# Experimental and Finite Element Analysis to Investigate the Vibration of Oblique-Stud Stator Frame in a Large Hydropower Generator Unit

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## Abstract

**:**

## 1. Introduction

## 2. Field Experimental Tests

#### 2.1. The Investigated Stator Frame

#### 2.2. Three Sets of Experimental Tests

#### 2.3. Results of the Experimental Tests

_{2}(3.125 Hz). The integral multiple of rotation frequency f

_{1}, and f

_{3}–f

_{6}are also significant in the spectrum, and the influence on vibration caused by these harmonic components decreases with the increase of frequency. The minor-amplitude (f

_{7}and f

_{8}) and low-frequency component exist due to the hydraulic vibration passing through the base of stator.

## 3. Finite Element Analysis

#### 3.1. Methodology

#### 3.2. A 2D Generator Model for Electromagnetic Analysis

#### 3.3. A 3D Stator Model for Mechanical Analysis

**M**,

**C**and

**K**are the matrices of mass, damping and stiffness, respectively.

**F**stands for the column vector of external forces.

_{boundry}stands for the constraints originated from the bolt connections between stator pack and brackets, which are considered as a fixed support.

## 4. Comparative Analyses of Different Models

#### 4.1. Eccentric Rotor–Stator Model

#### 4.1.1. Electromagnetic Field Analysis

_{r}is the rotational frequency of rotor, and f

_{d}is the frequency of dynamic eccentricity model.

#### 4.1.2. Transient Structure Analysis

#### 4.1.3. Harmonic Response Analysis

#### 4.2. Structural Comparative Analysis

#### 4.2.1. Simulation of Different Structures

#### 4.2.2. Research of Different Structures

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 4.**Vibration peak value of stator frame of experimental tests: (

**a**) excitation test at no-load and rated speed condition; (

**b**) rotation speed test at no-load and 100% excitation condition; and (

**c**) load test at rated speed and 100% excitation condition.

**Figure 8.**B-H (B stands for magnetic field intensity, while H represent magnetic induction intensity) curve of silicon steel 50W250.

**Figure 12.**Magnetic flux density at the center of air-gap with different eccentric models: (

**a**) concentric model; (

**b**) static eccentric model; and (

**c**) dynamic eccentric model.

**Figure 13.**Electromagnetic force densities at the center of air-gap with different eccentricity: (

**a**) concentric model; (

**b**) static eccentric model; and (

**c**) dynamic eccentric model.

**Figure 14.**Fast fourier transformation (FFT) of electromagnetic force density with different eccentric models.

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

Radius of rotor (mm) | 6430 |

Outer diameter of stator (mm) | 13,700 |

Inner diameter of stator (mm) | 12,900 |

Height of stator core (mm) | 2340 |

No. of parallel branches of stator winding | 4 |

No. of stator’s slots | 528 |

No. of poles | 64 |

Rotate speed (r/min) | 93.75 |

Item | Simulation | Experiment | Error |
---|---|---|---|

Peak of line voltage | 21.87 kV | - | - |

Peak of line current | 14.72 kA | - | - |

Voltage | 15.44 kV | 15.76 kV | 2.0% |

Current | 10.41 kA | 10.1826 kA | 2.2% |

Power | 250.6 MW | 250.1 MW | 0.33% |

Item | Material | ρ (kg/m^{−3}) | E (×${10}^{11}$ Pa) | μ (-) |
---|---|---|---|---|

Stator core | Silicon steel 50W250 | 7650 | 1.9 | 0.28 |

Coils | Red Cooper | 3580 | 1.5 | 0.34 |

Stator frame | Steel Q235A | 7850 | 2.1 | 0.3 |

Cooler | Aluminum alloy | 2770 | 0.71 | 0.33 |

Mode | Natural Frequency | Description |
---|---|---|

1 | 28.2 Hz | Horizontal elliptical deformation |

2 | 29.6 Hz | Horizontal circular displacement |

3 | 41.4 Hz | Horizontal triangular tensile deformation |

4 | 52.1 Hz | Horizontal quadrangular tensile deformation |

Item | The Studied Stator Frame | Contrast Model |
---|---|---|

Structures | Oblique-stud structure | Radial-stud structure |

Characteristic | flexible | rigid |

Natural frequency of 1st mode | 28.2 Hz | 32.2 Hz |

Description of 1st mode shape | Horizontal elliptical deformation | Horizontal circular displacement |

Maximum amplitude | 2.1 µm | 1.4 µm |

Station | No. of Unit | Capacity (MW) | Vibration Amplitude (µm) | Type |
---|---|---|---|---|

Three Gorges | 15 | 700 | 18 | rigid |

24 | 700 | 50 | flexible | |

Laxiwa | 1 | 700 | 120 | flexible |

Goupitan | 3 | 600 | 60 | rigid |

4 | 600 | 200 | flexible | |

pubugou | 1 | 600 | 6 | rigid |

4 | 600 | 28 | rigid |

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## Share and Cite

**MDPI and ACS Style**

Zhou, J.; Peng, X.; Li, R.; Xu, Y.; Liu, H.; Chen, D.
Experimental and Finite Element Analysis to Investigate the Vibration of Oblique-Stud Stator Frame in a Large Hydropower Generator Unit. *Energies* **2017**, *10*, 2175.
https://doi.org/10.3390/en10122175

**AMA Style**

Zhou J, Peng X, Li R, Xu Y, Liu H, Chen D.
Experimental and Finite Element Analysis to Investigate the Vibration of Oblique-Stud Stator Frame in a Large Hydropower Generator Unit. *Energies*. 2017; 10(12):2175.
https://doi.org/10.3390/en10122175

**Chicago/Turabian Style**

Zhou, Jianzhong, Xuanlin Peng, Ruhai Li, Yanhe Xu, Han Liu, and Diyi Chen.
2017. "Experimental and Finite Element Analysis to Investigate the Vibration of Oblique-Stud Stator Frame in a Large Hydropower Generator Unit" *Energies* 10, no. 12: 2175.
https://doi.org/10.3390/en10122175