In this paper, a theoretical analysis of an axial magnetic coupling is presented, leading to new closed-form expressions for the magnetic axial force and torque. These expressions are obtained by using a 2-D approximation of the magnetic coupling geometry (mean radius model). The analytical method is based on the solution of Laplace's and Poisson's equations by the separation of variables method. The influence of geometrical parameters such as number of pole pairs and air-gap length is studied. Magnetic field distribution, axial force, and torque computed with the proposed 2-D analytical model are compared with those obtained from 3-D finite elements simulations and experimental results.

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Simple Analytical Expressions for the Force and Torque of Axial Magnetic Couplings

Analytical study of a quasi-zero stiffness coupling using a torsion magnetic spring with negative stiffness

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.

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Steady-State and Transient Performance of Axial-Field Eddy-Current Coupling

This paper presents some improved analytical expressions of the magnetic fleld produced by arc-shaped permanent magnets whose polarization is radial with the amperian current model. First, we show that the radial component of the magnetic fleld produced by a ring permanent magnet whose polarization is radial can be expressed in terms of elliptic integrals. Such an expression is useful for optimization purposes. We also present a semi-analytical expression of the axial component produced by the same conflguration. For this component, we discuss the terms that are di-cult to integrate analytically and compare our expression with the one established by Furlani (1). In the second part of this paper, we use the amperian current model for calculating the magnetic fleld produced by a tile permanent magnet radially magnetized. This method was in fact still employed by Furlani for calculating the magnetic fleld produced by radially polarized cylinders. We show that it is possible to obtain a fully analytical expression of the radial component based on elliptic integrals. In addition, we show that the amperian current model allows us to obtain a fully analytical expression of the azimuthal component. All the expressions determined in this paper are compared with the ones established by Furlani (1) or in previous works carried out by the authors.

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Comparison of the Coulombian and Amperian Current Models for Calculating the Magnetic Field Produced by Radially Magnetized Arc-Shaped Permanent Magnets

This paper presents three-dimensional expressions for the optimization of permanent-magnet couplings. First, we give a fully analytical expression of the azimuthal field created by one arc-shaped permanent magnet radially polarized which takes into account its magnetic pole volume density. Such an expression has a very low computational cost and is exact for all points in space. Then, we propose two semianalytical expressions of the azimuthal force and the torque exerted between two arc-shaped permanent magnets. These expressions are valid for thick or thin arc-shaped permanent magnets. Furthermore, this approach allows us to realize easily parametric studies and optimizations. The analytical approach taken in this paper, based on the Coulombian model, is a good alternative compared to the finite element method generally used to study such configurations.

/pdf/permanent-magnet-couplings-field-and-torque-three-4zaoreh9wm.pdf

Permanent Magnet Couplings: Field and Torque Three-Dimensional Expressions Based on the Coulombian Model

An analytical method adapted to calculating the forces between permanent magnets is developed, and applied to the torque calculation of synchronous couplings. The method is based on the forces exerted between two elementary barshaped magnets. The curvature effect is taken into account by a corrective coefficient, and the yokes by magnetic images. The method is relatively simple and gives accurate results which are very useful for optimization of the coupling shape. >

E. Rulliere

Papers

Analytical calculation of permanent magnet couplings