Maximization of Acoustic Levitating Force for a Single-Axis Acoustic Levitation System Using the Finite Element Method

We investigate single-axis acoustic levitation using standing waves to levitate particles freely in a medium bounded by a driver and a reflector. The acoustic pressure at the pressure antinode of the standing wave counteracts the downward gravitational force of the levitating object. The optimal relationship between the air gap and the driving frequency leads to resonance and hence maximization of the levitating force. Slight deviation from the exact resonance condition causes a reduction in acoustic pressure at the pressure antinodes. This results in a significant reduction of the levitating force. The driving frequency is kept constant while the air gap is varied for different conditions. The optimal air gap for maximizing the levitation force is studied for first three resonance modes. Furthermore, a levitating particle is introduced between the driver and the reflector. The dependence of the resonance condition on the size of the levitating particle as well as the position of the particle between the driver and the reflector has also been studied. As the size of the levitating particle increases, the resonance condition also gets modified. Finite element results show a good agreement with the validated results available in the literature. Furthermore, the finite element approach is also used to study the variation of acoustic pressure at the pressure antinode with respect to the size of the reflector. The optimum diameter of the reflector is calculated for maximizing the levitating force for three resonance modes.

UAQ4 Magnetic Levitating Train： Propulsion System for Urban Transportation

This paper discusses the design of the propulsion system of the UAQ4 （University of L＇Aquila, model 4） magnetic levitating train which is used for transportation applications in urban environments. UAQ4 is the only magnetic levitating vehicle with resistance motion, except for aerodynamic drag and with energy consumption near zero at low speed. The feasibility of the system has been successfully verified and tested in the laboratory. Propulsion and braking are provided by a novel direct-current linear stepper motor, with the primary formed by permanent magnets distributed on central beam of the track, and the secondary by coils on board the vehicle, instead of the present alternate current linear motors that have well-known disadvantages. The motor working principles are described, and its performances are analyzed, by a finite element numerical model which allows modifying the most important parameters of the system. The main components of a full scale motor for urban transportation are measured and discussed.

Modeling and Validation of Diamagnetic Rotor Levitated by Permanent Magnetics

As an innovative,low-power consuming,and low-stiffness suspension approach,the diamagnetic levitation technique has attracted considerable interest because of its potential applicability in miniaturized mechanical systems.The foundation of a diamagnetic levitation system is mathematical modeling,which is essential for operating performance optimization and stability prediction.However,few studies on systematic mathematical modeling have been reported.In this study,a systematic mathematical model for a disc-shaped diamagnetically levitated rotor on a permanent magnet array is proposed.Based on the proposed model,the magnetic field distribution characteristics,diamagnetic levitation force characteristics(i.e.,levitation height and stiffness),and optimized theoretical conditions for realizing stable levitation are determined.Experiments are conducted to verify the feasibility of the proposed mathematical model.Theoretical predictions and experimental results indicate that increasing the levitation height enlarges the stable region.Moreover,with a further increase in the rotor radius,the stable regions of the rotor gradually diminish and even vanish.Thus,when the levitation height is fixed,a moderate rotor radius permits stable levitation.This study proposes a mathematical modeling method for a diamagnetic levitation system that has potential applications in miniaturized mechanical systems.

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.

Efficient loading of cesium atoms in a magnetic levitated dimple trap

We report a detailed study of magnetically levitated loading of ultracold ^(133)Cs atoms in a dimple trap.The atomic sample was produced in a combined red-detuned optical dipole trap and dimple trap formed by two small waist beams crossing a horizontal plane.The magnetic levitation for the ^(133)Cs atoms forms an effective potential for a large number of atoms in a high spatial density.Dependence of the number of atoms loaded and trapped in the dimple trap on the magnetic field gradient and bias field is in good agreement with the theoretical analysis.This method has been widely used to obtain the Bose–Einstein condensation atoms for many atomic species.

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.

Temperature-free mass tracking of a levitated nanoparticle

Mass measurement is an essential analytical tool in the characterization of materials.Here we present a method for measuring the mass of an individual nanoparticle which has a fg-level mass.This method enables a temperatureindependent mass measurement with the assistance of a sinusoidal electrostatic driving force.With this approach,we successfully track the change in properties of an optically levitated nanoparticle,such as mass,temperature,and electric charge,with air pressure.An abrupt change in the mass of silica nanoparticles is found to violate the Zhuravlev model.This method can be utilized to extend the mass analysis of materials,such as thermogravimetric analysis,to individual microor nano-particles.

Effect of thickness on magnetic properties of single domain GdBCO bulk superconductors

To study the influence of thickness on the magnetic properties of ReBCO(Re = Y, Gd, Sm, Nd, etc.) bulk superconductors, a single domain gadolinium barium copper oxide(GdBCO) bulk superconductor fabricated by the Re + 011 top seeded infiltration growth(Re + 011 TSIG) method was continuously sliced along the bottom to obtain samples of different thickness. The levitation force and attractive force of these samples were tested at 77 K in the zero-field-cooled(ZFC)state. It is found that as the sample thickness decreases, the levitation force decreases gradually whereas the attractive force increases. This is related to the varied ability to resist the penetration of magnetic field occasioned by varying sample thickness, which are deeply revealed by combining with the characteristics of the non-ideal type-II superconductor. Further,the levitation force exhibits a trend of slow initial change followed by rapid change, which may be attributed to the growth of the sample. Measurement of the trapped field shows that a similar distribution of trapped field at the top and bottom surfaces can be achieved by removing some materials from the bottom of the bulk. These results provide a reference for meeting the actual requirements of ReBCO bulks of different thicknesses and greatly contribute to practical designs and applications.

The Classical Description of the Meissner Effect: Theory and Applications

When we place a superconductor above a magnet, we observe a levitation of the superconductor above the magnet. But when placing a perfect diamagnetic material above a magnet, no levitation is observed. This difference in behavior between the superconductor and the perfect diamagnetic in the presence of an external magnetic field is explained by the classical description of the Meissner effect implemented in this article. We have shown here that the Meissner effect is nothing more than an electromagnetic interaction between the magnetic field created by the superconductor and the magnetic field of the magnet. This classical description of the Meissner effect also allowed us to give a more realistic explanation of the expansion of the universe. We have shown that this expansion is a phenomenon that simply results from a Meissner effect between superconducting dark matter and the magnetic fields of stars. We also pointed out that this expansion is accelerated because the gravitational force between dark matter and the stars around it decreases as these stars move away from the superconducting dark matter. We also used this classical description of the Meissner effect to propose a new method of remote sensing in space in which the superconducting satellite is in perpetual levitation on the night side of the earth and a new and more efficient way to discover new particles through a superconducting detector levitating in the upper atmosphere.

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。

Rapid solidification of Cu_(60)Co_(30)Cr_(10) alloy under different conditions

Metastable liquid phase separation and rapid solidification in a metastable miscibility gap were investigated on the Cu60Co30Cr10 alloy by using the electromagnetic levitation and splat-quenching.It is found that the alloy generally has a microstructure consisting of a（Co,Cr）-rich phase embedded in a Cu-rich matrix,and the morphology and size of the（Co,Cr）-rich phase vary drastically with cooling rate.During the electromagnetic levitation solidification processing the cooling rate is lower,resulting in an obvious coalescence tendency of the（Co,Cr）-rich spheroids.The（Co,Cr）-rich phase shows dendrites and coarse spheroids at lower cooling rates.In the splat quenched samples the（Co,Cr）-rich phase spheres were refined significantly and no dendrites were observed.This is probably due to the higher cooling rate,undercooling and interface tension.

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.

Modeling and Analysis of a Micromotor with an Electrostatically Levitated Rotor

The modeling and evaluation of a prototype rotary micromotor where the annular rotor is supported electrostatically in five degrees of freedom is presented in order to study the behavior of this levitated micromotor and further optimize the device geometry. The analytical torque model is obtained based on the principle of a planar variable-capacitance electrostatic motor while the viscous damping caused by air film between the stator and rotor is derived using laminar Couette flow model. Simulation results of the closed-loop drive motor, based on the developed dynamic model after eliminating mechanical friction torque via electrostatic suspension, are presented. The effects of the high-voltage drive, required for rotation of the rotor, on overload capacity and suspension stiffness of the electrostatic bearing system are also analytically evaluated in an effort to determine allowable drive voltage and attainable rotor speed in operation. The analytical results show that maximum speed of the micromotor is limited mainly by viscous drag torque and stiffness of the bearing system. Therefore, it is expected to operate the device in vacuum so as to increase the rotor speed significantly, especially for those electrostatically levitated micromotors to be used as an angular rate micro-gyroscope.

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.

Saturation influence of control voltage on maglev stationary self-excited vibration

This work addresses the saturation influence of control voltage on the occurring of self-excited vibration of maglev vehicle-bridge interaction system, which greatly degrades the stability of the levitation control, decreases the ride comfort, and restricts the cost of the whole system. Firstly, the interaction model of vehicle-bridge system is developed. Based on the interaction model, the relationship between the control voltage and vibration frequency is solved. Then, the variation of the effective direct component and fundamental harmonic are discussed. Furthermore, from the perspective of energy transmission between the levitation system and bridge, the principle underlying the self-excited vibration is explored, and the influence on the stability is discussed. Finally, in terms of the variation of the characteristic roots, the influence is analyzed further and some conclusions are obtained. This study provides a theoretical guidance for mastering the self-excited vibration problems.

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.

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.