# Experimental Study on the Vibration Reduction Performance of the Spindle Rotor of a Rubbing Machine Based on Aluminium Foam Material

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Theoretical Basis

#### 2.1. Modal Theory

#### 2.2. Attenuated Vibration Theory

- where n is called the attenuation coefficient, and the unit is 1/s; ${p}_{n}$ is the undamped vibration inherent in the system. The above equations can be written as follows:$$\ddot{x}+2n\dot{x}+{p}_{n}^{2}x=0$$

## 3. Materials and Methods

#### 3.1. Modal Test and Finite Element Simulation Analysis of Main Shaft Rotor of Rubbing Machine

#### 3.1.1. Modal Test of Main Shaft Rotor of Rubbing Machine

#### 3.1.2. Finite Element Simulation Analysis of Rubbing Machine Spindle Rotor

^{−3}. The connection mode of each part of the spindle was set to be welded, and the grid was divided, as shown in Figure 6.

#### 3.2. Vibration Reduction Optimisation and Test Verification of the Main Shaft Rotor

## 4. Results

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Three-dimensional model of the spindle rotor. (1) Spindle; (2) disc cutter; (3) hammer frame; (4) hammer; (5) throwing blade; (6) support plate.

**Figure 7.**Mode shape diagram of each order. (

**a**) The 7th order; (

**b**) the 8th order; (

**c**) the 9th order; (

**d**) the 10th order; (

**e**) the 11th order; (

**f**) the 12th order.

**Figure 9.**The installation position of the foamed aluminium material of the throwing blade. (1) Throwing blade; (2) steel plate; (3) triangular aluminium foam; (4) square aluminium foam.

**Figure 10.**Mounting position of the damping ring of the hob shaft sleeve. (1) Hob shaft sleeve; (2) damping ring.

**Figure 11.**Installation position of the support plate damping ring. (1) Support plate; (2) damping ring.

**Figure 12.**Site of the steel ball impact vibration test. (

**a**) Sensor placement; (

**b**) steel ball impact vibration test system.

**Figure 13.**Axial vibration acceleration before and after vibration reduction optimisation. (

**a**) Axial vibration acceleration before optimisation; (

**b**) axial vibration acceleration after optimisation.

**Figure 14.**Comparison of shock and vibration test results before and after spindle rotor reduction optimisation: (

**a**) 150 mm test; (

**b**) 550 mm test.

**Figure 15.**Comparison of time domain data difference in all directions of bearing before and after vibration reduction optimisation.

Order | Frequency/Hz | Damping/% |
---|---|---|

1 | 113.59 | 0.90 |

2 | 138.59 | 0.24 |

3 | 143.83 | 0.39 |

4 | 154.31 | 2.34 |

5 | 233.34 | 5.66 |

6 | 262.38 | 3.72 |

Modal Test Results | Simulation Test Results | Error/% | ||
---|---|---|---|---|

Order | Frequency Hz | Order | Frequency/Hz | |

1 | 113.59 | 7 | 116.77 | 2.8 |

2 | 138.59 | 8 | 139.03 | 0.3 |

3 | 143.83 | 9 | 144.54 | 0.5 |

4 | 154.31 | 10 | 156.04 | 1.1 |

5 | 233.34 | 11 | 223.53 | 4.2 |

6 | 262.38 | 12 | 285.22 | 8.7 |

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**MDPI and ACS Style**

Yue, Y.; Tian, H.; Li, D.; Liu, F.; Wang, X.; Ren, X.; Zhao, K.
Experimental Study on the Vibration Reduction Performance of the Spindle Rotor of a Rubbing Machine Based on Aluminium Foam Material. *Processes* **2023**, *11*, 1038.
https://doi.org/10.3390/pr11041038

**AMA Style**

Yue Y, Tian H, Li D, Liu F, Wang X, Ren X, Zhao K.
Experimental Study on the Vibration Reduction Performance of the Spindle Rotor of a Rubbing Machine Based on Aluminium Foam Material. *Processes*. 2023; 11(4):1038.
https://doi.org/10.3390/pr11041038

**Chicago/Turabian Style**

Yue, Yao, Haiqing Tian, Dapeng Li, Fei Liu, Xin Wang, Xianguo Ren, and Kai Zhao.
2023. "Experimental Study on the Vibration Reduction Performance of the Spindle Rotor of a Rubbing Machine Based on Aluminium Foam Material" *Processes* 11, no. 4: 1038.
https://doi.org/10.3390/pr11041038