Abstract
This work is an in-depth analysis of frictional phenomena including macroscopic stick–slip and mode coupling instabilities, which can occur at different scales ranging from earthquakes to vibrational issues in machining processes. The paper presents a comparison between experimental observations of frictional macroscopic behaviours reproduced in a dedicated laboratory set-up and numerical simulations, obtained by transient finite element simulations able to reproduce the contact dynamics. The explicit finite element code PLASTD has been used to perform numerical transient analysis of two elastic bodies in frictional contact. On the other hand an experimental set-up has been used to investigate the macroscopic response of two blocks of polycarbonate in relative motion, highlighting how the contact frictional behaviour is affected by the imposed boundary conditions. Time evolution of global contact forces has been investigated; macroscopic stick–slip, modal instability behaviours and the transition to continuous sliding as a function of the system parameters have been observed. The frequency and time analysis of experimental phenomena exhibits a good agreement with numerical results obtained through transient contact simulations. The numerical analysis allows for explaining the interaction between local contact behaviour and system dynamics, which is at the origin of the different frictional scenarios. Maps of the instability scenarios are drawn as a function of boundary conditions or system parameters.
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References
Andreaus U, Casini P (2001) Dynamics of friction oscillators excited by a moving base and/or driving force. J Sound Vib 245:685–699
Hoffmann N, Fischer M, Allgaier R, Gaul L (2002) A minimal model for studying properties of the mode-coupling type instability in friction induced oscillations. Mech Res Commun 29:197–205
Renouf M, Cao HP, Nhu VH (2011) Multiphysical modeling of third-body rheology. Tribol Int 44:417–425
Andreaus U, Casini P (2002) Friction oscillator excited by moving base and colliding with a rigid or deformable obstacle. Int J Non-Linear Mech 37:117–133
D’Annibale F, Luongo A (2013) A damage constitutive model for sliding friction coupled to wear. Contin Mech Thermodyn 25:503–522
Rubinstein SM, Cohen G, Fineberg J (2007) Dynamics of precursors to frictional sliding. Phys Rev Lett 98:226103
Voisin C, Renard F, Grasso J-R (2007) Long term friction: from stick–slip to stable sliding. Geophys Res Lett 34:L13301
Rubinstein SM, Cohen G, Fineberg J (2004) Detachment fronts and the onset of dynamic friction. Nature 430:1005–1009
Rubinstein SM, Cohen G, Fineberg J (2009) Visualizing stick–slip: experimental observations of processes governing the nucleation of frictional sliding. J Phys D 42:214016
Hervé B, Sinou JJ, Mahé H, Jezequel L (2008) Analysis of squeal noise and mode coupling instabilities including damping and gyroscopic effects. Eur J Mech-A 27:141–160
Ouyang H, Nack W, Yuan Y, Chen F (2005) Numerical analysis of automotive disc brake squeal: a review. Int J Veh Noise Vib 1:207–231
Sinou JJ (2010) Transient non-linear dynamic analysis of automotive disc brake squeal—on the need to consider both stability and non-linear analysis. Mech Res Commun 37:96–105
Dezi M, Forte P, Frendo F (2014) Motorcycle brake squeal: experimental and numerical investigation on a case study. Meccanica 49:1011–1021
Weiss C, Gdaniec P, Hoffmann NP, Hothan A, Huber G, Morlock MM (2010) Squeak in hip endoprosthesis systems: an experimental study and a numerical technique to analyze design variants. Med Eng Phys 32:604–609
Heckl MA, Abrahams ID (2000) Curve squeal of train wheels, part 1: mathematical model for its generation. J Sound Vib 229:669–693
Goodman R, Sundaram PN (1978) Fault and system stiffnesses and stick–slip phenomena. Pure Appl Geophys 116:873–887
Shi Z, Ben-Zion Y (2006) Dynamic rupture on a bimaterial interface governed by slip-weakening friction. Geophys J Int 165:469–484
Di Bartolomeo M, Massi F, Baillet L, Culla A, Fregolent A, Berthier Y (2012) Wave and rupture propagation at frictional bimaterial sliding interfaces: from local to global dynamics, from stick–slip to continuous sliding. Tribol Int 52:117–131
Tonazzi D, Massi F, Culla A, Baillet L, Fregolent A, Berthier Y (2013) Instability scenarios between elastic media under frictional contact. Mech Syst Signal Process 40:754–766
Di Bartolomeo M, Meziane A, Massi F, Baillet L, Fregolent A (2010) Dynamic rupture at a frictional interface between dissimilar materials with asperities. Tribol Int 43:1620–1630
Radiguet M, Kammer DS, Gillet P, Molinari J-F (2013) Survival of heterogeneous stress distributions created by precursory slip at frictional interfaces. Phys Rev Lett 111:164302
Adams GG (1998) Steady sliding of two elastic half-spaces with friction reduction due to interface stick–slip. J Appl Mech 65:470–475
Adams GG, Nosonovsky M (2001) Elastic waves induced by the frictional sliding of two elastic half-spaces. In: Dowson D, Priest M, Dalmaz G (eds) Tribology series, vol 39. Elsevier, Amsterdam, pp 47–54
Massi F, Baillet L, Giannini O, Sestieri A (2007) Brake squeal: linear and nonlinear numerical approaches. Mech Syst Signal Process 21:2374–2393
Massi F, Rocchi J, Culla A, Berthier Y (2010) Coupling system dynamics and contact behaviour: modelling bearings subjected to environmental induced vibrations and ‘false brinelling’ degradation. Mech Syst Signal Process 24:1068–1080
Magnier V, Brunel JF, Dufrénoy P (2014) Impact of contact stiffness heterogeneities on friction-induced vibration. Int J Solids Struct 51:1662–1669
Meziane A, D’Errico S, Baillet L, Laulagnet B (2007) Instabilities generated by friction in a pad–disc system during the braking process. Tribol Int 40:1127–1136
Meziane A, Baillet L, Laulagnet B (2010) Experimental and numerical investigation of friction-induced vibration of a beam-on-beam in contact with friction. Appl Acoust 71:843–853
Maegawa S, Suzuki A, Nakano K (2010) Precursors of global slip in a longitudinal line contact under non-uniform normal loading. Tribol Lett 38:313–323
Nielsen S, Taddeucci J, Vinciguerra S (2010) Experimental observation of stick–slip instability fronts. Geophys J Int 180:697–702
Baillet L, Sassi T (2002) Finite element method with Lagrange multipliers for contact problems with friction. CR Math 334:917–922
Carpenter NJ, Taylor RL, Katona MG (1991) Lagrange constraints for transient finite element surface contact. Int J Numer Meth Eng 32:103–128
Renouf M, Massi F, Fillot N, Saulot A (2011) Numerical tribology of a dry contact. Tribol Int 44:834–844
Ben-David O, Fineberg J (2011) Static friction coefficient is not a material constant. Phys Rev Lett 106:254301
Baillet L, Link V, D’errico S, Berthier Y (2005) Influence of sliding contact local dynamics on macroscopic friction coefficient variation. In: Elemént RED (ed.), vol. 14/2-3, pp 305–321.
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Tonazzi, D., Massi, F., Baillet, L. et al. Experimental and numerical analysis of frictional contact scenarios: from macro stick–slip to continuous sliding. Meccanica 50, 649–664 (2015). https://doi.org/10.1007/s11012-014-0010-2
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DOI: https://doi.org/10.1007/s11012-014-0010-2