Journal of Applied Nonlinear Dynamics
Minimal Model to Investigate ViscoElastic Contact Effect on FrictionInduced Vibration and Squeal
Journal of Applied Nonlinear Dynamics 11(2) (2022) 473485  DOI:10.5890/JAND.2022.06.014
Alborz Niknam, Kambiz Farhang
Department of Mechanical Engineering and Energy Processes, Southern Illinois University Carbondale, 1263\addressNewline Lincoln Drive, Carbondale 629016899, USA
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Abstract
A wellknown 2DOF massonbelt model is used to investigate frictioninduced vibration. By employing a KelvinVoigt definition to simulate viscoelastic contact interface, effects of contact modeling on the stability of a linearized system and sustain vibrations of the nonlinear system, such as stickslip and contact detachment are studied. In addition, the effect of a hardening nonlinear contact stiffness on transient and steadystate system responses has been discussed. Horizontal friction force is a function of vertical displacement and velocity through viscoelastic definition of contact. Contact detachment, where friction force disappears, is another source of nonlinearity and considered in governing equations. Eigenvalue analysis is performed to show the effect of viscoelastic/nonlinear contact on the stability of a linearized system. Numerical analysis is employed to solve Filippov systems of equations of motion with different possible phases in a cycle, i.e. slip, stick and separation. Results show that viscoelasticity at the contact interface plays a crucial role in the local stability of the linearized system and vertical sustained oscillation.
References

[1]  Berger, E. (2002), Friction Modeling for Dynamic System Simulation,
Applied Mechanics Reviews, 55(6), p. 535.


[2]  Ibrahim, R.A. (1994), FrictionInduced Vibration, Chatter, Squeal, and
ChaosPart I: Mechanics of Contact and Friction, Applied Mechanics
Reviews, 47(7), pp. 209226.


[3]  Ibrahim, R.A. (1994), FrictionInduced Vibration, Chatter, Squeal, and
ChaosPart II: Dynamics and Modeling, Applied Mechanics Reviews,
47(7),
pp. 227253.


[4]  Niknam, A. (2018), Vibration instability in frictionally driven elastic
mechanical system, Southern Illinois University, Carbondale, IL.


[5]  Niknam, A. and Farhang, K. (2018), Vibration Instability in a Large
Motion Bistable Compliant Mechanism Due to Stribeck Friction, Journal of
Vibration and Acoustics.


[6]  Thomsen, J.J. and Fidlin, A. (2003), Analytical Approximations for
Stickslip Vibration Amplitudes, International Journal of NonLinear
Mechanics, 38(3), pp. 389403.


[7]  Niknam, A. and Farhang, K. (2019), Frictioninduced vibration due to modecoupling and intermittent contact loss,
Journal of Vibration and Acoustics, 141(2).


[8]  Li, Z., Ouyang, H., and Guan, Z. (2016), Nonlinear FrictionInduced
Vibration of a SliderBelt System, Journal of Vibration and Acoustics,
138(4), p. 041006.


[9]  Zhang, Z., Oberst, S., and Lai, J.C.S. (2019), A NonLinear Friction
Work Formulation for the Analysis of SelfExcited Vibrations, Journal of
Sound and Vibration, 443, pp. 328340.


[10]  Sinou, J.J., Thouverez, F., and Jezequel, L. (2003), Analysis of
Friction and Instability by the Centre Manifold Theory for a NonLinear
SpragSlip Model, Journal of Sound and Vibration,
265(3), pp. 527559.


[11]  Hoffmann, N., Fischer, M., Allgaier, R., and Gaul, L. (2002), A
Minimal Model for Studying Properties of the ModeCoupling Type Instability
in Friction Induced Oscillations, Mechanics Research Communications,
29(4), pp. 197205.


[12]  Kang, J., Krousgrill, C.M., and Sadeghi, F. (2009), Oscillation
Pattern of StickSlip Vibrations, International Journal of NonLinear
Mechanics, 44(7), pp. 820828.


[13]  Hoffmann, N., Bieser, S., and Gaul, L. (2004), Harmonic Balance and
Averaging Techniques for StickSlip LimitCycle Determination in
ModeCoupling Friction SelfExcited Systems, Technische Mechanik, pp.
185197.


[14]  Sinou, J.J. and J{e}z{e}quel, L. (2007), Mode Coupling
Instability in FrictionInduced Vibrations and Its Dependency on System
Parameters Including Damping, European Journal of Mechanics, A/Solids,
26(1), pp. 106122.


[15]  Hoffmann, N. and Gaul, L. (2003), Effects of Damping on ModeCoupling
Instability in Friction Induced Oscillations, ZAMM Zeitschrift fur
Angewandte Mathematik und Mechanik, 83(8), pp. 524534.


[16]  Farhang, K. and Lim, A.L. (2005), A NonPhenomenological Account of
Friction/Vibration Interaction in Rotary Systems, Journal of Tribology,
128(1), pp. 103112.


[17]  Farhang, K. and Lim, A. (2007), A Kinetic Friction Model for
Viscoelastic Contact of Nominally Flat Rough Surfaces, Journal of
Tribology, 129(3), pp. 684688.


[18]  Hetzler, H. and Willner, K. (2012), On the Influence of Contact
Tribology on Brake Squeal, Tribology International, 46(1), pp. 237246.


[19]  Leine, R.I. and Nijmeijer, H. (2004), Dynamics and Bifurcations of
NonSmooth Mechanical Systems, SpringerVerlag Berlin Heidelberg.


[20]  Nayfeh, A.H. and Mook, D.T. (2008), Nonlinear Oscillations, John
Wiley & Sons.
