K. Wang

Torque Enhancement of Surface-Mounted Permanent Magnet Machine Using Third-Order Harmonic

This work presents a permanent magnet (PM) shaping technique with optimal third harmonic to improve the output torque without deteriorating the torque ripple in surface-mounted PM (SPM) machines. The optimal value of third harmonic injected into the sinusoidal PM shape for maximum torque improvement is analytically derived and confirmed by finite-element analysis. Further, the influence of magnet edge thickness on the airgap field distribution is investigated and utilized to compensate the inter-pole flux leakage and curvature effect. It is found that the optimal third harmonic is 1/6 of the fundamental one. For the SPM machines having rotors without shaping, Sine shaping, Sine shaping with third harmonic injected, the electromagnetic performance, including the back-EMF waveforms, cogging torque, average torque, and torque ripple are compared. It is demonstrated that the average torque in the machine of a Sine shaping with an optimal third harmonic injected can be improved by >9%, while the torque ripple remains similar to that of the one with Sine shaping. Finally, the machines with both conventional (without shaping) and optimal third harmonic PM rotors are prototyped and measured to validate the analyses.

Average Torque Improvement of Interior Permanent-Magnet Machine Using Third Harmonic in Rotor Shape

A rotor shaping technique with optimal third harmonic is presented to enhance the average torque of interior permanent-magnet (IPM) machines in this paper. The optimal value of third harmonic injected into the rotor outer surface shape has been derived and further confirmed by both finite-element analyses and experiments. The impact of the optimal third harmonic to the rotor shape on the electromagnetic performance, including harmonics in the back electromotive forces, cogging torque, average torque, and torque ripple, is investigated. It is demonstrated that without any modification of the costly rare earth permanent magnet employed for the inverse-cosine-shaped rotor, the average torque of the machine of an inverse cosine injected with an optimal third-harmonic-shaped rotor can be improved by 6%. Simultaneously, the torque ripple remains almost unchanged, and the saliency ratio is also improved, further boosting the average torque. Finally, the machines with both conventional and optimal third harmonic rotors are prototyped and tested to validate the analysis.

Optimal slot/pole and flux-barrier layer number combinations for synchronous reluctance machines

AC synchronous reluctance machine (SynRM) or permanent magnet assisted synchronous reluctance machine presently receives a great deal of interest, since there is less or even no rare earth permanent magnet in the rotor. Most of SynRM machines employ a stator that is originally designed for a standard squirrel cage induction motor for a similar output rating and application, or the SynRM machine with 24-slot, 4-pole are often directly chosen for investigation in most of the available literature. Therefore, it is necessary to investigate the influence of stator and rotor pole number combinations together with the flux-barrier layers number on the performance of SynRM machine with emphasis on output torque capability and torque ripple. In order to investigate the impact of slot/pole number combinations on performance of SynRM machine, the same ratio of rotor insulation width to the rotor iron width has been used for all the slot and pole number combinations machines. In addition, the effect of flux-barrier layer number of this machine on average torque and torque ripple has also been investigated.

Torque Improvement of Five-Phase Surface-Mounted Permanent Magnet Machine Using Third-Order Harmonic

Summary form only given. This paper presents optimal third harmonics in both permanent magnet (PM) shaping and current waveform to improve the output torque of five-phase surface-mounted PM (SPM) machines. The optimal value of third harmonic injected into the sinusoidal PM shape and current waveform for maximum torque improvement is analytically derived and validated by both finite element (FE) analyses and experiments. It is found that the optimal third harmonic is 1/6 of the fundamental one for both PM shape and current waveform. For the five-phase SPM machines having rotors without shaping, Sine shaping, or Sine shaping with third harmonic injected, the electromagnetic performance including the back EMF waveform, cogging torque, average torque, torque ripple, copper loss, iron loss, impact on power inverter, and demagnetization withstand capability are compared. It is demonstrated that, although the copper loss and iron loss increase due to additional third harmonic in the winding current and magnet shape, the average torque with optimal third harmonics injected in PM shaping and current waveform can be improved by >30% while the torque ripple and remains similar to that of the one with Sine shaping. In addition, this will reduce the dc bus voltage while maintaining the machine torque density. Furthermore, the machine with Sine and Sine+3rd rotors presents much better demagnetization withstand capability performance than conventional rotor.

Electromagnetic Performance of an 18-Slot/10-Pole Fractional-Slot Surface-Mounted Permanent-Magnet Machine

This paper investigates the electromagnetic performance of an 18-slot/10-pole fractional-slot surface-mounted permanent-magnet (SPM) machine and compares its performance with conventional fractional-slot 9-slot/10-pole, 12-slot/10-pole, and integer-slot 30-slot/10-pole SPM machines by 2-D finite-element (FE) analysis (FEA). The winding factors of the 18-slot/10-pole machine are first analyzed, and then its back electromagnetic force, average torque, cogging torque, and torque ripple are investigated. In addition, the influence of stator current excitation on the average torque and torque ripple, the impact of end windings on the average torque, the flux-weakening capability, the fault-tolerant capability, the magnet loss, and the mutual coupling between phases are also studied by 2-D FEA. The results show that the torque ripple can be suppressed in the 18-slot/10-pole SPM machine, whereas the average torque can be improved compared with the 12-slot/10-pole SPM machine. The unbalanced magnetic force in the 9-slot/10-pole SPM machine can be eliminated. Although the flux-weakening and fault-tolerant capabilities are reduced compared with the conventional 9-slot/10-pole and 12-slot/10-pole machine, the mutual coupling between phases can be eliminated. The magnet loss is slightly higher than that of a 30-slot/10-pole machine but significantly lower than those in both 9-slot/10-pole and 12-slot/10-pole machines. Finally, the experimental results are given for validation of theoretical analyses and FE results.

Synthesis of High Performance Fractional-Slot Permanent-Magnet Machines With Coil-Pitch of Two Slot-Pitches

This paper presents feasible slot/pole number combinations of machines with two slot-pitches. They are becoming popular since they not only exhibit the low torque ripple but also the low harmonic content of the magnetomotive force. Some examples of such windings are reported in the literature, but they are limited to a specific slot/pole combination. On the contrary, a general theory is presented in this paper. The main rules for the design of such windings are illustrated and the relationship of slot (Ns) and pole (2p) number, and winding topologies for machines with two slot-pitches is derived. Then, the average torque, torque ripple, eddy current magnet loss, and saliency ratio of machines with slot/pole combinations Ns = 2(2p ± 1) and Ns = 2(2p ± 2) are investigated by the finite-element method and compared with the conventional one. The Ns = 2(2p ± 1) machines have the high average torque and the low-torque ripple compared with Ns = 2(2p ± 2) machines. In addition, the eddy current magnet losses for both machines are limited, and the saliency ratio of the interior permanent magnet (IPM) machine is improved compared with the conventional slot/pole number combinations. Finally, the experimental results on surface-mounted permanent magnet and IPM machines are given for validation of theoretical analyses and finite element (FE) results.

Torque ripple reduction of synchronous reluctance machines: using asymmetric flux-barrier

Purpose – The purpose of this paper is to reduce the torque ripple but not to decrease the average torque of synchronous reluctance machines by using one step or more than two axially laminated rotors with asymmetric flux-barrier. Design/methodology/approach – A 24-slot four-pole synchronous reluctance machine with overlapping windings and asymmetric flux-barrier in the rotor is, first, described and designed by finite element (FE) method for maximizing average torque. The dimensions of asymmetric flux-barrier including the pole span angle and flux-barrier angle will be optimized to minimize the torque ripple and its influence on the average torque is also investigated by FE analysis. The impact of current angle on the average torque and torque ripple are also analysed. The step laminations together with the asymmetric flux-barrier are employed for further torque ripple reduction which can consider the both rotation directions. Findings – The torque ripple of synchronous reluctance machine can be signific...

Design and experimental verification of an 18-slot/10-pole fractional-slot surface-mounted permanent-magnet machine

This paper investigates the torque characteristics of an 18-slot/10-pole fractional-slot surface-mounted permanent-magnet (SPM) machine and presents its comparison with conventional 9-slot/10-pole and 12-slot/10-pole SPM machines by analytical and two-dimensional (2-D) finite element analysis (FEA). The winding factors of the 18-slot/10pole machine are firstly analyzed, and then, its back-EMF, average torque, cogging torque, and torque ripple are investigated. In addition, the influence of magnetic saturation due to stator current excitation on the average torque and torque ripple is also studied by 2-D FEA. The results show that the torque ripple can be suppressed while the average torque can be improved in the 18-slot/10-pole SPM machine compared with the 12-slot/10-pole SPM machine, while the unbalanced magnetic force in the 9-slot/10-pole SPM machine can be eliminated. Finally, the experimental results are given for validation of theoretical analyses and FE results.

Torque ripple reduction of synchronous reluctance machines : Optimal slot/pole and flux-barrier layer number combinations

Purpose – The purpose of this paper is to investigate the influence of stator and rotor pole number combinations together with the flux-barrier layers number on the performance of synchronous reluctance machine with emphasis on output torque capability and torque ripple. Design/methodology/approach – AC synchronous reluctance machine (SynRM) or permanent magnet assisted SynRM presently receives a great deal of interest, since there is less or even no rare-earth permanent magnet in the rotor. Most of SynRM machines employ a stator that is originally designed for a standard squirrel cage induction motor for a similar output rating and application, or the SynRM machine with 24-slot, four-pole are often directly chosen for investigation in most of the available literature. Therefore, it is necessary to investigate the influence of stator and rotor pole number combinations together with the flux-barrier layers number on the performance of SynRM machine with emphasis on output torque capability and torque rippl...

Using Third Harmonic for Shape Optimization of Flux Density Distribution in Linear Permanent-Magnet Machine

This paper presents a sinusoidal permanent magnet (PM) shaping technique with third harmonic to improve the electromagnetic thrust force in linear slotless PM machines without sacrificing the thrust force ripple. Slotless PM linear machine possesses relatively low thrust force ripple due to the absence of cogging force, compared with slotted topology. However, thrust force ripple of the machine with rectangular PM shape still exists due to nonsinusoidal airgap flux density distribution produced by PMs. Sinusoidal shaping techniques can be used to reduce the thrust force ripple but the average thrust force is reduced as well. Therefore, a simple PM shaping technique with optimal 3rd harmonic is presented to improve the output thrust force but not to increase the thrust force ripple. The sinusoidal plus 3rd harmonic shaping technique is analytically demonstrated together conventional sinusoidal shaping method and verified with finite element method. The results show that the electromagnetic performance can be significantly improved.