[IEEE Trans. on Mag.] Comparison of main magnetic force computation methods for noise and vibration assessment in electrical machines

AuthorsRaphaël Pile; Emile Devillers; Jean Le Besnerais
StatusPublished in: IEEE Transactions on Magnetics ( Volume: 54, Issue: 7, July 2018 )
KeywordsElectromagnetic forces, Maxwell Tensor, Virtual Work Principle, Semi-analytical, Finite Element analysis, Electrical Machines, Electromagnetic noise


This paper presents a comparison of several methods to compute the magnetic forces experienced by the stator teeth of electrical machines. In particular, the comparison focuses on the Virtual Work Principle (VWP) based nodal forces and the Maxwell Tensor (MT) applied on different surfaces. The VWP is set as the reference. The magnetic field is computed either with Finite Element Analysis (FEA) or with the semi-analytical Subdomain Method (SDM). Firstly, the magnetic saturation in iron cores is neglected (linear B-H curve). Then, the saturation effect is discussed in a second part. Homogeneous media are considered and all simulations are performed in 2D. The link between slot’s magnetic flux and tangential force harmonics is also highlighted. The comparison is performed on the stator of a Surface-Mounted Permanent Magnet Synchronous Machine (SPMSM). While the different methods disagree on the local distribution of the magnetic forces at the stator surface, they give similar results concerning the integrated forces per tooth, referred as Lumped Forces. This conclusion is mitigated for saturated cases: the time harmonics are correctly computed with any of the presented Lumped Force methods but the amplitude of each harmonic is different between methods. Nonetheless, the use of semi-analytical Subdomain Method remains accurate with Maxwell Tensor in the air-gap even with saturation for design and diagnostic of electromagnetic noise in electrical machines. However, for more accurate studies based on local magnetic pressure, the Virtual Work Principle is strongly recommended.

Preprint and full paper

The preprint can be found here:

Comparison of main magnetic force computation methods for noise and vibration assessment in electrical machines

The published version can be found on IEEE Xplore.


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