Ces travaux s’inscrivent dans le cadre des recherches destinées à réduire ou à éliminer le bruit de crissement émis par les véhicules ferroviaires en courbe ou au freinage. Ces bruits peuvent en effet atteindre des niveaux sonores très élevés, jusqu’à 105 dB(A) à proximité des rames en cas de freinage par exemple, et constituent une gêne importante pour les usagers et les riverains. Afin d’apporter des solutions de réduction de ce bruit de crissement, on se concentre sur la modélisation des vibrations auto-entretenues de structures avec contact frottant ainsi que sur la compréhension des mécanismes à l’origine du crissement résultant, en particulier dans le cas d’un frein à disque ferroviaire. On fait l’hypothèse que les vibrations ont pour origine un couplage de modes de la structure dans les directions tangentielles et normale à l’interface en contact frottant. Ce couplage entraîne une instabilité de l’équilibre quasi-statique glissant du système et l’apparition de vibrations auto-entretenues. On cherche à déterminer ces vibrations par le calcul ce qui s’effectue en deux étapes. Dans un premier temps, l’analyse de stabilité de l’équilibre quasi-statique du système permet de déterminer l’occurrence des vibrations. Dans cette thèse, deux hypothèses de modélisation du frottement – plan ou rectiligne – sont comparées dans le cas d’un modèle académique minimal. Dans le cas non-amorti, on montre que l’hypothèse simplificatrice du frottement rectiligne tend à stabiliser le système. Dans le cas amorti, on constate que les résultats établis dans la littérature pour un frottement rectiligne, en particulier le paradoxe de déstabilisation, ne sont pas facilement généralisables au cas du frottement plan bien que des similitudes existent. Dans un deuxième temps, une analyse non-linéaire est nécessaire pour déterminer les amplitudes et le contenu fréquentiel précis des vibrations auto-entretenues. Cette étape est généralement effectuée à l’aide d’une intégration temporelle numérique à partir de conditions initiales données, proches de l’équilibre glissant. En examinant l’évolution temporelle des vibrations obtenues à l’aide de cette technique, on peut distinguer d’une part le régime transitoire au cours duquel les non-linéarités apparaissent et stabilisent progressivement la solution instable, et d’autre part le régime stationnaire (ou régime de fonctionnement) où les amplitudes vibratoires sont stabilisées. Dans le cas du modèle académique, une analyse rigoureuse des échanges énergétiques au cours de l’évolution temporelle permet de mettre en évidence l’origine de la stabilisation des vibrations, en particulier la baisse du taux de puissance injectée au contact résultant de l’accumulation des événements fortement non-linéaires : décollements, adhérences ou chocs. L’intégration temporelle directe n’est toutefois pas adaptée à des modèles numériques comportant de nombreux degrés de liberté et pour lesquels la détermination du régime stationnaire est généralement suffisante pour proposer des solutions de réduction. Le surcoût de calcul engendré par le régime transitoire est en effet très limitant. C’est pourquoi, une méthode est proposée pour approximer directement le régime stationnaire dans le cas d’un système mono-instable. Cette méthode combine une technique de tir à une initialisation basée sur les observations énergétiques ci-dessus. Elle est d’abord validée sur le modèle minimal puis adaptée au modèle éléments finis de frein ferroviaire moyennant une approximation originale de la technique de tir : la réduction de l’espace des phases des conditions initiales. Les approximations des régimes stationnaires sont comparées avec ceux obtenus par l’intégration temporelle directe. Les avantages et les limitations de la méthode sont discutés. / This work is part of research intended to mitigate or eliminate the squeal noise produced by railway vehicles in curves or during braking. For instance, brake noise can reach very high sound levels up to 105 dB(A) close to the trains and constitutes an important nuisance for passengers and residents in the station. In order to provide some mitigation measures, the study focuses on the modelling of self-sustained structural vibrations in presence of frictional contact and the understanding of the squeal generation mechanism, especially for of a railway disc brake. It is assumed that vibration is due to structural mode coupling in the normal and tangential directions at the frictional interface. This coupling leads to instability of the sliding quasistatic equilibrium of the system and the occurrence of self-sustained vibrations. Two steps are necessary to calculate these vibrations. Firstly, the occurrence of the vibrations is determined through the stability analysis of the quasi-static equilibrium. In this thesis, two modelling assumptions for the friction law – planar or rectilinear – are compared in the case of an academic model. Without damping, the simplified rectilinear friction law tends to stabilize the system. With damping, the results established in the literature in case of rectilinear friction, especially the destabilization paradox, cannot be applied generally in case of planar friction even if similarities may be observed. Secondly, a nonlinear analysis is necessary and performed to calculate the amplitudes and the detailed spectral content of the self-sustained vibrations. This step is generally performed by using numerical time integration from given initial conditions, close to the equilibrium. Taking a look at the vibrations time histories obtained by this technique, two different states may be distinguished. In the transient state, nonlinear forces appear and gradually stabilize the unstable solution whereas in the steady (stationary) state, vibrations are stabilized. In the case of the academic model, the cause of the stabilization is highlighted thanks to a rigorous analysis of energy exchanges, especially the decrease of the power rate injected via the contact interface resulting from the accumulation of strongly nonlinear events like loss of contact, stick or impacts. However, direct time integration is not very appropriate in the case of large numerical models with many degrees of freedom. Indeed, the additional computational cost due to the transient state is very high although the determination of the steady state is generally sufficient from a practical point of view. Consequently, a method is proposed in order to directly approximate the steady state in case of mono-instability. This method combines a shooting technique with an initialization based on the above energy considerations. It is first validated on the minimal model and then transposed to the finite element model of a railway disc brake through an original approximation of the shooting technique : the reduction of the initial conditions phase space. The estimations of the steady states are compared with those obtained by direct time integration. The advantages and the limitations of the method are discussed.

Dither control is a method of introducing high frequency control efforts into a system to suppress a lower frequency disturbance. Dither control is an effective means of suppressing automotive brake squeal. Brake squeal is a problem that has plagued the automotive industry for years. In fact many makers of materials for brake pads spend up to 50% of their engineering budgets on noise, vibration and harshness issues. A normal dither signal may be introduced to an automotive braking system by placing a piezoceramic stack actuator in the piston of a floating caliper brake. Many theoretical models indicate a reduction in the braking torque due to the dither signal. Under the assumption of Hertzian contact stiffness the loss in braking torque is due to lowering of the average normal force. There are also theories that the dither signal eliminates the stick-slip oscillation causing an effective decrease in the friction force. Yet another theory indicates that the effective contact area is reduced, lowering the mean coefficient of friction. It is not apparent whether any of these models accurately portrays the interaction of the brake pads and rotor.

Esta tese estuda a emissão de ruído de alta frequência em freios automotivos, conhecida como squeal. Para tanto, uma série de ensaios foram executados em sistemas de freio em um dinamômetro inercial. Foram colocados acelerômetros na pastilha e no caliper em três direções ortogonais, e foram testados dois diferentes tipos de sistemas de freio comerciais. Os ensaios revelaram que, durante os períodos silenciosos, o movimento vibratório da pastilha acontece tanto na direção tangencial radial quanto na direção radial no plano definido pelo disco, além da direção axial. Estas vibrações ocorrem de modo independente, não mostrando acoplamento entre os movimentos. Durante os períodos de emissão sonora intensa, os valores de vibração aumentam significativamente e ocorre o acoplamento dos movimentos nas direções tangencial e radial, que passam a apresentar sincronismo de fase e de frequência. O movimento da pastilha na direção radial é explicado pelos modos de vibração do disco, e pastilha e disco são tratados como dois osciladores fracamente acoplados. Para o tratamento de osciladores, utiliza-se o modelo de Kuramoto. O sincronismo, neste modelo, ocorre devido ao acoplamento entre os osciladores e devido à proximidade das frequências naturais de pastilha e disco. A aplicação do modelo nos sistemas ensaiados mostrou boa aderência aos dados experimentais. Finalmente, é proposta a utilização de um coeficiente adimensional de maneira a incluir no estudo dinâmico do sistema variáveis puramente tribológicas. / This paper studies friction induced high frequency noise in automotive brakes, known as squeal. Aiming this purpose, a series of experiments were performed using brake systems in an inertial dynamometer. Accelerometers were installed on pad and caliper, measuring in three orthogonal directions, in two different commercial brake systems. The tests showed that, during the silent runs, pad vibration happens in tangential and radial directions, besides the axial direction, considering the coordinate reference frame on the plane defined by the brake disc. These vibrations happen in an independent fashion, indicating no coupling between motions in different directions. During the squeal periods, however, vibration amplitudes increase sharply and phase and frequency synchronization between tangential and radial vibrations is observed, indicating vibration coupling. Pad movement in radial direction is caused by disc in-phase vibration mode. Pad and disc are treated as two harmonic oscillators according to Kuramoto model. In this model, synchronization is caused by weak coupling between pad and disc natural frequencies, due to frequency proximity. A numerical simulation of Kuramoto model was able to emulate the experimental data. Finally, a new non-dimensional coefficient is proposed in order to include in this dynamic model the influence of pure tribological effects.

<p>Applications relying on a high static friction include various types of fixtures, couplings, bolted joints, torsion joints, etc. The common characteristic of these applications is that they rely on the friction force to maintain the relative position of two mating surfaces. Also applications relying on high dynamic friction are common, the main example being brakes, where a low friction could be devastating.</p><p>The plateau model for the friction of brakes has been refined. By using advanced electron microscopy, it has been shown that during braking a partly amorphous friction film, comprising nanosized iron oxide agglomerates, dissipates the friction energy. The film is only about 100 nm thick. It is separated from the underlying less mobile material by a thin boundary. The actual braking power is thus localised to this very thin film, leading to remarkably high power densities. In a typical case it was estimated to 40 GW/dm3.</p><p>Squeal and vibrations are critical problems for brakes. The present work has shown that a textured disc pattern may counteract squeal efficiently. The most successful pattern has spiral shaped arms in which wear resistant ceramic particles are embedded. The different wear characteristics of treated and untreated disc surface lead to an elevation of the patterned area above the rest of the disc. In a related experiment, laser technique was used to inject the particles deeper into the disc surface, and thus prolonging the time of silence. </p><p>Textured diamond surfaces have been used to study the influence of load, repeated scratching and surface roughness on the static coefficient of friction. It was shown that these surfaces were remarkably stable at high friction levels. A maximum load limit was found above which the coefficient of friction falls. This and a number of other factors were found important for the successful design of high-friction joints.</p>

Applications relying on a high static friction include various types of fixtures, couplings, bolted joints, torsion joints, etc. The common characteristic of these applications is that they rely on the friction force to maintain the relative position of two mating surfaces. Also applications relying on high dynamic friction are common, the main example being brakes, where a low friction could be devastating. The plateau model for the friction of brakes has been refined. By using advanced electron microscopy, it has been shown that during braking a partly amorphous friction film, comprising nanosized iron oxide agglomerates, dissipates the friction energy. The film is only about 100 nm thick. It is separated from the underlying less mobile material by a thin boundary. The actual braking power is thus localised to this very thin film, leading to remarkably high power densities. In a typical case it was estimated to 40 GW/dm3. Squeal and vibrations are critical problems for brakes. The present work has shown that a textured disc pattern may counteract squeal efficiently. The most successful pattern has spiral shaped arms in which wear resistant ceramic particles are embedded. The different wear characteristics of treated and untreated disc surface lead to an elevation of the patterned area above the rest of the disc. In a related experiment, laser technique was used to inject the particles deeper into the disc surface, and thus prolonging the time of silence. Textured diamond surfaces have been used to study the influence of load, repeated scratching and surface roughness on the static coefficient of friction. It was shown that these surfaces were remarkably stable at high friction levels. A maximum load limit was found above which the coefficient of friction falls. This and a number of other factors were found important for the successful design of high-friction joints.

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.

O conforto acústico é um fator que, ultimamente, tem ganhado importância na indústria automobilística, especialmente porque o ruído de freio tem se apresentado como uma das principais causas de desconforto acústico para os usuários. Com isso, o material de atrito é alvo de contínuas pesquisas, com intenção de reduzir os ruídos, mas o sistema de freio também tem responsabilidade no ruído. O ruído de freio tipo squeal ocorre em altas frequências e destaca-se por ser o ruído de freio mais economicamente importante, pois gera elevados custos de acionamento da garantia do veículo. O squeal é induzido pelo efeito do atrito, existindo técnicas de simulação numérica para avaliar esse fenômeno, que se baseiam na análise de autovalores complexos (CEA) do sistema de freio. Os trabalhos encontrados na literatura tratam quase exclusivamente sobre sistemas de freio a disco. Diante disso, esse trabalho visa apresentar uma metodologia de análise de instabilidade dinâmica em sistemas de freio a tambor, considerando os efeitos de amortecimento. É utilizado o programa ANSYS e o Método dos Elementos Finitos para realizar esse estudo. Ao longo do trabalho são apresentadas discussões sobre fatores de influência nas frequências auto excitadas, como amortecimento, coeficiente de atrito e pressão de acionamento. A técnica de CEA é aplicada a dois sistemas de freio a tambor, com geometrias diferentes, sendo os dois casos validados através da comparação com resultados veiculares. Os modelos numéricos são ferramentas muito úteis, e a referida análise fornece grande vantagem no desenvolvimento de um sistema de freio acusticamente confortável. No entanto, os parâmetros de entrada no modelo numérico precisam ser coerentes e cuidadosamente definidos. A metodologia se mostrou adequada para avaliar o fenômeno de acoplamento modal induzido por atrito. / Acoustic comfort has become increasingly important nowadays, especially because brake noise is one of the major causes of acoustic discomfort to the users. Thus, the friction material is a continuous research target, intended to reduce noise, but bearing in mind that the brake system also has responsibility in noise. The squeal noise occurs at high frequencies and stands out for being the most economically important type of brake noise, because it generates high costs of the activation of the vehicle warranty. Squeal noise is induced by friction, and there are numerical simulation techniques to assess this phenomenon, which are based on the complex eigenvalues analysis (CEA). Studies in the literature deal almost exclusively on disc brake systems. Therefore, the present work addresses the dynamic instability analysis methodology applied to drum brake systems, where the damping effect is considered. It is used ANSYS and the Finite Element Method program to perform this study. The influence of damping, friction coefficient and working pressure on the self-excited frequencies of the brake system are discussed throughout this work. CEA technique is applied to two drum brake systems, which have different geometries. These two cases are validated by comparison with results obtained in vehicle tests. The numerical models are very useful tools, and this analysis provides great advantage in developing an acoustically comfortable brake system. However, the input parameters in the numerical model must be carefully defined and consistent. The methodology proved to be adequate to evaluate the modal coupling phenomenon induced by friction in drum brake systems.

A presente dissertação descreve o desenvolvimento e análise de um experimento concebido para avaliar a contribuição de materiais de fricção sobre vibrações induzidas na superfície de um disco de freio. O aparato proposto é equipado com um excitador modal (shaker), utilizado para promover e controlar o sinal de excitação que foi aplicado sobre os materiais de fricção avaliados. A resposta dessa excitação na superfície do disco de freio foi mensurada através de acelerômetros. Além da aplicação sobre o experimento proposto, foram avaliados o coeficiente de atrito e a distribuição de asperezas da superfície das oito amostras utilizadas. A característica modal do disco utilizado foi descrita através das suas frequências naturais, amortecimento e formas modais, parâmetros identificados através da aplicação de análise modal experimental. O experimento proposto foi utilizado para identificar as principais características de resposta do disco quando a excitação é realizada através do material de fricção. Essa condição também foi comparada com aquela em que a excitação foi aplicada diretamente no disco A métrica mais adequada para avaliação desse experimento foi identificada como o valor médio da magnitude da Função Resposta em Frequência (FRF), calculado através do estimador H3. O aparato proposto se mostrou capaz de identificar diferenças nas amostras avaliadas quanto à propensão dessas à produção de vibrações na superfície do disco. As amostras foram avaliadas no experimento proposto nas condições sem e com filme tribológico sobre a sua superfície, as quais correspondem ao estado das amostras antes e depois, respectivamente, do processo de caracterização do coeficiente de atrito destas, utilizando o tribômetro do LATRIB/UFRGS. Foi observado que as amostras com filme produziram maior vibração do que as amostras sem filme. Os resultados obtidos demonstraram uma forte correlação entre a propensão das amostras à produção de vibrações e a distribuição de asperezas da superfície das amostras. Esses resultados indicam que materiais de fricção com superfícies planas são capazes de transmitir mais vibração à superfície do disco do que aqueles com superfícies mais rugosas. / The present work describes the development and analysis of an experimental apparatus designed to evaluate the contribution of friction materials in vibrations induced on the surface of a brake disc. The proposed apparatus is equipped with a modal exciter (shaker), which was used to promote and control the excitation signal applied in the evaluated friction material. The response of this excitation in the disc surface was measured with accelerometers. The eight samples evaluated in this study was also characterized in terms of its friction coefficient and the asperity distribution of its surface. The modal characteristic of the disc was described in terms of its natural frequencies, damping and modal shapes, whose parameters were obtained by application of experimental modal analysis. The proposed apparatus was used to identify the main characteristics of the disc response when the excitation is applied throw the friction material. This case was also compared to the condition in which the disc was excited directly by the shaker. The most adequate metric to evaluate this experiment was selected as the mean value of the Frequency Response Function (FRF) spectrum, calculated by the H3 estimator The proposed apparatus showed being capable of identifying differences between the evaluated samples, regarding its propensity to produce vibrations on the disc surface. The samples were evaluated in with and without tribological film deposited on its surface. It was shown that the analyzed samples had the vibration increased with tribological film compared to the condition without the film. The obtained results demonstrated a strong correlation between the samples propensity to the production of vibration and the asperity distribution of the samples surfaces. These results indicate that friction materials with flat surfaces are capable to transmit more vibrations to the disc surface than those samples with rough asperity distribution.

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.