Literatura académica sobre el tema "Brake squeal instability"

The purpose of this paper is to investigate the squealing mechanism of band brakes in order to develop effective treatments for the reduction or elimination of squeal noise. With increasing rotational drum speed, squeal frequency increases up to a constant frequency. This constant squeal frequency coincides precisely with the frequency of instability obtained by a linear analysis of the motion of a band on an elastic foundation when the frictional force between the lining of the band and the drum is taken into account. Through experiments and analyses, it will be demonstrated that squeals are induced by the coupling between two modes of the band.

Eliminating brake noises generated during brake application is an important issue in the improvement of comfort in vehicles. Brake noises (frequency 1–15 kHz) are often called brake squeal. On the other hand, brake noises (frequency 200–500 Hz) are often called brake groan noise. The studies on drum brake squeal, disc brake squeal and disc brake groan noise have already been presented in references (2), (3) and (4), where theoretical analyses on these brake noises were described. This paper shows that the equations of motion are represented by the same type of equations. Based on these analyses. It is clear that drum brake squeal, disc squeal and disc brake groan noise are generated by the same cause—dynamic instability of the brake system with friction force variations.

On the basis of fuzzy random variables, a universal approach to squeal analysis of the disc brakes involving various types of uncertainty is proposed in this paper. In the proposed approach, first, the brake stability analysis function related to reliability is constructed with fuzzy random variables. Next, the fuzziness represented by fuzzy random variables is decomposed into interval uncertainties by using a level-cut strategy. Then, the expectations and the variances of the brake stability analysis function are approximately solved by the random moment method at different cut levels, and the lower bounds and the upper bounds of the expectations and the variances are calculated by using a first-order Taylor expansion and a subinterval analysis. Finally, by combining the different interval solutions with the corresponding cut levels, the fuzzy solutions of the brake stability analysis function are obtained, which can be employed to evaluate the brake squeal instability. The proposed approach provides a universal framework for dealing with various types of uncertainty that may exist in automotive brakes. The universality, the accuracy and the efficiency of the proposed approach to the squeal instability analysis of the brakes involving various types of uncertainty are verified by the analysis results from nine different numerical examples.

The problem brake squeal is one of the important areas of application in the automotive industry. Most brake squeal is produced by vibration (resonance instability) of the brake components, especially the pads and discs are known as force-coupled excitation. Until now have many research about predict vibration and noise of disc brake but unfortunate the results is not satisfied. This paper presents model for prediction stability of disc brake for a model four degrees of freedom. The result shows stability of system and when occurrence brake squeal.

Despite substantial research efforts in the past two decades, the prediction of brake squeal propensity, as a significant noise, vibration and harshness (NVH) issue to automotive manufactures, is as difficult as ever. This is due to the complexity of the interacting mechanisms (e.g. stick-slip, sprag-slip, mode coupling and hammering effect) and the uncertain operating conditions (temperature, pressure). In particular, two major aspects in brake squeal have attracted significant attention recently: nonlinearity and uncertainty. The fugitiveness of brake squeal could be attributed to a number of factors including the difficulty in accurately modelling friction. In this paper, the influence of the uncertainty arising from the tribological aspect in brake squeal prediction is analysed. Three types of friction models, namely the Amonton-Coulomb model, the velocity-dependent model and the LuGre model, are randomly assigned to a group of interconnected oscillators which model the dynamics of a brake system. The complex eigenvalue analysis, as a standard stability analysis tool, and the friction work calculation are performed to investigate the probability for instability arising from the uncertainty in the friction models. The results are discussed with a view to apply this approach to the analysis of the squeal propensity for a full brake system.

This paper introduces the velocity-dependent friction law with the Stribeck effect in a moving load model for the vibration and squeal of a car disc brake. Simulated numerical results produce a bounded region of instability for the rotating speed of the disc which is compatible with observed squeal phenomenon.

The brake squeal reduction has been extensively investigated in many academic and industrial researchers. Friction-induced vibrations can be considered as a dynamic instability problem. Generally, automotive engineers and researchers working in the domain of disk brake noise treat instabilities due to the force of friction as a friction-induced vibration. In the case of squeal noise, mode coupling may cause instability of the system. The aim of this article is to propose a minimal two degree of freedom disk brake model in order to investigate the effects of different parameters on mode-coupling instability. This model takes into account self-excited vibration, gyroscopic effect, friction-induced damping, and brake pad geometry. Thus, a stability analysis of equilibrium by calculating complex eigenvalues is presented to investigate the influence of the main parameters on the stability zone such as the opening angle of the brake pad and preload. For the validation of the stability analysis, squeal index and time domain response are used. The results obtained show the importance of optimizing the physical and geometrical parameters of the brake and that some of these parameters have greater effects compared to the others to reduce noise.

In this study, a bespoke small-scale brake dynamometer was developed to simulate the braking conditions of a railway disc brake system. Braking squeal experiments were performed with this brake dynamometer at different braking pressures and disc rotation speeds, and the influence of these braking parameters on the generation and characterization of the squeal noise was evaluated and discussed. The obtained results show that both the braking pressure and the disc rotation speed have a significant influence on the generation and evolution of the squeal noise. Higher rotation speeds are found to result in higher sound pressures and more complicated squeal noise spectra, except at a particular braking pressure, for which the highest sound pressure level is found at various disc rotation speeds. This phenomenon indicates that a combination of specific braking parameters may lead to a strong instability of the brake system and consequently to squeal noise. Additionally, a possible correlation of the squeal noise characteristics with the pressure distribution at the braking interface was found and discussed.

Friction-induced vibrations (brake squeal) produced during braking applications have been one of the major problems in the transportation for many years. It can be the most troublesome for passengers because of its high frequency and acoustic pressure. The role of frictional contact surface geometry on the occurrence of squeal was investigated recently by some researchers. However, it has never been systematically studied at different scales simultaneously. Contact localizations are induced on the one hand by macro effects such as thermal dilatation (macroscopic scale) and on the other hand, by the heterogeneity of third body (tribolayer) generated by friction (mesoscopic scale). The aim of this paper is to investigate the effect of contact localization at both scales through stability analysis on a simplified pad on disc system. The model has been developed numerically by the finite element method (FEM) to introduce a non-uniform contact at macroscopic and mesoscopic scales. The results showed a strong dependency between squeal frequencies and effective contact zone at macroscopic and mesoscopic scales for the investigated configuration. Especially, it is found that squeal frequencies depend on the contact area at a macroscopic scale whereas the probability of occurrence of squeal frequency strongly relies on mesoscopic contact distribution.

This study proposes a three-layer brake pad design, on which a six-DOF dynamic model of brake disc-brake pad is established, and the factors affecting the system instability are analyzed. The analysis shows that the change of mass and stiffness of the brake pad will affect the stability of the system. From the linear complex eigenvalue analysis, the unstable vibration modes of the brake system are predicted, and the effectiveness of the complex mode analysis model is verified by the brake system bench test. Brake pads with different structural shapes are designed, and their influence on the stability of the brake system is analyzed. The results show that the design of the three-layer structure and the slotting design of the brake pad can effectively reduce the occurrence of the brake squeal, especially that of the high-frequency squeal noise.

En tant que radiations acoustiques intenses impliquant de conséquentes nuisances environnementales ainsi que de nombreux retours clients, le crissement des systèmes de freinage est un problème de vibration induite par frottement dépendant indubitablement de problématiques multi-physiques et multi-échelles. Parmi ces dernières, la structure du système, les paramètres opérationnels de freinage, les interfaces de contact frottant, couplés à une dépendance en température, ainsi que les non-linéarités de contact ou les aspects tribologiques, sont des éléments affectant considérablement le crissement, faisant de ce déplaisant bruit un sujet complexe à appréhender. Au sein de ce travail, le système complet de freinage est considéré, et plusieurs tendances principales sont identifiées au regard de l'influence des localisations de contact sur les émissions acoustiques.Des essais NVH sont réalisés, cette analyse implique différentes échelles d'intérêt visant à changer les caractéristiques de contact : les plaquettes de freinage sont modifiées d'une part à l'échelle macroscopique -avec la volonté de varier implicitement les zones de portance-, d'autre part à l'échelle mésoscopique -tendant à impacter l'évolution du circuit tribologique-. Le but inhérent est d'identifier les paramètres patins influençant le crissement, en affectant l'interface tribologique et engageant des différences de signatures acoustiques entre les expériences conduites.Des tests fortement instrumentés sont réalisés à l'échelle du système de frein complet, se focalisant sur différentes formes patins : le développement d'une instrumentation enrichie au travers d'un suivi in-operando des surfaces de contact via mesures thermiques, autorise l'accès à des informations de sollicitation supplémentaires, permettant le suivi des zones de portance supposées. L'emploi de méthodes de clustering est considéré afin d'analyser les données thermiques.Des simulations en stabilité impliquant corrélations expérimental / numérique sont effectuées. Des analyses sous-jacentes sont réalisées, en investiguant l'impact de caractéristiques de chanfreins sur le crissement, l'influence du coefficient de frottement, ou l'implémentation de formes globales d'usures. Qui plus-est, les simulations thermomécaniques sont ici d'intérêt, et l'introduction des zones de contact issues des méthodes de clustering est discutée.Bien que la considération du frein complet puisse impliquer de sévères dispersions expérimentales, des corrélations initiales entre les patins modifiés à différentes échelles -via des formes de patins à l'échelle macroscopique et des traitements thermiques à l'échelle mésoscopique- et les caractéristiques de bruit sont observées. Les essais avec instrumentation enrichie concluent que les localisations de contact peuvent varier pendant les tests NVH, dépendant des paramètres de sollicitation. Un lien particulier entre les conditions opérationnelles de freinage (pression, température), les localisations de contact, et le crissement est établi au travers des méthodes de clustering. Également, les tendances observées en simulation tendent à suivre celles expérimentales, et l'enrichissement des modèles via une description plus précise du contact peut présenter des améliorations quant à la capacité de prédiction du crissement de telles simulations<br>As intense acoustic radiations implying consequent environmental nuisances and customer complaints, squeal noises in brake systems are friction-induced vibration issues indubitably depending on multiphysics and multiscales problematics. Among these latter, system structure, braking operational parameters, frictional contact interfaces, coupled to temperature dependency, as well as contact non-linearities or tribological aspects, are elements considerably affecting squeal, making from this unpleasant noise a complex problem to apprehend. In this work, the full scale system is considered, and several principal tendencies are identified regarding the influence of contact localizations on acoustic emissions.NVH tests are conducted, this analysis involves several scales of interest aiming at changing contact characteristics: pads are modified either at the macroscopic scale -with the will of implicitly varying load bearing areas-, or at the mesoscopic one -tending to impact evolution of the tribological circuit-. The inherent purpose is to identify pads parameters influencing squeal, by affecting tribolayer as well as engaging noise signature differences between conducted experiments.Heavily instrumented tests are realized on a full scale brake system, focusing on different pad shapes: the development of an enriched instrumentation through in-operando thermal surface tracking allows to access to supplementary solicitation informations, permitting to follow the assumed load bearing area. The employment of clustering methods is considered to manage the analysis of thermal datas.Experimental / numerical correlated stability simulations are conducted. Subsequent analyses are realized, by investigating pads chamfer characteristic impact on squeal, influence of coefficient of friction, or implementation of global pads wear shapes. Furthermore, thermomechanical simulations are of interest, and the introduction of previously clustered-defined contact areas into models is realized.Although the full brake system consideration can involve severe experimental dispersions, initial correlations between modified pads at different scales -via pad shapes for the macroscopic one, and thermal treatments of friction material focusing on the mesoscopic level- and noise characteristics are observed. Enriched instrumented tests lead to the conclusion that contact localizations can evolve during NVH tests, depending on solicitation variables. A particular link between braking operational parameters (pressure, temperature), contact localizations, and squeal features is established through clustering. Finally, observed simulated tendencies tend to follow experimental ones, and model enrichment via a more accurate contact description could present improvements regarding squeal prediction capability of such simulation

Les systèmes de freins sont parfois sujets au crissement qui sont des vibrations auto-entretenues induites par le frottement et caractérisées par un contenu fréquentiel formé de raies à hautes fréquences supérieures à 1kHz. Ces vibrations et bruits intenses sont une source de gêne pour les usagers automobile, un problème de santé publique pour les riverains de gares lors du freinage de TGV et peuvent amener à l'endommagement du train d'atterrissage sur les avions.Afin de comprendre ce phénomène et pour le reproduire numériquement, une stratégie complète d'étude est développée. Elle se base sur l'observation expérimentale d'essais de crissement sur un banc d'essais qui permet de formuler des hypothèses de modélisation. Ces dernières sont un guide pour la construction d'un modèle numérique de frein simple. Une méthode de Double Synthèse Modale est appliquée au modèle afin d'en réduire la taille et de permettre des simulation numériques en temps raisonnable et ne nécessitant pas trop de ressources informatiques.La démarche numérique qui suit commence classiquement par une analyse de stabilité par la méthode CEA où les valeurs propres du modèle linéarisé autour de la position d'équilibre glissante sont évaluées. Puis une intégration temporelle est effectuée dans les cas détectés comme instables afin de calculer les niveaux de vibrations. L'étude se termine par une estimation du champ acoustique rayonné par la structure complète.Dans chacune des phases de l'analyse numérique, des outils spécifiques sont utilisés pour comparer le modèle de référence aux modèles obtenus par les deux étapes de réduction. Un critère d'erreur sur les valeurs propres et un critère de MAC sont utilisés pour l'analyse de stabilité. Pour l'étude temporelle, les allures des signaux sont comparées, ainsi que leurs cycles limites et leurs spectrogrammes. Les participations des modes instables sont également calculées pour observer le régime transitoire. En ce qui concerne la partie acoustique, les signaux sont comparés dans un premier temps de façon qualitative pour observer les différences entre les champs émis en fonction des différentes tailles de bases de réduction. Puis un outil basé sur une décomposition en 2D par wavelet des motifs acoustiques est introduit et appliqué pour estimer de façon quantitative les convergences des champs rayonnés<br>Brake systems are sometimes prone to squeal noise, which is due to friction-induced self-sustained vibrations, characterized by a set of frequencies above 1kHz. Those vibrations and resulting noises are a source of perturbations for car occupants, which can be nowadays considered as a health issue.This thesis deals with a global strategy to better understand this phenomenon from an experimental point of view and to propose the prediction of squeal noise by numerical approaches. Moreover, experimental observations of squeal occurrences are analyzed to lead to assumptions about the modelisation of numerical finite element models for squeal prediction. A Double Modal Synthesis is also applied to reduce the size of the discrete finite element model of brake system and to save computational time and ressources. The proposed numerical approach starts with a stability analysis with the classical CEA method. Then the determination of nonlinear self-excited vibrations are performed for the unstable cases detected via the CEA method. Finally the acoustic field emitted by the brake system is computed to predict squeal noise.Specific tools are applied for each computational step to assess the efficiency of reduced model versus the reference model: criteria based on the mean error on eigenvalues and the Modal Assurance Criterion analysis (MAC) are used for the stability analysis; comparisons of the limit cycles, spectrograms and the modal contributions of unstable modes are undertaken for the transient responses; patterns of the acoustic intensity are computed on several observations surfaces and a decomposition based on the theory of 2D wavelets is introduced and applied to assess the convergence of patterns

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.

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<br>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

Abstract The purpose of this paper is to investigate the squealing mechanism of a wheel brake with double shoes to develop effective treatments for the reduction. Detailed observations reveal that the squeal frequencies are closely related to the natural frequencies of the system. These squeal frequencies coincide with the frequencies of instability obtained by a linear analysis of the system. It is demonstrated that squeals are induced by the coupling of the modes of the disk and both beams, two modes of a single beam and the modes of the disk and a single beam.

Abstract Several experiments and analyses have carried out in the field of brake squeal and there are many suggestions to be found in the literature as to the cause of brake squeal. In this paper a mathematical model for friction-induced vibration and noise generation is used to study the influence of these different squeal excitation types. Squealing brakes are excited by the friction forces in the interface between the drum and the linings. This friction and its interaction with the brake structure can be modeled in many different ways. In this paper, different self-excitation types identified in the literature are tested — each one having the potential of generating instabilities. The drum brake model used for the analysis is two-dimensional, and consists of a drum and two shoes with linings. The same brake geometry and material properties are used for all computations, which means that the influence of each mechanism can be estimated. The results from this analysis show that, among the friction models analyzed, the constant coefficient of friction model gives the largest contribution to the instability level of squealing drum brakes. The contribution from the negative μ-velocity slope is shown to be minor. For the constant coefficient of friction model, there are different excitation types. Among these, lining deformation induced instabilities are shown to generate large instabilities, follower forces show a negligible contribution to the instabilities generated and self-locking is shown to be impossible for the brake analyzed.

Abstract The squeal noise arising due to friction-induced vibrations in brakes continues to be a major challenge for automotive manufacturers. To predict one of the mechanisms behind disc brake squeal, an analytical model is developed for the disc brake system. The brake rotor is represented by a thin plate of equivalent modal characteristics and the backing plates are modeled as thin annular sector plates using Rayleigh-Ritz approach. The two structural models are then coupled using linear elastic springs and Coulomb friction at the interface, and Lagrangian approach is used to derive the equations of motion of the coupled system. The resulting linear equations are solved by using complex eigenvalue analysis. The study shows that squeal is a flutter-type instability caused by coupling between the modes of structural components with very close natural frequencies. The sensitivity to friction material stiffness and the influence of hydraulic cylinder stiffness at backing plates are also discussed.

Rotors show very rich dynamical behavior especially when friction is involved. Due to the interaction of nonconservative, dissipative and gyroscopic forces a very interesting stability behavior can be observed. Instability of the rotor can yield severe problems, for example in the context of brakes and clutches it causes squeal, in the process of paper calendering the duration of the rollers is decreased substantially. This paper deals with the problem of how to design a rotor such that it is robust against friction induced vibrations using structural optimization. The problem is addressed using discrete and continuous models for disk brake squeal. It is shown that a proper design of the brake rotor can passively suppress squeal without introduction of additional damping into the system. Many of the qualitative results carry over to other problems of friction induced vibrations in rotors.

&lt;div class="section abstract"&gt;&lt;div class="htmlview paragraph"&gt;As the vehicle electrification progresses and the demand for acoustic comfort increases, the NVH performance of brakes becomes more important theme. In-plane squeal of disc brake is one of phenomena that is difficult to countermeasure. In this study, we used array microphones to search for sound sources of in-plane squeal in order to elucidate the mechanism. The Microphones were set in the out-of-plane direction and the lateral direction of a disc in brake components on a full-sized dynamometer. In the vibration mode in which in-plane stretch vibration was dominant, the sparse and dense parts showed high sound pressure. 3D laser vibrometer was used to check displacements of the disc, and the result indicated a possibility that the sparse and dense parts could vibrate in the out-of-plane direction and generate the sound. Then, complex eigenvalue analysis (CEA) and acoustic simulation were conducted to validate the experimental results. Firstly, frequency of instability mode occurred in CEA was almost the same as that of the actual brake squeal and the mode was identified as in-plane squeal mode. Secondary, acoustic simulation resulted that areas near the sparse and dense parts in a disc had high sound pressure as similar to the sound source identified by array microphones. Finally, parametric studies of friction material property showed correlation between the CEA results and the sound pressure distribution obtained by acoustic simulation.&lt;/div&gt;&lt;/div&gt;

&lt;div class="section abstract"&gt;&lt;div class="htmlview paragraph"&gt;Disc brake squeal is always a challenging multidisciplinary problem in vehicle noise, vibration, and harshness (NVH) that has been extensively researched. Theoretical analysis has been done to understand the mechanism of disc brake squeal due to small disturbances. Most studies have used linear modal approaches for the harmonic vibration of large models. However, time-domain approaches have been limited, as they are restricted to specific friction models and vibration patterns and are computationally expensive. This research aims to use a time-domain approach to improve the modeling of brake squeal, as it is a dynamic instability issue with a time-dependent friction force. The time-domain approach has been successfully demonstrated through examples and data.&lt;/div&gt;&lt;/div&gt;

Automotive brake squeal which is generated during brake application has become a major concern in automotive industry. Warranty costs for brake noise have been greatly increasing in recent years. Brake noise and vibration control are important for the improvement of vehicle quietness and passenger comfort. In this work, the mode coupling instability mechanism is discussed, and a method to estimate the critical value of friction coefficient is presented to predict the onset of brake squeal. A modal expansion method is developed to calculate eigenvalue and eigenvector sensitivities. Different types of mode couplings and their relationships with squeal are discussed. A reduced-order characteristic equation method based on the statically coupled eigenvalues and their derivatives is presented to estimate the critical value of friction coefficient. The significance of this method is that the critical value of friction coefficient can be predicted accurately without the need for a full complex eigenvalue analysis, making it possible to determine the sensitivity of system stability with respect to design parameters directly.

In this paper, the friction-induced vibration of a simple disc brake model during decelerated sliding is investigated. A three-degree-of-freedom physical model of a disc brake system is considered; the brake pads are modeled as rigid blocks interacting with a rigid translating strip (rotor) through friction. This model simulates the transient dynamics of the longitudinal motions (in the direction of sliding) of the pads during braking. A Coulomb-type friction model is adopted, with the coefficient of friction approximated by an analytical function of the sliding speed at the rotor-pads interface. The coupled equations of motion for the longitudinal vibrations of the sliding strip and the pads are solved simultaneously. Effects of the friction model and other physical parameters on the transient dynamics and instability of the system are examined through the numerical results. Implication of these results to brake squeal generation is also discussed.