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

Baiko, A.V.; Voevodskii, Konstantin E.; Kochetkov, V.M.

doi:10.1016/0011-2275(80)90052-1

Cited by 8 publications

(6 citation statements)

References 3 publications

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“…It is well known that electrodynamic suspension systems are highly underdamped [9]. Davis and Wilkie [10] analytically studied the dynamics of a long wire moving above a thin continuously uniform nonferromagnetic conducting plate while Baiko et al [11] studied the dynamics using a rectangular coil. Both authors calculated that positive vertical damping is present at low-speeds while at high-speed the vertical damping can become negative.…”

Section: Introductionmentioning

confidence: 99%

“…However, the damping values greatly reduce at high speed. Davis and Wilkie [10] and Yoshida and Takakura [12] calculated the forces utilizing a thin-sheet approximation approach in which the current is assumed to be constant throughout the plate thickness while Baiko et al [11] and Urankar [13] accounted for current variation throughout the plate thickness.…”

Section: Introductionmentioning

confidence: 99%

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Modeling the Dynamic Electromechanical Suspension Behavior of an Electrodynamic Eddy Current Maglev Device

Paudel¹,

Bird²

2013

PIER B

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Abstract-A 2-D analytic based eddy-current transient model for a conducting plate is derived that is capable of accounting for continuous changes in the input conditions. Only the source field on the surface of the conducting plate needs to be known. In addition, a 2-D steady-state analytic based eddy-current model that is capable of accounting for frequency and velocity changes in two directions is derived. Both analytic based models have been validated using finite element code. The transient and steady-state models are integrated into an electromechanical system where the magnetic source is a Halbach rotor. The accuracy of both calculation methods is compared. The stiffness and damping coefficients are derived using the steadystate model.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Modeling the Dynamic Electromechanical Suspension Behavior of an Electrodynamic Eddy Current Maglev Device

Paudel¹,

Bird²

2013

PIER B

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“…In the absence of any enhanced damping, the magnetic damping inherent in a magnet-moving conductor system is generally referred to as intrinsic magnetic damping. Several aspects of magnetic damping have been studied: magnetic damping as a function of velocity (Moon [9], Iwamoto et al [7], Yamada et al [11]); damping constant as a function of frequency (Saitoh et al, 1992); passive damping (Iwamoto et al [7]); and the effects 1 The submitted manuscript has been created by the University of Chicago as Operator of Argonne National Laboratory ("Argonne") under Contract No. W-31-109-ENG-38 with the U.S. Department of Energy.…”

Section: Introductionmentioning

confidence: 99%

“…However, for a large enough velocity v, this dissipative force can become destabilizing. The subject of eddy current damping in the context of levitation problems was studied by Davis and Wilkie [5], Iwamoto et al [7], Moon [8], and Baiko et al [1]. When the levitation height varies sinusoidally, the perturbed lift force component, F L , proportional to sinusoidal height u(t) with respect to the original height h 0 is found to be…”

Section: Introductionmentioning

confidence: 99%

Magnetic Damping For Maglev

Zhu

Cai

Rote

et al. 1998

Shock and Vibration

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Magnetic damping is one of the important parameters that control the response and stability of maglev systems. An experimental study to measure magnetic damping directly is presented. A plate attached to a permanent magnet levitated on a rotating drum was tested to investigate the effect of various parameters, such as conductivity, gap, excitation frequency, and oscillation amplitude, on magnetic damping. The experimental technique is capable of measuring all of the magnetic damping coefficients, some of which cannot be measured indirectly.

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“…2) and the 3-degree of freedom velocity motion is accounted for . Apart from [2] most other 3-D analytical eddy current force models consider only the source on the top conductive plate [4][5][6][7][8][9][10] . By using the reflected field modeling approach the force equations can be clearly derived allowing damping and stiffness terms to be determined [11] .…”

mentioning

confidence: 99%

A 3-D analytical model for a double Halbach linear array electrodynamic suspension system

Chen¹,

Paul

Bird

et al. 2015

2015 IEEE Magnetics Conference (INTERMAG)

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By translationally moving a magnetic source above a conductive plate guideway both levitation and drag forces are created . Unfortunately, the electrodynamic drag force can be quite high [1] . Kratz studied a double Halbach array topology, such as shown in Fig 1 [1], and used a simple curve fitting approximation to model the forces . Kratz experimentally showed that a significant reduction in drag force can be created when using this "null current" approach . Much earlier Urankar derived analytic equations for a similar double coil system [2] . In this paper an exact 3-D eddy current force model is derived that accounts for both velocity and frequency changes in the source field both above and below the conductive plate . For validation purposes the source field is assumed to be created by a linear Halbach array, as shown in Fig 1 . However, the equations are written in a general form, so as to be useful to other researchers . A 3-D second order vector potential (SOVP) formulation is used to calculate the fields and force components . The SOVP is related to the magnetic vector potential A and magnetic flux density, B, by (1)-(3) [3] . In this model the conducting plate is assumed to be finite in thickness and the plate width and length are sufficiently large that the edge effects on the conducting plate (but not source) are neglected (therefore Wb=0) . The authors believe that the presented formulation is new because the force equations on both the top and bottom conductive plate are derived by using a reflected and transmitted eddy current field approach (see Fig . 2) and the 3-degree of freedom velocity motion is accounted for . Apart from [2] most other 3-D analytical eddy current force models consider only the source on the top conductive plate [4][5][6][7][8][9][10] . By using the reflected field modeling approach the force equations can be clearly derived allowing damping and stiffness terms to be determined [11] .Using the values shown in Table I the derived 3-D eddy current model was validated using a finite element analysis model . The analytic model has been used to study parameter trade-offs . For instance, Fig 3 shows how the Halbach array magnet width, thickness and pole-pitch effect the levitation-to-weight ratio . While Fig 4 shows the trade-off in levitation/weight and levitation/drag ratios when using the double and a single Halbach array topology . The full paper will provide the detailed mathematical derivation of the field and force values as well as more detail on model validation .

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

Cited by 8 publications

References 3 publications

Modeling the Dynamic Electromechanical Suspension Behavior of an Electrodynamic Eddy Current Maglev Device

Modeling the Dynamic Electromechanical Suspension Behavior of an Electrodynamic Eddy Current Maglev Device

Magnetic Damping For Maglev

A 3-D analytical model for a double Halbach linear array electrodynamic suspension system

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