# Optimal Design Method of Post-Assembly Magnetizing Device with Field–Circuit Coupling Analysis

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## Abstract

**:**

## 1. Introduction

## 2. Investigated Magnetizing Fixture and Design Guidelines

#### 2.1. Structure of Investigated Post-Assembly Magnetizing Device

#### 2.2. Design Guidelines

## 3. Equivalent Models and Field–Circuit Coupling Analysis

#### 3.1. Magnetic Equivalent Circuit Model of Rotor

#### 3.2. Magnetic Equivalent Circuit Model of Stator

#### 3.3. Equivalent Circuit of Eddy Currents in Permanent Magnet

- The applied magnetic field is uniform and perpendicular to the surface of the PMs.
- ${\mu}_{\mathrm{PM}}$ and ${\gamma}_{\mathrm{PM}}$ are constant.

#### 3.4. Field–Circuit Coupling Analysis

## 4. Optimization Design of Auxiliary Stator-Type Magnetizing Device

## 5. Experiment

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

PM | Permanent Magnet |

FEA | Finite Element Analysis |

FCCA | Field–Circuit Coupling Analysis |

IPMSM | Interior Permanent Magnet Synchronous Motor |

MEC | Magnetic Equivalent Circuit |

SPMSM | Surface-Mounted Permanent Magnet Synchronous Motor |

MMF | Magnetomotive Force |

FE | Finite Element |

GA | Genetic algorithm |

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**Figure 1.**Auxiliary stator-type post-assembly magnetizing device: (

**a**) Quarter cross-section of the rotor to be magnetized and the auxiliary stator. (

**b**) Power circuit structure of magnetizer.

**Figure 4.**Influence of auxiliary stator structure on the rotor MEC model: (

**a**) ${B}_{\mathrm{r}3}$–${F}_{\mathrm{r}3}$ curve with different pole widths and 4.4 mm pole length. (

**b**) ${B}_{\mathrm{r}3}$–${F}_{\mathrm{r}3}$ curve with different pole lengths and 23.5° pole width.

**Figure 6.**Distribution of flux lines around the auxiliary stator slot: (

**a**) One of the magnetic branches with saturated iron core. (

**b**) Geometric relationship of ${\theta}_{\mathrm{o}\mathrm{f}\mathrm{f}\mathrm{s}\mathrm{e}\mathrm{t}\mathit{j}}$, ${B}_{\mathrm{t}\mathrm{a}\mathrm{n}\mathit{j}}$, and ${B}_{\mathrm{n}\mathrm{o}\mathrm{r}\mathit{j}}$.

**Figure 8.**Comparison between ${\phi}_{\mathrm{re}}$ and ${\widehat{\phi}}_{\mathrm{re}}$ at different frequencies: (

**a**) Reaction flux with $f=1$ kHz and ${R}_{\mathrm{e}}=35.8\phantom{\rule{0.166667em}{0ex}}\mathrm{m}\mathsf{\Omega}$. (

**b**) Reaction flux with $f=10$ kHz and ${R}_{\mathrm{e}}=37.2\phantom{\rule{0.166667em}{0ex}}\mathrm{m}\mathsf{\Omega}$. (

**c**) Reaction flux with $f=100$ kHz and ${R}_{\mathrm{e}}=42.5\phantom{\rule{0.166667em}{0ex}}\mathrm{m}\mathsf{\Omega}$. (

**d**) Reaction flux with $f=1$ MHz and ${R}_{\mathrm{e}}=90.0\phantom{\rule{0.166667em}{0ex}}\mathrm{m}\mathsf{\Omega}$. (

**e**) Variation of ${R}_{\mathrm{e}}$ with frequency.

**Figure 10.**Dynamic results obtained with FCCA and FEA: (

**a**) Current with time. (

**b**) Flux linkage with time. (

**c**) Eddy currents losses with time. (

**d**) Capacitor voltage with time.

**Figure 14.**Comparison of the two device designs when the capacitance is 2 mF and discharge voltage is 700 V. (

**a**) Flux density map of empirical design. (

**b**) Flux density map of optimized design.

**Figure 17.**Flux generated by post-magnetized PMs with discharge voltage for empirical design and optimized design.

**Figure 18.**Flux density of post-assembly PMs at different sampling points. (

**a**) Positions of sampling points of a PM. (

**b**) Comparison of the flux density at different sampling points under empirical design and optimal design.

**Figure 19.**Measured flux density distribution at the rotor surface with pre-magnetized PMs, and with the PMs post-magnetized with the optimized and empirically designed devices.

Parameter Name | Parameter Value |
---|---|

Power | 1300 W |

Speed | 15,000 r/min |

Number of poles | 4 |

Rotor outer diameter | 42 mm |

Rotor stack length | 46.2 mm |

Magnet thickness | 2.8 mm |

Magnet width | 11.2 mm |

Iron core material | FeSi laminations |

PM material | Nd-Fe-B (N42SH) |

Parameter Name | Parameter Value |
---|---|

Number of poles | 4 |

Air gap length | 0.5 mm |

Auxiliary stator outer diameter | 72.4 mm |

Auxiliary stator inner diameter | 43 mm |

Auxiliary stator length | 46.2 mm |

Pole angle | 43 degree |

Pole length | 4.4 mm |

Yoke thickness | 6.6 mm |

Number of coil layers | 2 |

Number of turns per coil | 10 |

Number of parallel branches | 1 |

Wire gauge | 1.8 mm |

Bare wire diameter | 1.5 mm |

Magnetizer capacitance | 2 mF |

Discharging voltage | 700 V |

Auxiliary stator material | Silicon Laminations |

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## Share and Cite

**MDPI and ACS Style**

Zhu, Z.-A.; Wang, Y.-C.; Qin, X.-F.; Yao, L.; Gyselinck, J.; Shen, J.-X.
Optimal Design Method of Post-Assembly Magnetizing Device with Field–Circuit Coupling Analysis. *Actuators* **2023**, *12*, 383.
https://doi.org/10.3390/act12100383

**AMA Style**

Zhu Z-A, Wang Y-C, Qin X-F, Yao L, Gyselinck J, Shen J-X.
Optimal Design Method of Post-Assembly Magnetizing Device with Field–Circuit Coupling Analysis. *Actuators*. 2023; 12(10):383.
https://doi.org/10.3390/act12100383

**Chicago/Turabian Style**

Zhu, Zi-Ang, Yun-Chong Wang, Xue-Fei Qin, Lei Yao, Johan Gyselinck, and Jian-Xin Shen.
2023. "Optimal Design Method of Post-Assembly Magnetizing Device with Field–Circuit Coupling Analysis" *Actuators* 12, no. 10: 383.
https://doi.org/10.3390/act12100383