An overview of analytical methods for magnetic field computation

Curti, Mitrofan; Paulides, Jjh Johannes; Lomonova, E. A.

doi:10.1109/ever.2015.7112938

Cited by 35 publications

(26 citation statements)

References 17 publications

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“…To model magnetic fields, a basic way is to calculate and integrate the magnetic flux density produced by each charge or small segment of currents. However, boundary conditions are not considered in this method [20]. In real machines, boundaries exist and the magnetic field is the result of PMs, changing electric fields and magnetized ferrimagnets.…”

Section: Magnetic Field Modelingmentioning

confidence: 99%

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Analytical Field and Torque Analysis of a Reaction Sphere

2018

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In recent years, the increasing need in small satellite solutions triggers the miniaturization of attitude control systems. Reaction spheres were proposed as promising replacements of conventional reaction wheels for their 4π rotations. Since the generated control torques could be about any desired axes, a single reaction sphere is sufficient for three-axis stabilizations of spacecraft. This paper presents an innovative design of reaction spheres. Its driving unit is a combination of permanent magnets (PMs) and electromagnetic induction. This enables the generation of torques about three principle axes simultaneously. Meanwhile, a contactless bearing is integrated into the actuator design. Detailed designs and working principles of the reaction sphere are described. To investigate performance characteristics of the actuator, field modeling is of great importance and provides the basis for dynamics modeling. In this paper, an improved analytical model for dynamic fields excited by slotless distributed windings is presented for the first time. To study the cross coupling between PMs and electromagnetic induction, the static field generated by PMs is also modeled analytically. These developed models are validated through comparisons with numerical simulations. Electromagnetic torques generated by the actuator are calculated through the approaches of the Maxwell stress tensor and the Lorentz force law. Torque calculations based on the analytical field models deviate from those based on the numerical model slightly, with the maximum error within 4%. This means the presented analytical models allow to predict the electromagnetic field distribution and torques precisely.

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Section: Magnetic Field Modelingmentioning

confidence: 99%

“…Unknowns in the general solutions can be solved by boundary conditions. Alternatively, mapping methods such as the Schwarz-Christoffel transformation and magnetic equivalent circuit [22] can be useful but are limited to special cases [20].…”

Section: Magnetic Field Modelingmentioning

confidence: 99%

Analytical Field and Torque Analysis of a Reaction Sphere

2018

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“…Although there are a lot of papers in this area, the modeling approach is still a challenging and attractive research topic. Some comprehensive reviews on the models of electrical machines for magnetic field calculations can be found in [1][2][3][4][5][6], and their references, with their (dis)advantages. The modeling techniques can thus be classified in various categories:…”

Section: Context Of This Papermentioning

confidence: 99%

New Scientific Contribution on the 2-D Subdomain Technique in Cartesian Coordinates: Taking into Account of Iron Parts

Dubas¹,

Boughrara²

2016

Preprint

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The most significant assumptions in the subdomain technique (i.e., based on the formal resolution of Maxwell's equations applied in subdomain) is defined by: "The iron parts (i.e., the teeth and the back-iron) are considered to be infinitely permeable, i.e., µ iron → +∞, so that the saturation effect is neglected". In this paper, the author presents a new scientific contribution on improving of this method in two-dimensional (2-D) and in Cartesian coordinates by focusing on the consideration of iron. The subdomains connection is carried out in the two directions (i.e., xand y-edges). The improvement was performed by solving magnetostatic Maxwell's equations for an air-or iron-core coil supplied by a direct current. To evaluate the efficacy of the proposed technique, the magnetic flux density distributions have been compared with those obtained by the 2-D finite-element analysis (FEA). The semi-analytical results are in quite satisfying agreement with those obtained by the 2-D FEA, considering both amplitude and waveform.3 of 37 has been applied to surface-mounted/-inset magnets machines [32][33][34][35], surface-inset magnet machines [33], and others electrical machines.-Concept wave impedance: They are based on a direct solution of Maxwell's field equations in homogeneous multi-layers of magnetic material properties, viz., the magnetic permeability and the electrical conductivity. This approach, developed by Mishkin (1953) [36], was first applied to squirrel-cage induction machine in Cartesian coordinates with three-layers (i.e., stator slotting, air-gap, and rotor slotting). It was used and enhanced by many authors, viz., * simplification of the electromagnetic theory [37]; * extended with an infinite number of layers [38]; * converted into equivalent circuits and terminal impedance [39]; * included the curvature effect with the magnetizing current [40]; * incorporated spatial harmonics in the multi-layers theory by considering isotropic and anisotropic (e.g., laminated, composite, and toothed) regions [41,42]; * introduced the nonlinear B(H) curve in homogenous layers by an iterative procedure [43,44]; * taking account of the effect of slot openings [45], i.e., the multi-layers model is combined with the subdomain technique for slotted structures by assuming infinitely permeable tooth tips; * included the current penetration effect in conductive layers [43,46]. The analytical solution for the electromagnetic field in conductive layers is then defined by Bessel functions.

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“…Although there are many papers in this scientific domain, the modeling approach is still a challenging and attractive research topic. Some comprehensive reviews on the models of electrical machines for magnetic field calculations along with their advantages and disadvantages can be found in [1][2][3][4][5][6] and the accompanying references. The modeling techniques can thus be classified in various categories:…”

Section: Context Of This Papermentioning

confidence: 99%

New Scientiﬁc Contribution on the 2-D Subdomain Technique in Cartesian Coordinates: Taking into Account of Iron Parts

Dubas

Boughrara

2017

MCA

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Abstract:The most significant assumptions in the subdomain technique (i.e., based on the formal resolution of Maxwell's equations applied in subdomain) is defined by: The iron parts (i.e., the teeth and the back-iron are considered to be infinitely permeable, i.e., µ iron → +∞, so that the saturation effect is neglected. In this paper, the authors present a new scientific contribution on improving of this method in two-dimensional (2-D) and in Cartesian coordinates by focusing on the consideration of iron. The subdomains connection is carried out in the two directions (i.e., x-and y-edges). For example, the improvement was performed by solving magnetostatic Maxwell's equations for an air-or iron-cored coil supplied by a direct current. To evaluate the efficacy of the proposed technique, the magnetic flux density distributions have been compared with those obtained by the 2-D finite-element analysis (FEA). The semi-analytical results are in quite satisfying agreement with those obtained by the 2-D FEA, considering both amplitude and waveform.

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An overview of analytical methods for magnetic field computation

Cited by 35 publications

References 17 publications

Analytical Field and Torque Analysis of a Reaction Sphere

Analytical Field and Torque Analysis of a Reaction Sphere

New Scientific Contribution on the 2-D Subdomain Technique in Cartesian Coordinates: Taking into Account of Iron Parts

New Scientiﬁc Contribution on the 2-D Subdomain Technique in Cartesian Coordinates: Taking into Account of Iron Parts

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