Unbalanced Magnetic Forces in Permanent-Magnet Brushless Machines With Diametrically Asymmetric Phase Windings

By Windings, Z. Q. Zhu, D. Ishak, David Howe, Jintao T. Chen. IEEE transactions on industry applications, 2005

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Effect of Pole and Slot Combination on Noise and Vibration in Permanent Magnet Synchronous Motor (2010, methodology): “As the component of total force, the radial force of PMSM can be well calculated in the Maxwell stress tensor method [5].”
Force Calculations in 3-D Cylindrical Structures Using Fourier Analysis and the Maxwell Stress Tensor (2013, methodology): “By means of these two force components, the magnetic pull between two concentric cylinders is defined [31]–[33].”
An Accurate Subdomain Model for Magnetic Field Computation in Slotted Surface-Mounted Permanent-Magnet Machines (2010, background): “The unbalanced magnetic force can be calculated by [73]:”
An Improved Subdomain Model for Predicting Magnetic Field of Surface-Mounted Permanent Magnet Machines Accounting for Tooth-Tips (2011, methodology): “The 2-D slotless analytical model received extensive applications in the permanent-magnet machines [6]–[10] for predicting electromagnetic performance [11], [12], losses [13]–[15], radial force [16], [17], and unbalanced magnetic force [18], [19] etc.”
Unbalanced Magnetic Pull Due to Asymmetry and Low-Level Static Rotor Eccentricity in Fractional-Slot Brushless Permanent-Magnet Motors With Surface-Magnet and Consequent-Pole Rotors (2010, methodology): “In [8], it was shown that the asymmetrical winding dominates the UMP and this has a vibration of which is twice the supply frequency.”