# Performance Analysis and Simulation of a Novel Brushless Double Rotor Machine for Power-Split HEV Applications

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## Abstract

**:**

## 1. Introduction

**Figure 4.**Typical operation states of the power-split hybrid drive system: (

**a**) Pure electric mode; (

**b**) ICE starter mode; (

**c**) CVT mode; (

**d**) Acceleration and hill climbing mode; (

**e**) Braking mode.

_{c}is the mechanical speed of the claw-pole rotor (rad/s); Ω

_{p}is the mechanical speed of the permanent-magnet rotor 1 (rad/s); ω

_{s}the angular frequency of the stator winding current (rad/s); p is the pole-pair number of the BDRM.

_{CM}is the torque of the CM, which can be positive and negative, depending on the torque difference between the ICE and output demand, and Τ

_{BDRM}is the torque of the BDRM.

_{ICE}is the input mechanical power of the ICE, Ρ

_{battery}is the input power of the battery, P

_{CM}is the electromagnetic power of the CM and P

_{BDRM}is the electromagnetic power of the BDRM.

## 2. Basic Topology and Magnetic Circuit Model of the BDRM

## 3. Reactance Parameters of the BDRM

_{eeσ}is the leakage flux passing through R

_{eeσ}.

_{ccσ}is the leakage flux passing through R

_{ccσ}.

_{a}is the main flux passing through R

_{qg}

_{1}.

## 4. Sizing and Torque Equations of the BDRM

_{ef}is the effective axial length of single-phase BDRM.

^{’}is the output apparent power, D

_{1}is the inner diameter of the claw-pole rotor, n is the synchronous speed, m is the phase number, K

_{w}is the winding factor, α

_{p}’ is the effective pole arc coefficient, B

_{δ}

_{1}is the maximum flux density in the inner air gap, σ

_{1}is the leakage factor of the flux from the inner air gap into the outer air gap, σ

_{2}is the leakage factor of the flux from the outer air gap into the stator core.

_{A}remains unchanged, the output apparent power P’ is proportional to the inner diameter of the claw-pole rotor D

_{1}, the pole-pair number p, the synchronous speed n, and the square of the motor axial length l

_{ef}. Special size characteristics of the BDRM can be drawn from analysis of Equations (13) and (14):

_{ef}, which means that a larger l

_{ef}can lead to a higher power density. Appropriate reduction of the inner diameter of the claw-pole rotor D

_{1}can increase the power density. The MMF of the winding per phase is proportional to the number of turns per phase and the changes of the pole-pair number p will not affect the MMF.

## 5. Power Factor Analysis of the BDRM

_{d}= 0, where E

_{0}and E

_{δ}are the fundamental back electromotive forces (BEMFs) at no-load and load operations, I

_{d}, I

_{q}are the d- and q-axis armature currents, R

_{1}is the armature resistance, U is the voltage fed by external circuit, L

_{q}is the q-axis inductance, ω is the radian frequency, θ is the torque angle and φ is the power factor angle.

_{i}is the flux induced by armature current only, Φ

_{m}is the flux induced by permanent magnets only.

_{m}is fixed, the power factor will be enhanced and the torque density of BDRM will fall at the same time. By reducing the pole number of BDRM when the leakage flux between the claws is reduced, the power factor is slightly enhanced. For both methods, a compromise between the torque density and the power factor must be made. Another effective way to improve the power factor and enhance torque density at the same time is to simply enhance Φ

_{m}, but more permanent magnets increase the cost of the machine, and this is clearly not attractive in practice, so in order to obtain the best performance, a compromise among all parameters should be made.

_{0}. This raises the question whether such timing adjustment could be used to improve power factor in BDRM.

_{0}, I

_{d}= I∙sinψ, I

_{q}= I∙cosψ, then the power factor could be expressed as:

_{d}, X

_{q}are the d- and q-axis synchronous reactance.

_{0}, X

_{d}, X

_{q}into Equation (18), variation of power factor with respect to $\psi $ is shown in Figure 9.

_{0}, and a greater d-axis current means that sacrifice of torque is inevitable. The compromise between the torque density and the power factor must also be made.

## 6. Practical Design Methodology

#### 6.1. Performance Evaluation by 3D Field Calculation

#### 6.2. Determination of the 2D Equivalent Structure

Number of elements | Computation time for magnetostatic field | Computation time for transient field | System | |
---|---|---|---|---|

2D FEM | 9254 | 19 s | 6 min/3 s | 2.31 GHz AMD Phenom with 2.75 GB RAM |

3D FEM | 125392 | 7 min/37 s | 5 h/59 min/35 s |

**Figure 16.**No-load BEMF and average torque from 2D FEM and 3D FEM: (

**a**) Models with different pole arc coefficients of the claw tip; (

**b**) Models with different axial lengths of single-phase; (

**c**) Models with different thickness of stator cores.

#### 6.3. Flowchart of the Design Methodology

## 7. Optimization of the BDRM

#### 7.1. Pole-Pair Number

#### 7.2. Shape of the Claws

**Figure 20.**Variation of average torque and torque ripple with pole arc coefficient of the claw root.

#### 7.3. Permanent-Magnet Rotor Structure

Types of permanent-magnet rotors | Radial surface-mounted | Radial embedding | Tangential embedding |
---|---|---|---|

Amplitude of fundamental BEMF (V) | 102.19 | 83.42 | 165.27 |

THD of BEMF (%) | 5.60 | 18.31 | 18.84 |

Peak-peak value of cogging torque (Nm) | 1.14 | 2.16 | 3.85 |

Average torque (Nm) | 24.55 | 21.42 | 38.90 |

Torque ripple (%) | 4.63 | 5.90 | 6.39 |

**Figure 22.**Inner air gap flux density: (

**a**) Radial surface-mounted structure; (

**b**) Radial embedding structure; (

**c**) Tangential embedding structure.

#### 7.4. Optimized Prototype of the BDRM

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

Rated power (kW) | 10 |

Number of phase | 3 |

Rated speed (rpm) | 2800 |

Rated current (A) | 35 |

Number of poles | 12 |

Rated efficiency (%) | 89.8 |

Rated power factor | 0.69 |

Stator outer diameter (mm) | 189 |

Shaft diameter (mm) | 48 |

Axial length of BDRM (mm) | 126 |

Outer air gap length (mm) | 0.7 |

Inner air gap length (mm) | 0.7 |

Winding turns in series per phase | 31 |

Amplitude of fundamental no-load BEMF (V) | 140.81 |

THD of BEMF (%) | 17.73 |

Peak-peak value of cogging torque (Nm) | 3.46 |

## 8. Conclusions

## Acknowledgments

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**MDPI and ACS Style**

Zheng, P.; Wu, Q.; Zhao, J.; Tong, C.; Bai, J.; Zhao, Q.
Performance Analysis and Simulation of a Novel Brushless Double Rotor Machine for Power-Split HEV Applications. *Energies* **2012**, *5*, 119-137.
https://doi.org/10.3390/en5010119

**AMA Style**

Zheng P, Wu Q, Zhao J, Tong C, Bai J, Zhao Q.
Performance Analysis and Simulation of a Novel Brushless Double Rotor Machine for Power-Split HEV Applications. *Energies*. 2012; 5(1):119-137.
https://doi.org/10.3390/en5010119

**Chicago/Turabian Style**

Zheng, Ping, Qian Wu, Jing Zhao, Chengde Tong, Jingang Bai, and Quanbin Zhao.
2012. "Performance Analysis and Simulation of a Novel Brushless Double Rotor Machine for Power-Split HEV Applications" *Energies* 5, no. 1: 119-137.
https://doi.org/10.3390/en5010119