# Practical Modal Analysis of a Prototyped Hydrogenerator

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Analytical Model

#### 2.2. Finite-Element Model

#### 2.3. Validation Measurements on a Prototyped Hydrogenerator

## 3. Results

#### 3.1. Comparison between Models Using Different Input Parameters

#### 3.2. Experimental Results

## 4. Discussion and Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**FE model: (

**a**) Stator core and winding; (

**b**) Frame parts replaced by shell elements; (

**c**) Contact between the stator yoke and the double-dovetail bars.

**Figure 7.**Calculated mode shapes: (

**a**) General view of mode orders 2 and 3 with frame; (

**b**) Mode orders 2 and 3, hiding the frame from the plot; (

**c**) Mode orders 2 and 3 for the model without the frame.

**Figure 8.**Effect of stator frame with bonded and frictionless contact between core and double-dovetail bars.

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

Rated output | 732 kVA |

Rated speed | 375 rpm |

Number of poles | 16 |

Number of stator slots | 96 |

Stator core outer diameter | 1640 mm |

Stator core total length | 330 mm |

Ventilation ducts | 11 × 6 mm |

Parameter | Core | Winding | Frame |
---|---|---|---|

$\rho $ (kg/m³) | 7600 | 7965.5 | 7850 |

${E}_{x}$$,{E}_{y}$ (GPa) | 180 | 0.1...67.4 | 200 |

${E}_{z}$ (GPa) | 1...180 | ||

${G}_{xy}$ (GPa) | 69.23 | 0.04...25.15 ^{1} | 76.92 |

${G}_{xz}$$,{G}_{xz}$ (GPa) | 0.99...69.23 ^{1} | ||

${\mu}_{xy}$ | 0.3 | 0.34 | 0.3 |

${\mu}_{xz}$$,{\mu}_{yz}$ | 0.0017...0.3 ^{1} |

^{1}Calculated based on defined values of Young’s modulus according to Equations (3)–(5).

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## Share and Cite

**MDPI and ACS Style**

de Barros, A.; Galai, A.; Ebrahimi, A.; Schwarz, B.
Practical Modal Analysis of a Prototyped Hydrogenerator. *Vibration* **2021**, *4*, 853-864.
https://doi.org/10.3390/vibration4040048

**AMA Style**

de Barros A, Galai A, Ebrahimi A, Schwarz B.
Practical Modal Analysis of a Prototyped Hydrogenerator. *Vibration*. 2021; 4(4):853-864.
https://doi.org/10.3390/vibration4040048

**Chicago/Turabian Style**

de Barros, Allan, Ahmed Galai, Amir Ebrahimi, and Babette Schwarz.
2021. "Practical Modal Analysis of a Prototyped Hydrogenerator" *Vibration* 4, no. 4: 853-864.
https://doi.org/10.3390/vibration4040048