[Open Physics] Analytical Study of Air-Gap Surface Force – Application to Electrical Machines


AuthorsRaphaël Pile; Jean Le Besnerais; Guillaume Parent; Yvonnick Le Menach; Emile Devillers; Thomas Henneron; Jean-Philippe Lecointe
KeywordsMaxwell Tensor, Magnetic pressure, Electrical machines, Magneto-mechanical, Vibration, Magnetic forces; Noise and vibration; Air gaps


The Maxwell stress tensor (MST) method is commonly used to accurately compute the global efforts, such as electromagnetic torque ripple and unbalanced electromagnetic forces in electrical machines. The MST has been extended to the estimation of local magnetic surface force for the vibroacoustic design of electrical machines under electromagnetic excitation. In particular, one common air-gap surface force (AGSF) method based on MST is to compute magnetic surface forces on a cylindrical shell in the air gap. However, the AGSF distribution depends on the radius of the cylindrical shell. The main contribution of this study is to demonstrate an analytic transfer law of the AGSF between the air gap and the stator bore radius. It allows us to quantify the error between the magnetic surface force calculated in the middle of the air gap and the magnetic force computed on the stator teeth. This study shows the strong influence of the transfer law on the computed tangential surface force distribution through numerical applications with induction and synchronous electrical machines. Finally, the surface force density at stator bore radius is more accurately estimated when applying the new transfer law on the AGSF.


The published version is available in open-access here.

The article pre-print can be found here: