# Comparative Analysis and Design of Double-Rotor Stator-Permanent-Magnet Motors with Magnetic-Differential Application for Electric Vehicles

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## Abstract

**:**

## 1. Introduction

- Provided a review of major differential systems in the market and discussed both their pros and cons;
- Proposed two novel motors for MagD systems, namely, the DSPM and FRPM motors with MC windings tactfully located in the motors;
- Thoroughly investigated the performances of three major types of stator-PM motors for the MagD application by using the 3D FEA simulation;
- Compared three motors and suggested suitable motor types on the basis of various application scenarios;
- Fabricated a motor prototype to conduct experimentations to validate the aforementioned theoretical analysis and simulation.

## 2. Motor Structures, Operation Principles, and Optimization

#### 2.1. Topologies and Operation Principles

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

_{s}is the stator-slot number, and m is the phase number. Moreover, its stator-slot number Z

_{s}should follow [21]:

_{w}is the pole pairs of armature windings, and k is a positive odd number. Lastly, for the FSPM motor, the relationship between its winding pole pairs, rotor-pole number, and stator PM pole pairs P

_{s}observes [23]:

#### 2.2. Optimization

_{rs}, MC winding arc B

_{mc}, and armature winding arc B

_{ac}are calculated based on the centerline, as shown in Figure 3b. In the case of the DSPM motor, its MC winding arc and PM arc are both equal to the armature winding arc B

_{ac}. The optimization of the DSPM and FRPM motor follows the same practice used for the FSPM motor in [17], aiming at providing a reasonably large torque and suppressing the torque ripple. Additionally, the analysis is conducted by 3D simulation using the FEA software JMAG. To make the comparison fair enough, all motors take on the same constraints in [17], that is, 420 mm outer diameter D

_{o}for the motor, 0.6 mm air-gap length g, and 186.4 mm stack length L

_{stk}. The slot filling factor is selected as 0.6.

_{em}is the electromagnetic torque, B

_{ave}is the average flux density in the air gap, A

_{in}is the electrical loading, k

_{d}is the distribution factor, and k

_{io}is the ratio of inner and outer diameter or the split ratio that equals D

_{i}/D

_{o}. From Equation (5), one can see that, apart from the constraints, the split ratio k

_{io}is the key factor for determining the motor torque. Thus, the split ratio should be optimized priorly. Next, the PM thickness L

_{pm}, rotor slot arc B

_{rs}, armature winding arc B

_{ac}, thickness of the rotor yoke and teeth L

_{ry}and L

_{rt}, and stator yoke thickness L

_{sy}are optimized orderly, and the results are shown in Figure 4. Note that arcs are in degree and lengths are in mm.

_{io}increasing, the torque drops while its ripple goes up. Here, the torque refers to the summation of the left and right rotor torque. Note that the smaller the k

_{io}, the heavier the motor, since the motor volume is mainly determined by it. Thus, taking the torque density into consideration, it can be seen that k

_{io}= 0.4 is a reasonable option for both motors to achieve large torque while maintaining a relatively low torque ripple. Initially, the PM thickness L

_{pm}for the DSPM and FRPM motors are 30 and 5 mm, respectively. According to Figure 4d, given that the PM materials are expensive, they are optimized to be 24 and 5 mm after optimization.

_{ac}and the rotor slot arc B

_{rs}, play important roles in the determination of motor torque performance. For the proposed DSPM motor, its constraints on the stator arc parameters are:

_{pm}, B

_{mc}, and B

_{st}are the PM arc, MC winding arc, and stator teeth arc, respectively. When B

_{ac}increases, the current flowing through the winding slot will increase, and so does the space to accommodate PM materials. Thus, the torque performance will be mainly restrained by saturation of stator and rotor yokes. From Figure 4e, it can be found that the torque increases together with B

_{ac}. However, as regards the proposed FRPM motor, its stator arc parameters are governed by:

_{ac}will take up more space for locating PM materials and accelerate the saturation of the stator. In this case, there exists a B

_{ac}to obtain the optimal torque output, as shown in Figure 4f. In terms of the rotor slot arc, one can see from Figure 4e,f that the torque increases at the beginning and then decreases with the growth of B

_{rs}. Consequently, B

_{ac}and B

_{rs}are optimized as 16° and 27.5° for the DSPM motor and 12° and 27.5° for the FRPM motor.

_{ry}and rotor teeth length L

_{rt}, which significantly influence the armature winding area, stator volume, and saturation in both the stator and rotor, are also taken into consideration in the optimization. As shown in Figure 4g,h, with the increase in both L

_{ry}and L

_{rt}, the torque rises first and then drops. This is because the increase in the stack length of the rotor will reduce the armature winding area, which limits the input power. Additionally, the stator is more likely to saturate due to its shrinking size. As a result, the optimal L

_{ry}is 17.5 mm for both motors. Further, L

_{rt}is optimized as 12.5 mm for the DSPM motor and 15 mm for the FRPM motor.

_{sy}increment. According to the optimization results, the optimized design parameters of the proposed DSPM and FRPM motors are listed in Table 1, while that of the FSPM motor will be adopted from [17]. Note that the height of MC winding, L

_{mc}, is kept constant during the optimization.

## 3. Comparison of Motor Performance

^{2}, and the rotor speed is chosen to be 900 rpm. The simulation results are presented in the following.

#### 3.1. No-Load EMF

#### 3.2. Electromagnetic Torque

^{2}current density J

_{ac}, the torque performances of the motors are shown in Figure 6a. Similar to the traditional comparison of these three motors, the FSPM motor shows the best torque performance, that is, the highest torque and lowest torque ripple, while the DSPM motor is inferior to the other two counterparts. Additionally, the average torque versus J

_{ac}is evaluated as depicted in Figure 6b, where all motors saturate more or less when the current density increases.

#### 3.3. Differential Torque

#### 3.4. Efficiency and Loss

## 4. Experimental Results

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 2.**Operation principles of three AF-DR motors with rotors. (

**a**) Aligned position: (

**i**) DSPM, (

**ii**) FRPM, (

**iii**) FSPM. (

**b**) Unaligned position: (

**i**) DSPM, (

**ii**) FRPM, (

**iii**) FSPM.

**Figure 3.**Sketch of the AF-DR FRPM motor with key design parameters: (

**a**) cylindrical view; (

**b**) top view.

**Figure 4.**Optimization results. (

**a**) k

_{io}—DSPM, (

**b**) k

_{io}—FRPM, (

**c**) torque ripple vs. k

_{io}, (

**d**) torque vs. L

_{pm}, (

**e**) B

_{rs}and B

_{ac}—DSPM, (

**f**) B

_{rs}and B

_{ac}—FRPM, (

**g**) L

_{ry}and L

_{rt}—DSPM, (

**h**) L

_{ry}and L

_{rt}—FRPM, (

**i**) L

_{sy}—DSPM, (

**j**) L

_{sy}—FRPM.

**Figure 6.**Torque performances of three AF-DR motors without MC current: (

**a**) J

_{ac}= 6 A/mm

^{2}; (

**b**) different armature current densities.

**Figure 7.**Torque performances of three AF-DR motors under different MC current densities: (

**a**) DSPM, (

**b**) FRPM, (

**c**) FSPM, (

**d**) total torque.

**Figure 8.**Efficiency and iron loss of three AF-DR motors under different MC current densities: (

**a**) efficiency; (

**b**) iron loss.

Parameters | DSPM | FRPM | Parameters | DSPM | FRPM |
---|---|---|---|---|---|

Outer diameter | 420 mm | Rotor slot arc | 27.5° | ||

Inner diameter | 168 mm | AC winding arc | 16° | 12° | |

Air-gap length | 0.6 mm | MC winding arc | 16° | 6° | |

Axial stack length | 186.4 mm | Turns per AC coils | 20 | ||

Rotor yoke length | 17.5 mm | Turns per MC coils | 30 | ||

Rotor teeth length | 12.5 mm | 15 mm | Slot filling factor | 0.6 | |

PM thickness | 24 mm | 5 mm | PM material | N35SH | |

Stator yoke thickness | 60 mm | 35 mm | SMC material | Somaloy 700-3P | |

Height of MC winding | 22 mm | 20 mm | No. of rotor slots | 8 | 16 |

Characteristics | DSPM | FRPM | FSPM |
---|---|---|---|

SMC volume (L) | 14.38 | 12.65 | 12.90 |

PM volume (L) | 1.37 | 0.47 | 1.75 |

Frequency (Hz) | 120 | 240 | 150 |

Back-EMF amplitude (V) | 150.2 | 165.3 | 298.7 |

Current (rms, A) | 73.5 | 89.8 | 89.4 |

Total torque (Nm) | 526.6 | 628.2 | 950.1 |

Torque ripple | 62.3% | 18.2% | 7.8% |

Total torque/PM volume (Nm/L) | 384.4 | 1336.6 | 542.9 |

Torque density (Nm/kg) | 3.58 | 4.51 | 6.04 |

Output power (kW) | 49.62 | 59.21 | 89.54 |

Loss (kW) | 5.81 | 10.57 | 4.29 |

Efficiency | 89.5% | 84.9% | 95.4% |

Power density (kW/kg) | 0.34 | 0.43 | 0.57 |

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

Outer diameter | 220 mm | Turns per AC coils | 60 |

Inner diameter | 128 mm | Turns per MC coils | 64 |

Air-gap length | 1.0 mm | Slot filling factor | 0.4 |

Axial stack length | 88 mm | PM remanence | 1.14 T |

Stator poles no. | 12 | PM volume | 163 cm^{3} |

Rotor poles no. | 10 | SMC materials | Somaloy 700-3P |

Coil type | AWG 22 | Outer frame material | Aluminum |

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**MDPI and ACS Style**

Yang, T.; Chau, K.T.; Liu, W.; Ching, T.W.; Cao, L.
Comparative Analysis and Design of Double-Rotor Stator-Permanent-Magnet Motors with Magnetic-Differential Application for Electric Vehicles. *World Electr. Veh. J.* **2022**, *13*, 199.
https://doi.org/10.3390/wevj13110199

**AMA Style**

Yang T, Chau KT, Liu W, Ching TW, Cao L.
Comparative Analysis and Design of Double-Rotor Stator-Permanent-Magnet Motors with Magnetic-Differential Application for Electric Vehicles. *World Electric Vehicle Journal*. 2022; 13(11):199.
https://doi.org/10.3390/wevj13110199

**Chicago/Turabian Style**

Yang, Tengbo, Kwok Tong Chau, Wei Liu, Tze Wood Ching, and Libing Cao.
2022. "Comparative Analysis and Design of Double-Rotor Stator-Permanent-Magnet Motors with Magnetic-Differential Application for Electric Vehicles" *World Electric Vehicle Journal* 13, no. 11: 199.
https://doi.org/10.3390/wevj13110199