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Research Papers

Nonlinear Friction-Induced Vibration of a Slider–Belt System

[+] Author and Article Information
Zilin Li

State Key Laboratory of Structural Analysis of
Industrial Equipment,
Dalian University of Technology,
Dalian 116024, China;
School of Engineering,
University of Liverpool,
Liverpool L69 3GH, UK
e-mail: canydao@liverpool.ac.uk

Huajiang Ouyang

State Key Laboratory of Structural Analysis of
Industrial Equipment,
Dalian University of Technology,
Dalian 116024, China;
School of Engineering,
University of Liverpool,
Liverpool L69 3GH, UK
e-mail: huajiang.ouyang@gmail.com

Zhenqun Guan

State Key Laboratory of Structural Analysis of
Industrial Equipment,
Dalian University of Technology,
Dalian 116024, China
e-mail: guanzhq@dlut.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 September 24, 2015; final manuscript received March 9, 2016; published online May 19, 2016. Assoc. Editor: Walter Lacarbonara.

J. Vib. Acoust 138(4), 041006 (May 19, 2016) (9 pages) Paper No: VIB-15-1405; doi: 10.1115/1.4033256 History: Received September 24, 2015; Revised March 09, 2016

A mass–spring–damper slider excited into vibration in a plane by a moving rigid belt through friction is a major paradigm of friction-induced vibration. This paradigm has two aspects that can be improved: (1) the contact stiffness at the slider–belt interface is often assumed to be linear and (2) this contact is usually assumed to be maintained during vibration (even when the vibration becomes unbounded at certain conditions). In this paper, a cubic contact spring is included; loss of contact (separation) at the slider–belt interface is allowed and importantly reattachment of the slider to the belt after separation is also considered. These two features make a more realistic model of friction-induced vibration and are shown to lead to very rich dynamic behavior even though a simple Coulomb friction law is used. Both complex eigenvalue analyses of the linearized system and transient analysis of the full nonlinear system are conducted. Eigenvalue analysis indicates that the nonlinear system can become unstable at increasing levels of the preload and the nonlinear stiffness, even if the corresponding linear part of the system is stable. However, they at a high enough level become stabilizing factors. Transient analysis shows that separation and reattachment could happen. Vibration can grow with the preload and vertical nonlinear stiffness when separation is considered, while this trend is different when separation is ignored. Finally, it is found that the vibration magnitudes of the model with separation are greater than the corresponding model without considering separation in certain conditions. Thus, ignoring the separation is unsafe.

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Figures

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Fig. 1

A two degrees-of-freedom model with nonlinear stiffness

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Fig. 5

The real (right) and imaginary parts (left) of the eigenvalues versus the friction coefficient μ for various nonlinear stiffness with nonproportional damping. The imaginary parts are the frequencies and real parts are growth rates (F = 100 N).

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Fig. 4

The real (right) and imaginary parts (left) of the eigenvalues versus the friction coefficient μ for various nonlinear stiffness. The imaginary parts are the frequencies and real parts are growth rates (F = 100 N).

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Fig. 3

The real (right) and imaginary parts (left) of the eigenvalues versus the friction coefficient μ for various nonlinear stiffness. The imaginary parts are the frequencies and real parts are growth rates (F = 20 N).

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Fig. 2

Vertical displacements of equilibrium points versus normal precompression force F (a) and nonlinear stiffness knl (b)

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Fig. 6

Evolution of the critical friction coefficient against the precompression force

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Fig. 7

Evolution of the critical friction coefficient against the nonlinear stiffness

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Fig. 8

Evolution of the critical friction coefficient against the precompression force

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Fig. 9

Evolution of the critical friction coefficient against the nonlinear stiffness

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Fig. 10

Time-domain results of the contact force during the time period [0–100 s]

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Fig. 11

Time response of the horizontal displacement during the time period [0–100 s]

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Fig. 12

Time response of the vertical displacement during the time period [0–100 s]

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Fig. 13

Maximum vertical amplitudes against normal precompression forces (knl = 20 N/m3)

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Fig. 14

Maximum vertical amplitudes against normal precompression forces (knl = 100 N/m3)

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Fig. 15

Maximum vertical amplitudes for various nonlinear stiffness values (F = 40 N)

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Fig. 16

Maximum vertical amplitudes for various nonlinear stiffness values (F = 60 N)

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