Fractional-slot Surface-mounted Permanent Magnet Research Articles

Performance Comparisons of Fractional Slot Surface-Mounted Permanent Magnet Machines With Slot-Harmonic-Only Windings

Fractional-slot slot harmonic only windings (SHOW), featured by multi-layer and varied coil turn ratios, contain only the torque-generating component and its slot harmonics in stator magnetomotive force (MMF), which makes them attractive. This paper establishes general design principles of SHOW considering different slot/pole combinations and makes detailed comparisons between SHOW and double layer (DL) windings for surface-mounted permanent magnet (SPM) machines. Firstly, fractional slot windings are classified into several categories. Similarity in distribution factors of MMF harmonics is illustrated, based on which, harmonics elimination principle of SHOW is explained. Then, general equations for calculating optimal coil turn ratios for SHOW are derived. Practical ratios approximating the optimal ones are also presented and evaluated. Furthermore, in order to show the superiorities of SHOW, 12-slot/10-pole (12s10p) and 24S10P SPM machines with SHOW are comprehensively studied and compared with their DL counterparts in terms of torque ripple, overload capability, rotor magnet loss, stator iron loss and radial electromagnetic force harmonics. Finally, 12S10P and 24S10P prototypes with SHOW are fabricated and tested for verifications.

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

The common analytical models for the no-load iron loss of permanent magnet(PM) motors usually neglect the iron loss caused by the rotating magnetic field in the tooth tips and the harmonics of the magnetic fields in the teeth and yokes. This paper presents an analytical model for no-load iron loss of a fractional-slot surface-mounted permanent magnet motor. According to the existing analytical model of the magnetic field distribution in the slotted air gap, the magnetic flux densities considering the harmonics of the stator tooth and yoke are both derived based on the continuity of magnetic flux. Due to the complexity of the magnetic field in the tooth tip, the tangential flux density of the tooth tip is approximated by an equivalent sine wave and the radial component is regarded to be the same as that of the corresponding tooth. After obtaining the magnetic fields in stator different regions, the analytical iron loss is calculated by using the Bertotti model and the orthogonal decomposition model. A 20-pole/24-slot PM synchronous motor is taken as an example. The maximum error between the analytical model and finite element model(FEM) is 5.46%, which verifies the validity of the proposed method.

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

This paper investigates the influence of concentrated winding configurations and stator core structures on torque performance of fractional-slot surface-mounted permanent magnet (SPM) machines. From analyzing the separated torque components of prototype SPM machines with 12-slot/10-pole (12S/10P) combination by frozen permeability (FP) method, it can be found that the torque ripple is closely related with local saturation in fully closed slot (FCS) machines. Besides, the heavier local saturation will also jeopardize the merit of using alternate teeth wound windings, such as obtaining higher average torque than electrical machines with all teeth wound windings. The further analysis of stator tooth relative permeability variation over one electrical period demonstrates that the major reason for torque ripple difference among these electrical machines with different stator topologies is the asymmetric saturation between the adjacent teeth. Both the subharmonic due to armature reaction (determined by winding connection and current value) and the asymmetry of stator core structure contribute to such asymmetric saturation. In order to more clearly verify this, the complementary slot/pole number combination (12S/14P) is also analyzed. The conclusion is effective for electrical machines with other slot/pole number combinations as well. Experiments have been carried out to validate the predictions.

Effectiveness of Terminal Voltage Distortion Minimization Methods in Fractional Slot Surface-Mounted Permanent Magnet Machines Considering Local Magnetic Saturation

Terminal voltage distortion in surface-mounted permanent magnet machines caused by local magnetic saturation significantly influences the machine performance. Thus, this paper focuses on the minimization methods for such phenomenon. The traditional harmonics minimization methods, such as rotor skewing and nonuniform airgap (rotor and stator shaping), are investigated. However, neither of them can effectively reduce the terminal voltage distortion since the local magnetic saturation in tooth-tips always exists, especially for designs with small or closed slot openings. This paper proposes that the terminal voltage distortion could be essentially reduced when larger slot opening width is adopted, since the local magnetic saturation by tooth-tip leakage flux decreases as a consequence. A design trade-off on slot opening is recommended to balance the terminal voltage distortion and other performance, e.g., the torque quality and flux weakening capability. The results show that the optimal trade-off should be made according to the machines most frequent operation conditions. Two prototypes with different design tradeoffs have been manufactured and tested as examples to validate the analyses.

Design Tradeoff Between Cogging Torque and Torque Ripple in Fractional Slot Surface-Mounted Permanent Magnet Machines

In designing the fractional slot surface-mounted permanent magnet (SPM) machines for servo and direct-drive applications, the cogging torque and on-load torque ripple are both major design considerations. Nevertheless, since the torque ripple depends on load conditions, the optimal tooth-tip design for the smallest cogging torque may not be the same for the smallest torque ripple as well. Usually cogging torque will reduce with slot opening width (b 0 ) [1] as shown in Fig.1(a). However, the variations of torque ripple are more complicated. With the help of frozen permeability method [2], the on-load torque can be seen as composed by PM torque (T PM ), reluctance torque (T r ) and on-load cogging torque (T cog ), which all contribute to torque ripple, Fig.1(b). The variation of these components against different b 0 under full-load are shown in Figs.1(c) and (d). It can be seen that the average torque for T r will not be zero even in SPM machines due to cross-coupling saturation. With the reducing of b 0 , the leakage flux will increase, which reduces the average torque and makes the fluctuations of T cog even increase under full-load condition. However, under half-load condition, the variation of torque components against b 0 is totally different, Figs.1(e) and (f). It reveals that the cross-coupling effect under half-load becomes unobvious while T cog reduces when b 0 is small.

On-Load Voltage Distortion in Fractional Slot Surface-Mounted Permanent Magnet Machines Considering Local Magnetic Saturation

The on-load voltage distortion in fractional slot surface-mounted permanent magnet machines refers to the phase terminal voltage distorted by armature reaction. With the aid of frozen permeability method, the mechanism of this phenomenon has been investigated based on a 12-slot/8-pole model as an example, showing that the local magnetic saturation in tooth-tips is the main cause, especially when small or closed slot openings are adopted. Then, its impacts on machine performance under vector control have been investigated. If the dc-link voltage is sufficient to satisfy all distorted voltage, i.e., operating in constant torque region, the phenomenon mainly contributes to torque ripple. However, it becomes more problematic in the flux weakening region if the dc-link voltage is limited. Both base-speed and torque-speed curve will significantly differ from the expected results calculated by fundamental voltages. Meanwhile, if the machine operates beyond the base speed, or considering the limited bandwidth in real systems, the phase currents may be distorted, which consequently increase the current harmonics and reduce the average torque. Finally, a prototype machine is manufactured and tested to validate the analyses.

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.

Sensorless Capability of Fractional-Slot Surface-Mounted PM Motors

This paper investigates the capability of sensorless rotor position detection by means of injection of a high-frequency (HF) signal of fractional-slot surface-mounted permanent-magnet (PM) motors. In order to create an HF anisotropy, such motors are characterized by the presence of a ring around each pole. For the sake of completeness, different windings are considered: a distributed coil winding and a concentrated coil winding. The effect of eddy currents in the magnets, due to the HF signal, is also considered. The effect of the slot opening is also taken into consideration. Finally, the comparison with two different PM rotor topologies is addressed: an interior PM motor and an INSET motor.

An Analytical Model of Unbalanced Magnetic Force in Fractional-Slot Surface-Mounted Permanent Magnet Machines

We present an analytical model of unbalanced magnetic force (UMF) in fractional-slot surface-mounted permanent magnet (PM) machines having diametrically asymmetrical winding distribution but no static/dynamic rotor eccentricities. It is based on a 2-D analytical field model and accounts for the influence of both the radial and tangential force waves under any load condition. It is capable of providing insight into the generation, harmonic contents, and characteristics of the UMF and accurately predicting the magnitudes, rotation directions, phase angles of its harmonics and various components, such as the UMFs due to armature reaction only, mutual interaction between both PM and armature reaction fields, and radial and tangential force waves. The cancellation and additive effects between the UMF components resulting from the radial and tangential force waves are revealed for the first time by the analytical model. We show that such effects strongly depend on the UMF harmonic order, slot/pole number combinations, and the internal/external rotor machine topologies. We have validated the analytical model by finite-element analyses and partially by experimental results.

The steering effect PM motor drives for automotive systems

The steer-by-wire (SBW) system requires the use of enhanced fuel economy, assist action given two motor drives, the first for the mechanical steering system and the second for the torque feedback to the steering wheel. An interior permanent magnet (IPM) synchronous motor is used for the steering actuator whereas a fractional-slot surface-mounted permanent magnet (SPM) synchronous motor is used for the torque feedback.