# Influence of Different Rotor Teeth Shapes on the Performance of Flux Switching Permanent Magnet Machines Used for Electric Vehicles

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Machine Topologies and Torque Analysis

#### 2.1. Flux Switching Permanent Magnet Machine Main Parameters

**Figure 1.**Schematic of the proposed flux switching permanent magnet (FSPM) machine: (

**a**) all poles wound cross section; and (

**b**) one model.

Symbol | Machine parameter | Value | Unit |
---|---|---|---|

P | Phase number | 3 | - |

N_{s} | Stator pole number | 12 | - |

N_{r} | Rotor pole number | 11 | - |

N | Coil number per stator slot | 78 | - |

PM | Magnet material | NTP40UH | - |

B_{r} | Magnet remanence (20 °C) | 1.26 | T |

D_{so} | Stator outer diameter | 132 | mm |

D_{ro} | Rotor outer diameter | 72 | mm |

g | Air gap length | 0.3 | mm |

b_{m} | Magnet thickness | 4.75 | mm |

h_{p} | Rotor tooth height | 9.5 | mm |

l_{a} | Machine stack length | 59 | mm |

n_{r} | Rated rotational speed | 600 | rpm |

T_{ra} | Rated output torque | 15 | N·m |

I_{a} | Peak value of rated phase current | 15.4 | A |

U_{dc} | DC link voltage | 110 | V |

#### 2.2. Torque Analysis

**Figure 2.**Electromagnetic torques of the FSPM machine with different current amplitudes and inner power factor angles.

_{em}of the FSPM machine can be derived by co-energy [23], the W

_{coenergy}can be expressed as:

_{field}is the field energy; ψ

_{PM}(θ) is the flux linkage produced by PMs; and W

_{PM}is the energy produced by PMs.

_{em}is defined as [23]:

_{PM}is produced by the interaction of the flux generated by PMs and the armature reaction; T

_{rm}is produced by the machine inductance which changes with the rotor position; and T

_{cog}is cogging torque generated by PMs and rotor teeth.

_{PM}, T

_{rm}and T

_{cog}. However, the cogging torque T

_{cog}will not produce effective average torque but only cause torque ripple.

_{r}is defined by:

_{avg}, T

_{max}and T

_{min}are average, maximal and minimal torques, respectively.

## 3. The Influence of Different Rotor Teeth Shapes on Torque Performance

#### 3.1. Rotor with Notched Teeth

_{1}, the depth of v-shape notch L, the width of v-shape notch h

_{2}, are shown in Figure 5. Considering that the teeth top has a great influence on the cogging torque, the notch position should not be too far from the teeth top, so the parameter h

_{1}is selected from 0 mm to 3.0 mm. In addition, as the notches are on the sides of the teeth, the depth and width of the v-shape notch influence the magnetic reluctance directly. Thus, the depth L and width h

_{2}of the v-shape notch should be small in order to obtain higher average torque. In this paper, L is selected from 0.1 mm to 0.8 mm, and h

_{2}is selected from 0.04 mm to 0.36 mm.

_{1}at an interval of 0.5 mm from 0 mm to 3.0 mm with h

_{2}= 0.2 mm and L = 0.5 mm as shown in Step (1) of Figure 5, the waveforms of electromagnetic torques, cogging torques and torque ripples are shown in Figure 6a. It should be noted that the torque data of point h

_{1}= 0 mm represents the torque data of the initial structure. At the point of h

_{1}= 1.0 mm, both the cogging torque and torque ripple reach their minimum values with the average torque reduced only by 0.72%.

_{1}= 1.0 mm and h

_{2}= 0.2 mm as shown in Step (2) of Figure 5, the torque data versus L is shown in Figure 6b. The torque ripple reaches its minimum value at L = 0.5 mm, while the cogging torque is also small.

_{2}at an interval of 0.04 mm from 0.04 mm to 0.36 mm with h

_{1}= 1.0 mm and L = 0.5 mm as shown in Step (3) of Figure 5, and selecting the final parameters of the v-shape notch from Figure 6c, they are h

_{1}= 1.0 mm, L = 0.5 mm, and h

_{2}= 0.28 mm, respectively.

**Figure 6.**Average torques, torque ripples, cogging torques according to: (

**a**) the height of h

_{1}; (

**b**) the depth of L; and (

**c**) the width of h

_{2}.

Optimizing procedure | Cogging torque (mN·m) | Torque ripple (%) | Average torque (N·m) |
---|---|---|---|

Initial structure | 187.11 | 4.09 | 15.04 |

Optimized structure with h_{1} = 1.0 mm, L = 0.5 mm, and h_{2} = 0.28 mm | 158.97 | 2.56 | 14.89 |

#### 3.2. Rotor with Stepped Teeth

_{s}and height H

_{s}. Within one model, each step has equal width and equal height, e.g., h

_{21}= h

_{22}and L

_{21}= L

_{22}= L

_{23}= L

_{24}= L

_{25}in S2.

Optimizing procedure | Cogging torque (mN·m) | Torque ripple (%) | Average torque (N·m) |
---|---|---|---|

Initial structure | 187.11 | 4.09 | 15.04 |

Two step structure | 177.45 | 3.62 | 14.93 |

#### 3.3. Rotor with Eccentric Teeth

_{e}. As shown in Figure 9, fixing O, the eccentric distance h

_{e}varies as O’ moves. The minimum air gap is decreasing as h

_{e}is increasing, so the eccentric distance h

_{e}should not be too large in order to ensure the air-gap length.

_{e}= 16.5 mm. With the increase of eccentric distance, the electromagnetic torque keeps increasing, while the torque ripple firstly decreases and then increases, and the cogging torque firstly increases, then decreases and finally increases again.

_{e}of 16.5 mm is more preferred to improve the torque characteristics. Torque characteristics before and after the eccentric teeth optimization are shown in Table 4. It can be seen that the effect of improving the torque characteristics by eccentric teeth is not satisfactory enough.

Optimizing procedure | Cogging torque (mN·m) | Torque ripple (%) | Average torque (N·m) |
---|---|---|---|

Initial structure | 187.11 | 4.09 | 15.04 |

Optimized structure with h_{e} = 16.5 mm | 180.08 | 3.85 | 15.12 |

#### 3.4. Rotor with the Combination of Stepped and Notched Teeth

_{1}= 0 mm in Figure 12a represents the torque data of the stepped teeth S

_{2}scheme.

_{1}= 1.5 mm, L = 0.4 mm, h

_{2}= 0.16 mm are selected after carefully comparing the results.

**Figure 12.**Average torques, torque ripples, cogging torques according to: (

**a**) the height of h

_{1}; (

**b**) the depth of L; and (

**c**) the width of h

_{2}.

**Table 5.**Torque characteristics before and after optimizing the stepped and notched teeth combination.

Optimizing procedure | Cogging torque (mN·m) | Torque ripple (%) | Average torque (N·m) |
---|---|---|---|

Initial structure | 187.11 | 4.09 | 15.04 |

Optimized structure with h_{1} = 1.5 mm, L = 0.4 mm, h_{2} = 0.16 mm, and stepped teeth S2 | 127.65 | 2.49 | 14.79 |

#### 3.5. Rotor with the Combination of Eccentric and Notched Teeth

_{1}= 0 mm, in Figure 14a represents the torque data with only the eccentric teeth and without notched teeth.

_{1}= 1.0 mm, L = 0.2 mm, h

_{2}= 0.28 mm, in this combination. Torque characteristics before and after optimizing the eccentric and notched teeth combination are compared in Table 6. Compared to the initial scheme, the cogging torque is just decreased by 10 mN·m, but the torque ripple is greatly reduced by 37.24%, while the average electromagnetic torque is slightly increased by 0.59%.

**Figure 14.**Average torques, torque ripples, cogging torques according to: (

**a**) the height of h

_{1}; (

**b**) the depth of L; and (

**c**) the width of h

_{2}.

**Table 6.**Torque characteristics before and after optimizing the eccentric and notched teeth combination.

Optimizing procedure | Cogging torque (mN·m) | Torque ripple (%) | Average torque (N·m) |
---|---|---|---|

Initial structure | 187.11 | 4.09 | 15.04 |

Optimized structure with h_{1} = 1.0 mm, L = 0.2 mm, h_{2} = 0.28 mm, h_{e} = 16.5 mm | 177.00 | 2.57 | 15.12 |

## 4. Rotor Comparison

#### 4.1. Cogging Torque

**Figure 15.**Cogging torque: (

**a**) cogging torque at rated speed, 600 rpm; and (

**b**) maximal and minimal values.

#### 4.2. Electromagnetic Torque

#### 4.3. Flux Linkage

#### 4.4. Back Electromotive Force

#### 4.5. Summary of the Results

**Table 7.**Comparatively comparison of the performances of T0–T5 schemes. THD: total harmonic distortion.

Performance | T0 | T1 | T2 | T3 | T4 | T5 |
---|---|---|---|---|---|---|

Cogging torque (mN·m) | 187.11 | 158.97 | 176.13 | 172.87 | 127.65 | 177.00 |

Average torque (N·m) | 15.04 | 14.89 | 14.93 | 15.19 | 14.79 | 15.12 |

Torque ripple (%) | 4.09 | 2.57 | 3.62 | 3.85 | 2.49 | 2.57 |

THD of EMF (%) | 14.24 | 15.09 | 14.02 | 14.90 | 14.25 | 15.32 |

THD of EMF without three harmonic (%) | 1.23 | 1.33 | 1.18 | 1.24 | 1.19 | 1.24 |

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

- Fei, W.Z.; Luk, P.C.K.; Miao, D.-M.; Shen, J.-X. Investigation of torque characteristics in a novel permanent magnet flux switching machine with an outer-rotor configuration. IEEE Trans. Magn.
**2013**, 45, 4656–4659. [Google Scholar] - Fei, W.; Luk, P.C.K.; Shen, J.X.; Wang, Y.; Jin, M. A novel permanent-magnet flux switching machine with an outer-rotor configuration for in-wheel light traction applications. IEEE Trans. Ind. Appl.
**2012**, 48, 1496–1506. [Google Scholar] [CrossRef][Green Version] - Ahmad, M.Z.; Sulaiman, E.; Haron, Z.A.; Kosaka, T. Preliminary studies on a new outer-rotor permanent magnet flux switching machine with hybrid excitation flux for direct drive EV applications. In Proceedings of the 2012 IEEE International Conference on Power and Energy (PECon), Kota Kinabalu, Malaysia, 2–5 December 2012; pp. 928–933.
- Hwang, C.-C.; Chang, C.-M.; Hung, S.-S.; Liu, C.-T. Design of high performance flux switching PM machines with concentrated windings. IEEE Trans. Magn.
**2014**, 50. [Google Scholar] [CrossRef] - Xue, X.; Zhao, W.; Zhu, J.; Liu, G.; Zhu, X.; Cheng, M. Design of five phase modular flux switching permanent magnet machines for high reliability applications. IEEE Trans. Magn.
**2013**, 49, 3941–3944. [Google Scholar] [CrossRef] - Abdollahi, S.E.; Vaez-Zadeh, S. Back EMF analysis of a novel linear flux switching motor with segmented secondary. IEEE Trans. Magn.
**2014**, 50, 1–9. [Google Scholar] - Zulu, A.; Mecrow, B.C.; Armstrong, M. Permanent-magnet flux-switching synchronous motor employing a segmental rotor. IEEE Trans. Ind. Appl.
**2012**, 48, 2259–2267. [Google Scholar] [CrossRef] - Thomas, A.S.; Zhu, Z.Q.; Owen, R.L.; Jewell, G.W.; Howe, D. Multiphase flux-switching permanent-magnet brushless machine for aerospace application. IEEE Trans. Ind. Appl.
**2009**, 45, 1971–1981. [Google Scholar] [CrossRef] - Thomas, A.S.; Zhu, Z.Q.; Jewell, G.W. Proximity loss study in high speed flux-switching permanent magnet machine. IEEE Trans. Magn.
**2009**, 45, 4748–4751. [Google Scholar] [CrossRef] - Sulaiman, E.; Kosaka, T.; Matsui, N. Parameter optimization study and performance analysis of 6S-8P permanent magnet flux switching machine with field excitation for high speed hybrid electric vehicles. In Proceedings of the 2011-14th European Conference on Power Electronics and Applications (EPE 2011), Birmingham, UK, 30 August–1 September 2011; pp. 1–9.
- Hua, W.; Cheng, M.; Zhang, G. A novel hybrid excitation flux-switching motor for hybrid vehicles. IEEE Trans. Magn.
**2009**, 45, 4728–4731. [Google Scholar] [CrossRef] - Wang, Y.; Sun, J.; Zou, Z.; Wang, Z.; Chau, K.T. Design and analysis of a HTS flux-switching machine for wind energy conversion. IEEE Trans. Appl. Supercond.
**2013**, 23. [Google Scholar] [CrossRef] - Zhang, G.; Cheng, M.; Hua, W.; Dong, J. Analysis of the oversaturated effect in hybrid excited flux-switching machines. IEEE Trans. Ind. Magn.
**2011**, 47, 2827–2830. [Google Scholar] [CrossRef] - Raminosoa, T.; Gerada, C.; Galea, M. Design considerations for a fault-tolerant flux-switching permanent-magnet machine. IEEE Trans. Ind. Electron.
**2011**, 58, 2818–2825. [Google Scholar] [CrossRef] - Li, G.; Ojeda, J.; Hoang, E.; Gabsi, M. Double and single layers fault-tolerant flux-switching permanent-magnet motor: Fault tolerant model for critical applications. In Proceedings of the 2011 International Conference on Electrical Machines and Systems (ICEMS), Beijing, China, 20–23 August 2011.
- Raminosoa, T.; Gerada, C. Fault tolerant winding technology comparison for flux switching machine. In Proceedings of the 2010 XIX International Conference on Electrical Machines (ICEM), Rome, Italy, 6–8 September 2010; pp. 1–6.
- Zhao, W.; Cheng, M.; Chau, K.T.; Hua, W.; Jia, H.; Ji, J.; Li, W. Stator-flux-oriented fault-tolerant control of flux-switching permanent-magnet motors. IEEE Trans. Magn.
**2011**, 47, 4191–4194. [Google Scholar] [CrossRef][Green Version] - Chen, J.T.; Zhu, Z.Q. Winding configurations and optimal stator and rotor pole combination of flux-switching PM brushless AC machines. IEEE Trans. Energy Convers.
**2010**, 25, 293–302. [Google Scholar] [CrossRef] - Chen, J.T.; Zhu, Z.Q. Comparison of all- and alternate-poles-wound flux-switching PM machines having different stator and rotor pole numbers. IEEE Trans. Ind. Appl.
**2010**, 46, 1406–1415. [Google Scholar] [CrossRef] - Zheng, P.; Zhao, J.; Han, J.; Wang, J.; Yao, Z.; Liu, R. Optimization of the magnetic pole shape of a permanent-magnet synchronous motor. IEEE Trans. Magn.
**2007**, 43, 2531–2533. [Google Scholar] [CrossRef] - Zhao, W.; Lipo, T.A.; Kwon, B. Material-efficient permanent-magnet shape for torque pulsation minimization in SPM motors for automotive applications. IEEE Trans. Ind. Electron.
**2014**, 61, 5779–5787. [Google Scholar] [CrossRef] - Fei, W.; Luk, P.C.K.; Shen, J. Torque analysis of permanent-magnet flux switching machines with rotor step skewing. IEEE Trans. Magn.
**2012**, 48, 2664–2673. [Google Scholar] [CrossRef][Green Version] - Fei, W.; Luk, P.C.K.; Shen, J.X.; Xia, B.; Wang, Y. Permanent-magnet flux-switching integrated starter generator with different rotor configurations for cogging torque and torque ripple mitigations. IEEE Trans. Ind. Appl.
**2011**, 47, 1247–1256. [Google Scholar] [CrossRef][Green Version] - Wang, D.; Wang, X.; Jung, S.-Y. Reduction on cogging torque in flux-switching permanent magnet machine by teeth notching schemes. IEEE Trans. Magn.
**2012**, 48, 4228–4231. [Google Scholar] [CrossRef] - Abdollahi, S.E.; Vaez-Zadeh, S. Reducing cogging torque in flux switching motors with segmented rotor. IEEE Trans. Magn.
**2013**, 49, 5304–5309. [Google Scholar] [CrossRef] - Zhu, Z.Q.; Chen, J.T.; Pang, Y.; Howe, D.; Iwasaki, S.; Deodhar, R. Analysis of a novel multi-tooth flux-switching PM brushless AC machine for high torque direct-drive applications. IEEE Trans. Magn.
**2008**, 44, 4313–4316. [Google Scholar] [CrossRef] - Cai, J.; Lu, Q.; Jin, Y.; Chen, C.; Ye, Y. Performance investigation of multi-tooth flux-switching PM linear motor. In Proceedings of the 2011 International Conference on Electrical Machines and Systems (ICEMS), Beijing, China, 20–23 August 2011.
- Xu, W.; Lei, G.; Wang, T.; Yu, X.; Zhu, J.; Guo, Y. Theoretical research on new laminated structure flux switching permanent magnet machine for novel topologic plug-in hybrid electrical vehicle. IEEE Trans. Magn.
**2012**, 48, 4050–4053. [Google Scholar] [CrossRef] - Zhao, W.; Cheng, M.; Chau, K.T.; Cao, R.; Ji, J. Remedial injected-harmonic-current operation of redundant flux-switching permanent-magnet motor drives. IEEE Trans. Ind. Electron.
**2013**, 60, 151–159. [Google Scholar] [CrossRef][Green Version] - Zhao, W.; Cheng, M.; Hua, W.; Jia, H.; Cao, R. Back-EMF harmonic analysis and fault-tolerant control of flux-switching permanent-magnet machine with redundancy. IEEE Trans. Ind. Electron.
**2011**, 58, 1926–1935. [Google Scholar] [CrossRef] - Zhao, W.; Cheng, M.; Cao, R.; Ji, J. Experimental comparison of remedial single-channel operations for redundant flux-switching permanent magnet motor drive. Prog. Electromagn. Res.
**2012**, 123, 189–204. [Google Scholar] [CrossRef]

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## Share and Cite

**MDPI and ACS Style**

Zhao, J.; Yan, Y.; Li, B.; Liu, X.; Chen, Z. Influence of Different Rotor Teeth Shapes on the Performance of Flux Switching Permanent Magnet Machines Used for Electric Vehicles. *Energies* **2014**, *7*, 8056-8075.
https://doi.org/10.3390/en7128056

**AMA Style**

Zhao J, Yan Y, Li B, Liu X, Chen Z. Influence of Different Rotor Teeth Shapes on the Performance of Flux Switching Permanent Magnet Machines Used for Electric Vehicles. *Energies*. 2014; 7(12):8056-8075.
https://doi.org/10.3390/en7128056

**Chicago/Turabian Style**

Zhao, Jing, Yashuang Yan, Bin Li, Xiangdong Liu, and Zhen Chen. 2014. "Influence of Different Rotor Teeth Shapes on the Performance of Flux Switching Permanent Magnet Machines Used for Electric Vehicles" *Energies* 7, no. 12: 8056-8075.
https://doi.org/10.3390/en7128056