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.

The Maxwell Tensor (MT) method is widely used to compute global forces or local surface forces for vibroacoustic design of electrical machines under electromagnetic excitation. In particular the air-gap Maxwell Tensor method is based on a cylindrical shell in the middle of the air-gap. This paper proposes to quantify the differences between the air-gap MT and the magnetic force wave experienced by the stator. In particular the air-gap to stator transfer and the tooth mechanical modulation effects are studied. A new formula is proposed to extend the tooth modulation effect to tangential forces. A numerical application is performed with a turbo-alternator to illustrate the respective and combined effects of both phenomena. The paper highlights that the tooth mechanical modulation is relevant even for electrical machines with a high number of teeth. Additionally the combination of the two phenomena has a clear impact on the calculated surface force. Therefore, it is recommended to take into account the air-gap transfer for any study of the tooth mechanical modulation effect.