# 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

- Xiao, M.; Zhang, H.; Zhou, S.; Wang, K.; Ling, C. Research progress and trend of agricultural machinery fault diagnosis technology. J. Nanjing Agric. Univ.
**2020**, 43, 979–987. [Google Scholar] - Solecki, L. Preliminary recognition of whole body vibration risk in private farmers working environment. Ann. Agric. Environ. Med.
**2007**, 6, 299–304. [Google Scholar] - Chu, T.; Yang, Z.; Han, L. Analysis on satisfied degree and advantage degree of agricultural crop straw feed utilization in China. Trans. Chin. Soc. Agric. Eng.
**2016**, 32, 1–9. [Google Scholar] - Chen, C.; Yang, Y.; Xie, G. Study of the development of crop straw management policy in China. J. China Agric. Univ.
**2016**, 21, 1–11. [Google Scholar] - Yang, L.; Gao, Y. Bottlenecks of efficient utilization of corn straw feed and its solutions. J. Jilin Agric. Univ.
**2016**, 38, 634–638+644. [Google Scholar] - Wang, J.; Xu, C.; Xu, Y.; Wang, J.; Zhou, W.; Wang, Q.; Tang, H. Resonance analysis and vibration reduction optimization of agricultural machinery frame—Taking vegetable precision seeder as an example. Processes
**2021**, 9, 1979. [Google Scholar] [CrossRef] - Ji, J.; Chen, K.; Jin, X.; Wang, Z.; Dai, B.; Fan, J.; Lin, X. High-efficiency modal analysis and deformation prediction of rice transplanter based on effective independent method. Comput. Electron. Agric.
**2020**, 168, 105126. [Google Scholar] - Son, G.; Kim, B.; Cho, S.; Park, Y. Optimization of the housing shape design for radiated noise reduction of an agricultural electric vehicle gearbox. Appl. Sci.
**2020**, 10, 8414. [Google Scholar] [CrossRef] - Wang, J. Study on Noise Analysis of Rubbing and Breaking Machine; Inner Mongolia Agricultural University: Hohhot, China, 2010. [Google Scholar]
- Wang, J.; Wang, C.; Han, X.; Zhai, Z. The noise research of 9R-40 rub and breaking machine. J. Agric. Mech. Res.
**2010**, 32, 212–214+218. [Google Scholar] - Wang, J.; Wang, C.; Wang, F. Numerical simulation on three-dimensional turbulence air flow of 9R-40 rubbing and breaking machine based on fluent software. Trans. Chin. Soc. Agric. Eng.
**2010**, 26, 165–169. [Google Scholar] - Zhai, Z.; Zhang, L.; Liu, C.; Li, H.; Cui, H. Numerical simulation and experimental validation of radiation noise from vibrating shell of stalk impeller blower. Trans. Chin. Soc. Agric. Eng.
**2017**, 33, 72–79. [Google Scholar] - Zhai, Z.; Wang, C. Numerical simulation and optimization for air flow in impeller blower. Trans. Chin. Soc. Agric. Mach.
**2008**, 39, 84–87. [Google Scholar] - Zhai, Z.; Li, H.; Zhao, Y.; Liang, H. Analysis of stress-strain and structure optimization for impeller blower of the stalk rubbing machine. Mach. Des. Manuf.
**2017**, 07, 37–40. [Google Scholar] - Zhai, Z.; Zhao, Y.; Wang, L. Stress-strain analysis of throwing impeller based on ABAQUS. Mach. Des. Manuf.
**2015**, 10, 42–45. [Google Scholar] - Zhai, Z.; Zhou, L.; Yang, Z.; Zhao, Y.; Gan, S. Analysis on vibration characteristics of throwing impeller of stalk impeller blower. Trans. Chin. Soc. Agric. Eng.
**2015**, 31, 17–25. [Google Scholar] - Wang, J.; Dong, H.; Zhai, Z.; Cheng, H.; Kang, X.; Wu, Y. Modal analysis and structure optimization of the rotors of forage rubbing and breaking machine. Noise Vib. Control
**2018**, 38, 52–56+61. [Google Scholar] - Lan, Z.; Zhang, L.; Zhai, Z.; Li, Z.; Li, C. Analysis of the influences of structure parameters on pneumatic noise of the impeller blower of the stalk rubbing machine. J. Agric. Mech. Res.
**2020**, 42, 34–38+63. [Google Scholar] - Kováčik, J.; Nosko, M.; Mináriková, N.; Simančík, F.; Jerz, J. Closed-cell powder metallurgical aluminium foams reinforced with 3 vol.% sic and 3 vol.% graphite. Processes
**2021**, 9, 2031. [Google Scholar] [CrossRef] - Fiedler, T.; Sulong, M.A.; Mathier, V.; Belova, I.V.; Younger, C.; Murch, G.E. Mechanical properties of aluminium foam derived from infiltration casting of salt dough. Comput. Mater. Sci.
**2014**, 81, 246–248. [Google Scholar] [CrossRef] - Belardi, V.G.; Fanelli, P.; Trupiano, S.; Vivio, F. Multiscale analysis and mechanical characterization of open-cell foams by simplified FE modeling. Eur. J. Mech. A: Solids
**2021**, 89, 104291. [Google Scholar] [CrossRef] - Norbert, O.; Attila, S.; Alexandra, K.; Domonkos, K. Compressive mechanical properties of low-cost, aluminium matrix syntactic foams. Compos. Part A Appl. Sci. Manuf.
**2020**, 135, 105923. [Google Scholar] - Su, L.; Liu, H.; Yao, G.; Zhang, J. Experimental study on the closed-cell aluminum foam shock absorption layer of a high-speed railway tunnel. Soil Dyn. Earthq. Eng.
**2019**, 119, 331–345. [Google Scholar] [CrossRef] - Rajak, D.; Mahajan, N.; Selvaraj, S.K. Fabrication and experimental investigation on deformation behaviour of AlSi
_{10}Mg foam-filled mild steel tubes. Trans. Indian Inst. Met.**2020**, 73, 587–594. [Google Scholar] [CrossRef] - Fomin, O.; Lovska, A.F.; Skok, P.O.; Rybin, A.V. Feasibility study for using the fillers in the bearing structure components of a gondola car. Nauk. Visnyk Natsionalnoho Hirnychoho Universytetu
**2022**, 1, 51–56. [Google Scholar] [CrossRef] - Lu, X.; Sun, W.; Liang, J.; Xie, J.; Lu, Z. Experimental research on exhaust silencer of foamed aluminum alloy. Trans. Chin. Soc. Agric. Mach.
**1999**, 5, 36–40. [Google Scholar] - Ashby, M.F.; Evans, A.; Fleck, N.A.; Gibson, L.J.; Hutchinson, J.W.; Wadley, H.N.G. Metal foams: A design guide: Butterworth-Heinemann. Mater. Des.
**2002**, 23, 119. [Google Scholar] [CrossRef] - Crupi, V.; Epasto, G.; Guglielmino, E. Impact response of aluminum foam sandwiches for light-weight ship structures. Metals
**2011**, 1, 98–112. [Google Scholar] [CrossRef][Green Version] - Banhart, J. Light-metal foams-history of innovation and technological challenges. Adv. Eng. Mater.
**2013**, 15, 82–111. [Google Scholar] [CrossRef] - Jia, R.; Zhao, G. Progress in constitutive behavior of aluminum foam. Chin. J. Theor. Appl. Mech.
**2020**, 52, 603–622. [Google Scholar] - Wan, T.; Liu, Y.; Zhou, C.; Chen, X.; Li, Y. Fabrication, properties, and applications of open-cell aluminum foams: A review. J. Mater. Sci. Technol.
**2021**, 62, 11–24. [Google Scholar] [CrossRef] - Albertelli, P.; Esposito, S.; Valerio, M.; Massimo, G.; Michele, M. Effect of metal foam on vibration damping and its modelling. Int. J. Adv. Manuf. Technol.
**2021**, 117, 2349–2358. [Google Scholar] [CrossRef] - Wang, J.; Xu, H.; Ma, N. Investigation on simulation and response of impact between flexible cantilever and steel ball. Chin. J. Appl. Mech.
**2010**, 27, 471–475+638. [Google Scholar] - Bapat, C.; Popplewell, N. Several similar vibroimpact systems. J. Sound Vib.
**1987**, 113, 17–28. [Google Scholar] [CrossRef] - Qin, Z.; Lu, Q. Analysis of process model based on restitution coefficient. J. Dyn. Control
**2006**, 12, 294–297. [Google Scholar] - Zhu, D.; Xing, Y. Analytical solution of point elastic impact between structures. Chin. J. Theor. Appl. Mech.
**1996**, 28, 99–103. [Google Scholar] - Yousuf, L.S. Influence of nonlinear dynamics behavior of the roller follower on the contact stress of polydyne cam profile. Processes
**2022**, 10, 585. [Google Scholar] [CrossRef] - Li, W.; Chen, T.; Hu, X.; Huang, X. Computer simulation of vibroimpact absorbers. J. Xi’an Jiaotong Univ.
**1998**, 32, 32–35. [Google Scholar] - Xing, Y. Analytical solution of linear elastic collision of beam structure. J. Beijing Univ. Aeronaut. Astronaut.
**1998**, 24, 633–637. [Google Scholar] - Li, F. Experiment and Simulation Study of Sub-Impact in Beam Struck by Sphere; Anhui University of Technology: Hefei, China, 2016. [Google Scholar]
- Qi, X.; Yin, X.; Yang, H.; Jin, T. Study of sub-impact in simply supported beam struck by steel sphere. J. Mech. Strength
**2015**, 37, 45–51. [Google Scholar] - Wang, P.; Li, G.; Li, X. Vibration characteristics analysis of o-shaped damping ring to balance damping gear transmission system for three-cylinder engine. Processes
**2022**, 10, 1685. [Google Scholar] [CrossRef]

**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