital Fractional Order PID Controller Using Optimal Pole-Zero Approximation Method for Magnetic Levitation System

The aim of this paper is to employ fractional order proportional integral derivative(FO-PID)controller and integer order PID controller to control the position of the levitated object in a magnetic levitation system(MLS),which is inherently nonlinear and unstable system.The proposal is to deploy discrete optimal pole-zero approximation method for realization of digital fractional order controller.An approach of phase shaping by slope cancellation of asymptotic phase plots for zeros and poles within given bandwidth is explored.The controller parameters are tuned using dynamic particle swarm optimization(d PSO)technique.Effectiveness of the proposed control scheme is verified by simulation and experimental results.The performance of realized digital FO-PID controller has been compared with that of the integer order PID controllers.It is observed that effort required in fractional order control is smaller as compared with its integer counterpart for obtaining the same system performance.

Analysis and Calculation for Heating and Temperature Rise of Magnetic Levitation Device

准确的热分析是磁悬浮系统电磁装置优化设计、防止过热的前提。提出了基于等效热路模型的电磁装置发热及温升计算方法,并与基于＂场＂的仿真分析结果进行比较,验证其正确性。首先,利用ANSYS软件建立电磁装置的瞬态温度场模型,并将装置中动铁心随大轴旋转时与空气产生的风摩擦损耗包含在模型中,通过仿真分析,得到电磁装置温度分布;然后,通过对散热路径的分析建立了电磁装置的等效热路模型,从＂路＂的角度计算出本电磁装置各位置的温升;最后,将基于＂路＂的计算结果与基于＂场＂的仿真结果进行了比较分析,各部分温升误差均在允许范围内,验证了等效热路模型计算电磁装置发热及温升方法的准确性和可行性。在基于＂场＂和＂路＂的两种分析中,均考虑了电阻率随温升的变化,散热分析中均计及了导热系数和对流散热系数随温度的变化。

Real Magnetic Charges in the Substance, Ferrogravitation and Technical Levitation

Experimental and theoretical investigations by author of the present article (period: 1968-2013) have shown that the magnetic spinor particles (magnetic charges) are real structural components of atoms and substance and are immediate sources of all magnetic fields in Nature. Joint orbital currents of electric and magnetic charges within atomic shells are the natural sources of gravitational field which is a vortex electromagnetic field. The vector character of the elementary gravitational field is similar to the vortex magnetic field that allows entering in the submission of such fundamental states of the gravitational field, as a paragravitation and ferrogravitation. Physical masses (atoms, nucleons, substance, etc.), which emit ferrogravitational field are repelled off from sources paragravitational field, for example, from Earth. It is a manifestation of the effect of levitation, which was discovered by the author of this article. Technical forces levitation, that induced by technical ferrogravitational fields, could be used in transport, lifting and space technology, power engineering and many other areas of human activity. The main reasons that real magnetic charges are “buried alive” in modern theoretical notions are as physics their of confinement in the structures of atoms and substance which are radically different from the confinement of electrons so and fallacious electromagnetic concept Maxwell in which the magnetic field is by mistake deprived of its own source of the magnetic pole or of the magnetic charge.