# A Novel Surface Inset Permanent Magnet Synchronous Motor for Electric Vehicles

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## Abstract

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## 1. Introduction

## 2. The Proposed SIPMSM

#### 2.1. Structure Design

#### 2.2. Infulence on Cogging Torque

_{a}is the axial length of the motor; R

_{1}is the outer arc radius of unequal thickness magnetic poles; h is the vertical distance from the center of the outer arc to the permanent magnet; n is an integer that makes (nz/2p) an integer.

_{max}is the maximum thickness of permanent magnet; ${h}_{m}^{\prime}$ is the minimum thickness of permanent magnet; d is the width of permanent magnet.

_{d}is auxiliary slot in rotor, and k = 1.

#### 2.3. Influence of Notching Auxiliary Slots

_{d}is the voltage of d axis; u

_{q}is the voltage of q axis; R

_{s}is the resistance of armature winding; i

_{d}is the current of d axis; i

_{q}is the current of q axis; Ψ

_{d}is the flux linkage of d axis; Ψ

_{q}is the flux linkage of q axis; ω is the angular speed of rotor rotation.

_{q}= 0. The ideal maximum speed of the motor can be expressed as

_{c}is the magnetomotive of permanent magnet; R

_{M}is the magnetic resistance of magnetic circuit through which the self-induction flux; N is the number of turns of conductor.

_{r}is the magnetic resistance at the maximum thickness of permanent magnet steel; R

_{z}is the rotor core magnetic resistance between the permanent magnet steel and the air-gap; R

_{a}is the magnetic resistance of the air-gap; R

_{s}is the magnetic resistance of stator; R

_{y}is the magnetic resistance of the stator yoke.

_{d}is the magnetic resistance of auxiliary slot.

## 3. Optimization Model

_{max}, the depth of auxiliary slot X

_{d}, the cogging torque T

_{cog}and the flux weakening expansion rate ρ can be obtained by the combination of RSM and finite element method. The experimental arrangements and finite elements results are shown in Table 2, where X

_{1}and X

_{2}are the factor coded values, Y

_{1}is the cogging torque, and Y

_{2}is the flux weakening expansion rate. The second-order model can be expressed as follows:

_{i}is the coded variables; β

_{i}is the linear effect of x

_{i}; β

_{ij}is the interaction between x

_{i}and x

_{j}; β

_{ii}is the quadratic effect of x

_{i}.

_{1}and Y

_{2}are analyzed using Design-Expert software. According to the regression model equation, the response surface and contour map of the interaction factors to peak value of cogging torque and flux magnetic speed expansion can be established, as shown in Figure 4 and Figure 5.

_{1}varies from 5 to 7 mm, the peak value of the cogging torque decreases first and then increases. If x

_{1}is fixed at a certain level, the peak value of the cogging torque decreases first and then increases. Therefore, according to the analysis of partial regression equation and contour plot, the effect of the depth of auxiliary slot in rotor on the flux magnetic speed expansion is greater than the maximum thickness of the permanent magnet.

_{1}changes from 5 to 7 mm, the value of flux weakening expansion ratio of the motor increases first and then decreases. If x

_{1}is fixed at a certain level, with the increase in x

_{2}, the peak value of cogging torque trends to decrease. Therefore, according to the analysis of partial regression equation and the contour plot, the effect of the maximum thickness of the permanent magnet is greater than the depth of auxiliary slot in the rotor.

_{max}, X

_{d}) = (6.40, 7). The optimal response is (T

_{cog}, ρ) = (1.16, 2.08).

## 4. Experimental Validation

## 5. Conclusions

- (1)
- The mathematical model of cogging torque of the novel SIPMSM is established, and the influence factors of the cogging torque and flux weakening speed expansion of the novel SIPMSM were deduced. Combining the RSM and finite element method, the multi-objective optimization design of the influencing factors was carried out. The optimization results show that when the maximum thickness of magnetic poles is 6.4mm and the depth of rotor slot is 7mm, the peak value of cogging torque is 1.16 nm and the flux weakening speed rate is 2.08.
- (2)
- The prototype test shows that—compared with the traditional SIPMSM—the new SIPMSM not only enhances the output torque and reduces the torque ripple, but also improves the performance of flux weakening speed expansion. At the same time, the high efficiency range of the constant power operation is widened, and more in line with the performance requirements of PMSM for electric vehicles. Therefore, the novel SIPMSM is more suitable for electric vehicles.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Schematic diagram of typical SIPMSM and tile shape magnetic poles. (

**a**) Schematic diagram of traditional SIPMSM; (

**b**) Schematic diagram of tile shape magnetic poles.

**Figure 2.**Schematic diagram of the novel SIPMSM and unequal thickness magnetic poles. (

**a**) Schematic diagram of the novel SIPMSM; (

**b**) Schematic diagram of unequal thickness magnetic poles.

**Figure 4.**Effect of interaction factors on peak value of cogging torque Y

_{1}: (

**a**) 3D and (

**b**) 2D contours.

**Figure 5.**Effect of interaction factors on peak value of cogging torque Y

_{2}: (

**a**) 3D and (

**b**) 2D contours.

Parameters | Numberical Value | Parameters | Numberical Value |
---|---|---|---|

Rated voltage (V) | 60 | Rated speed (r/min) | 3000 |

Rated power (kW) | 3 | Rated torque (N·m) | 89 |

Number of pole pairs | 4 | Rotor outer diameter (mm) | 30 |

Number of slots | 24 | Rator inner diameter (mm) | 70 |

Stator inner diameter (mm) | 90 | Number of turns per slot | 12 |

Stator outer diameter (mm) | 145 | Magnet width | 29 |

Maximun magnet thickness (mm) | 6 | Slot width of rotor/mm | 7 |

Minimum magnet thickness(mm) | 4 | Slot depth of rotor/mm | 5 |

No. | Experimental Factor | Code Conversion | T_{cog} | ρ | ||
---|---|---|---|---|---|---|

h_{max} | X_{d} | x_{1} | x_{2} | Y_{1} | Y_{2} | |

1 | 5 | 5 | −1 | −1 | 1.82 | 2.07 |

2 | 7 | 5 | 0 | −1 | 0.75 | 1.95 |

3 | 5 | 9 | −1 | 1 | 2.04 | 1.98 |

4 | 7 | 9 | 1 | 1 | 1.32 | 2.06 |

5 | 5 | 7 | −1 | 0 | 2.05 | 1.87 |

6 | 7 | 7 | 1 | 0 | 0.73 | 2.03 |

7 | 6 | 5 | 0 | −1 | 1.51 | 1.91 |

8 | 6 | 9 | 0 | 1 | 2.19 | 2.02 |

9 | 6 | 7 | 0 | 0 | 1.90 | 1.93 |

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## Share and Cite

**MDPI and ACS Style**

Qu, B.; Yang, Q.; Li, Y.; Sotelo, M.A.; Ma, S.; Li, Z.
A Novel Surface Inset Permanent Magnet Synchronous Motor for Electric Vehicles. *Symmetry* **2020**, *12*, 179.
https://doi.org/10.3390/sym12010179

**AMA Style**

Qu B, Yang Q, Li Y, Sotelo MA, Ma S, Li Z.
A Novel Surface Inset Permanent Magnet Synchronous Motor for Electric Vehicles. *Symmetry*. 2020; 12(1):179.
https://doi.org/10.3390/sym12010179

**Chicago/Turabian Style**

Qu, Baojun, Qingxin Yang, Yongjian Li, Miguel Angel Sotelo, Shilun Ma, and Zhixiong Li.
2020. "A Novel Surface Inset Permanent Magnet Synchronous Motor for Electric Vehicles" *Symmetry* 12, no. 1: 179.
https://doi.org/10.3390/sym12010179