Instabilities generated by friction in a pad–disc system during the braking process

Méziane, Anissa; d'Errico, Salvatore; Baillet, Laurent; Laulagnet, Bernard

doi:10.1016/j.triboint.2006.11.005

Cited by 36 publications

(12 citation statements)

References 18 publications

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“…(31), though the calculation is lengthy. We thus conclude that the finite size H of the sliding system has significant implications for its stability, in particular it implies the existence of an instability with a wavelength determined by H. This instability should be relevant to a broad range of systems, for example an elastic brake pad sliding over a much stiffer substrate, for which recent numerical results demonstrated dominant instability modes directly related to the intrinsic vibrational modes of the pad (Behrendt et al, 2011;Meziane et al, 2007). The universal existence of this finite H instability does not immediately mean that it will be indeed observed since other instabilities, which do not necessarily satisfy kH ∼ O(1), might exist and feature a larger growth rate (when several instabilities coexist, the one with the largest growth rate will be the dominant one).…”

Section: Analysis Of the Spectrum In The Small Kh Limitmentioning

confidence: 77%

Dynamic instabilities of frictional sliding at a bimaterial interface

Brener

Weikamp

Spatschek

et al. 2016

Journal of the Mechanics and Physics of Solids

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Understanding the dynamic stability of bodies in frictional contact steadily sliding one over the other is of basic interest in various disciplines such as physics, solid mechanics, materials science and geophysics. Here we report on a two-dimensional linear stability analysis of a deformable solid of a finite height H, steadily sliding on top of a rigid solid within a generic rate-and-state friction type constitutive framework, fully accounting for elastodynamic effects. We derive the linear stability spectrum, quantifying the interplay between stabilization related to the frictional constitutive law and destabilization related both to the elastodynamic bi-material coupling between normal stress variations and interfacial slip, and to finite size effects. The stabilizing effects related to the frictional constitutive law include velocity-strengthening friction (i.e. an increase in frictional resistance with increasing slip velocity, both instantaneous and under steady-state conditions) and a regularized response to normal stress variations. We first consider the small wave-number k limit and demonstrate that homogeneous sliding in this case is universally unstable, independently of the details of the friction law. This universal instability is mediated by propagating waveguidelike modes, whose fastest growing mode is characterized by a wave-number satisfying kH ∼ O(1) and by a growth rate that scales with H −1 . We then consider the limit kH → ∞ and derive the stability phase diagram in this case. We show that the dominant instability mode travels at nearly the dilatational wave-speed in the opposite direction to the sliding direction. In a certain parameter range this instability is manifested through unstable modes at all wave-numbers, yet the frictional response is shown to be mathematically well-posed. Instability modes which travel at nearly the shear wave-speed in the sliding direction also exist in some range of physical parameters. Previous results obtained in the quasi-static regime appear relevant only within a narrow region of the parameter space. Finally, we show that a finite-time regularized response to normal stress variations, within the framework of generalized rate-and-state friction models, tends to promote stability. The relevance of our results to the rupture of bi-material interfaces is briefly discussed.

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Section: Analysis Of the Spectrum In The Small Kh Limitmentioning

confidence: 77%

Dynamic instabilities of frictional sliding at a bimaterial interface

Brener

Weikamp

Spatschek

et al. 2016

Journal of the Mechanics and Physics of Solids

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“…This scheme has been successfully applied by Carpenter and al [12] and Meziane and al. [27]. The time is first discretized with a constant step τ, the time sequence being t 0 = 0,t 1 = τ, ...,t n = nτ.…”

Section: Time Integration Schemementioning

confidence: 99%

Direct numerical simulation of the dynamics of sliding rough surfaces

et al. 2013

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The noise generated by the friction of two rough surfaces under weak contact pressure is usually called roughness noise. The underlying vibration which produces the noise stems from numerous instantaneous shocks (in the microsecond range) between surface micro-asperities. The numerical simulation of this problem using classical mechanics requires a fine discretization in both space and time. This is why the finite element method takes much CPU time. In this study, we propose an alternative numerical approach which is based on a truncated modal decomposition of the vibration, a central difference integration scheme and two algorithms for contact: The penalty algorithm and the Lagrange multiplier algorithm. Not only does it reproduce the empirical laws of vibration level versus roughness and sliding speed found experimentally but it also provides the statistical properties of local events which are not accessible by experiment. The CPU time reduction is typically a factor of 10.

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“…They presented how structural damping influences the global instability mode varying from stick-slip phenomenon to stable slip. The finite element method is also used for the simulation of engineering applications involving frictional behavior such as braking processes [35]. However, limited studies can be found on finite element modeling of rate and state dependent frictional interfaces.…”

Section: Introductionmentioning

confidence: 99%

Finite element modeling of dynamic frictional rupture with rate and state friction

Rezakhani

Barras

Brun

et al. 2020

Journal of the Mechanics and Physics of Solids

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Numerous laboratory experiments have demonstrated the dependence of the friction coefficient on the interfacial slip rate and the contact history, a behavior generically called rate and state friction. Although numerical models have been widely used for analyzing rate and state friction, in general they consider infinite elastic domains surrounding the sliding interface and rely on boundary integral formulations. Much less work has been dedicated to modeling finite size systems to account for interactions with boundaries. This paper investigates rate and state frictional interfaces in the context of finite size systems with the finite element method in explicit dynamics. It is shown that due to the highly non-linear nature of rate and state friction and its sensitivity to numerical noise, the time integration step to achieve an accurate steady state solution is orders of magnitude smaller compared to the stable time step required in boundary integral formulations. We provide evidence that the noise, which is source of instability in the finite element solution, originates from internal discretization nodes. We then investigate the long term behavior of the sliding interface for two different friction laws: a velocity weakening law, for which the friction monotonously decreases with increasing sliding velocity, and a velocity weakening-strengthening law, for which the friction coefficient first decreases but then increases above a critical velocity. We show that for both friction laws at finite times, that is before wave reflections from the boundaries come back to the sliding interface, a temporary steady state sliding is reached, with a well-defined stress drop at the interface. This stress drop gives rise to a stress concentration and leads to an analogy between friction and fracture. However, at longer times, that is after multiple wave reflections, the stress drop is essentially zero, resulting in losing the analogy with fracture mechanics. Finally, the simulations reveal that velocity weakening is unstable at long time scales, as it results in an acceleration of the sliding blocks. On the other hand, velocity weakening-strengthening reaches a steady state sliding configuration.

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Instabilities generated by friction in a pad–disc system during the braking process

Cited by 36 publications

References 18 publications

Dynamic instabilities of frictional sliding at a bimaterial interface

Dynamic instabilities of frictional sliding at a bimaterial interface

Direct numerical simulation of the dynamics of sliding rough surfaces

Finite element modeling of dynamic frictional rupture with rate and state friction

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