Extended Formulas to Compute Resultant and Contact Electromagnetic Force and Torque From Maxwell Stress Tensors

Bermúdez, Alfredo; Aguilar, Rodríguez; Villar, Irma

doi:10.1109/tmag.2016.2633316

Cited by 24 publications

(22 citation statements)

References 14 publications

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“…Spargo et al [103] developed a semi-numerical method to calculate the harmonic torque components based on the MST theory which provides a simple algebraic expression. Bermúdez et al [104] extended the MST method to consider the nonlinear magnetic media and local force distribution. The resultant electromagnetic force was verified well.…”

Section: Maxwell Stress Tensormentioning

confidence: 99%

Review of Electromagnetic Vibration in Electrical Machines

Han

Chu

2018

Energies

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Electrical machines are important devices that convert electric energy into mechanical work and are widely used in industry and people's life. Undesired vibrations are harmful to their safe operation. Reviews from the viewpoint of fault diagnosis have been conducted, while summaries from the perspective of dynamics is rare. This review provides systematic research outlines of this field, which can help a majority of scholars grasp the ongoing progress and conduct further investigations. This review mainly generalizes publications in the past decades about the dynamics and vibration of electrical machines. First the sources of electromagnetic vibration in electrical machines are presented, which include mechanical and electromagnetic factors. Different types of air gap eccentricity are introduced and modeled. The analytical methods and numerical methods for calculating the electromagnetic force are summarized and explained in detail. The exact subdomain analysis, magnetic equivalent circuit, Maxwell stress tensor, winding function approach, conformal mapping method, virtual work principle and finite element analysis are presented. The effects of magnetic saturation, slot and pole combination and load are discussed. Then typical characteristics of electromagnetic vibration are illustrated. Finally, the experimental studies are summarized and the authors give their thoughts about the research trends.Energies 2018, 11, 1779 2 of 33 vibration mechanism can be helpful for the design of electrical machines. Therefore, the study of the electromagnetic vibration of electrical machines has practical significance.Electromagnetic vibrations are usually generated by the distorted air-gap field of an eccentric rotor in electrical machines. The uneven air-gap is directly related to the eccentricity, which is common in rotating electrical machines. Eccentricity can be caused by several reasons, such as relative misalignment of the rotor and stator in the fixing stage, misalignment of the load axis and rotor shaft, elliptical stator inner cross section, wrong placement or rubbing of ball bearings, mechanical resonance, and unbalanced loads [1,2]. Eccentricities can be further subdivided into two categories: circumferential unequal air gaps and axial unequal air gaps. The former can be grouped into static eccentricity and dynamic eccentricity. In the case of static eccentricity, the rotor rotates around its own geometric axis, which is not the geometric axis of the stator. In the case of dynamic eccentricity, the rotor is not concentric and rotates around the geometric axis of the stator. In reality, both static eccentricity and dynamic eccentricity tend to coexist. An inherent static eccentricity exists, even in newly manufactured machines, due to the build-up of tolerances during the manufacturing and assembly procedure, as has been reported in [3]. Unequal air gaps cause unbalanced magnetic forces (UMFs) [4] on the rotor, which lead to mechanical stress on some part of the shaft and bearing. After prolonged operation, these fac...

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Section: Maxwell Stress Tensormentioning

confidence: 99%

Review of Electromagnetic Vibration in Electrical Machines

Han

Chu

2018

Energies

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“…1+t∇ sym v and r v (t, x)b 1+t/2 (rotv)×b, where ∇ sym v is the symmetrized 2-tensor (∂ i v j + ∂ j v i )/2. This amounts to neglecting terms in t 2 and higher order in the Taylor expansion of −ψ v about t = 0, which doesn't affect the result: (8) as obtained when one substitutes B(x) for b. The appearance of H there is due to the fact that H = ∂ b ψ.…”

Section: Magnetic Energy During a Virtual Motionmentioning

confidence: 99%

“…Remarkably, the result is generic: Whatever the B-H law, one has the same three terms in the expression of the magnetic force (in addition to the (rotH) × B force): An inhomogeneity term ∇ψ (generalizing the |B| 2 /2 ∇ν we had when ψ was ψ(x, s, b) = 1 / 2 ν(x)|b| 2 whatever s), a magnetostrictive term div(σ M ), and an anisotropy term − 1 / 2 rot(H × B). All of these, of course, to be interpreted as distributions, so we aim now at a Maxwell-like tensor 2 whose divergence would be the term between square brackets in (8).…”

Section: Magnetic Energy During a Virtual Motionmentioning

confidence: 99%

Bulk Forces and Interface Forces in Assemblies of Magnetized Pieces of Matter

Bossavit¹

2016

IEEE Trans. Magn.

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When two magnets are stuck together, where do magnetic forces operate and which formulas should one apply to compute them? Such frequently asked questions do not find immediate answers in the literature on forces, mainly because the force field is obtained, by the Virtual Power Principle (VPP), as a (mathematical, vector-valued) distribution, not as a plain vector field, which would be more convenient for practical computation. We intend to show, in a few important cases of contact (between two linear materials with different permeabilities, between magnet and magnetizable metal, linear or not, between two hard magnets, etc.), how to represent this single distribution by two vector fields, one of them borne by the bulk of the matter, the other one localized at material interfaces where discontinuities of permeability, of magnetization, etc., do occur. Suitable extensions of the classical Maxwell tensor play an important role in the computation (by the so-called 'pillbox trick') of this interface vector field.

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“…The information regarding the magnetic field in the air around the active materials can be obtained by calculation but has a cost. Thus the classical methods of force computation (Maxwell Stress Tensor [7], Virtual Works method [5]) are not usable (or at least not as efficient as with the FEM) and we must find specialy adapted techniques to compute the forces. First we will provide and demonstrate an expression of the magnetic co-energy (which can be used to compute the magnetic force [6]) that requires only the information of the magnetic field inside the active materials.…”

Section: Introductionmentioning

confidence: 99%

An expression of the magnetic co-energy adapted to magnetostatic volume integral formulations - application to the magnetic force computation

Debray

Meunier

Chadebec

et al. 2019

JAE

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This paper provides a new expression of the magnetic co-energy for ferromagnetic materials. This expression is very well suited to integral methods but can as well be used as a post function for the Finite Elements Method (FEM). First the context of this work and the expression of the co-energy will be introduced. Second, two examples will be treated with the proposed method and the performances will be compared with the FEM.

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Extended Formulas to Compute Resultant and Contact Electromagnetic Force and Torque From Maxwell Stress Tensors

Cited by 24 publications

References 14 publications

Review of Electromagnetic Vibration in Electrical Machines

Review of Electromagnetic Vibration in Electrical Machines

Bulk Forces and Interface Forces in Assemblies of Magnetized Pieces of Matter

An expression of the magnetic co-energy adapted to magnetostatic volume integral formulations - application to the magnetic force computation

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