Vibrations induites par le frottement : sensibilité aux paramètres de contrôle

Le grincement est un bruit induit par le frottement dont la nature fugace est très souvent mise en avant expérimentalement. Cet article présente l'étude menée sur un modèle de principe, contenant deux masses en contact frottant et obtenu suite à l'évolution du modèle classique de stick-slip par une démarche de complexité croissante. Alors que l'étude temporelle menée sur ce modèle permet de mettre en évidence l'extrême sensibilité du grincement vis-à-vis des paramètres de contrôle, l'étude modale permet de comprendre l'origine de cette sensibilité grâce au concept d'instabilité modale

Robust stability analysis of brake squeal based on a parametric finite element model

International audienceBrake squeal is an instability phenomenon, which is severely dependent on many parameters. This study attempts to assess the effects of their variability on brake squeal behavior through FE computation. A detailed FE model of a commercial brake corner has been built up in order to predict its nominal squeal behavior. This analysis includes a non-linear preloading step to predict the system working-point and a complex eigenvalue analysis to assess its stability. A parametric study has been conducted in order to estimate the dependency with respect to the friction coefficient. The FE model has been parameterized to investigate the effect of variability. The process includes geometry simplifications to reduce CPU time, allowing far more configurations to be computed. Several parametric studies have been conducted to assess the effects of the friction coefficient, of the rotating direction, of the friction induced damping and of the hydraulic pressure. A numerical matrix test has been undertaken to synthesize the brake behavior in the wide variety of conditions it may encounter. Then, a full factorial design of experiments has been conducted with respect to the friction coefficient and the disc Young Modulus. This analysis shows biparametric coupling patterns and stability charts. Finally, it is possible to rank the parameters with respect to their influence and to assess the performance and the robustness of the system

Effet de l'amortissement sur les motifs de coalescence impliqués dans le crissement de frein

International audienceBrake squeal is a friction induced instability phenomenon that belongs to the flutter instability class. Most studies tend to prove that damping is a key parameter in brake squeal modelling. A finite element model of the brake has been used to investigate the effects of damping on the coalescence patterns. If the two modes involved in the coalescence are equally damped, a " lowering effect " that tends to stabilize the system is observed. If the two modes are not equally damped, both " lowering " and " smoothing " effects occur. If the " smoothing effect " prevails, added damping may act in an unintuitive way by destabilizing the system. To further study this point, stability areas have been plotted to find the most stable configuration in terms of damping distribution.Le crissement de frein est un phénomène d'instabilité induit par frottement qui entre dans la catégorie des instabilités de flottement. La plupart des études tendent à montrer que l'amortissement est un paramètre clé dans la modélisation du crissement. Un modèle éléments finis du frein a été utilisé pour étudier l'effet de l'amortissement sur le phénomène de coalescence. Si les deux modes impliqués dans la coalescence sont également amortis, un "effet abaissant" qui tend à stabiliser le système est observé. Si les deux modes ne sont pas également amortis, des effets à la fois "abaissant" et "lissant" se produisent. Dans le cas d'un effet "lissant", l'ajout d'amortissement peut agir d'une manière non-intuitive en déstabilisant le système. Afin d'étudier plus en profondeur ces différents aspects, des zones de stabilité ont été tracées pour définir la configuration la plus stable vis à vis de la distribution d'amortissement

Investigation of the relationship between damping and mode-coupling patterns in case of brake squeal

International audienceBrake squeal is a friction induced instability phenomenon that has to be addressed during the development process. The mechanism is considered a mode coupling phenomenon also referred to as coalescence. The system eigenvalues have been computed using a technique based on the finite element method. The coalescence patterns were then determined in relation to the friction coefficient. The effects of damping on the coalescence patterns have been investigated. If the two modes involved in the coalescence are equally damped, a "lowering effect" that tends to stabilize the system is observed. If the two modes are not equally damped, both "lowering" and "smoothing" effects occur. If the "smoothing effect" prevails, added damping may act in an unintuitive way by destabilizing the system. To further study this point, stability areas have been plotted and a metric is proposed to find the most stable configuration in terms of damping distribution. In the squeal frequency range, coalescence patterns often involve more than two modes. In this case, the effect of damping is far more complicated since several modes are coupled both in terms of friction and damping

Effects of damping on brake squeal coalescence patterns - application on a finite element model

International audienceBrake squeal is referred to, in most publications, as a flutter instability triggered by a mode coupling phenomenon. A lot of clues tend to prove that damping would be a key parameter in brake squeal modelling. This study aims at investigating the effects of damping on coalescence patterns, that is to say on the way the modes couple. A finite element model of the whole brake corner has been used to compute the brake modal behaviour. Then a complex eigenvalue analysis has been undertaken to assess the brake stability as a function of the friction coefficient. Different kinds of damping spreading over the modes have been studied. Two main effects have been noticed: a shifting effect and a smoothing effect. The first one always stabilize the brake, whereas this is not the case of the second one. The combination of the two effects may make the brake more unstable depending on the spreading of the additionnal damping

Non-linear dynamics of a whole vehicle FE Model using a Harmonic Balance Method

International audienceThe aim of the present paper is to apply the Harmonic Balance Method (HBM) to a Finite Element Model of a complete vehicle (body, engine and engine mounts) in order to calculate the non-linear response of the assembly. The non-linear effects come from the amplitude-dependent stiffness of the engine mounts. First, the Harmonic Balance Method is presented. A condensation process on the non-linear degrees-of-freedom is also proposed. This processreduces the original non-linear system by focusing only on the solution of the non-linear equations associated with the system's non-linear components. Secondly, the engine mount stiffness dependency with amplitude is measured on a test bench to estimate a polynomial stiffness law. Finally, the numerical analysis is performed to analyze the non-linear response of the whole vehicle using the Harmonic Balance Method algorithm with appropriate condensation located only on the non-linear coordinates of the system in order to minimize computer time

Robust active noise control in a car cabin: evaluation of achievable performances with a feedback control scheme

International audienceThe application dealt with in this paper is the active attenuation of broadband noise (produced by the tire/road contact) in a car cabin, using only a feedback control scheme (1-DOF (one degree of freedom)). The objective of the proposed control methodology is to evaluate achievable performances according to the frequency bandwidth in which attenuation is desired. This is investigated numerically, by seeking a multi-input multi-output (MIMO) active noise control solution that reaches the best attenuation level, under explicit robustness constraints. The paper aims to i) formalize the underlyingoptimization problem including performance and robustness indicators as well as industrial constraints, ii) perform an effective MIMO identification, and iii) provide an a priori control structure and then proceed to direct optimization of some meaningful parameters using a well-suited nonsmooth optimization solver. Finally, the simulation and experimental results obtained following the proposed methodology are shown and discussed

Parameter analysis of brake squeal using finite element method

International audienceBrake Squeal is a friction induced instability phenomenon known to be one of the most annoying noise for drivers. This paper focuses on the mode coupling aspect of brake squeal by means of a multi parametric analysis. The study is based on a Finite Element model of the whole brake corner. A complex eigenvalue analysis is undertaken, with a modal projection technique, to detect the stable and unstable modes. Following this process, the brake stability is assessed as a function of the friction coefficient. The results highlight accurately the modecoupling phenomenon also referred to as coalescence. Then, the emphasis is put on the disc Young modulus variability by launching a numerical design of experiment. Finally, the brake robustness is displayed as functions of the friction coefficient and of the disc Young modulus.Le crissement de frein est un phénomène d'instabilité vibratoire induit par le frotte-ment, connu comme l'un des bruits les plus gênants pour le conducteur. Cet article se focalise, grâce à une analyse multiparamétrique, sur la coalescence de modes lors du crissement. L'étude se base sur un modèle éléments finis du système de freinage complet. Une analyse aux valeurs propres complexes est réalisée, avec une technique de projection modale, afin de déterminer quels sont les modes stables et instables. Une étude paramétrique permet de déterminer la stabilité du système en fonction de la valeur du coefficient de frottement. Les résultats décrivent avec précision le phénomène de coalescence. Enfin, un plan d'expérience est lancé afin d'évaluer l'influence du frottement et du module d'Young du disque sur la stabilité du système

Broadband Active Noise Control Design through Nonsmooth Hinfinity Synthesis

International audienceThis paper deals with active control of a broadband noise in a car cabine. It aims to study the achievable performance of such control in the SISO feedback case. The main limitations involved, known as waterbed effect, are critical for such problem due to the presence of non-minimum phase zeros. To evaluate the intrinsic limitations due to these non-minimum phase zeros, a multi-objective control synthesis is proposed, allowing to cope with classical specifications (performance and robustness), without pessimism. The control synthesis is based on a H1 criterion to be minimized under some decoupled constraints. It consists in a non-convex and non-smooth optimization problem, for which a local optimum may be efficiently obtained. A particular control structure is considered in order to reduce the number of decision variables, to set relevant bounds on these parameters and to choose appropriateinitial conditions. Then the optimization problem is solved using recent results on non-smooth optimization. The whole design process is detailed, including the identification of the synthesis model. The control strategy is then applied to an instrumented cavity, which shares most of the acoustic characteristics of a car cabin. Finally, the analysis of the results gives clear conclusions on SISO feedback possibilities, and paves the way for an efficient multivariable design case