Closed Analytical Formulae for Multi-Pole Magnetic Rings

Ausserlechner, Udo

doi:10.2528/pierb11112606

Cited by 16 publications

(20 citation statements)

References 36 publications

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“…Yet in the sequel we need a closed summation formula to study the influence of p on the torque. Therefore we assume that the driving disc has infinite outer diameter, which allows for closed summation over all p pole pairs as shown in Section 6 of [1]. Of course this simplified model over-estimates the magnetic field and the torque.…”

Section: Definitionsmentioning

confidence: 99%

“…Before the torque can be computed one has to compute the magnetic field generated by one of the two discs. This can be done in numerous ways [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. In the majority of these publications the contributions of all segments are summed up numerically.…”

Section: Introductionmentioning

confidence: 99%

“…In the majority of these publications the contributions of all segments are summed up numerically. Only [1,9,11,12] present formulae where the summation was done in closed form. The torque computation means integrating over the force density of these fields.…”

Section: Introductionmentioning

confidence: 99%

“…This work is based on [1], where closed analytical formulae for the magnetic field components of axially magnetized multi-pole discs and rings are given. There also the torque of axial magnetic couplings is studied in the limit of infinitely thin discs.…”

Section: Introductionmentioning

confidence: 99%

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The Maximum Torque of Synchronous Axial Permanent Magnetic Couplings

Ausserlechner¹

2012

PIER B

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Abstract-Axial permanent magnetic couplings are composed of two discs with a small air-gap in-between. Each disc consists of several segments in the shape of slices of cakes. The segments are polarized in axial direction with alternating polarity. In this work the homogeneous magnetization in the segments is replaced by equivalent currents on the surface of the segments (Amperean model). In a simplified model we consider only radial currents whereas azimuthal currents along the perimeter of the discs are discarded. This corresponds to the arrangement where one of the discs has much larger diameter than the other disc. Compared to the case of two equal discs it leads to a notable error in the magnetic field near the perimeter, yet it has only a small effect on the torque, especially for the case of optimum couplings. This trick allows for summing up the fields of all segments in closed form. A concise double integral over the radial magnetic field component describes the torque. An investigation of this integral reveals many properties of axial magnetic couplings: A diagram is introduced and areas in this diagram are identified where the torque shows overshoot, rectangular pulse shape or sinusoidal dependence versus twist angle between both discs. The diagram contains also a curve for maximum torque and one point on this curve is of considerable economic significance: It denotes the global maximum of torque over magnet mass.

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Section: Definitionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The Maximum Torque of Synchronous Axial Permanent Magnetic Couplings

Ausserlechner¹

2012

PIER B

Self Cite

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“…A new geometry with a V section, defined by an angle α is proposed, with arbitrary generic magnetisation directions on the inner and outer elements (Figure 1). Such a geometry may offer advantageous configurations with respect to the most common passive bearing solutions limited to rectangular/annular shapes with axial and radial magnetisations [7][8][9][10][11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

Permanent Magnet Bearings: Analysis of Plane and Axisymmetric v-Shaped Element Design

Puccio¹,

Bassani²,

Ciulli³

et al. 2012

PIER M

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Abstract-Applications of permanent magnets bearings have gained a new interest thanks to the development of rare earth materials, characterised by residual magnetic induction greater than 1 T. The present paper proposes a new geometry for permanent magnets bearings with V-shaped elements, both for a plane slide and for cylindrical bearings. The aim of this geometry is to give new possibilities to the application of these bearing systems, by reducing its inherent instability. A design method, involving Finite Elements and Magnetic Field Integral Equations analyses, is also described for defining the most suitable V-opening angle and the two magnetisation directions. These parameters can be varied in order to reduce the unstable force in the coupling, and to reach the desired force and stiffness in the stable direction. The design is founded on the evaluation of four "geometric" vectors, that depend on the geometry of the elements. Some results are reported for a reference geometry for both the slide and the cylindrical bearings.

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The Magnetic Field from Cylindrical Arc Coils and Magnets: A Compendium with New Analytic Solutions for Radial Magnetization and Azimuthal Current

Forbes,

Robertson,

Zander

et al. 2024

Advanced Physics Research

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This study provides analytic solutions for the magnetic field of coils and magnets that have a non‐axisymmetric cylindrical geometry with a rectangular cross‐section. New analytic solutions are provided for radially magnetized permanent magnet arcs, thin coil disc sectors, and thick coil sectors. If components of the 3D field are not representable in closed‐form or as canonical Legendre elliptic integrals, the exact solution is given in terms of a series of regularized beta functions. The limit and hence spatial convergence is found to these series, giving a well‐defined and fast solving algorithm for computation. The equations can be readily applied to find the magnetostatic field in linear or non‐linear systems that contain a large set of elements. Example applications are provided to demonstrate how the field can be used to calculate forces and benchmark computational efficiency of the equations. A thorough review of the preceding literature and background theory is provided before a detailed methodology obtaining the analytic solutions contained in this compendium, and further related geometries in cylindrical or spherical coordinates. This is the first study to comprehensively solve the field equations for this collection of electromagnetic geometries.

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Closed Analytical Formulae for Multi-Pole Magnetic Rings

Cited by 16 publications

References 36 publications

The Maximum Torque of Synchronous Axial Permanent Magnetic Couplings

The Maximum Torque of Synchronous Axial Permanent Magnetic Couplings

Permanent Magnet Bearings: Analysis of Plane and Axisymmetric v-Shaped Element Design

The Magnetic Field from Cylindrical Arc Coils and Magnets: A Compendium with New Analytic Solutions for Radial Magnetization and Azimuthal Current

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