Application Limits of the Airgap Maxwell Tensor

Airgap Maxwell tensor is widely used in numerical simulations to accurately compute global magnetic forces and torque but also to estimate magnetic surface force waves, for instance when evaluating magnetic stress harmonics responsible for electromagnetic vibrations and acoustic noise in electrical machines. This article shows that airgap surface forces based on Maxwell tensor with a circular contour depend on the radius of application. The dependence of surface forces on radius is analytically explained using an academic case of a slotless electric machine. The corrective coefficients that should be applied to transfer the airgap surface forces to stator (or rotor) bore radius are presented. The coefficients depend on the airgap geometry and surface forces wavenumber. The use of transfer coefficients is recommended to quantify the deviation due to the radius of application in the airgap. In addition, the transfer coefficients could be applied to correct the radial surface force component on the tip of the teeth assuming infinite permeability.