Mixed finite element formulation in large deformation frictional contact problem

International audienceThis paper presents a mixed variational framework and numerical examples to treat a bidimensional friction contact problem in large deformation. Two different contact algorithms with friction are developed using the 2D finite element code PLAST2. The first contact algorithm is the classical node-on-segment, and the second one corresponds to an extension of the mortar element method to a unilateral contact problem with friction. In this last method, the discretized normal and tangential stresses on the contact surface are expressed by using either continuous piecewise linear or piecewise constant Lagrange multipliers in the saddle-point formulation. The two algorithms based on Lagrange multipliers method are developed and compared for linear and quadratic elements

Numerical analysis of squeal instability

International audienceThe name “brake squeal” groups a large set of high frequency sound emissions from brake systems, generated during the braking phase and characterized by a periodic or harmonic spectrum. This paper presents two different numerical approaches to identify the mechanism bringing to the dynamic instability, producing squeal noise. The first approach performs a finite element modal analysis on the brake system, to identify the eigenfrequencies of the components and to relate them to the squeal frequencies. The second one uses a specific finite element program, Plast3, appropriate for non-linear dynamic analysis in the time domain and particularly addressed to contact problems with friction between deformable bodies. The use of this program allows to verify the behavior of the components and to link results obtained from the time analysis and the modal one. The study presented is carried on a simple model, composed by a disc, a small pad and a beam supporting the pad, to simplify the behavior of its components

Influence de la géométrie des premiers corps sur les instabilités de contact - cas du crissement

International audienceThe squeal is often studied because it is uncomfortable for the user and the environment of the vehicle although not harming the operation of the brake mechanism. A preceding study showed experimentally that, for a convenient value of the coefficient of friction and an adequate third body, the appearance of the squeal can be directly related to the geometry of the first bodies. The results presented here deal with the evolution of the tendencies (amplitude, frequency...) of the vibrations induced by friction according to the relative angle between the surfaces of the first bodies. This is a first stage to propose modifications of the first bodies to solve the problems of squeal

Propositions pour le développement d'une méthodologie d'évaluation quantitative de l'aléa rocheux A new methodology for quantitative rock fall hazard assessment

Document de travail (3 pages) Working paperAn innovative methodology is proposed for assessing rock fall hazard. Diffuse hazard can be assessed from rock fall frequency obtained by laser scanner or photogrammetry. For located hazards, the probability of occurrence is difficult to estimate quantitatively, due to two key problems: (a) the poor knowledge of the internal rock mass structure (or geometry); (b) the poor knowledge of the processes which lead to failure. A new approach is proposed to constraint the geometrical and mechanical model of the rock wall, which is based on the dynamic response of the potentially unstable rock compartments to seismic noise. To describe the temporal evolution of the stability and predict the time to failure, a simple rheological law is suggested. It is proposed to fit the rheological parameter of this law, by taking into account the expected number of rock falls in the studied rock wall, derived from the rock fall frequency. The study of the dynamic response is also suggested as an innovative method for monitoring of unstable rock masses

Instabilités de frottement : Approches temporelle et fréquentielle

International audienceThe vibrations generated at the interface between the two bodies in friction are responsible for various noises such as squealing, juddering, hammering, hooting, etc... In order to model and understand friction-induced vibration phenomenon, two approaches are compared in this article: temporal approach and modal approach. This analysis has been made on a simplified system composed of two beams in contact. The two different approaches have been programmed using Finite Element method. Assumptions on the contact calculation are different for the two approaches. Modal approach consists in calculating eigenvalues of the friction coupled system. Instabilities appear when a pair of modes merges. Eigenvalues with positive real parts are identified as potentially unstable modes. Temporal approach calculates the evolution of displacements, velocities, accelerations, forces ... One speaks about instabilities when stick or separation zones appear in the contact surfaces. With this approach frequencies which are excited during instability are obtained. Results have been compared and both methods give coherent and complementary results

Numerical and experimental study of C/C composites under tribological loading

International audienceThis work is devoted to the numerical study of a composite under dynamic tribological loading. The aim of this study is to define an homogeneous model, obtained for static loading and built from an heterogeneous one, that represents the real behavior of the composite. The equivalence of the vibratory behavior between homogeneous and heterogeneous models is emphasized. This equivalence has been studied under dynamical loading without contact. Then a non linear dynamical explicit finite element model is used to check if the homogeneous model represents the heterogeneous ones under dynamic tribological loading. Finally an experimental work, that confirms presence of high frequencies obtained numerically, is discussed

Experimental and numerical investigation of friction-induced vibration of a beam-on-beam in contact with friction

International audienceThe vibrations generated by friction are responsible for various noises such as squealing, squeaking and chatter. Although these phenomena have been studied for a long time, it is not well-understood. In this study, an experimental and numerical study of friction-induced vibrations of a system composed of two beams in contact is proposed. The experimental system exhibits periodic steady state vibrations of different types. To model and understand this experimental vibratory phenomenon, complex eigenvalue and dynamic transient analyses are performed. In the linear complex eigenvalue analysis, flutter instability occurs via the coalescence of two eigenmodes of the system. This linear study provides an accurate value of the experimental frequency of vibration. To understand what happens physically during friction-induced instability, a dynamic transient analysis that takes account of the non-linear aspect of a frictional contact is performed. In this analysis, friction-induced instability is characterized by self-sustained vibrations and by stick, slip and separation zones occurring at the surface of the contact. The results stemming from this analysis show that good correlation between numerical and experimental vibrations can be obtained (in time and frequency domains). Moreover, time domain simulations permit understanding the physical phenomena involved in two different vibratory behaviours observed experimentally. (C) 2010 Elsevier Ltd. All rights reserved

Homogenization in non-linear dynamics due to frictional contact

International audienceThis work is devoted to a study of the classical homogenization process and its influence on the behavior of a composite under non-linear dynamic loading due to contact and friction. First, the general problem of convergence of numerical models subjected to dynamic contact with friction loading is addressed. The use of a regularized friction law allows obtaining good convergence of such models. This study shows that for a dynamic contact with friction loading, the classical homogenization process, coupled with an homogenization of the frictional contact, enables replacing the entire heterogeneous model by a homogenized one. The dynamic part of the frictional contact must be homogenized by modifying the dynamic parameter of the friction law. Modification of the dynamic parameter of the friction law is function of the type and regime of instability. A calculation of a homogenized friction coefficient is presented in view to homogenizing the static part of the frictional contact when the friction coefficient is not constant over the contact surface. Finally matrix and heterogeneities stresses in the heterogeneous models are identified by using the relocalization process and a frictional contact dynamic analysis of a homogeneous model

Influence of sliding contact local dynamics on macroscopic friction coefficient variation

International audienceThe aim of this paper is to present a means of analysing "friction instabilities". The explicit dynamic finite element software PLAST3 in 3D is used to simulate the behaviour of the two bodies (pin and disk) of a tribometer during frictional contact. Coulomb's friction law is used at the contact surface. The phenomenon of relay between the instantaneous contact zone, the contact stresses distribution and the kinematics of the contact surfaces are presented. As the friction coefficient and velocity of the disk are considered constants in the simulations, the contact zone (stick, slip) and separation depend on a "dynamic effect". This generates wave propagation in the interface and involves a variation of normal contact stress. Definitions of macroscopic and local friction coefficients are given. The interfacial instabilities due to the dynamic effect produce a macroscopic friction coefficient that is less than the local friction coefficient. The influence of disk velocity on the macroscopic friction coefficient is also investigated

Experimental analysis on squeal modal instability

International audienceIn this paper, an experimental analysis performed on a simplified brake apparatus is presented. Brake squeal is a major concern in braking design. During past years a common approach for squeal prediction was the complex eigenvalues analysis. Squeal phenomenon is treated like a dynamic instability. When two modes of the brake system couple at the same frequency, one of them becomes unstable leading to increasing vibration. The presented experimental analysis is focused on correlating squeal characteristics with the dynamic behavior of the system. The experimental modal identification of the set-up is performed and different squeal conditions and frequencies are reproduced and analyzed. Particular attention is addressed to the system dynamics in function of the driving parameters on squeal occurrence. Squeal events are correlated with the modal behavior of the system in function of the main parameters, like contact pressure, friction material properties and system geometry. The robustness of the obtained squeal events permits a further analysis on the triggering of the squeal instability during braking, including the values of parameters that bring to instability. The obtained results agree with the modal coupling approach for squeal prediction, and confirm the characterization of squeal as dynamic instabilit