The present paper investigates friction-induced self-excited vibration of a bistable compliant mechanism. A pseudo-rigid-body representation of the mechanism is used containing a hardening nonlinear spring and a viscous damper. The mass is suspended from above with the spring-damper combination leading to the addition of geometric nonlinearity in the equation of motion and position- and velocity-dependent normal contact force. Friction input provided by a moving belt in contact with the mass. An exponentially decaying function of sliding velocity describes the friction coefficient and, thereby, incorporates Stribeck effect of friction. Eigenvalue analysis is employed to investigate the local stability of the steady-state fixed points. It is observed that the oscillator experiences pitchfork and Hopf bifurcations. The effects of the spring nonlinearity and precompression, viscous damping, belt velocity, and the applied normal force on the number, position, and stability of the equilibrium points are investigated. Global system behavior is studied by establishing trajectory maps of the system. Critical belt speed is derived analytically and shown to be only the result of Stribeck effect of friction. It is found that one equilibrium point dominates the steady-state response for very low damping and negligible spring nonlinearity. The presence of damping and/or spring nonlinearity tends to diminish this dominance.
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December 2018
Research-Article
Vibration Instability in a Large Motion Bistable Compliant Mechanism Due to Stribeck Friction
Alborz Niknam,
Alborz Niknam
Department of Mechanical Engineering and
Energy Processes,
Southern Illinois University Carbondale,
Carbondale, IL 62901
e-mail: alborz@siu.edu
Energy Processes,
Southern Illinois University Carbondale,
Carbondale, IL 62901
e-mail: alborz@siu.edu
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Kambiz Farhang
Kambiz Farhang
Department of Mechanical Engineering and
Energy Processes,
Southern Illinois University Carbondale,
Carbondale, IL 62901
e-mail: farhang@siu.edu
Energy Processes,
Southern Illinois University Carbondale,
Carbondale, IL 62901
e-mail: farhang@siu.edu
Search for other works by this author on:
Alborz Niknam
Department of Mechanical Engineering and
Energy Processes,
Southern Illinois University Carbondale,
Carbondale, IL 62901
e-mail: alborz@siu.edu
Energy Processes,
Southern Illinois University Carbondale,
Carbondale, IL 62901
e-mail: alborz@siu.edu
Kambiz Farhang
Department of Mechanical Engineering and
Energy Processes,
Southern Illinois University Carbondale,
Carbondale, IL 62901
e-mail: farhang@siu.edu
Energy Processes,
Southern Illinois University Carbondale,
Carbondale, IL 62901
e-mail: farhang@siu.edu
1Corresponding author.
Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received April 16, 2018; final manuscript received May 31, 2018; published online July 5, 2018. Assoc. Editor: Stefano Lenci.
J. Vib. Acoust. Dec 2018, 140(6): 061017 (9 pages)
Published Online: July 5, 2018
Article history
Received:
April 16, 2018
Revised:
May 31, 2018
Citation
Niknam, A., and Farhang, K. (July 5, 2018). "Vibration Instability in a Large Motion Bistable Compliant Mechanism Due to Stribeck Friction." ASME. J. Vib. Acoust. December 2018; 140(6): 061017. https://doi.org/10.1115/1.4040513
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