An Investigation of Zeroth-Order Radial Magnetic Forces in Low-Speed Surface-Mounted Permanent Magnet Machines

Zeroth mode of vibration is investigated in low-speed high-torque surface-mounted permanent magnet (PM) machines with non-overlapping concentrated windings. Magnetic field distribution in the air gap is computed using time-stepping finite-element analysis, and Maxwell stress tensor is then employed to calculate the radial force density. Based on the time variation of the mean value of the radial force density spatial distribution, the zeroth-order radial forces are studied. Simple structural equations are used to compare the stator deformations for the machines under investigation. Contribution of the zeroth mode to produce vibration is analyzed and compared with the lowest non-zero mode. The influence of pole and slot combinations and the effect of rectifier load are discussed. This paper is carried out to investigate whether or not the zeroth-order radial forces can be of importance in the presented surface-mounted PM machines that are not connected to pulsewidth modulation (PWM) converters.