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RESEARCH PAPERS

Effect of Tangential Dither Signal on Friction Induced Oscillations in an SDOF Model

[+] Author and Article Information
Michael A. Michaux, Aldo A. Ferri, Kenneth A. Cunefare

School of Mechanical Engineering, The Georgia Institute of Technology, Atlanta, GA 30332-0405

J. Comput. Nonlinear Dynam 2(3), 201-210 (Feb 12, 2007) (10 pages) doi:10.1115/1.2727486 History: Received July 20, 2005; Revised February 12, 2007

This work examines how friction-induced oscillations in a traditional mass-on-a-moving-belt system are affected by high-frequency excitations, commonly referred to as dither signals. Two different friction laws are considered: a Stribeck friction law governed by a relationship that is cubic in the slip velocity, and an exponentially-based friction law that steadily decreases with slip velocity. Although in both cases the friction force has an initial negative slope versus relative velocity, their stability characteristics are quite different. In particular, it is shown that tangential dither can either stabilize or destabilize an initially stable system, depending on the nature of the friction law, and on other system and dither parameters. The behavior of the systems is studied through use of an averaging technique and through direct numerical simulation. The numerical study validates the stability predictions from the averaging method, and quantifies the partial-cancellation performance of tangential dither.

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Copyright © 2007 by American Society of Mechanical Engineers
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Figures

Grahic Jump Location
Figure 2

Comparison of Stribeck and decreasing friction laws. Parameters: μs=0.4, μm=0.2857.

Grahic Jump Location
Figure 3

System responses with the decreasing friction model, displacements x(τ) (top row), velocities v(τ) (middle row), and magnitude of X(ω) in dB (bottom row) for three values of tangential dither amplitude DT. (⋯) Reference case without dither excitation; (—) dithered system. Parameters: ω0=1, ζ=0.005, F=1, v0=0.05, vm=0.2, μs=0.4, μm=0.2857, RT=10, and (a)DT=0.3, (b)DT=0.4, (c)DT=0.5.

Grahic Jump Location
Figure 4

Effective Stribeck friction model for five values of tangential dither amplitude αT. Parameters: μs=0.4, μm=0.2857, and (a)αT∕vm=0, (b)αT∕vm=0.25, (c)αT∕vm=0.5, (d)αT∕vm=0.75, (e)αT∕vm=1.

Grahic Jump Location
Figure 5

Effective decreasing friction model for five values of tangential dither amplitude αT. Parameters: μs=0.4, μm=0.2857, and (a)αT∕vm=0, (b)αT∕vm=0.25, (c)αT∕vm=0.5, (d)αT∕vm=0.75, (e)αT∕vm=1.

Grahic Jump Location
Figure 6

Stability map for the Stribeck friction model. Parameters: ζ=0.005, F=1, vm=0.2, μs=0.4, and μm=0.2857.

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Figure 8

Reduction ratio using the Stribeck friction model for four values of belt velocity v0. (Solid line is the stability boundary using the averaging technique.) Parameters: ω0=1, ζ=0.005, F=1, vm=0.2, μs=0.4, μm=0.2857, and (a)v0=0.05, (b)v0=0.1, (c)v0=0.125, (d)v0=0.15.

Grahic Jump Location
Figure 9

Reduction ratio using the decreasing friction model for four values of belt velocity v0. (Solid line is the stability boundary using the averaging technique.) Parameters: ω0=1, ζ=0.005, F=1, vm=0.2, μs=0.4, μm=0.2857, and (a)v0=0.05, (b)v0=0.1, (c)v0=0.125, (d)v0=0.15.

Grahic Jump Location
Figure 10

System displacement response with the decreasing friction model for six values of tangential dither amplitude DT. Parameters: ω0=1, ζ=0.005, F=1, v0=1, vm=0.2, μs=0.4, μm=0.2857, RT=10, (a)DT=0, (b)DT=2.5, (c)DT=3, (d)DT=4, (e)DT=9, (f)DT=10.

Grahic Jump Location
Figure 11

Poincaré plots for the decreasing friction model for six values of tangential dither amplitude DT. Parameters: ω0=1, ζ=0.005, F=1, v0=1, vm=0.2, μs=0.4, μm=0.2857, RT=10, (a)DT=0, (b)DT=2.5, (c)DT=3, (d)DT=4, (e)DT=9, (f)DT=10.

Grahic Jump Location
Figure 7

Stability map for the decreasing friction model. Parameters: ζ=0.005, F=1, vm=0.2, μs=0.4, and μm=0.2857.

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