Les instabilités vibratoires, telles que le crissement de frein, sont souvent étudiées par des analyses aux valeurs propres complexes sur des modèles éléments finis (EF). L'objectif de cette thèse est d'enrichir ces modèles en prenant en compte la viscoélasticité dont les effets sont l'amortissement et la rigidification des matériaux en fonction de la fréquence. Pour cela un viscoanalyseur a été développé. Il permet de caractériser en cisaillement les matériaux entre 100 et 3500Hz, sans utiliser les équivalences temps-température. Ce viscoanalyseur permet d'alimenter en paramètres le modèle rhéologique de Maxwell généralisé par le biais d'une nouvelle méthode d'identification particulièrement robuste. Le modèle de Maxwell généralisé est ensuite introduit dans les modèles EF grâce à un modèle d'état projeté sur un sous-espace adéquat. Ces modèles améliorés prédisent moins d'instabilités du fait de l'amortissement, mais ils montrent également que la viscoélasticité peut avoir des effets de déstabilisation du fait de la rigidification. / The vibratory instabilities, such as the brake squeal noise, are often studied by complex Eigenvalues analysis (CEA) on finite elements models (FE). The purpose of this thesis is to improve these models by taking the material viscoelasticity into account which induces damping and stiffening of materials according to the frequency.For that a tester was developed. It makes it possible to characterize the shearing behavior of materials between 100 and 3500Hz, without using time-temperature equivalences. This tester allows feeding in parameters the rheological model of generalized Maxwell by the means of a new robust identification method. The generalized Maxwell model is then introduced into FE models thanks to a state-space model on an accurate subspace.These improved models predict less instability occurrences because of damping, but they also show that viscoelasticity may induce destabilization because of stiffening.

The main objective of this research is to address the relationship between formulation of friction lining materials and their propensity to friction induced noise generation. The basic idea was formulated earlier by Dr. Filip, who showed that the friction layer plays the relevant role when noise is observed during braking. It was shown that when newly formed patches (parts of the friction layer) exhibit a large difference in the coefficient of friction, brake lining is stretched and released repeatedly, which leads to significant vibrations and corresponding noise when coupled with the vibration mode of the system. Farhang ,on the other hand, demonstrated that noise can be related to specific surface roughness parameters and when properties of friction lining and friction layer (such as compressibility, stiffness and modulus of elasticity) fit into certain specific value ranges, noisy behavior occurs. This research will address the braking related to friction induced noise in relation to the properties of the bulk lining material and the character and properties of the friction layer. The friction tests will be performed using the CAFS-developed (Szary and Lee) real time noise measurement system compatible with the major part of SAEJ2521 standard (note that the system does not allow for reliable measurement of frequencies lower than 900 Hz). The mechanical properties of fourteen samples will be investigated. Of the fourteen samples, friction layer of three of the samples will be investigated by several analytical techniques developed by Dr. Filip [1]. They include polarized light microscopy, scanning and transmission electron microscopy equipped with energy dispersive microanalysis, and X-ray diffraction. This research summarizes data from the J2521 dynamometer test of the Dodge Caravan samples exhibiting specific compressibility, porosity and hardness. Also, this research provides the results of friction surface analysis by SEM with energy dispersive microanalysis, light microscopy, surface roughness, and X ray diffraction. Of the fourteen samples, Bendix has the largest occurrence of noisy braking. Based on techniques developed by Dr. Filip, the characteristics of the friction layer strongly influence brake noise propensity. The friction layer characteristics are dependent on brake formulation. As predicted, "noisy stop" and "quiet stop" samples exhibit completely different friction surfaces.

Squeal noise has been an on-going concern with automotive brake systems since their inception. Even after many decades of research no single theory exists that adequately describes the phenomenon, and no general methods for eliminating squeal noise exist. Broadly speaking, three primary methods of analysis have been applied to understanding and eliminating brake squeal: analytical, experimental and numerical. Analytical models provide some insight into the mechanisms involved when a brake squeals, but have limitations in applicability to specific brake systems. Experimental methods provide the backbone of brake squeal investigations, especially in an industrial environment. However, the core focus of this thesis is to use a large scale finite element analysis (FEA) model to investigate brake squeal. Initially the FEA model was developed and the dynamic characteristics were validated against experimental modal analysis results. A complex eigenvalue analysis was performed to identify potential squeal modes which appear as unstable system vibration modes. Further techniques are described that allow the deeper probing of unstable brake system modes. Feed-in energy, which is the conversion of friction work into vibrational energy during the onset of squeal, is used to determine the relative contribution of each brake pad to the overall system vibration. The distribution of the feed-in energy across the face of a brake pad is also calculated. Component strain energy distributions are determined for a brake system as a guide to identifying which components might best be modified in addressing an unstable system mode. Finally modal participation is assessed by calculating the Modal Assurance Criterion (MAC) between component free modes and the component in the assembly during squeal. This allows participating modes to be visualised and aids in the development of countermeasures. The majority of the work in this thesis was performed using the commercial FEA code MSC.Nastran with user defined friction interfaces. An alternative approach using a contact element formulation available in Abaqus was also implemented and compared to the MSC.Nastran results. This analysis showed that considerable differences were noted in the results even though the overall predicted stability correlated relatively well to observed squeal. Abaqus was also used in a case study into the design of a brake rotor in a noisy brake system. The results of this study provided good correlation to observed squeal and facilitated effective rotor countermeasures to be developed. Some success was achieved in the main aims of predicting brake squeal and developing countermeasures. However, while the tools presented do allow a deeper probing of system behaviour during squeal, their use requires good correlation to observed squeal on brake system to be established. As such, their use as up-front design tools is still limited. This shortcoming stems from the complexity of brake squeal itself and the limitations in modelling the true nature of the non-linearities within a brake system.

Brake squeal is a common noise problem encountered in the automotive industry. Higherfriction coefficients and weight reduction recently led to higher vibration levels in the audiblefrequency range. This quality issue becomes economic due to penalties imposed to the brakesupplier although no robust design method exists. The industrial practice thus relies on costlyprototyping and adjustment phases. The evolution of computational power allows computationof large mechanical assemblies, but non-linear time simulations generally remain out of reach.In this context, the thesis objective is to provide numerical tools for squeal resolution at earlydesign stages.Parameterized reduction methods are developed, using system real modes as Rayleigh-Ritzvectors, and allow very compact reduced models with exact real modes. The proposed ComponentMode Tuning method uses the components free/free modes as explicit degrees of freedom.This allows very quick sensitivity computation and reanalyzes of an assembly as function oflocal component-wise parameters. Non-linear time simulations are made possible through twoingredients. A modified non-linear implicit Newmark scheme and a fixed Jacobian are adaptedfor contact vibrations. The brake is reduced keeping a superelement with exact real modes anda local non-linear finite element model in the vicinity of the pad/disc interaction.A set of design tools is illustrated for a full industrial brake model. First, instant stabilitycomputations and complex mode trajectories are studied. Modal interactions and non-linearphenomena inside the limit cycles are thus well understood. Time/frequency correlations areperformed using transient modal identification and space-time decomposition. A time domainmodal damping model is also shown to be very useful. The modification of a critical componentfor squeal resolution is finally tested and validated.

Le crissement de frein est une nuisance sonore classique dans l’automobile. L’augmentationdes coefficients de friction et la réduction de la masse mènent aujourd’hui à de hauts niveauxvibratoires dans les fréquences auditives, et ces problèmes de qualité se traduisent par des pénalités économiques aux équipementiers, bien qu’il n’existe pas de méthode robuste de conception.La pratique industrielle repose donc sur de coûteuses phases de prototypage et d’ajustement.L’évolution de la puissance de calcul permet le calcul de grands assemblages mécaniques mais lesétudes vibratoires non-linéaires restent généralement hors de portée. Dans ce contexte, l’objectifde la thèse est de fournir, dès les phases de conception, des outils de conception numérique d’aideà la résolution du crissement.Une méthode de réduction paramétrée utilisant comme base de Rayleigh-Ritz les modes réelsdu système assemblé permet la génération de modèles réduits très compacts, avec modes réelsexacts. La méthode proposée d’ajustement des modes de composants utilise les modes libresde composants comme degrés de liberté explicites. L’étude des sensibilités et la réanalyse d’unassemblage en fonction de modifications à l’échelle d’un composant deviennent possibles. Lesétudes temporelles non-linéaires sont rendues possibles par deux développements. Un schémade Newmark non-linéaire modifié et un Jacobien fixe adapté aux vibrations de contact sontintroduits. Le frein est réduit en un superélément avec modes réels exacts et une zone nonréduite au niveau du contact.Un ensemble d’outils de conception est illustré sur un modèle industriel de frein. La stabilitéinstantanée et les trajectoires de modes complexes sont étudiées. Les interactions modales et lesphénomènes non-linéaires au sein des cycles limites sont alors mieux compris. Des corrélationstemps/fréquence sont obtenues par l’identification modale instantanée et une décompositionespace-temps. La grande utilité d’un modèle temporel d’amortissement modal est illustrée.Enfin, la modification d’un composant critique au crissement est testée et validée. / Brake squeal is a common noise problem encountered in the automotive industry. Higherfriction coefficients and weight reduction recently led to higher vibration levels in the audiblefrequency range. This quality issue becomes economic due to penalties imposed to the brakesupplier although no robust design method exists. The industrial practice thus relies on costlyprototyping and adjustment phases. The evolution of computational power allows computationof large mechanical assemblies, but non-linear time simulations generally remain out of reach.In this context, the thesis objective is to provide numerical tools for squeal resolution at earlydesign stages.Parameterized reduction methods are developed, using system real modes as Rayleigh-Ritzvectors, and allow very compact reduced models with exact real modes. The proposed ComponentMode Tuning method uses the components free/free modes as explicit degrees of freedom.This allows very quick sensitivity computation and reanalyzes of an assembly as function oflocal component-wise parameters. Non-linear time simulations are made possible through twoingredients. A modified non-linear implicit Newmark scheme and a fixed Jacobian are adaptedfor contact vibrations. The brake is reduced keeping a superelement with exact real modes anda local non-linear finite element model in the vicinity of the pad/disc interaction.A set of design tools is illustrated for a full industrial brake model. First, instant stabilitycomputations and complex mode trajectories are studied. Modal interactions and non-linearphenomena inside the limit cycles are thus well understood. Time/frequency correlations areperformed using transient modal identification and space-time decomposition. A time domainmodal damping model is also shown to be very useful. The modification of a critical componentfor squeal resolution is finally tested and validated.

Le crissement de frein résulte d’une instabilité vibratoire du système de freinage induite par le frottement des garnitures sur le disque. Ce phénomène se traduit par des bruits hautes fréquences, de 1kHz à 20kHz, et pouvant atteindre des niveaux de 110dB. L’objectif de cette thèse est d’enrichir la filière de simulation actuelle afin de mieux prédire ce phénomène. La taille grandissante des modèles de calcul est aujourd’hui un frein à l’utilisation de méthodes, plus complexes que la classique analyse de stabilité et coûteuses en temps de calcul. De plus, ces modèles ne rendent pas compte du comportement viscoélastique de certains composants. Dans un premier temps, l’analyse expérimentale du crissement nous permet d’identifier les points clés de la modélisation du phénomène. Ensuite, une stratégie de réduction de la taille des modèles, via la réduction de l’interface de contact et la génération de super-élément est mise au point. Puis, une méthode d’implémentation du comportement viscoélastique dans les calculs de stabilité est proposée. Enfin, une analyse de sensibilité est menée afin d’identifier les paramètres fortement influents sur l’estimation des instabilités. / Brake squeal is due to a vibrational instability of the brake system induced by the friction between the pads and the disc. It results in a high frequency noise of 1kHz to 20kHz, up to 110 dB. The objective of this thesis is to enrich the current numerical process to better predict the squeal noise. The growing size of the numerical models is now an obstacle to the use of methods, more complex than the conventional stability analysis, but time consuming. Moreover, these models do not take into account the viscoelastic behavior of some component. First, the experimental analysis of squeal allows us to identify the key points of the modeling of brake squeal. Then, a strategy in order to minimize the size of the model, thanks to the reduction of the contact interface and super-element generation is developed. Then, a method for integrating viscoelastic behaviour in stability analysis is proposed. Finally, a sensitivity analysis is performed to identify highly influential parameters on the estimation of instabilities.

This Diploma Thesis is dedicated to solve the source of noise, observed during braking processes on tested vehicle, called Gouki noise and has been worked out in corporation with Federal Mogul company. The aim of this work to create test methology, which allows to experimentally detect the source of undesirable noise and eventually suggest next steps in its prevention.

Les freins aéronautiques sont soumis à des instabilités vibratoires induites par le frottement. Il en résulte des vibrations qui présentent un risque pour la structure du frein et de l’atterrisseur et posent des problèmes d’intégration. Safran Landing Systems doit donc répondre à des spécifications avionneurs strictes sur les niveaux des vibrations générées par son équipement. Le respect de ces spécifications est actuellement contrôlé par la réalisation d’essais de freinage longs et coûteux. L’objectif de ces travaux de recherche est de reproduire numériquement ces phénomènes vibratoires via des outils intégrables au processus de conception d’un frein. Le crissement de frein, bien qu’il soit l’objet de recherches depuis le début du XXe siècle, demeure un phénomène assez mal compris, notamment dans l’aéronautique. Des vibrations instables apparaissent régulièrement sur l’ensemble de la plage fréquentielle 0-2 kHz. Au cours de la dernière décennie, une instabilité vibratoire vers 200 Hz dénommée whirl 2 s’est manifestée de manière récurrente et souvent critique sur la plupart des nouveaux freins développés. On cherche donc à mettre en place une méthode permettant de simuler l’apparition et les amplitudes des instabilités vibratoires, notamment du mode de whirl 2. Dans une première partie, on présente des analyses d’essais vibratoires réalisés en conditions opérationnelles et expérimentales. On décrit ensuite la modélisation par la méthode des éléments finis du frein instable au sens de Lyapunov. La stabilité du système linéarisé est étudiée et on montre une corrélation en fréquence et déformée entre le modèle et les essais. Ce modèle éléments finis est trop volumineux en l’état pour permettre la simulation d’amplitudes de vibrations non linéaires. On propose donc dans une seconde partie deux méthodes de réduction adaptées à l’architecture complexe d’un système de freinage aéronautique et permettant la prise en compte du frottement. La première est une méthode semi-analytique qui se révèle très performante jusqu’à 500 Hz. La seconde méthode de réduction mise en oeuvre est la double synthèse modale. Elle est implémentée dans sa version classique, puis une amélioration est proposée avec succès : la double synthèse modale complexe. La troisième partie est consacrée à l’étude de la dynamique non linéaire du whirl 2 par la réalisation d’intégrations temporelles. La simulation des amplitudes de vibration nécessite la prise en compte réaliste du comportement non linéaire du frein. Or, on fait d’abord le constat que, contrairement à une hypothèse communément admise, les non-linéarités de contact situées aux interfaces frottantes ne suffisent pas à expliquer à elles seules la saturation des amplitudes vibratoires constatée expérimentalement. La recherche des phénomènes physiques non linéaires influents nous amène a considérer l’interaction de la structure vibrante avec le circuit hydraulique de commande du frein. La modélisation du couplage hydrodynamique fournit alors des éléments de compréhension inédits et permet de formuler des règles de conception. Enfin on étudie l’impact du frottement sec dans les contacts périphériques des disques de freinage avec la structure. Ce phénomène, jusque là négligé, apparaît largement prépondérant. Des études d’influences, présentant une bonne corrélation avec les essais, permettent de mettre en évidence de manière robuste l’influence du design et des scénarios de freinage sur les amplitudes vibratoires. / These vibrations are a threat for the brake and landing-gear structural integrity and represent an issue in terms of integration. Thus Safran Landing Systems has to comply with aircraft manufacturers’ strict requirements on the vibration amplitude its product is likely to generate. Compliance to these requirements is assessed by long and costly braking test campaigns. The objective of the research presented here is to reproduce by simulation the brake dynamic instabilities with numerical tools that could be integrated in the design process. Brake squeal has been a research topic since the early XXth century. However it remains a rather ill-understood phenomenon, especially in aeronautics. Unstable vibrations regularly appear on the whole 0-2kHz frequency spectrum. In the last decade, an instability located around 200 Hz called whirl 2 persistently appeared on the newly developed wheel and brake assemblies, sometimes exhibiting critical vibration amplitudes. Consequently, Safran Landing Systems wishes to develop numerical tools able to simulate both the occurrence and the amplitudes associated with friction-induced instabilities, especially with the whirl 2 mode. In the first part of this report, an experimental analysis of the brake is conducted, on both laboratory and in operational set-ups. The modelling of the wheel and brake assembly using the finite element method is then described. The system stability in a Lyapunov’s sense is studied and shows good correlation in both frequencies and mode shapes with the experiments. This finite element model is too big to be used to perform the transient simulation of the nonlinear amplitudes. In the second part, two reduction methods, tailored to the complex aircraft brakes architectures, are thus presented. The first method is a semi-analytical. It shows excellent performances up to 500 Hz. The second reduction method is the double modal synthesis, implemented under its classical version. It is then successfully improved and called "complex double modal synthesis". The third part is dedicated to the study of the nonlinear dynamics of the whirl 2 through transient analyses. The nonlinear amplitudes simulation requires taking into account the relevant nonlinear brake behavior. However, it is first observed that, contrary to a commonly accepted hypothesis, the contact nonlinearities located at the friction interfaces cannot single-handedly account for the vibration amplitudes saturation observed in the tests. The need to identify the relevant physical phenomena leads then to consider the interaction between the squealing brake structure and its hydraulic command circuit. The modelling of the hydro-mechanical coupling provides an unprecedented insight and allows to prescribe design rules. Finally, we study the impact of dry friction in the peripheral contacts between the braking discs and the structure. This phenomenon, neglected until now, appears to have a major influence. Sensitivity studies exhibit a good correlation with tests, allowing to highlight, in a robust manner, the impact of brake design and braking scenarii on the nonlinear vibration amplitudes.

Brake squeal is an old and well-known problem in the vehicle industry and is a frequent source for customer complain. Although, brake squeal is not usually affecting the performance of the brakes, it is still important to address the problem and to predict the brakes tendency to squeal on an early stage in the design process. Brake squeal is usually defined as a sustained, high-frequency vibration of the brake components, due to the braking action. By using simulation in finite element (FE) method it should be possible to predict at what frequencies the brakes tend to emit sound. The method chosen for the analysis was the complex eigenvalues analysis (CEA) method, since it is a well-known tool to predict unstable modes in FE analysis. The results from the CEA were evaluated against measured data from an earlier study. Even though there are four main mechanism formulated in order to explain the up come of squeal, the main focus in this project was modal coupling, since it is the main mechanism in the CEA. A validation of the key components in model was performed before the analysis, in order to achieve better correlation between the FE model and reality. A parametric study was conducted with the CEA, to investigate how material properties and operating parameters effected the brakes tendency to squeal. The following parameters was included in the analysis; coefficient of friction, brake force, damping, rotational velocity, and Young’s modulus for different components. The result from the CEA did not exactly reproduce the noise frequencies captured in experimental tests. The discrepancy is believed to mainly be due to problems in the calibration process of the components in the model. The result did however show that the most effective way to reduce the brakes tendency for squeal was to lower the coefficient of friction. The effect of varying the Young’s modulus different components showed inconsistent results on the tendency to squeal. By adding damping one of the main disadvantages for the CEA, which the over-prediction of the number of unstable modes, where minimized.