Effects of Loading and Slot Harmonic on Radial Magnetic Forces in Low-Speed Permanent Magnet Machine With Concentrated Windings

This paper investigates the effects of loading and slot harmonic on radial magnetic forces in a low-speed permanent magnet (PM) machine with non-overlapping concentrated windings. Vibration level of the PM machines with concentrated windings can be potentially higher compared with that of the traditional machines with distributed windings. It is mainly due to the presence of low-order spatial harmonics in radial force density distribution. In this paper, magnetic flux density distribution in the air-gap of a 120-slot/116-pole machine is computed using finite-element method. Maxwell's stress tensor method is then employed to calculate radial and tangential forces in the air-gap. Flux density and radial and tangential force distributions are studied in different loading conditions and the effect of d-and q-axis currents are investigated. It is shown how the lowest mode of vibration is produced by different harmonic pairs in the flux density. It is found that d-axis current significantly changes the amplitude of the lowest spatial harmonic of the radial force distribution and consequently the vibration behavior. The main reason is found to be the changes in the amplitude of the slot harmonic, which is heavily affected by loading. Experimental tests are carried out to compare the vibration level of a PM generator supplying resistive, inductive, and capacitive loads. There is a good agreement between simulations and experimental results.