Analytical Calculation of Yoke Flux Patterns in Fractional-Slot Permanent Magnet Machines

Abstract

Machine design problems are often solved under the assumption of no-load when calculating iron flux densities. However, it is particularly important to account for the fluxes from the stator currents, the armature reaction, in fractional-slot machines. The fluxes from the permanent magnets and the armature reaction both vary in time with the electrical frequency. By studying the flux that flows along the stator yoke behind every slot in such a machine, it is revealed that the armature reaction flux does not have the same amplitude behind all slots. In addition, it is revealed that the time-varying no-load and armature reaction fluxes are shifted in time, with different phase shifts behind different slots. The sum of the no-load and armature reaction fluxes, namely, the load flux, depends on both the amplitudes of the fluxes and the phase shift between them. The resulting load flux behind each slot varies significantly. In four investigated machines, the ratio of the highest to the lowest load flux amplitude ranges between 1.6 and 6. The load flux can be significantly higher than the no-load flux. The flux calculations are verified through finite-element analysis in all four machines, and the error in the maximum load flux ranges between 2% and 6%.

No-load iron loss model for a fractional-slot surface-mounted permanent magnet motor based on magnetic field analytical calculation

“…(10) can be obtained by discrete Fourier transform(DFT). Then the magnetic field in the slotted air gap can be expressed according to (5).…”

“…However, the analytical model is not compared with the FEM. The other way is to build the equivalent magnetic circuit of the motor and obtain the magnetic flux density of each node in the stator core directly [4][5] . Reference [4] built an equivalent magnetic circuit of the interior permanent magnet synchronous machine.…”

“…Because of the irregular shape of the stator yoke, the magnetic field of the yoke is not introduced. An armature reaction magnetic circuit was built in reference [5]. The study showed that the amplitude of the load flux density of the stator yoke is different due to the winding configuration of the fractional-slot motor.…”

Comparison between 2‐D and 0‐D analytical models for slotless double‐sided inner armature linear permanent magnet synchronous machines

“…Although FEM is accurate and is used for complex geometries with nonlinear characteristics, it has a high computational burden compared to that of analytical methods. 7,8 Therefore, for optimization problems especially with too many iterations, analytical methods are the preferred option.…”

Influence of Stator Topologies on Average Torque and Torque Ripple of Fractional-Slot SPM Machines With Fully Closed Slots

“…Although the authors [18] analyzed both aspects, only single 3-phase all teeth wound winding was shown. The influence of saturation caused by subharmonic was also stressed in [19], whereas only vibration was emphasized. Most of the above papers focused on machines with slot openings and quite a few researchers have investigated the influence of slot opening on torque performances [20]- [22].…”