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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 or with the semi-analytical subdomain method (SDM). First, 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 2-D. The link between the slot's magnetic flux and the tangential force harmonics is also highlighted. The comparison is performed on the stator of a surface-mounted permanent-magnet synchronous machine. 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 the SDM remains accurate with MT in the air gap even with saturation for design and diagnostic of electromagnetic noise in electrical machines. However, for more accurate studies based on the local magnetic pressure, the VWP is strongly recommended.
Pile et al. (Wed,) studied this question.