# Influence of Geometric Dimensions on the Performance of Switched Reluctance Machine

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## Abstract

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## 1. Introduction

- We describe our approach to geometric influence by analyzing the behavior of SRM output quantities (flux linkage and torque) by finite element simulation for two motors, a three-phase 6/4 SRM and a four-phase 8/6 SRM. This study encompasses the effect of eight dimensions on machine performance, which are individually analyzed to determine its influence on the average torque value and saturation.
- We present a novel perspective of evaluating the performance of SRM through constructing and analyzing performance graphs, which help the designer to understand which geometric dimensions should be modified for specific applications.

## 2. SRM Design Considerations

#### 2.1. Revisit the Selection of SRM Dimensions

#### 2.2. Simulated Motors

## 3. Analysis of the Influence of Geometrical Dimensions

#### 3.1. Stator Polar Arc

#### 3.2. Rotor Polar Arc

#### 3.3. Stator Yoke Thickness

#### 3.4. Rotor Yoke Thickness

#### 3.5. Inner Diameter

#### 3.6. Outer Diameter

#### 3.7. Air Gap

#### 3.8. Number of Turns

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 2.**Feasible pole arcs for the stator and rotor poles of an (

**a**) 6/4 SRM three-phase (

**b**) 8/6 SRM four-phase.

**Figure 20.**Influence of number of turns ($NT$) variation on torque and flux linkage of 6/4 and 8/6 SRM.

Variable | 6/4 SRM | 8/6 SRM | ||||
---|---|---|---|---|---|---|

${\mathit{\beta}}_{s}\mathbf{=}{\mathbf{30}}^{\circ}$ | ${\mathit{\beta}}_{s}\mathbf{=}{\mathbf{37.5}}^{\circ}$ | ${\mathit{\beta}}_{s}\mathbf{=}{\mathbf{45}}^{\circ}$ | ${\mathit{\beta}}_{s}\mathbf{=}{\mathbf{15}}^{\circ}$ | ${\mathit{\beta}}_{s}\mathbf{=}{\mathbf{22.5}}^{\circ}$ | ${\mathit{\beta}}_{s}\mathbf{=}{\mathbf{30}}^{\circ}$ | |

Average torque $(N\xb7m)$ | 3.280 | 3.367 | 3.360 | 3.956 | 4.966 | 5.029 |

$|{B}_{1}|$$\left(T\right)$ | 1.935 | 1.936 | 1.940 | 1.720 | 1.966 | 1.965 |

$|{B}_{2}|$$\left(T\right)$ | 2.772 | 2.790 | 2.795 | 2.421 | 2.776 | 2.797 |

Variable | 6/4 SRM | 8/6 SRM | ||||
---|---|---|---|---|---|---|

${\mathit{\beta}}_{\mathit{r}}\mathbf{=}{\mathbf{30}}^{\circ}$ | ${\mathit{\beta}}_{\mathit{r}}\mathbf{=}{\mathbf{45}}^{\circ}$ | ${\mathit{\beta}}_{\mathit{r}}\mathbf{=}{\mathbf{60}}^{\circ}$ | ${\mathit{\beta}}_{\mathit{r}}\mathbf{=}{\mathbf{22.5}}^{\circ}$ | ${\mathit{\beta}}_{\mathit{r}}\mathbf{=}{\mathbf{30}}^{\circ}$ | ${\mathit{\beta}}_{\mathit{r}}\mathbf{=}{\mathbf{37.5}}^{\circ}$ | |

Average torque $(N\xb7m)$ | 3.160 | 3.538 | 3.200 | 4.722 | 5.358 | 5.053 |

$|{B}_{1}|$$\left(T\right)$ | 1.957 | 1.580 | 1.223 | 1.966 | 1.881 | 1.649 |

$|{B}_{2}|$$\left(T\right)$ | 2.781 | 2.343 | 2.061 | 2.712 | 2.649 | 2.371 |

Variable | 6/4 SRM | 8/6 SRM | ||||
---|---|---|---|---|---|---|

${\mathit{c}}_{\mathit{s}}\mathbf{=}\mathbf{0.5}$ | ${\mathit{c}}_{\mathit{s}}\mathbf{=}\mathbf{0.75}$ | ${\mathit{c}}_{\mathit{s}}\mathbf{=}\mathbf{1.0}$ | ${\mathit{c}}_{\mathit{s}}\mathbf{=}\mathbf{0.5}$ | ${\mathit{c}}_{\mathit{s}}\mathbf{=}\mathbf{0.75}$ | ${\mathit{c}}_{\mathit{s}}\mathbf{=}\mathbf{1.0}$ | |

Average torque $(N\xb7m)$ | 3.259 | 3.318 | 3.332 | 4.859 | 4.974 | 4.994 |

$|{B}_{1}|$$\left(T\right)$ | 1.924 | 1.943 | 1.949 | 1.866 | 1.962 | 1.949 |

$|{B}_{2}|$$\left(T\right)$ | 2.702 | 2.820 | 2.934 | 2.609 | 2.781 | 2.729 |

Variable | 6/4 SRM | 8/6 SRM | ||||
---|---|---|---|---|---|---|

${\mathit{c}}_{\mathit{r}}\mathbf{=}\mathbf{0.5}$ | ${\mathit{c}}_{\mathit{r}}\mathbf{=}\mathbf{0.75}$ | ${\mathit{c}}_{\mathit{r}}\mathbf{=}\mathbf{1.0}$ | ${\mathit{c}}_{\mathit{r}}\mathbf{=}\mathbf{0.5}$ | ${\mathit{c}}_{\mathit{r}}\mathbf{=}\mathbf{0.75}$ | ${\mathit{c}}_{\mathit{r}}\mathbf{=}\mathbf{1.0}$ | |

Average torque $(N\xb7m)$ | 3.214 | 3.446 | 3.387 | 4.577 | 4.995 | 5.309 |

$|{B}_{1}|$$\left(T\right)$ | 1.939 | 1.818 | 1.650 | 1.952 | 1.939 | 1.865 |

$|{B}_{2}|$$\left(T\right)$ | 2.745 | 2.627 | 2.430 | 2.759 | 2.779 | 2.5955 |

Variable | 6/4 SRM | 8/6 SRM | ||||
---|---|---|---|---|---|---|

${\mathit{D}}_{\mathit{i}}\mathbf{=}82$ | ${\mathit{D}}_{\mathit{i}}\mathbf{=}91.1$ | ${\mathit{D}}_{\mathit{i}}\mathbf{=}100.2$ | ${\mathit{D}}_{\mathit{i}}\mathbf{=}82$ | ${\mathit{D}}_{\mathit{i}}\mathbf{=}91.1$ | ${\mathit{D}}_{\mathit{i}}\mathbf{=}100.2$ | |

Average torque $(N\xb7m)$ | 3.109 | 3.280 | 3.416 | 4.702 | 4.966 | 5.187 |

$|{B}_{1}|$$\left(T\right)$ | 1.919 | 1.935 | 1.948 | 1.934 | 1.966 | 1.982 |

$|{B}_{2}|$$\left(T\right)$ | 2.659 | 2.772 | 2.798 | 2.694 | 2.776 | 2.683 |

Variable | 6/4 SRM | 8/6 SRM | ||||
---|---|---|---|---|---|---|

${\mathit{k}}_{{\mathit{D}}_{\mathbf{0}}}\mathbf{=}\mathbf{0.4}$ | ${\mathit{k}}_{{\mathit{D}}_{\mathbf{0}}}\mathbf{=}\mathbf{0.55}$ | ${\mathit{k}}_{{\mathit{D}}_{\mathbf{0}}}\mathbf{=}\mathbf{0.7}$ | ${\mathit{k}}_{{\mathit{D}}_{\mathbf{0}}}\mathbf{=}\mathbf{0.4}$ | ${\mathit{k}}_{{\mathit{D}}_{\mathbf{0}}}\mathbf{=}\mathbf{0.55}$ | ${\mathit{k}}_{{\mathit{D}}_{\mathbf{0}}}\mathbf{=}\mathbf{0.7}$ | |

Average torque $(N\xb7m)$ | 3.226 | 3.277 | 3.312 | 4.893 | 4.959 | 5.023 |

$|{B}_{1}|$$\left(T\right)$ | 1.875 | 1.924 | 1.957 | 1.939 | 1.943 | 1.977 |

$|{B}_{2}|$$\left(T\right)$ | 2.523 | 2.709 | 2.958 | 2.517 | 2.715 | 2.827 |

Variable | 6/4 SRM | 8/6 SRM | ||||
---|---|---|---|---|---|---|

$\mathit{g}\mathbf{=}\mathbf{0.3}$ | $\mathit{g}\mathbf{=}\mathbf{0.4}$ | $\mathit{g}\mathbf{=}\mathbf{0.5}$ | $\mathit{g}\mathbf{=}\mathbf{0.3}$ | $\mathit{g}\mathbf{=}\mathbf{0.4}$ | $\mathit{g}\mathbf{=}\mathbf{0.5}$ | |

Average torque $(N\xb7m)$ | 3.322 | 2.895 | 2.509 | 5.024 | 4.338 | 3.732 |

$|{B}_{1}|$$\left(T\right)$ | 1.935 | 1.861 | 1.775 | 1.966 | 1.883 | 1.795 |

$|{B}_{2}|$$\left(T\right)$ | 2.772 | 2.666 | 2.544 | 2.776 | 2.683 | 2.541 |

Variable | 6/4 SRM | 8/6 SRM | ||||
---|---|---|---|---|---|---|

$\mathit{NT}=\mathbf{50}$ | $\mathit{NT}=\mathbf{62}$ | $\mathit{NT}=\mathbf{74}$ | $\mathit{NT}=\mathbf{50}$ | $\mathit{NT}=\mathbf{62}$ | $\mathit{NT}=\mathbf{74}$ | |

Average torque $(N\xb7m)$ | 2.376 | 3.280 | 4.204 | 3.594 | 4.966 | 6.365 |

$|{B}_{1}|$$\left(T\right)$ | 1.865 | 1.940 | 1.978 | 1.897 | 1.966 | 2.002 |

$|{B}_{2}|$$\left(T\right)$ | 2.652 | 2.772 | 2.853 | 2.663 | 2.776 | 2.855 |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Mamede, A.C.F.; Camacho, J.R.; Araújo, R.E. Influence of Geometric Dimensions on the Performance of Switched Reluctance Machine. *Machines* **2019**, *7*, 71.
https://doi.org/10.3390/machines7040071

**AMA Style**

Mamede ACF, Camacho JR, Araújo RE. Influence of Geometric Dimensions on the Performance of Switched Reluctance Machine. *Machines*. 2019; 7(4):71.
https://doi.org/10.3390/machines7040071

**Chicago/Turabian Style**

Mamede, Ana Camila F., José Roberto Camacho, and Rui Esteves Araújo. 2019. "Influence of Geometric Dimensions on the Performance of Switched Reluctance Machine" *Machines* 7, no. 4: 71.
https://doi.org/10.3390/machines7040071