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Research Papers

Friction-Induced Vibration Due to Mode-Coupling and Intermittent Contact Loss

[+] Author and Article Information
Alborz Niknam

Department of Mechanical
Engineering and Energy Processes,
Southern Illinois University Carbondale,
1263 Lincoln Drive,
Carbondale, IL 62901-6899
e-mail: alborz@siu.edu

Kambiz Farhang

Mem. ASME
Department of Mechanical Engineering and
Energy Processes,
Southern Illinois University Carbondale,
1263 Lincoln Drive,
Carbondale, IL 62901-6899
e-mail: farhang@siu.edu

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received March 15, 2018; final manuscript received October 2, 2018; published online November 14, 2018. Assoc. Editor: Maurizio Porfiri.

J. Vib. Acoust 141(2), 021012 (Nov 14, 2018) (10 pages) Paper No: VIB-18-1113; doi: 10.1115/1.4041671 History: Received March 15, 2018; Revised October 02, 2018

A two degrees-of-freedom (2DOFs) single mass-on-belt model is employed to study friction-induced instability due to mode-coupling. Three springs, one representing contact stiffness, the second providing lateral stiffness, and the third providing coupling between tangential and vertical directions, are employed. In the model, mass contact and separation are permitted. Therefore, nonlinearity stems from discontinuity due to dependence of friction force on relative mass-belt velocity and separation of mass-belt contact during oscillation. Eigenvalue analysis is carried out to determine the onset of instability. Within the unstable region, four possible phases that include slip, stick, separation, and overshoot are found as possible modes of oscillation. Piecewise analytical solution is found for each phase of mass motion. Then, numerical analyses are used to investigate the effect of three parameters related to belt velocity, friction coefficient, and normal load on the mass response. It is found that the mass will always experience stick-slip, separation, or both. When separation occurs, mass can overtake the belt causing additional nonlinearity due to friction force reversal. For a given coefficient of friction, the minimum normal load to prevent separation is found proportional to the belt velocity.

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References

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Figures

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Fig. 1

The mechanical model proposed to study the friction self-excited vibration [15]

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Fig. 2

Real part (upper graph) and imaginary part (lower graph) of eigenvalue (μcr=0.25): Γ=0.8,Γc=0.2,andζ1=ζ2=0.0074

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Fig. 3

(a) Phase plane for pure slip oscillation. V=0.5, n=0.4, μ=0.3 (solid line), and μ=0.6 (dash line). The horizontal line shows the belt velocity; (b) time history of x1t at μ=0.3; (c) time history of x2t at μ=0.3. The horizontal line shows the separation boundary (x2=0); (d) phase plane (x1,dx1/τ) at μ=0.3; (e) time history of x1t at μ=0.6; (f) time history of x2t at μ=0.6; (g) phase plane (x1,dx1/τ) at μ=0.6. The horizontal line shows the separation boundary (x2=0).

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Fig. 4

Time history of friction force: V=0.5, n=0.4, andμ=0.3

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Fig. 5

Phase plane for different coefficients of friction. It is obvious that greater friction coefficient expands phase portrait: V=0.5 and n=0.4.

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Fig. 6

Mass oscillation with overshoot: (a) friction force and (b) mass motion. V=0.5, n=0.4, and μ=0.6.

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Fig. 7

Phase plane of the oscillator at different belt velocities. μ=0.3 and n=0.4.

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Fig. 8

(a) Investigating separation and stick. The solid line stands for the tangential velocity (v1=dx1/dτ) of the oscillator and dash line shows the normal displacement; (b) investigating the relation between vertical velocity (v2=dx2/dτ) and onset of slip; (c) zoom-in view of transient response. V=0.05, μ=0.3, and n=0.4.

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Fig. 9

Phase plot for the different normal loads when V=0.2 and μ=0.3. Greater normal load the greater amplitude of vibration.

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Fig. 10

Normal force versus belt velocity. The region above the line separation does not happen. μ=0.3.

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Fig. 11

Normal force versus belt velocity. The region above the line separation does not happen.

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Fig. 12

Phase plot for the different friction coefficients when V=0.2 and n=1.2

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