Injected Rotor Shape for Five - Phase Surface - Mounted Permanent Magnet

I . Introduction Multi-phase machines offer several key features, such as high reliability, high torque density, and high efficiency . Therefore, they are obtained wide applications from automotive to aerospace [1][2] . One of them is the five-phase PM machine, where the torque density can be improved by injecting third harmonic current . However, in order to maintain high torque density and remain low torque ripple, the shaping methods utilizing 3rd harmonic is commonly employed [3]-[8] . The sinusoidal together with the 3rd harmonic shaping method is proposed to achieve higher fundamental EMFs than the conventional sinusoidal shaping method [3] . The optimal 3rd harmonic into the magnet shape is analytically derived [4] [5] and applied both interior PM (IPM) machines and linear PM machines [6] [7] . Alternatively, in multiphase machines, the 5th harmonic current can be eliminated in line-line back-EMF and cannot result in torque ripple . Similarly, it can be employed to improve the fundamental and 3rd harmonic airgap flux density, resulting in further torque improvement . This paper will investigate a five-phase SPM machine with harmonics injected magnets and the amount of increased torque with associated harmonics will also be discussed . Compared to the machine with conventional sinusoidal and sinusoidal with 3rd harmonic shaped PM magnets, the average torque is increased since the space for PM is fully utilized, whilst the torque ripple can be maintained significantly low, resulting in both high torque density and low torque ripple . The FEA predicted back-EMF, cogging torque, torque-current characteristic are validated by experiments on the prototype machines . II .SPM Machines with Various PM Shapes The 10-slot/8-pole SPM machine with double-layer non-overlapping winding is employed to investigate the impact of harmonics injection on the torque improvement . Fig . 1 (a) shows the stator together with the winding connections used for all the machines, whilst the rotors with different harmonics injected PM shapes are shown in Fig . 1 (b), (c), (d), and (e), respectively . These rotors are designated as the conventional rotor, Sine rotor, Sine+3rd rotor, and Sine+3rd+5th rotor, to capture the key injected harmonics features . Approximate sinusoidal or sinusoidal with specific harmonics airgap flux density distributions can be achieved by sinusoidally shaping or sinusoidally with harmonics shaping the PMs, respectively, as shown in Fig . 1 (f), (g), and (h) . Fig . 1 (f) shows the variation of PM thickness with the rotor positions θ . The maximum thickness of the arc magnet is constant . All of them are functions of rotor position θ . nhm(θ)=nmab[sin(pθ)+asin(3pθ)+bsin(5pθ)] (1) where, a, and b are the parameters to be determined . a and b are the amplitude of injected 3rd and 5th harmonic, while varies with the value of injected 3rd and 5th harmonic in order to maintain the same maximum magnet thickness . It can be theoretically predicted that the optimal a and b are 1/6 and 0 .019 and this will be given in the full paper . The P1 in the PM contour increases from (Sine shaped) to 1 .15 (Sine+3rd shaped) and 1 .17 (Sine+3rd+5th shaped), as shown in Fig . 1 (f), (g), and (h) . Correspondingly, the torque can be improved as the harmonics injected . Meanwhile, the additional 3rd harmonic airgap flux density can also be used for torque production in five-phase machines . In order to compensate inter-pole flux leakage and curvature effect, PM edge thickness ∆t is introduced and is optimized for achieving nearly sinusoidal and sinusoidal with harmonics airgap flux density distribution . Then, the magnet thickness with such compensation is given by: hm(θ)=nt+nhm(θ) (2) The maximum thickness of the magnet is kept to be constant, 3mm . Hence, Δm will be varied with Δt . Fig . 2 shows the variation of torque with rotor position for the four machines where the supplied phase currents with and without 3rd harmonic current injection are in phase with its phase backEMFs . It shows that the conventional rotor SPM machine supplied with Sine+3rd current has the highest average torque but Sine shaped rotor SPM machine has the lowest average torque . The average torque for Sine+3rd+5th shaped rotor SPM machine has been improved by >17% compared with that of Sine shaped rotor SPM machine . Meanwhile, the torque ripples of Sine shaped, Sine+3rd, Sine+3rd+5th shaped machines are similar, but lower than that of the conventional rotor SPM machine . Low harmonics in the back-EMF together with low cogging torque result in low torque ripple . Most importantly, the average torque has been improved . The detail analysis will be given in the full paper .