# Design Optimization of a New Hybrid Excitation Drive Motor for New Energy Vehicles

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## Abstract

**:**

## 1. Introduction

## 2. Structure and Magnetic Circuit Analysis of HEDM

#### 2.1. Motor Structure

#### 2.2. Magnetic Circuit Analysis of HEDM

#### 2.2.1. Magnetic Circuit Analysis of the Combined Magnetic Pole PM Rotor

_{mt}and F

_{mc}is the magneto-motive force generated by tangential permanent magnet steel and radial permanent magnet steel, G

_{mt}and G

_{mc}is the equivalent internal magnetic conductivity of tangential permanent magnetic steel and radial permanent magnetic steel, ${G}_{\mathsf{\delta}\mathrm{t}}$ is the flux leakage conductance at the outer and inner ends of tangential permanent magnet steel, ${G}_{\mathsf{\delta}\mathrm{c}}$ is the magnetic flux leakage conductance at the left and right ends of radial permanent magnet steel, G

_{r1}and G

_{r2}is the magnetic conductivity of the rotor core of effective magnetic circuit Ⅰ and effective magnetic circuit Ⅱ, G

_{rp}is the magnetic conductivity of the rotor core between two adjacent radial permanent magnetic steels in effective magnetic circuit Ⅱ, G

_{air}is the main air gap permeability, G

_{1}is the magnetic conductivity of stator teeth and stator yoke of the combined magnetic pole permanent magnet motor, F

_{d1}is the magneto-motive force under the straight axis of the armature reaction under the no-load state of the motor, ${\Phi}_{\mathrm{pmt}}$ and ${\Phi}_{\mathrm{pmc}}$ is the magnetic flux generated by tangential permanent magnet steel and radial permanent magnet steel, ${\Phi}_{\mathsf{\delta}\mathrm{t}}$ and ${\Phi}_{\mathsf{\delta}\mathrm{c}}$ is the flux leakage generated by tangential and radial permanent magnetic steels, ${\Phi}_{\mathsf{\delta}1}$ is the effective main flux of effective magnetic circuit Ⅰ and effective magnetic circuit Ⅱ.

#### 2.2.2. Magnetic Circuit Analysis of the Claw Pole Rotor

_{e}is the magnetomotive force generated by the claw electro-excitation winding, and G

_{m}is the equivalent internal magnetic conductivity of the claw pole electric excitation winding, F

_{d2}is the induced electromotive force generated by the armature reaction of the claw pole electric excitation winding, ${G}_{\mathsf{\delta}\mathrm{n}}$ is the magnetic conductivity of the yoke of the electric excitation claw pole, G

_{pf}is the magnetic conductivity of the flange, G

_{pt}is the magnetic conductivity of the claw pole teeth, G

_{pn}is the magnetic conductivity of the excitation support opposite the flange, G

_{2}is the leakage conductance in flux path 2, G

_{3}is the leakage conductance in flux path 3, G

_{4}is the leakage conductance in flux path 4, G

_{5}is the leakage conductance in flux path 5, G

_{air}is the magnetic conductivity of the main air gap, G

_{1}is the magnetic conductivity of the stator teeth and stator yoke of the brushless electric excitation claw pole motor, ${\Phi}_{\mathrm{m}}$ is the magnetic flux generated by the claw pole electric excitation winding, ${\Phi}_{\mathsf{\delta}1}$ is the main flux of magnetic circuit 1, ${\Phi}_{\mathsf{\delta}2}$ is the leakage flux in flux path 2, ${\Phi}_{\mathsf{\delta}3}$ is the leakage flux in flux path 3, ${\Phi}_{\mathsf{\delta}4}$ is the leakage flux in flux path 4, ${\Phi}_{\mathsf{\delta}5}$ is the leakage flux in flux path 5. According to the equivalent magnetic circuit of brushless electric excitation claw pole motor, the following relationship can be established:

## 3. Structure Optimization of HEDM

#### 3.1. Structure Optimization of Combined Magnetic Pole PM Rotor

_{cog}), average torque (T

_{avg}), and distortion rate of back EMF (THD) are the main indexes to evaluate its performance, while ensuring that the torque fluctuation coefficient does not increase. Therefore, the distortion rate of back EMF becomes the primary optimization objective, the groove torque is the second optimization objective, the average torque is the third optimization objective, and the torque fluctuation coefficient is the constraint condition. The magnetic barrier structure of the combined magnetic pole PM rotor is optimized. Therefore, it is necessary to ensure that T

_{cog}and THD are as small as possible and T

_{avg}is as large as possible. Cogging torque (T

_{cog}), average torque (T

_{avg}), and distortion rate of back EMF (THD) are calculated as follows:

_{ef}is the effective axial length, ${B}_{\mathsf{\sigma}}^{2}$ represents the square of air gap magnetic density, R

_{1}and R

_{2}are the inner and outer diameters of the air gap, N

_{p}represents the pole number, N

_{s}is the slot number, N

_{L}is the least common multiple between N

_{p}and N

_{s}, b

_{0}is the angle of slot opening, ${\mathsf{\alpha}}_{\mathrm{p}}$ is the magnetic-pole embrace, ${\mathsf{\alpha}}_{\mathrm{s}}$ is the angle of the stator skew, $\mathsf{\alpha}$ is the rotor position, K

_{sk}is the skewing factor, T

_{max}and T

_{min}are the maximum and minimum output torques, U

_{1}represents the fundamental component, and U

_{n}is the nth harmonic amplitude.

^{4}= 486 experiments need to be carried out, with a large number of experiments and a long design cycle. The L

_{18}orthogonal table is selected to design the orthogonal experimental scheme, and reliable results can be obtained from only 18 experiments. The orthogonal experimental design is shown in the table. Table 3 shows the established mixed-level orthogonal experimental matrix and T

_{cog}, T

_{avg}, and THD under various experimental conditions. The numbers (1, 2, 3, 4, 5, and 6) in the table represent the corresponding level values of each optimization factor in the table.

_{Pi1}~m

_{Pi3}is the Performance index values of 3 experiments at factor P level i.

_{cog}minimum, T

_{avg}maximum, and THD minimum are A5, B1, C2, D1, E3, A1, B3, C2, D3, E1, A6, B1, C3, D1, and E3, respectively. Obviously, the optimal combination of multiple parameters for each performance indicator is not uniform. Therefore, it is necessary to further conduct variance analysis on the experimental results to determine the proportion of influence of each optimization factor on each performance index, and then the optimal combination of multiple parameters can be obtained.

_{cog}, the change of A has the greatest influence on THD, and the changes of D and E have the greatest influence on T

_{avg}. Based on the optimization objectives of T

_{cog}minimum, T

_{avg}maximum, and THD minimum, the selection of D and E is based on the maximum size of T

_{avg}, the selection of A is based on the minimum THD, and the selection of B is based on the minimum T

_{cog}.

_{cog}minimum, T

_{avg}maximum, and THD minimum is A5, B1, C2, D1, E3; A1, B3, C2, D3, E1; and A6, B1, C3, D1, E3, respectively. Combined with variance and specific gravity analysis, the optimized level factor combination is determined as A6, B1, C3, D1, and E3. Namely, the pole surface offset (d) is 13 mm, the radius of the welding groove (b) is 0.3 mm, the height of the anchor type magnetic barrier (h) is 5.5 mm, the width of the anchor type magnetic barrier (l) is 9.5 mm, and the radius of the teeth of the anchor type magnetic barrier (a) is 12 mm.

#### 3.2. Structure Optimization of Claw Pole Rotor with Brushless Electric Excitation

_{c1}= 10.5 mm) is the best parameter. As shown in Figure 8b, within the scope of the exciting current, with the increase in the thickness of the claw tip, the air gap flux density is also increasing. When the thickness of the claw tip is greater than 4 mm, the growth rate of the peak value of the air gap magnetic density slows down because the increase in the thickness of the claw tip weakens the switching ability of the axial and tangential magnetic fields. When the thickness of the claw tip (h

_{c2}) is 4 mm, a larger air gap magnetic field intensity can be obtained, which is the best claw tip parameter.

_{c2}= 0.4 mm is the best parameter.

## 4. Simulation Analysis and Prototype Experiment

#### 4.1. Simulation Analysis of HEDM

#### 4.1.1. Simulation Analysis of Combined Magnetic pole PM Rotor

#### 4.1.2. Simulation Analysis of Brushless Electric Excitation Claw Pole Rotor

#### 4.2. Prototype Experiment of HEDM

#### 4.2.1. Cogging Torque Test

#### 4.2.2. Output Torque Performance Test

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**Comparison diagrams of flux paths. (

**a**) Magnetic flux path of initial structure. (

**b**) Magnetic flux path of improved structure.

**Figure 4.**Magnetic circuit diagram of claw pole motor with brushless electric excitation. (

**a**) Electric excitation main flux path with forward current. (

**b**) Electric excitation flux path with forward current.

**Figure 6.**Schematic diagram of optimization parameters of combined magnetic pole PM rotor. (

**a**) Initial structure and (

**b**) Improved structure.

**Figure 7.**Influence of optimization factor. (

**a**) Cogging torque; (

**b**) Output torque; and (

**c**) Back-EMF distortion rate.

**Figure 8.**Variation of air-gap flux density with the thickness of claw pole under different excitation currents. (

**a**) The thickness of claw heel; and (

**b**) The thickness of claw tip.

**Figure 9.**Variation of air gap magnetic density with pole arc coefficient under different excitation currents. (

**a**) Heel pole arc coefficient; and (

**b**) tip pole arc coefficient.

**Figure 10.**Comparison diagram of rotor before and after optimization. (

**a**) Rotor magnetic field line trend comparison before and after optimization. (

**b**) Rotor magnetic flux density comparison before and after optimization.

**Figure 11.**Wave and harmonic of no-load back EMF before and after optimization. (

**a**) Back-EMF wave. (

**b**) Harmonic amplitude.

**Figure 12.**Cogging torque and output torque before and after optimization. (

**a**) Cogging torque wave. (

**b**) Output torque wave.

**Figure 14.**Comparison of air-gap magnetic density waveforms of the claw pole motor before and after optimization.

**Figure 15.**The rotor structure of the HEDM. (

**a**) Structure of combined magnetic pole PM rotor. (

**b**) Structure of brushless electric excitation claw pole rotor.

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

Rated power | 5 kW | Outer diameter of rotor | 106 mm |

Rated voltage | 72 V | Inner diameter of rotor | 36 mm |

Rated speed | 3000 r/min | Diameter of conductor | 0.8 mm |

Phase | 3 | Number of conductors per slot | 8 |

Permanent magnet | NdFe35 | Winding pitch | 5 |

Number of PM poles | 8 | Number of parallel winding | 9 |

Number of claw poles | 12 | Number of excitation winding turns | 320 |

Outer diameter of stator | 160 mm | Excitation Winding Diameter | 0.8 mm |

Inner diameter of stator | 107 mm | Rated field current | 2A |

Parameters | A (mm) | B (mm) | C (mm) | D (mm) | E (mm) |
---|---|---|---|---|---|

level 1 | 3 | 0.3 | 4.5 | 9.5 | 10 |

level 2 | 5 | 0.4 | 5 | 10.5 | 11 |

level 3 | 7 | 0.5 | 5.5 | 11.5 | 12 |

level 4 | 9 | \ | \ | \ | \ |

level 5 | 11 | \ | \ | \ | \ |

level 6 | 13 | \ | \ | \ | \ |

A | B | C | D | E | T_{cog} (mN·m) | T_{avg} (N·m) | THD (%) | |
---|---|---|---|---|---|---|---|---|

i = 1 | 1 | 1 | 1 | 1 | 1 | 351.93 | 13.08 | 27.43 |

i = 2 | 1 | 2 | 2 | 2 | 2 | 352.36 | 13.17 | 27.41 |

i = 3 | 1 | 3 | 3 | 3 | 3 | 620.92 | 13.25 | 27.34 |

i = 4 | 2 | 1 | 1 | 2 | 2 | 243.52 | 12.57 | 22.08 |

i = 5 | 2 | 2 | 2 | 3 | 3 | 480.20 | 12.65 | 22.08 |

i = 6 | 2 | 3 | 3 | 1 | 1 | 710.16 | 12.44 | 22.61 |

i = 7 | 3 | 1 | 2 | 1 | 3 | 273.77 | 12.33 | 17.03 |

i = 8 | 3 | 2 | 3 | 2 | 1 | 629.16 | 12.76 | 17.51 |

i = 9 | 3 | 3 | 1 | 3 | 2 | 850.42 | 12.86 | 17.84 |

i = 10 | 4 | 1 | 3 | 3 | 2 | 520.13 | 12.69 | 12.92 |

i = 11 | 4 | 2 | 1 | 1 | 3 | 584.56 | 12.20 | 12.82 |

i = 12 | 4 | 3 | 2 | 2 | 1 | 936.71 | 12.74 | 13.67 |

i = 13 | 5 | 1 | 2 | 3 | 1 | 236.41 | 12.90 | 9.16 |

i = 14 | 5 | 2 | 3 | 1 | 2 | 308.08 | 12.48 | 8.81 |

i = 15 | 5 | 3 | 1 | 2 | 3 | 423.91 | 12.53 | 9.31 |

i = 16 | 6 | 1 | 3 | 2 | 3 | 252.89 | 12.53 | 4.80 |

i = 17 | 6 | 2 | 1 | 3 | 1 | 555.24 | 12.90 | 6.08 |

i = 18 | 6 | 3 | 2 | 1 | 2 | 603.66 | 12.58 | 5.64 |

T_{cog} (mN·m) | T_{avg} (N·m) | THD (%) | |
---|---|---|---|

Average value | 496.335 | 12.703 | 15.808 |

Factor | Horizontal Value | T_{cog} (mN·m) | T_{avg} (N·m) | THD (%) |
---|---|---|---|---|

A | 1 | 441.74 | 13.17 | 27.39 |

2 | 477.96 | 12.55 | 22.26 | |

3 | 584.45 | 12.65 | 17.46 | |

4 | 680.47 | 12.54 | 13.14 | |

5 | 322.80 | 12.64 | 9.09 | |

6 | 470.60 | 12.67 | 5.51 | |

B | 1 | 313.11 | 12.68 | 15.57 |

2 | 484.93 | 12.69 | 15.79 | |

3 | 690.96 | 12.73 | 16.07 | |

C | 1 | 501.60 | 12.69 | 15.93 |

2 | 480.52 | 12.73 | 15.83 | |

3 | 506.89 | 12.69 | 15.67 | |

D | 1 | 472.03 | 12.52 | 15.72 |

2 | 473.09 | 12.72 | 15.80 | |

3 | 543.89 | 12.88 | 15.90 | |

E | 1 | 569.94 | 12.80 | 16.08 |

2 | 479.70 | 12.73 | 15.80 | |

3 | 439.38 | 12.58 | 15.56 |

Parameter | T_{cog} (mN·m) | T_{avg} (N·m) | THD (%) | |||
---|---|---|---|---|---|---|

Variance | Proportion | Variance | Proportion | Variance | Proportion | |

A | 12,627.48 | 31 | 4.60 × 10^{−2} | 59.78 | 56.13 | 99.82 |

B | 23,860.12 | 58.58 | 4.76 × 10^{−4} | 0.62 | 0.0419 | 0.07 |

C | 129.75 | 0.32 | 3.56 × 10^{−4} | 0.46 | 0.0115 | 0.02 |

D | 1130.85 | 2.78 | 2.17 × 10^{−2} | 28.2 | 0.0054 | 0.01 |

E | 2979.43 | 7.32 | 8.42 × 10^{−3} | 10.94 | 0.0452 | 0.08 |

Parameter | Claw Heel Thickness | Claw Tip Thickness | Pole Arc at the Claw Heel | Pole Arc at the Claw Tip |
---|---|---|---|---|

1 | 9.5 | 2.5 | 0.9 | 0.3 |

2 | 10 | 3 | 1 | 0.4 |

3 | 10.5 | 3.5 | 1.1 | 0.5 |

4 | 11 | 4 | 1.2 | 0.6 |

5 | 11.5 | 4.5 | 1.3 | 0.7 |

Feature Points | Voltage (V) | Electric Current (A) | Torque (N·m) | Rotate Speed (r/min) | Efficiency (%) |
---|---|---|---|---|---|

Load point | 72.16 | 10.50 | 1.3 | 3256 | 57.3 |

Rated point | 72.03 | 79.79 | 15.8 | 3027 | 87.0 |

Maximum efficiency point | 71.80 | 100.9 | 21.1 | 2958 | 90.1 |

Maximum output point | 71.76 | 153.7 | 35.1 | 2665 | 88.7 |

Maximum torque point | 71.76 | 153.7 | 35.1 | 2665 | 88.7 |

End point | 71.76 | 153.7 | 35.1 | 2665 | 88.7 |

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## Share and Cite

**MDPI and ACS Style**

Yan, S.; Zhang, X.; Gao, Z.; Wang, A.; Zhang, Y.; Xu, M.; Hua, S.
Design Optimization of a New Hybrid Excitation Drive Motor for New Energy Vehicles. *World Electr. Veh. J.* **2023**, *14*, 4.
https://doi.org/10.3390/wevj14010004

**AMA Style**

Yan S, Zhang X, Gao Z, Wang A, Zhang Y, Xu M, Hua S.
Design Optimization of a New Hybrid Excitation Drive Motor for New Energy Vehicles. *World Electric Vehicle Journal*. 2023; 14(1):4.
https://doi.org/10.3390/wevj14010004

**Chicago/Turabian Style**

Yan, Shilong, Xueyi Zhang, Zhidong Gao, Aichuan Wang, Yufeng Zhang, Mingjun Xu, and Sizhan Hua.
2023. "Design Optimization of a New Hybrid Excitation Drive Motor for New Energy Vehicles" *World Electric Vehicle Journal* 14, no. 1: 4.
https://doi.org/10.3390/wevj14010004