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TECHNICAL PAPERS

The Role of Damping and Definition of the Robust Damping Factor for a Self-Exciting Mechanism With Constant Friction

[+] Author and Article Information
J-J. Sinou1

Laboratoire de Tribologie et Dynamique des Systèmes UMR-CNRS 5513, Ecole Centrale de Lyon, 36 avenue Guy de Collongue, 69134 Ecully Cedex, Francejean-jacques.sinou@ec-lyon.fr

G. Fritz, L. Jézéquel

Laboratoire de Tribologie et Dynamique des Systèmes UMR-CNRS 5513, Ecole Centrale de Lyon, 36 avenue Guy de Collongue, 69134 Ecully Cedex, France

1

Corresponding author.

J. Vib. Acoust 129(3), 297-306 (Oct 05, 2006) (10 pages) doi:10.1115/1.2730536 History: Received June 09, 2006; Revised October 05, 2006

This paper presents a linear two-degree-of-freedom model in order to analyze friction-induced instabilities that are governed by modal interaction. The role of structural damping on flutter instability is undertaken, and the effects of the structural damping ratio between the stable and unstable modes are investigated in order to clarify and to explain the mechanical process of flutter instability. In certain conditions, it is demonstrated that the merging scenario and the unstable mode may change due to this structural damping ratio. Discussions not only demontrate the role of strutural damping and the associated mechanical process but also define the robust damping factor in order to avoid design errors and to reduce flutter instability.

FIGURES IN THIS ARTICLE
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Copyright © 2007 by American Society of Mechanical Engineers
Topics: Damping , Friction
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Figures

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Figure 4

Evolution of the real parts; (a) μ=0.1 and η2=0.1, (b) μ=0.2 and η2=0.1, (c) μ=0.2 and η2=0.02, (d) μ=0.6 and η2=0.1

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Figure 1

Mechanical system

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Figure 2

Variability of frequencies and real parts (a, b): proportional damping c1=c2=0Nsm−1 (solid line); c1=c2=23.56Nsm−1 (dashed line); c1=c2=47.12Nsm−1 (dotted line); (c, d): nonproportional damping c1=c2=0Nsm−1 (solid line); c1=31.42Nsm−1; c2=23.56Nsm−1 (dashed line) c1=62.83Nsm−1; c2=47.12Nsm−1 (dotted line)

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Figure 3

Evolution of the frequencies and real parts versus the damping ratio η1∕η2 and the friction coefficient μ; (a, c) η2=0.02, (b, d) η2=0.1

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Figure 5

Evolution of the frequencies; (a) μ=0.1 and η2=0.1, (b) μ=0.2 and η2=0.1, (c) μ=0.2 and η2=0.02, (d) μ=0.6 and η2=0.1

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Figure 6

Variability of log(ΔR+1) and log(ΔF+1) for ω0,2∕ω0,1=0.75 and η2=0.02

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Figure 7

Variability of log(ΔR+1) and log(ΔF+1) (for μ=0.2 and η2=0.1)

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Figure 8

Evolution of the robust damping factor as a function of the pulsation ratio ω1∕ω2 and the damping ratio η1∕η2 (for μ=0.1); (a) η2=0.002, (b) η2=0.02, (c) η2=0.05, (d) η2=0.1

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Figure 9

Evolution of the robust damping factor as a function of the pulsation ratio ω1∕ω2 and the damping ratio η1∕η2 (for μ=0.4); (a) η2=0.002, (b) η2=0.02, (c) η2=0.05, (d) η2=0.1

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Figure 10

Evolution of the robust damping factor as a function of the friction coefficient μ and the damping ratio η1∕η2; (a) ω0,2∕ω0,1=1.33 and η2=0.02, (b) ω0,2∕ω0,1=1.33 and η2=0.1, (c) ω0,2∕ω0,1=0.66 and η2=0.02, (d) ω0,2∕ω0,1=0.66 and η2=0.1

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