# Back EMF Waveform Comparison and Analysis of Two Kinds of Electrical Machines

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## Abstract

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## 1. Introduction

## 2. Back EMF Analysis of FSPM Machine and VFMPM Machine

#### 2.1. Operation Principle Analysis

#### 2.2. Back EMF Waveform Analysis of Machine with Straight Slot and Skewed Slot

#### 2.3. Magnetization and Demagnetization Analysis of LNG52

## 3. Simulation of FSPM Machine and VFMPM Machine

#### 3.1. Back EMF Waveforms of FSPM Machine with Straight Slot and Skewed Slot

#### 3.2. Back EMF Waveforms of VFMPM Machine with Skewed Slot

## 4. Experimental Validation

## 5. Discussions of the Maximum Back EMF Waveform Amplitude Difference between FSPM Machine and VFMPM Machine

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**Relative position between rotor and stator of VFMPM machine, and the corresponding variation of flux linkage and phase back EMF. (

**a**) Position a; (

**b**) Position b; (

**c**) Position c; (

**d**) Position d; (

**e**) Phase flux linkage waveform; (

**f**) Phase back EMF waveform.

**Figure 4.**Back EMF waveform analysis of VFMPM machine. (

**a**) Straight-slot-type back EMF waveforms (0°, 1°, 2°, 3°, 4° and 5° are the initial rotation degrees of rotor); (

**b**) Skewed-slot-type back EMF waveform; (

**c**) Back EMF harmonics comparison of straight-slot type and skewed-slot type.

**Figure 6.**Simulation model and back EMF waveform comparison. (

**a**) Mesh dividing; (

**b**) Simulation model; (

**c**) Comparison of back EMF waveforms (1000 r/min); (

**d**) Harmonics comparison of back EMF waveforms.

**Figure 7.**Simulation models of weaken flux and enhance flux. (

**a**) Weaken flux model of VFMPM machine (magnetization of LNG52); (

**b**) Enhance flux model of VFMPM machine (demagnetization of LNG52).

**Figure 10.**Back EMF waveforms of FSPM machine and VFMPM machine. (

**a**) Back EMF waveform of FSPM machine; (

**b**) Back EMF waveform of VFMPM machine after enhance flux; (

**c**) Back EMF waveform of VFMPM machine after weaken flux.

**Figure 12.**Detailed analysis of mutual demagnetization effect in VFMPM machine. (

**a**) Variation of magnetic flux density (B); (

**b**) Variation of magnetic field strength (H); (

**c**) Key variation of magnetic flux density (B) and magnetic field strength (H); (

**d**) Decrease of magnetic field strength of LNG52.

Descriptions | FSPM | VFMPM | |
---|---|---|---|

Stator | Outer radius | 65.5 mm | 79.2 mm |

Inner radius | 35 mm | 35 mm | |

Tooth width | 8.22 deg | 8.22 deg | |

Axial length | 75 mm | 75 mm | |

Quantity of slots | 12 | 12 | |

Materials (iron core) | DW360_50 | DW360_50 | |

Rotor | Outer radius | 34.5 mm | 34.5 mm |

Tooth width | 10 deg | 10 deg | |

Axial length | 75 mm | 75 mm | |

Poles | 14 | 14 | |

Materials (iron core) | DW360_50 | DW360_50 | |

NdFeB35 | Thick | 3.5 mm | 3.5 mm |

Length | 15 mm | 15 mm | |

Magnet coercive force | 625 kA/m | 625 kA/m | |

LNG52 | Length | None | 12 mm |

Thick | None | 5 mm | |

Magnet coercive force | None | 56 kA/m | |

Others | Air gap wide | 0.5 mm | 0.5 mm |

Turns of armature winding per phase | 140 | 140 | |

Turns of field regulating winding per LNG52 | None | 60 | |

Maximum current of field regulating winding | None | 15 A | |

DC-link voltage | 220 A | 220 A | |

Rated current | 5 A rms | 5 A rms | |

Resistance per phase | 0.9 Ω | 0.9 Ω | |

Rated power (approximate value) | 1 kW | 1 kW | |

Rated speed | 3000 rpm | 3000 rpm |

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**MDPI and ACS Style**

Cui, Y.; Faizan, M.; Chen, Z.
Back EMF Waveform Comparison and Analysis of Two Kinds of Electrical Machines. *World Electr. Veh. J.* **2021**, *12*, 149.
https://doi.org/10.3390/wevj12030149

**AMA Style**

Cui Y, Faizan M, Chen Z.
Back EMF Waveform Comparison and Analysis of Two Kinds of Electrical Machines. *World Electric Vehicle Journal*. 2021; 12(3):149.
https://doi.org/10.3390/wevj12030149

**Chicago/Turabian Style**

Cui, Yingjie, Munawar Faizan, and Zhongxian Chen.
2021. "Back EMF Waveform Comparison and Analysis of Two Kinds of Electrical Machines" *World Electric Vehicle Journal* 12, no. 3: 149.
https://doi.org/10.3390/wevj12030149