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Technical Briefs

On Lugre Friction Model to Mitigate Nonideal Vibrations

[+] Author and Article Information
Jorge Luis Palacios Felix

Departamento de Estatística, Matemática Aplicada e Computação, Instituto de Geociências e Ciências Exatas, UNESP-Rio Claro, C. P. 178, Rio Claro, 13500-230 Sao Paolo, Braziljorgelpfelix@yahoo.com.br

José Manoel Balthazar

Departamento de Estatística, Matemática Aplicada e Computação, Instituto de Geociências e Ciências Exatas, UNESP-Rio Claro, C. P. 178, Rio Claro, 13500-230 Sao Paolo, Braziljmbaltha@rc.unesp.br

Reyolando M. L. R. F. Brasil

Escola Politécnica, USP-São Paulo, CP 61548, 05424-930 Sao Paolo, Brazilreyolando.brasil@poli.usp.br

Bento Rodrigues Pontes

Departamento de Engenharia Mecânica, UNESP-Bauru, Caixa Postal 473, Bauru, 17033-360 Sao Paolo, Brazilbrpontes@feb.unesp.br

J. Comput. Nonlinear Dynam 4(3), 034503 (May 21, 2009) (5 pages) doi:10.1115/1.3124783 History: Received April 09, 2008; Revised September 24, 2008; Published May 21, 2009

In this paper, a nonideal mechanical system with the LuGre friction damping model is considered. The mechanical model of the system is an oscillator not necessarily linear connected with an unbalanced motor of excitation with limited power supply. The control of motion and the attenuation of the Sommerfeld effect of the considered nonideal system are analyzed in this paper. The mathematical model of the system is represented by coupled nonlinear differential equations. The identification of some interesting nonlinear phenomenon in the transient and steady state motion of the system during the passage through resonance (using applied voltages at dc motor as control parameter) is investigated in detail using numerical simulation.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

Grahic Jump Location
Figure 1

Nonideal vibrating system with LuGre friction

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Figure 7

Time history of black line (gray line) without friction (with friction) for system 4: (a) angular velocity and (b) oscillator displacement for a=2.4, σ2∗=0.2, and μ1∗=0.8

Grahic Jump Location
Figure 6

Time history of black line (gray line) without friction (with friction) for system 4: (a) angular velocity and (b) oscillator displacement for a=2.4

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Figure 5

Amplitudes of (a) angular velocity and (b) oscillator versus control parameter for system 4: star line (triangle line) without friction (with friction)

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Figure 4

The relation between the LuGre friction FL∗ (dashed line) and the excitation force Fnef=q1(φ′2 cos φ+φ″ sin φ) (solid line) in system 3 for (a) a=1.8 and (b) a=2.4

Grahic Jump Location
Figure 3

Time history of black line (gray line) without friction (with friction) for system 3: (a) angular velocity and (b) oscillator displacement for a=2.4

Grahic Jump Location
Figure 2

Amplitudes of (a) angular velocity and (b) oscillator versus control parameter for system 3: star line (triangle line) without friction (with friction)

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