Analytical method for levitation force calculation of radial HTS magnetic bearings

Naseh, Mojtaba; Heydari, Hossein

doi:10.1049/iet-epa.2016.0070

Cited by 14 publications

(12 citation statements)

References 21 publications

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“…Starting from Maxwell's equations, one could arrive at the following system of PDEs [15, 16]

\nabla \times E = - \frac{\partial B}{\partial t} = - μ \frac{\partial H}{\partial t} = - μ_{0} μ_{r} \frac{\partial H}{\partial t}

({, \begin{matrix} 1em4pt \\ - \frac{1}{r} (\frac{\partial (r E_{φ})}{\partial z}) = - μ_{0} μ_{r} \frac{\partial H_{r}}{\partial t} \\ \frac{1}{r} (\frac{\partial (r E_{φ})}{\partial r}) = - μ_{0} μ_{r} \frac{\partial H_{z}}{\partial t} \end{matrix})

The complete form of the PLM reads [17]

\begin{matrix} right leftthickmathspace.5em \\ E_{φ} & = E_{normalc} {()(, \frac{J_{s normalc}}{J_{c} ()(, B, T)})}^{n (B, T)}, J_{normalc} (B, T) = \frac{J_{c 0} B_{0}}{B_{0} + |B|} \times \frac{1 - false(T / T_{c} false)}{1 - false(T_{0} / T_{c} false)} \\ n (B, T) & = (n_{1} + B_{0}) \end{matrix}

…”

Section: Multi‐physics Analysis Of Hts Bearingsmentioning

confidence: 99%

Thermo‐electromagnetic analysis of radial HTS magnetic bearings using a semi‐analytical method

Naseh¹,

Heydari²

2017

IET Electric Power Applications

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Nowadays, after passing more than three decades from discovery of high‐temperature superconductors, they are widely used in different fields including power industry. High‐temperature superconducting (HTS) bearing is an electromagnetic machine that provides frictionless operation and intrinsic stability without requiring control equipment. Before entering to the fabrication stage, an accurate simulating model can satisfactorily reveal many of practical considerations. This work is based on the results of their previous study, delving into time steps of multi‐physical simulations juxtaposing electromagnetic and thermal characteristics of an HTS bearing. This is attainable by using multi‐physics analysis of radial HTS bearings based on a semi‐analytical method called variational iteration method (VIM). This is accomplished by coupling of the Maxwell equations and thermal equilibrium. The electrical behaviour of the superconductor is described by means of a B–T‐dependent modified E–J power‐law relation. To verify VIM results, the multi‐physics equations are also numerically solved using finite‐element method. In this research, two case studies are examined; failure of the cryogenic system and incorporating new materials in the stator part of the bearing in order to improve the cooling efficiency.

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“…Starting from Maxwell's equations, one could arrive at the following system of PDEs [15, 16]

\nabla \times E = - \frac{\partial B}{\partial t} = - μ \frac{\partial H}{\partial t} = - μ_{0} μ_{r} \frac{\partial H}{\partial t}

({, \begin{matrix} 1em4pt \\ - \frac{1}{r} (\frac{\partial (r E_{φ})}{\partial z}) = - μ_{0} μ_{r} \frac{\partial H_{r}}{\partial t} \\ \frac{1}{r} (\frac{\partial (r E_{φ})}{\partial r}) = - μ_{0} μ_{r} \frac{\partial H_{z}}{\partial t} \end{matrix})

The complete form of the PLM reads [17]

\begin{matrix} right leftthickmathspace.5em \\ E_{φ} & = E_{normalc} {()(, \frac{J_{s normalc}}{J_{c} ()(, B, T)})}^{n (B, T)}, J_{normalc} (B, T) = \frac{J_{c 0} B_{0}}{B_{0} + |B|} \times \frac{1 - false(T / T_{c} false)}{1 - false(T_{0} / T_{c} false)} \\ n (B, T) & = (n_{1} + B_{0}) \end{matrix}

…”

Section: Multi‐physics Analysis Of Hts Bearingsmentioning

confidence: 99%

Thermo‐electromagnetic analysis of radial HTS magnetic bearings using a semi‐analytical method

Naseh¹,

Heydari²

2017

IET Electric Power Applications

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“…Using the T-Ω method, he analysed its levitation characteristics [13]. Naseh and Heydari [14] employed variational iteration method to calculate the levitation force of a radial-type HTSB in the 2D space. However, the more calculus formulae needed to be solved if using this method.…”

Section: Introductionmentioning

confidence: 99%

3D electromagnetic behaviours and discharge characteristics of superconducting flywheel energy storage system with radial‐type high‐temperature bearing

Feng

Sun

et al. 2020

IET Electric Power Applications

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The authors have built a 2 kW/28.5 kJ superconducting flywheel energy storage system (SFESS) with a radial‐type high‐temperature superconducting bearing (HTSB). Its 3D dynamic electromagnetic behaviours were investigated based on the H ‐method, showing the non‐uniform electromagnetic force due to unevenly distributed induced current may cause the superconducting magnet stator of the HTSB cracks. As the SFESS discharges, the amplitude and frequency of the discharge voltage decrease with speed, dropping by 55 and 58%, respectively, from the beginning phase (BP) to the middle phase (MP), by 41 and 37% from the MP to end phase. The decay rates of the discharge voltage and its fluctuation are both increased compared with the no‐load operation. During the BP to MP, the output power is higher, the power quality is better and the harmonics are less. The amplitude and frequency of radial vibration are proportional to speed, larger than that during the no‐load operation in the same case, and in the BP about 1.8 and 8.8% amplitude in the x and y directions, respectively. Its two norm is increasing by 2.6%, probably leading to the friction between the shaft and protective bearings, gradually becoming greater with speed.

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“…Creating of superconducting bearings [1][2][3][4][5][6][7][8], transportation systems (MagLev) [9][10][11][12][13][14], and other devices with HTS bulks requires the use of numerical calculation methods and specialized mathematical model describing their electromagnetic properties. Simulation of HTS bulks is a complex problem due to the necessity to consider the influence of nonlinear properties of superconducting material at work in magnetic fields and their interaction with the magnetic system.…”

Section: Introductionmentioning

confidence: 99%

Bulk High-Temperature Superconductors: Simulation of Electromagnetic Properties

Kurbatova¹,

Kurbatov²,

Sysoev³

2020

On the Properties of Novel Superconductors

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The chapter deals with the electromagnetic properties of bulk high-temperature superconductors (HTSs), which can be used in magnetic systems for various applications, in particular, in contactless magnetic suspensions. Magnetic levitation in HTS material has a different nature from permanent magnets. It is caused by induced superconducting currents inside the volume of material. Due to this, the levitation is self-stabilizing and does not require additional active control or mechanical stops in magnetic systems with HTS. HTS materials have nonlinear, anisotropic, hysteresis properties, which make the calculation of the superconducting devices very difficult. Here you can find a brief overview of existing approaches to modeling HTS materials by E-J characteristics. Authors propose the method of simulation intending for 3D numerical calculation, which represents the processes in HTS using two types of magnetic field sourcescurrent and magnetization. The chapter focuses on the analysis of sources inside the superconducting material and their influence on an external magnetic field and levitation properties of HTS. In addition to simulations, the experimental studies of the force interactions between HTS bulks and permanent magnet are presented and compared with the calculations to verify the proposed mathematical models.

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Analytical method for levitation force calculation of radial HTS magnetic bearings

Cited by 14 publications

References 21 publications

Thermo‐electromagnetic analysis of radial HTS magnetic bearings using a semi‐analytical method

Thermo‐electromagnetic analysis of radial HTS magnetic bearings using a semi‐analytical method

3D electromagnetic behaviours and discharge characteristics of superconducting flywheel energy storage system with radial‐type high‐temperature bearing

Bulk High-Temperature Superconductors: Simulation of Electromagnetic Properties

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