# Saturation-Induced Variable-Flux Characteristics in a 12-Slot 10-Pole Concentrated Winding Permanent-Magnet Motor

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## Abstract

**:**

## 1. Introduction

## 2. A Leakage-Flux Bypass CW Motor

## 3. A Saturation-Induced Variable-Flux CW Motor

#### 3.1. Magnetic Flux Density Distribution

#### 3.2. Variable-Flux Characteristics

#### 3.3. Motor Performances

## 4. Experimental Verification

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

CW | Concentrated winding |

EMF | Electromotive force |

FEM | Finite element method |

FSCW | Fractional-slot concentrated winding |

MTPA | Maximum torque per ampere |

MTPF | Maximum torque per flux-linkage |

PM | Permanent magnet |

## References

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**Figure 1.**Cross sections of 12-slot 10-pole PM motors that have (

**a**) a conventional stator and a conventional rotor (CONV), (

**b**) a conventional stator and a rotor with leakage-flux bypasses (LFBP), and (

**c**) a proposed stator and a conventional rotor (PROP).

**Figure 2.**Variable-flux characteristics of CONV: (

**a**) d-axis flux linkage, (

**b**) torque for q-axis current, and (

**c**) torque for flux linkage.

**Figure 3.**Variable-flux characteristics of LFBP: (

**a**) d-axis flux linkage, (

**b**) torque for q-axis current, and (

**c**) torque for flux linkage.

**Figure 5.**Magnetic flux density distribution in the MTPA operation with an armature current of $25\phantom{\rule{0.166667em}{0ex}}\mathrm{A}$ in LFBP.

**Figure 7.**Magnetic flux density distribution in the MTPA operation with an armature current of $25\phantom{\rule{0.166667em}{0ex}}\mathrm{A}$ in (

**a**) CONV and (

**b**) PROP.

**Figure 8.**Variable-flux characteristics of PROP: (

**a**) d-axis flux linkage, (

**b**) torque for q-axis current, and (

**c**) torque for flux linkage.

**Figure 10.**No-load line EMF at a rotational speed of $1500\phantom{\rule{0.166667em}{0ex}}{\mathrm{min}}^{-1}$ in CONV and PROP.

**Figure 11.**Line EMF in the MTPA operation with an armature current of $25\phantom{\rule{0.166667em}{0ex}}\mathrm{A}$ and a rotational speed of $1500\phantom{\rule{0.166667em}{0ex}}{\mathrm{min}}^{-1}$ in CONV and PROP.

**Figure 12.**Torque in the MTPA operation at an armature current of $25\phantom{\rule{0.166667em}{0ex}}\mathrm{A}$ in CONV and PROP.

**Figure 13.**Maximum torque for rotational speed under the conditions of a maximum armature current of $25\phantom{\rule{0.166667em}{0ex}}\mathrm{A}$ and a maximum line voltage of $140\phantom{\rule{0.166667em}{0ex}}\mathrm{V}$ in CONV and PROP.

**Figure 16.**No-load line EMF induced by the prototype at a rotational speed of $1500\phantom{\rule{0.166667em}{0ex}}{\mathrm{min}}^{-1}$.

**Figure 17.**Static torque produced by the prototype at a q-axis current of $15\phantom{\rule{0.166667em}{0ex}}\mathrm{A}$.

**Figure 18.**Variable-flux characteristics of the prototype at a rotational speed of $1500\phantom{\rule{0.166667em}{0ex}}{\mathrm{min}}^{-1}$ : (

**a**) torque for q-axis current and (

**b**) torque for line voltage.

CONV | LFBP | PROP | |
---|---|---|---|

Stack length | $50\phantom{\rule{0.166667em}{0ex}}\mathrm{mm}$ | $50\phantom{\rule{0.166667em}{0ex}}\mathrm{mm}$ | $50\phantom{\rule{0.166667em}{0ex}}\mathrm{mm}$ |

Stator outer diameter | $160\phantom{\rule{0.166667em}{0ex}}\mathrm{mm}$ | $160\phantom{\rule{0.166667em}{0ex}}\mathrm{mm}$ | $160\phantom{\rule{0.166667em}{0ex}}\mathrm{mm}$ |

Rotor outer diameter | $88\phantom{\rule{0.166667em}{0ex}}\mathrm{mm}$ | $88\phantom{\rule{0.166667em}{0ex}}\mathrm{mm}$ | $88\phantom{\rule{0.166667em}{0ex}}\mathrm{mm}$ |

Air gap length | $1\phantom{\rule{0.166667em}{0ex}}\mathrm{mm}$ | $1\phantom{\rule{0.166667em}{0ex}}\mathrm{mm}$ | $1\phantom{\rule{0.166667em}{0ex}}\mathrm{mm}$ |

Stator yoke width | $14\phantom{\rule{0.166667em}{0ex}}\mathrm{mm}$ | $14\phantom{\rule{0.166667em}{0ex}}\mathrm{mm}$ | $14\phantom{\rule{0.166667em}{0ex}}\mathrm{mm}$ |

Stator tooth width | $14\phantom{\rule{0.166667em}{0ex}}\mathrm{mm}$ | $14\phantom{\rule{0.166667em}{0ex}}\mathrm{mm}$ | $14\phantom{\rule{0.166667em}{0ex}}\mathrm{mm}$ |

Stator tooth tip base thickness | $7\phantom{\rule{0.166667em}{0ex}}\mathrm{mm}$ | $7\phantom{\rule{0.166667em}{0ex}}\mathrm{mm}$ | $2\phantom{\rule{0.166667em}{0ex}}\mathrm{mm}$ |

Stator tooth tip end thickness | $3\phantom{\rule{0.166667em}{0ex}}\mathrm{mm}$ | $3\phantom{\rule{0.166667em}{0ex}}\mathrm{mm}$ | $2\phantom{\rule{0.166667em}{0ex}}\mathrm{mm}$ |

Stator slot opening width | 5 | 5 | 4 |

Leakage-flux bypass thickness | — | $2\phantom{\rule{0.166667em}{0ex}}\mathrm{mm}$ | — |

Magnet thickness | $3.5\phantom{\rule{0.166667em}{0ex}}\mathrm{mm}$ | $3.5\phantom{\rule{0.166667em}{0ex}}\mathrm{mm}$ | $3.5\phantom{\rule{0.166667em}{0ex}}\mathrm{mm}$ |

Magnet width | $16\phantom{\rule{0.166667em}{0ex}}\mathrm{mm}$ | $16\phantom{\rule{0.166667em}{0ex}}\mathrm{mm}$ | $16\phantom{\rule{0.166667em}{0ex}}\mathrm{mm}$ |

Number of turns per coil | 30 | 30 | 30 |

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**MDPI and ACS Style**

Yokoi, Y.; Higuchi, T.
Saturation-Induced Variable-Flux Characteristics in a 12-Slot 10-Pole Concentrated Winding Permanent-Magnet Motor. *Machines* **2023**, *11*, 824.
https://doi.org/10.3390/machines11080824

**AMA Style**

Yokoi Y, Higuchi T.
Saturation-Induced Variable-Flux Characteristics in a 12-Slot 10-Pole Concentrated Winding Permanent-Magnet Motor. *Machines*. 2023; 11(8):824.
https://doi.org/10.3390/machines11080824

**Chicago/Turabian Style**

Yokoi, Yuichi, and Tsuyoshi Higuchi.
2023. "Saturation-Induced Variable-Flux Characteristics in a 12-Slot 10-Pole Concentrated Winding Permanent-Magnet Motor" *Machines* 11, no. 8: 824.
https://doi.org/10.3390/machines11080824