# Cogging Torque Reduction Based on a New Pre-Slot Technique for a Small Wind Generator

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## Abstract

**:**

## 1. Introduction

## 2. Machine Type and Main Parameters

## 3. Cogging Torque

_{c}in a PMSG is given by [7]

_{m}are, respectively, the reluctances viewed by the magnetomotive force and by the magnetic field, ∅

_{m}the flux due to the magnets crossing the air gap, and N the number of winding turns.

_{cog}

_{cog}, reluctance R should be independent of the rotor position. Therefore, a very low cogging torque design requires an almost constant value of R for any rotor position.

## 4. Cogging Torque Measurement

_{o}is the air gap permeability, L is the rotor depth, g is the air gap length, B

_{n}the normal flux density, B

_{t}the tangential flux density and r the radius from the center of the rotor to the center of the air gap [7].

## 5. Cogging Torque Reduction Methods

#### 5.1. Pre-Slot Method

#### 5.2. Manufacturing Aspects to Reduce the Cogging Torque

#### 5.3. Comparative Results

_{slots}= 36) and the number of poles (N

_{poles}= 20). The results in Figure 15 show the decrease in the cogging torque with the pre-slot triangular method and that this improvement is even better when combining this pre-slot installation technique with fractional skewing in the rotor, up to 84% less in the most realistic case of considering errors in manufacturing processes.

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Cross section area of the permanent magnet synchronous generator (PMSG): (

**a**) Original model; (

**b**) Model with centered holes.

**Figure 3.**Simulation results of cogging torque of the original model considering manufacturing errors.

**Figure 6.**Proposed cogging-torque reduction method: (

**a**) Pre-slot with separator; (

**b**) Pre-slot with triangular separator.

**Figure 10.**Magnetic field distribution (θ = 0°): (

**a**) Original model, without centered holes; (

**b**) Model with centered holes.

**Figure 15.**Cogging torque of the centered holes PMSG model, triangular pre-slot model and triangular pre-slot model with skewing (with manufacturing errors).

**Figure 16.**Air gap magnetic flux of the centered holes PMSG model, triangular pre-slot model, and triangular pre-slot model with skewing (with manufacturing errors).

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

Phase | 3 |

Pole number | 20 |

Slot number | 36 |

Rated speed | 232 rpm |

Rated power | 6300 W |

Rated voltage | 256.4 V |

Rated torque | 102 Nm |

Air gap | 1 mm |

Thickness of PM | 3 mm |

Rotor diameter | 180 mm |

Material of steel | M330-50A |

Material of PM | NdFeB |

Model | THD (%) |
---|---|

Original design | 1.54 |

Design with closed slot | 1.39 |

Design with pre-slot | 1.88 |

Design with triangular pre-slot | 1.33 |

**Table 3.**Comparison of the maximum cogging torque values obtained for the prototype and the different models considered in the study.

Model | Without Manufacturing Errors | Considering Manufacturing Errors | ||
---|---|---|---|---|

Nm | Reduction (%) | Nm | Reduction (%) | |

Original Design (without Centered Holes) | ||||

Prototype | 3.70 | - | - | - |

Original design | 2.32 | - | 3.92 | - |

Pre-slot with separation | 1.44 | 37.9 | 2.03 | 48.2 |

Triangular pre-slot | 1.21 | 47.8 | 1.90 | 51.5 |

Design with all Holes Centered | ||||

Original design | 0.86 | - | 3.31 | - |

Pre-slot with separation | 0.61 | 29.1 | 1.80 | 45.6 |

Triangular pre-slot | 0.59 | 31.4 | 1.76 | 46.8 |

**Table 4.**Comparison of the maximum cogging torque values of PMSG with centered holes and the different models considering skewing.

Model | Without Manufacturing Errors | Considering Manufacturing Errors | ||
---|---|---|---|---|

Nm | Reduction (%) | Nm | Reduction (%) | |

Design with centered holes | 0.86 | - | 3.31 | - |

Design with centered holes + Triangular pre-slot | 0.59 | 31.4 | 1.76 | 46.8 |

Design with centered holes + Skewing | 0.31 | 64.0 | 1.34 | 59.5 |

Design with centered holes + Triangular pre-slot + Skewing | 0.03 | 96.5 | 0.51 | 84.6 |

**Table 5.**Comparison of the electromotive force (EMF) and cogging torque values of PMSG with centered holes and the different models considering skewing.

Model | EMF (V) (p.u.) | Cogging Torque (Nm) | |
---|---|---|---|

Design with centered holes | 241.52 | 1.000 | 3.31 |

Design with centered holes + Skewing | 229.47 | 0.950 | 1.34 |

Design with centered holes + Triangular pre-slot | 247.73 | 1.026 | 1.76 |

Design with centered holes + Triangular pre-slot + Skewing | 233.04 | 0.965 | 0.51 |

© 2018 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**

García-Gracia, M.; Jiménez Romero, Á.; Herrero Ciudad, J.; Martín Arroyo, S. Cogging Torque Reduction Based on a New Pre-Slot Technique for a Small Wind Generator. *Energies* **2018**, *11*, 3219.
https://doi.org/10.3390/en11113219

**AMA Style**

García-Gracia M, Jiménez Romero Á, Herrero Ciudad J, Martín Arroyo S. Cogging Torque Reduction Based on a New Pre-Slot Technique for a Small Wind Generator. *Energies*. 2018; 11(11):3219.
https://doi.org/10.3390/en11113219

**Chicago/Turabian Style**

García-Gracia, Miguel, Ángel Jiménez Romero, Jorge Herrero Ciudad, and Susana Martín Arroyo. 2018. "Cogging Torque Reduction Based on a New Pre-Slot Technique for a Small Wind Generator" *Energies* 11, no. 11: 3219.
https://doi.org/10.3390/en11113219