Analysis of Cogging Torque in a Series Hybrid Variable Flux Machine for EV Using Lumped Magnetic Circuit

One of the major problems in the series hybrid variable flux machine (SVFM) is cogging torque. This article tries to compute cogging torque in a 36-slot 6-pole SVFM where the higher coercive force N48SH magnet is in series with the lower coercive force AlNiCo9 magnet. A lumped magnetic circuit for the SVFM including magnetic saturation is proposed and the analytical equations are developed to compute the air-gap flux density in an equivalent slot-less machine. The parameters of the lumped magnetic circuit are computed based on the magnetic flux lines in a slot-less machine obtained using the finite-element analysis (FEA) method. The air-gap flux density in the slot-less six-pole SVFM is calculated using the developed lumped magnetic circuit model at different magnetization levels of the AlNiCo9 magnet. The error between the analytical and FEA results of air-gap flux density is less than 4% at lower magnetization levels. Thus, the lumped magnetic circuit can be validated. The relative air-gap permeance function for the SVFM with the series magnets (N48SH and AlNiCo9) is defined. By utilizing the air-gap flux density in an equivalent slot-less machine and the relative air-gap permeance function, the cogging torque of the 36-slot 6-pole SVFM is computed and compared to the analytical and experimental results at different magnetization levels of the AlNiCo9 magnet. The results show that the computed cogging torque of the 36-slot 6-pole SVFM follows the FEA and experimental results at different magnetization levels of AlNiCo9 magnet. The back electromotive force, power factor, efficiency, and electromagnetic torque are analyzed including magnetic saturation in FEA and compared with analytically computed results at different magnetization levels of AlNiCo9 magnet.