Calculating the External Magnetic Field From Permanent Magnets in Permanent-Magnet Motors—An Alternative Method

Abstract-This paper presents an analytical method based on the coulombian model of a magnet for studying a ferrofluid seal in ironless electrodynamic loudspeakers. Such an approach differs from the ones generally used for studying such geometries because the ferrofluid used is submitted to a magnetic field greater than 1 T which saturates the ferrofluid. Consequently, its shape and its mechanical properties depend mainly on the magnetic field produced by the permanent magnets that constitute the ironless structure. The motor is constituted of outer stacked ring permanent magnets and the inner moving part is a piston. In addition, one ferrofluid seal is used for centering the moving part and ensuring the airtightness between the loudspeaker faces. The ferrofluid seal also exerts a pull back force on the moving piston. It is noted that this force depends on the lateral shape of the moving piston. Therefore, the piston profile is analytically studied in this paper. A peculiar attention is given to profiles that ensure the axial pull back force to be proportional to the piston displacement. Furthermore, a geometrical method is presented to design the shape of the ferrofluid seal according to the chosen piston profile. It can be noted that such a profile is elliptical in this study. Then, the magnetic energy of the ferrofluid seal is determined with the analytical expression of the magnetic energy density. Such an expression allows us to calculate the axial force created by the ferrofluid seal for a given profile.

“…Consequently, the integration limits are not constant but depend on the altitude z. The lower limit r(z) verifies (15).…”

Section: Energy Of the Ferrofluid Sealmentioning

confidence: 81%

“…Then, as ferrofluids have been improved, more and more engineering applications have been developed [8]. On the other hand, three-dimensional approaches for calculating the magnetic field produced by permanent magnets have been proposed [9][10][11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

Design of Ironless Loudspeakers With Ferrofluid Seals: Analytical Study Based on the Coulombian Model

Ravaud¹,

Lemarquand²

2009

“…Analytical approach is faster investigation method as compared to the latter ones for the parametric study. The analytical equations for determining the magnetic field [9][10][11][12][13][14], force and stiffness [15][16][17][18][19][20][21][22] in bearings with axial, radial and perpendicular polarizations are presented by the many researchers recently. However in these works, the ring magnets are concentric, which might not be prevailing in actual scenario.…”

Section: Introductionmentioning

confidence: 99%

Analysis of Radial Magnetized Permanent Magnet Bearing Characteristics

Bekinal¹,

Anil²,

Jana³

2013

Abstract-With an increase in the number of high speed applications, researchers have been concentrating on permanent magnet bearings due to their suitability. This paper presents a mathematical model of a permanent magnet bearing made of ring magnets with radial polarizations. Coulombian model and vector approach are used to estimate the force, moment and stiffness. A MATLAB code is developed for evaluating the envisaged parameters for three degrees (translational) of freedom of the rotor. Comparison of force and stiffness results of the presented model with that reported in the literature and also with the results of 3D finite element analysis shows good agreement. Then, it is extended to analyse stacked ring magnets with alternate radial polarizations. Finally, the cross coupled stiffness values in addition to the principal stiffness values are presented for the elementary structure and also for stacked structure with three ring permanent magnets with alternate radial polarizations.

“…Besides, this wall can be either a plane or a cylinder and so the airgap type determines two couplings families. Moreover, the study of magnetic couplings relies on the analytical expressions of the magnetic field created by permanent magnets of various shapes [12][13][14][15][16], and especially parallelepipeds [17,18], tiles [19][20][21][22], rings [23,24] and cylinders [25,26]. The first analytical formulations for the forces between cuboidal magnets was given by Akoun and Yonnet [27].…”

Section: Introductionmentioning

confidence: 99%

Magnetic Couplings With Cylindrical and Plane Air Gaps: Influence of the Magnet Polarization Direction.

Ravaud¹,

Lemarquand²

2009

Abstract-This paper presents a comparison of cylindrical and plane air gap magnetic couplings in which the tile permanent magnet polarizations can be either radial or tangential or axial.The expressions of the torque transmitted between the two rotors of each coupling are determined by using the colombian approach. All the calculations are performed without any simplifying assumptions. Consequently, the expressions obtained are accurate and enable a fast comparison between the structures presented in this paper.