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Research Papers

Random Vibration of Diamond-Beaded Rope Subject to a Concentrated Load

[+] Author and Article Information
Fei Wang

School of Mechanical Engineering,
Shandong University,
Jinan, Shandong 250061, China;
Stone Engineering Technologies Research Center,
Shandong Province,
Jinan, Shandong 250061, China;
Key Laboratory of High-Efficiency and Clean
Mechanical Manufacture (Shandong University),
Ministry of Education,
Jinan 250061, China
e-mail: jixie_me2011@126.com

Jinsheng Zhang

School of Mechanical Engineering,
Shandong University,
Jinan, Shandong 250061, China;
Stone Engineering Technologies Research Center,
Shandong Province,
Jinan, Shandong 250061, China;
Key Laboratory of High-Efficiency and Clean
Mechanical Manufacture (Shandong University),
Ministry of Education,
Jinan 250061, China
e-mail: zhangjs@sdu.edu.cn

Bo Huang

School of Mechanical Engineering,
Shandong University,
Jinan, Shandong 250061, China;
Stone Engineering Technologies Research Center,
Shandong Province,
Jinan, Shandong 250061, China;
Key Laboratory of High-Efficiency and Clean
Mechanical Manufacture (Shandong University),
Ministry of Education,
Jinan 250061, China
e-mail: huangbo@sdu.edu.cn

Zhi Wang

School of Mechanical Engineering,
Shandong University,
Jinan, Shandong 250061, China;
Stone Engineering Technologies Research Center,
Shandong Province,
Jinan, Shandong 250061, China;
Key Laboratory of High-Efficiency and Clean
Mechanical Manufacture (Shandong University),
Ministry of Education,
Jinan 250061, China
e-mail: wzhi@sdu.edu.cn

Jingkun Wang

School of Mechanical Engineering,
Shandong University,
Jinan, Shandong 250061, China;
Stone Engineering Technologies Research Center,
Shandong Province,
Jinan, Shandong 250061, China;
Key Laboratory of High-Efficiency and Clean
Mechanical Manufacture (Shandong University),
Ministry of Education,
Jinan 250061, China
e-mail: wangjk@sdu.edu.cn

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received January 10, 2015; final manuscript received August 25, 2015; published online October 15, 2015. Assoc. Editor: Nicole Kessissoglou.

J. Vib. Acoust 138(1), 011003 (Oct 15, 2015) (10 pages) Paper No: VIB-15-1015; doi: 10.1115/1.4031520 History: Received January 10, 2015; Revised August 25, 2015

In this work, the random vibration characteristics of a beaded rope under a concentrated load are investigated. A stochastic model describing the sawing force of a single diamond-beaded rope was established, based on the principle of volume invariability. The governing equations of the beaded rope were obtained using Hamilton's principle. Theoretical expressions were derived to calculate the response power spectral density (PSD), load-response cross-PSD and the mean square value of the beaded rope lateral displacement, for a beaded rope subject to a concentrated load. The influence of the parameters on the random vibration characteristics of a beaded rope was analyzed, including the effects of the linear speed of the beaded rope, the tension of the beaded rope, and the location of the concentrated load. Numerical examples are given. Results show that as the tension of the beaded rope increases, the PSD and mean square value of the rope displacement are reduced. However, as the linear velocity of the beaded rope increases, the PSD and mean square value of the rope displacement are also increased. During movement of the diamond-beaded rope, the mean square value of the transverse displacement fluctuates predominantly, because of the time-varying impact force caused by the diamond beads.

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References

Figures

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Fig. 2

Model of diamond-beaded rope movement system

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Fig. 1

(a) Force analysis of the processing zone of a beaded rope and (b) force analysis diagram of a beaded rope

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Fig. 4

The influence of velocity on the system PSD

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Fig. 5

The influence of tension on the system PSD

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Fig. 7

The influence of tension on the system PSD

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Fig. 6

Mean square response of the beaded rope transverse displacement with different locations of concentrated load

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Fig. 3

(a) The response analysis under a concentrated load at x0 = 150 mm and (b) relationship between the concentrated loading position and linear velocity

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