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Journal ArticleDOI

A General Analytical Model of Permanent Magnet Eddy Current Couplings

01 Jan 2014-IEEE Transactions on Magnetics (IEEE)-Vol. 50, Iss: 1, pp 1-9
TL;DR: In this article, an improved practical two-dimensional model for the analytical calculation of the magnetic field distributions in permanent magnet (PM) eddy current couplings is presented to obtain the torque characteristics.
Abstract: An improved practical two-dimensional model for the analytical calculation of the magnetic field distributions in permanent magnet (PM) eddy current couplings is presented to obtain the torque characteristics. By establishing the Cartesian coordinate reference system on the rotating conductor, the PM region is treated as a source of traveling wave magnetic field and then the multi-layer boundary value problem is solved. The formulation for the magnet blocks, the eddy current and saturation effects in the solid secondary back iron, and the equivalence relationships between typical PM shapes, are all reasonably taken into account. Calculation results produced by the proposed analytical model are compared with those from the nonlinear finite element method and experimental measurement.
Citations
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Journal ArticleDOI
TL;DR: This paper presents an approach for quick calculation of steady-state and transient performances of an axial-field eddy-current coupling based on a 2-D approximation of the magnetic field distribution and shows that good agreements are obtained.
Abstract: This paper presents an approach for quick calculation of steady-state and transient performances of an axial-field eddy-current coupling. Based on a 2-D approximation of the magnetic field distribution, a simple analytical expression for the transmitted torque is first developed. This expression is valid for low slip values, which correspond to the normal working area of such devices (high efficiency). The proposed torque formula is then used to study the steady-state (constant-speed operations) and the transient performances of the coupling (small variations of the slip speed). The results are compared with those obtained from 3-D finite elements simulations and tests. It is shown that good agreements are obtained.

84 citations


Cites background or methods from "A General Analytical Model of Perma..."

  • ...It has been shown in [18] that the first harmonic component plays a dominant role in the torque transmission for eddy-current couplings (around 98% of the total torque)....

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  • ...In order to predict accurately the torque-speed characteristic for larger slip values, a more complex model which takes into account the reaction field effect must be used [16]-[18], but this is out of the scope of the present paper....

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  • ...The induced currents in the conducting plate are computed by solving a 2D diffusion equation leading to a complex expression for the transmitted torque [16]-[18]....

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  • ...It has been shown in [18], [20] and [22] that the 3D endeffects cannot be neglected for such devices....

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Journal ArticleDOI
TL;DR: In this article, a 3D analytical model for axial-flux eddy-current couplings and brakes is presented, leading to closed-form expressions for the torque and the axial force.
Abstract: This paper presents a 3-D analytical model for axial-flux eddy-current couplings and brakes, leading to closed-form expressions for the torque and the axial force. The proposed model is valid under a steady-state condition (constant speed operation). It takes into account the reaction field due to induced currents in the moving conducting part. In order to simplify the analysis, we adopt the assumption of linearization at the mean radius, and the problem is then solved in 3-D Cartesian coordinates (curvature effects are neglected). The solution is obtained by solving the Maxwell equations with a magnetic scalar potential formulation in the nonconductive regions (magnets and air gap) and a magnetic field strength formulation in the conductive region (copper). Magnetic field distribution, axial force, and torque computed with the 3-D analytical model are compared with those obtained from the 3-D finite-element simulations and experimental results.

79 citations


Cites background or result from "A General Analytical Model of Perma..."

  • ...Indeed, the edge effects in the radial direction have a great importance on the torque–speed curve prediction, and cannot be neglected [19], [20]....

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  • ...It was shown in [20] that this additional torque is small compared with the one due to the copper plate....

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Journal ArticleDOI
TL;DR: A simple and practical magnetic equivalent circuit (MEC) based analytical technique for calculating the performance parameters of the permanent magnet (PM) eddy current coupling is presented and shows that in a considerably wide range of slip speeds, the torques predicted by the presented method match well with those obtained by both the three-dimensional finite element analysis and experimental measurement.
Abstract: A simple and practical magnetic equivalent circuit (MEC) based analytical technique for calculating the performance parameters of the permanent magnet (PM) eddy current coupling is presented. In the proposed MEC model built with the lumped parameters, the eddy current effects are inherently taken into account by introducing a branch magnetic circuit allowing for the magnetomotive force and the reaction magnetic flux. A complete formulation for the reaction flux which is treated as a kind of leakage flux is derived. A verification process is conducted and it is shown that in a considerably wide range of slip speeds, the torques predicted by the presented method match well with those obtained by both the three-dimensional finite element analysis and experimental measurement. The new MEC-based method also proves to be effective in the performance simulation of the PM eddy current coupling with different design parameters. In addition, the limitation of the proposed approach is also discussed and the reasons are fully investigated.

76 citations


Cites background or methods from "A General Analytical Model of Perma..."

  • ...The axial flux PM eddy current coupling studied in this section has the same basic structure and physical parameters as the 75 kW prototype with the double-sided structure described in [13]....

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  • ...The actual magnets with other shapes, such as circular shaped and fan-shaped magnets, can all be equalized to the corresponding rectangular shaped one with the same area and thickness [13]....

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Journal ArticleDOI
TL;DR: In this article, a 2D analytical model for the prediction of the magnetic field in permanent magnet (PM) eddy current couplings with a slotted conductor topology is proposed.
Abstract: In this paper, a 2-D analytical model for the prediction of the magnetic field in permanent magnet (PM) eddy current couplings with a slotted conductor topology is proposed. The originality of this paper lies in the fact that the influences of both the slots and the iron-core protrusions on the eddy currents induced in the slotted conductor are considered in the analytical computation, and the interactions between adjacent conducting spokes are considered. The magnetic field distribution is obtained by taking account of the eddy current reaction caused by the induced eddy currents in the slotted conductor. The moving PM field is treated as the source of a time-varying magnetic field, and both the effects of the time harmonics and spatial harmonics on the torque computation are analyzed. The results from this analytical model and nonlinear finite-element models are compared, and the effectiveness of the analytical method is demonstrated. The reason for the discrepancies between the results is discussed, and an eddy current clustering phenomenon is observed. The 2-D analytical method has the advantage of taking less computational time for a parametric study than the 3-D finite-element method, and can be a useful tool for design optimization.

68 citations


Cites background or methods from "A General Analytical Model of Perma..."

  • ...In addition, the very existence of a radial component of the magnetic field may be another reason [4]....

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  • ...This correction factor is widely applied in torque calculations for eddy current devices [4]–[9], [16]....

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  • ...To simplify the analytical modeling inspired by [1], [2], [4]–[6], [14], and [19], we can simplify real 3-D models of the axial-flux type to a 2-D model by imaging that the structure is cut in a radial direction and rolled out flat in the circumferential direction along an equivalent circle of magnets (at the equivalent radius Re with Re ∈ [Ri , Ro])....

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  • ...To facilitate the analytical treatment of the eddy current problem inspired by [4], [32], and [35], the PM magnetic field is treated as a time-harmonic field due to the relative motion (slip) between the PMs and the conductor....

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Journal ArticleDOI
TL;DR: An improved 3D analytical model for axial-flux permanent-magnet eddy-current couplings is presented in this paper, which directly takes into account the radial edge effects and the curvature effects on the torque prediction without the need of any correction factor.
Abstract: An improved 3-D analytical model for axial-flux permanent-magnet eddy-current couplings is presented in this paper. As the problem is solved in a 3-D cylindrical coordinate system, the proposed model directly takes into account the radial edge effects and the curvature effects on the torque prediction without the need of any correction factor. It is shown that, the new analytical model is very accurate, even for the geometries where the curvature effects are very pronounced. Another advantage of the proposed model is the great reduction of computation time compared to 3-D finite-elements simulations and an easier adaptation for parametric studies and optimization.

34 citations


Cites background from "A General Analytical Model of Perma..."

  • ...However, it has been shown that this correction factor is not always accurate [5], [6]....

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References
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Journal ArticleDOI
TL;DR: In this paper, the uniqueness of the vector potential is given special attention, and a numerically stable finite-element scheme that performs well at low and high frequencies, does not require an unduly high number of degrees of freedom, and is capable of treating multiple connected conductors is presented.
Abstract: Various magnetic vector potential formulations for the eddy-current problem are reviewed. The uniqueness of the vector potential is given special attention. The aim is to develop a numerically stable finite-element scheme that performs well at low and high frequencies, does not require an unduly high number of degrees of freedom, and is capable of treating multiple connected conductors. >

720 citations

Journal ArticleDOI
01 Apr 1958
TL;DR: In this paper, the problem of estimating the power losses in a cylindrical corrosion-resistant shell of a fly-by-fly RC motor is investigated. But the results are limited to the case where the rotor is separated from the stator by a thin, corrosion resistant shell.
Abstract: The problem of circulating corrosive liquids assumes a major importance in nuclear-engineering practice, where the standards of safety and reliability which are imposed demand sealed circulating systems. One method employs a completely enclosed centrifugal pump driven by a squirrel-cage induction motor in which the rotor is separated from the stator by a thin cylindrical corrosion-resistant shell which is situated in the air-gap of the machine and effectively forms part of the retaining wall of the circulating system. A precise assessment for design or development purposes depends on a knowledge of the power losses in the stationary shell and it is a solution of this eddy-current problem which is developed in this paper. Arguments more appropriate to field theory than to circuit theory lead to a classical boundary-value problem which takes into account the nature and thickness of the shell and the length of overhang, and provides formulae for current densities, flow lines and dissipated power in terms of ordinary machine parameters and the dimensions and electrical constants of the shell. Theoretical and practical results are compared and shown to be in close agreement. Some of the graphical results display a pronounced slot effect and suggest methods for making a more detailed investigation. The theory can be extended to correspond to a composite shell of complex structure and it has some bearing on the principles employed in drag-cup motors, to which it could be applied.

221 citations


"A General Analytical Model of Perma..." refers background in this paper

  • ...Reference [25] presented a correction factor which was derived from the ratio of the eddy current loss associated with a 2-D current distribution to that due to a 1-D current field (i....

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Journal ArticleDOI
01 May 1959
TL;DR: In this paper, a simple formula for the power factor (pf) that the magnetic circuit reflects into the magnetizing winding is presented, which enables the losses caused by eddy currents to be predicted with surprising accuracy.
Abstract: In this paper formulas are developed, on the basis of simple physical conceptions, for the calculation of eddy currents in solid and laminated iron, which, as the experiments presented show, enable the losses caused by eddy currents to be predicted with surprising accuracy. A simple formula for the calculation of the power factor (pf) that the magnetic circuit reflects into the magnetizing winding is also presented.

183 citations


"A General Analytical Model of Perma..." refers background in this paper

  • ...The empirical coefficient is set to 0.75, following Agarwal [24]....

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  • ...2) Limiting nonlinear theory Agarwal [24] suggested that the magnitude of the magnetic flux density may be considered constant if the magnetic field intensity is strong enough....

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  • ...The eddy current loss per unit area is (62) B. 2) Limiting nonlinear theory Agarwal [24] suggested that the magnitude of the magnetic flux density may be considered constant if the magnetic field intensity is strong enough....

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Journal ArticleDOI
TL;DR: In this paper, a detailed analytical study of rotational eddy-current couplers is presented, which consist of a permanent-magnet stator and a multilayer conductive rotor.
Abstract: We present a detailed analytical study of rotational eddy-current couplers. We provide a field solution by the variable separation method, and we analyze radial geometry structures. The couplers consist of a permanent-magnet stator and a multilayer conductive rotor. We present different analytical solutions in order to study single- and double-sided permanent-magnet frames. We validate the models by two-dimensional and three-dimensional (3-D) finite-element studies, and we perform an exhaustive parametric analysis to estimate the influence of the dimension parameters of the two structures. Finally, we present an analytical approach to a 3-D correction.

93 citations

Journal ArticleDOI
TL;DR: The present paper analyzes the impact of design parameters on the torque-speed curve of the eddy-current brake by the means of a three-dimensional finite element analysis.
Abstract: Eddy-current brakes as primary brakes in automobiles can potentially remedy the problems posed by conventional friction brakes. First, however, it will be necessary to analyze the effect of each design parameter on the performance of the eddy- current brake before designing a conceptual brake for a practical application and evaluating its behavior in real-life driving situations. In this paper, we analyze the effects of design parameters on the torque-speed curve of the eddy-current brake by the means of three-dimensional (2-D) finite-element analysis. The paper follows a previous work in which analysis was performed with a 2-D analytical model. The use of eddy-current brakes as primary brakes in automobiles has been proposed to remedy to the problems posed by conventional friction brakes. The analysis of the impact of each design parameter on the performance of the eddy-current brake is a necessary step before designing a conceptual brake for a practical application and analyzing its behavior in real-life driving situations. The present paper analyzes the impact of design parameters on the torque-speed curve of the eddy-current brake by the means of a three-dimensional finite element analysis. It follows a previously work where this analysis was performed with a two-dimensional analytical model.

83 citations


"A General Analytical Model of Perma..." refers background in this paper

  • ...The numerical approaches, however, are commonly hampered by the convergence of iteration calculation and the computational stability for high-speed cases by reason of high Peclet numbers, especially for 3-D problems [7], [8]....

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