# Analysis of Stator-Slot Circumferentially Magnetized PM Machines with Full-Pitched Windings

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Machine Topology, Operation Principle, and Slot/Pole Number Combination

_{d}= 0 control can be expressed as

_{r}ψ

_{PM}(i

_{q})i

_{q}∝N

_{r}φ

_{PM}(F

_{q})F

_{q}

_{r}is the rotor-pole number, ψ

_{PM}(i

_{q}) is the PM flux linkage and affected by the armature current i

_{q}, and φ

_{PM}(F

_{q}) is the PM flux and affected by the armature magnetomotive force (MMF) F

_{q}.

_{r}= iN

_{s}/2 ± P

_{a}(i = 1, 3, 5···)

_{r}is the rotor-pole number, N

_{s}is the stator-slot number, i is the odd number, and P

_{a}is the pole-pair number of armature windings. 12S-4R/8R/10R/11R/13R/14R/16R stator-slot PM machines are mentioned in [14], and the corresponding P

_{a}is 2, 2, 4, 5, 5, 4, and 2, respectively, but all with tooth-coil windings. However, there are other combinations, e.g., 12S-5R/7R, whose armature pole-pair number is 1, as shown in Table 1. In this paper, 12 stator-slots machines with FPW and different number of rotor poles are investigated. The coil pitches are 3, 6, 6, and 3 slot pitches, respectively. It should be noted that FPW is not restricted to 12 stator-slots machines.

_{w}can be expressed as

_{w}= k

_{d}k

_{p}

_{d}is the winding distribution factor, and k

_{p}is the pitch factor. k

_{d}is given by

_{d}= sin(Qvα/2)/(Q sin(vα/2))

_{p}is given by [16]

_{p}= cos(θ

_{c}/2 − π/2)

_{c}is the angular difference between two adjacent slot conductors for the v

^{th}harmonics and is expressed as v(2πN

_{r}/N

_{s}).

_{cu_total}), iron loss (P

_{iron}), PM eddy current loss (P

_{pm_eddy}), as

_{em}/(P

_{em}+ P

_{cu_total}+ P

_{iron}+ P

_{pm_eddy})

_{em}is the output power. The total copper loss includes the effective copper loss P

_{cu_eff}and the end-winding copper loss P

_{cu_end}. The end-winding length per turn l

_{end}is calculated as

_{end}= τ

_{c}π

_{c}is the average coil pitch of the machine. For FPW, τ

_{c}is calculated as

_{c}= 2πy(r

_{3}– yk − 0.5h

_{slot})/N

_{s}

_{c}is calculated as

_{c}=π(r

_{3}− yk − 0.5h

_{slot})/N

_{s}+ 0.5tw

_{3}is the stator outer radius, yk is the stator yoke width, h

_{slot}is the slot depth, tw is the tooth width, and y is the coil pitch in slot pitch.

## 3. Influence of Key Geometric Parameters

- (1)
- Both machines have the same stator outer diameter, stack length, PM material, and iron steel. The effective copper loss is fixed to 20 W.
- (2)
- All the optimizations are based on genetic algorithm (GA), and 30 individuals in each population with 35 generations have been employed.
- (3)
- The optimized parameters are stator yoke width, stator inner radius, stator tooth width, rotor tooth width, rotor slot depth, and PM thickness. Parameters of the optimized machines are listed in Table 2.

_{a}is fixed, there are different rotor-pole numbers that can satisfy (2). For example, when P

_{a}= 1, the rotor-pole number can be chosen as 5, 7, 17, or 19. Figure 5 shows that when the rotor pole number is 5 or 7, higher torque can be generated. Then, the influence of other geometric parameters in 12S-4R/5R/7R/8R machines is further investigated.

_{a}= 1 and P

_{a}= 2. When P

_{a}is smaller, the armature MMF is stronger, and more PM flux can be forced into the airgap and the rotor side under load condition. (1) shows that the average torque is greatly affected by the armature MMF. Hence, the stronger the armature MMF, the higher the PM flux and the thicker the PMs.

_{PM}(F

_{q}), as shown in (1).

## 4. Comparison of Stator-Slot PM Machines with Tooth-Coil and Full-Pitched Windings

_{q}can only force PM flux φ

_{PM}(F

_{q}) into the airgap, and excess PM flux makes the flux path more saturated. Aside from that, the stator slot area is reduced, and so is the armature MMF F

_{q}. Therefore, M3 generates lower torque than M2, as shown in Figure 15.

_{d}= 0 control. It should be noted that the SSCMPMMs have antisaturation capability. This antisaturation capability is due to the fact that most of the PM flux circulates within the stator core on open circuit, and the armature MMF forces the PM flux into the airgap and the rotor side at load condition. The magnetic flux path firstly becomes less saturated when the armature current increases. Then, the PM MMF and the armature MMF reach a balance, at which point the main flux path is least saturated. Afterward, the flux path becomes more and more saturated if the armature current is further increased. This phenomenon is indicated by the inductance variation versus armature current, as shown in Figure 21. The inductance variations also indicate that M2 has better overload capability.

_{s}+ h

_{end}. h

_{end}is the height of end-winding. The volume of the end-winding V

_{end}and the volume of the effective winding V

_{eff}satisfy (10).

_{end}/V

_{eff}= l

_{end}/l

_{s}

_{end}= π(r

_{b}

^{2}− r

_{t}

^{2})h

_{end}

_{eff}= S

_{slot}l

_{s}

_{b}is the radius of slot bottom, r

_{t}is the radius of slot top, and S

_{slot}is the total slot area.

## 5. Experiment Validation

_{a}= −2I

_{b}= −2I

_{c}= 10 A) into the three phase windings [22]. The FEA calculated and measured static torques are shown in Figure 30. The measured static torque is around 23.6% and 18% lower than the 2D and 3D FEA calculated values. Similarly, larger difference can be observed between 2D FEA calculated and measured torque versus current curves, as shown in Figure 31.

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

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N_{r} | P_{a} | iN_{s}/2 | Coil Pitch of Full Pitch |
---|---|---|---|

4 | 2 | 6 (i = 1) | 3 |

5 | 1 | 6 (i = 1) | 6 |

7 | 1 | 6 (i = 1) | 6 |

8 | 2 | 6 (i = 1) | 3 |

10 | 4 | 6 (i = 1) | 1 |

11 | 5 | 6 (i = 1) | 1 |

13 | 5 | 18 (i = 3) | 1 |

14 | 4 | 18 (i = 3) | 1 |

16 | 2 | 18 (i = 3) | 3 |

17 | 1 | 18 (i = 3) | 6 |

19 | 1 | 18 (i = 3) | 6 |

20 | 2 | 18 (i = 3) | 3 |

Symbol | 12S4R | 12S5R | 12S7R (M1) | 12S8R | 12S10R (M2) | 12S10R (M3) |
---|---|---|---|---|---|---|

Stator outer radius (mm) | 45 | |||||

Stack length (mm) | 25 | |||||

Airgap length (mm) | 0.5 | |||||

Rated speed (rpm) | 600 | |||||

PM material | N32EZ | |||||

B_{r}, μ_{r}@ 20 °C | 1.13 T, 1.05 | |||||

Winding pole pair number | 2 | 1 | 1 | 2 | 4 | 4 |

N_{ph} | 128 | 112 | 120 | 128 | 128 | 120 |

PM thickness (mm) | 3.5 | 5.0 | 4.6 | 3.45 | 2.75 | 3.74 |

Stator inner radius (mm) | 20.3 | 18.6 | 19.5 | 20.8 | 24.4 | 25.8 |

Stator tooth width (mm) | 3.6 | 4 | 3.45 | 3.64 | 4.85 | 4.67 |

Stator yoke width (mm) | 4.6 | 7.1 | 6.72 | 4.66 | 1.42 | 2.2 |

Rotor tooth width (mm) | 14 | 9.1 | 6.4 | 7 | 6.4 | 7 |

Rotor slot depth (mm) | 7.6 | 7.2 | 5.6 | 7.7 | 6.2 | 5.9 |

Rated current (Arms/Apeak) | 10/14.14 |

Symbol | 12S7R with y = 3 |
---|---|

Stator outer radius (mm) | 45 |

Stack length (mm) | 25 |

Airgap length (mm) | 0.5 |

Winding pole pair number | 1 |

Coil pitch (slot pitch) | 3 |

N_{ph} | 120 |

PM thickness (mm) | 4.8 |

Stator inner radius (mm) | 23 |

Stator tooth width (mm) | 4.8 |

Stator yoke width (mm) | 7 |

Rotor tooth width (mm) | 7.8 |

Rotor slot depth (mm) | 7.5 |

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**MDPI and ACS Style**

Qu, H.; Yang, H.; Zhu, Z.Q.
Analysis of Stator-Slot Circumferentially Magnetized PM Machines with Full-Pitched Windings. *World Electr. Veh. J.* **2021**, *12*, 33.
https://doi.org/10.3390/wevj12010033

**AMA Style**

Qu H, Yang H, Zhu ZQ.
Analysis of Stator-Slot Circumferentially Magnetized PM Machines with Full-Pitched Windings. *World Electric Vehicle Journal*. 2021; 12(1):33.
https://doi.org/10.3390/wevj12010033

**Chicago/Turabian Style**

Qu, Huan, Han Yang, and Zi Qiang Zhu.
2021. "Analysis of Stator-Slot Circumferentially Magnetized PM Machines with Full-Pitched Windings" *World Electric Vehicle Journal* 12, no. 1: 33.
https://doi.org/10.3390/wevj12010033