Les roulements à billes sont l’un des composants les plus importants et les plus critiques dans les turbomachines ou dans les éoliennes. Les butées à billes rencontrées dans les pieds de pales d’éoliennes doivent supporter des chargements très élevés, avec des bagues très fines par rapport aux dimensions du palier. Le roulement à quatre points de contact à haute vitesse est un autre exemple de bagues minces, où la cinématique interne est fortement liée à la géométrie des pistes qui elle, dépend de la rigidité des bagues et des logements. Pour cette application, les pistes intérieures et extérieures sont archées et bien souvent constituées de deux demi-bagues. La souplesse de ces dernières ainsi que celle du logement modifie la géométrie interne et l’interaction entre les composants. Il est proposé dans cette thèse un modèle permettant de dimensionner des roulements à billes à quatre points de contact, principalement dans le domaine d'application des turbines aéronautiques. Ce modèle est capable de rendre compte des déformations globales des bagues et de leur logement et environnement proche. Un ensemble de travaux existants et différentes possibilités envisagées pour la mise en place d’un modèle de roulement à bagues déformables est présenté pour définir une stratégie de couplage efficace entre un modèle analytique et un modèle éléments finis. La prise en compte de la souplesse des bagues s’appuie sur la résolution préalable d’un problème semi analytique de modélisation avec bagues rigides. Ensuite un couplage entre les résultats de ce modèle et un modèle éléments finis est réalisée pour prendre en compte la souplesse des bagues. Des choix sont nécessaires pour ce couplage, notamment sur la modélisation des contacts billes/bagues par l’utilisation de forces nodales pour simuler fidèlement ces contacts. Plusieurs méthodes sont ainsi évaluées pour calculer au mieux la nouvelle géométrie de la bague, en observant son comportement lorsqu'elle est soumise au contact d'une bille. Finalement, cette souplesse est intégrée au modèle semi analytique pour comparer le comportement d'un roulement à bagues rigides à celui d'un roulement à bagues souples. Des premiers résultats numériques sur une géométrie académique montrent des variations des grandeurs internes du roulement (angles de contact, ellipse de contact) ainsi qu’une meilleure répartition du chargement. Des essais ont été réalisés pour valider expérimentalement le modèle développé dans cette thèse. Les comparaisons par mesures du déplacement axial des bagues et des ondulations en surface des bagues montrent que la souplesse du support n’est pas négligeable, même dans le cas de bagues larges. Egalement, ces essais ont démontré la pertinence du couplage entre un modèle analytique et un modèle éléments finis pour rendre compte des déformations de bagues de roulements à billes à quatre points de contact. / Ball bearings are one of the most important and most critical part in turbomachine and wind turbine. They require a careful design in order to create reliability and economic relevance, which leads to compact bearings with high dynamic and static load capacity. Then ball bearing encountered in wind turbine must carry high loads, with thin rings regarding mean diameter of the bearing. High speed four point contact ball bearing is another example of thin rings, where internal kinematics is highly linked to raceway geometry, and raceway geometry depends on rings and housing stiffness. For this application, internal and external ring are arched and frequently made of two parts. There stiffness change the internal geometry and interaction with bearings components. It implies a change in load distribution and internal speed. As a consequence bearing and housing stiffness is an important parameter in order to estimate the admissible loads for the bearing. This thesis propose a model for the four point contact ball bearing, mainly for aeronautical turbine engine. This model can account for structural ring deformation as well as of housing deformation. Some existing work and different possibility for such a model are presented in order to define a coupling strategy between an analytical model and a finite element model. The accounting for ring stiffness rely on the resolution of a rigid ring semi analytical model. Then a coupling between this results and finite element results is done in order to account for ring stiffness. Some choices are made for the coupling, especially on ball/ring interaction by using nodal forces to model contact with fidelity. Some methods are evaluated to compute new ring geometry due to contacts with balls. Finally this stiffness is integrated in the semi analytical model in order to compare the behavior of rigid ring bearing with deformable ring bearing. First numerical results on an academic bearing shows change in internal parameter (contact angle, contact ellipse) and a better load distribution. Some experimental tests are made in order to validate the model presented in this thesis. Comparison on axial displacement and ring surface undulation shows that housing stiffness is not negligible even with large ring bearing. This tests show the relevance of a coupling between an analytical model and a finite element model in order to account for ring deformation in four point contact ball bearing.

Orientador: Katia Lucchesi Cavalca Dedini / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica / Made available in DSpace on 2018-08-22T07:50:24Z (GMT). No. of bitstreams: 1 Reis_VitorLuiz_M.pdf: 22501479 bytes, checksum: 7dcc42bed756f7cd1dc28e2f763f91ed (MD5) Previous issue date: 2013 / Resumo: Este trabalho apresenta o desenvolvimento de um modelo dinâmico para o mecanismo biela-manivela com folga na junta de revolução pino-pistão. As equações do movimento para este sistema são obtidas através do método de Lagrange e os efeitos relacionados ao contato, atrito e lubrificação que atuam nos elementos com folga são alvo de estudo. O modelo da força de contato utilizado baseia-se na formulação de Hertz, considerando a inclusão do efeito dissipativo associado ao impacto entre o pino e o pistão. A força de atrito adotada baseia-se no atrito de Coulomb, porém adaptada à abordagem da dinâmica multicorpos. Tais modelos são validados com os resultados encontrados na literatura recente. A pesquisa apresenta contribuição na avaliação do efeito introduzido pela lubrificação hidrodinâmica na junta com folga. Dois modelos de lubrificação hidrodinâmica são avaliados: o primeiro apresenta uma solução direta e de baixo custo computacional; o segundo modelo obtém uma solução numérica que leva em consideração o efeito da aceleração imposta ao fluido lubrificante pelo movimento do mecanismo. A resposta dinâmica é obtida sob a variação paramétrica do tamanho da folga e a velocidade de rotação da manivela. Ao final, agrega-se ao sistema um modelo simplificado de geração da curva de pressão para um motor de combustão interna típico. Observou-se que a inclusão do modelo de lubrificação proposto não garante a sustentação do pino-pistão em regime de lubrificação hidrodinâmica durante as simulações efetuadas. Desta maneira, faz-se necessário o desenvolvimento de um modelo de lubrificação hidrodinâmica e elastohidrodinâmica capaz de determinar o comportamento no contato pino-pistão de maneira mais realista / Abstract: This work presents the development of a dynamic model for the slider-crank mechanism with clearance on the piston-pin revolute joint. The equations of motion for this system are obtained by Lagrange's method and the effects related to contact, friction and lubrication at the elements that operate in the clearance are the targets of study. The contact force model used in this work is based on Hertz formulation, considering the inclusion of the dissipative effect associated with the impact between the pin and the piston. The frictional force adopted is based on the Coulomb friction but adapted to the multibody dynamics approach. Such models are validated with the results found in recent literature. The research presents contribution in evaluating the effect introduced by hydrodynamic lubrication in the revolute joint clearance. Two models of hydrodynamic lubrication are investigated: the first model presents a direct solution of low computational cost, the second model results in a numerical solution that consider the effect of the acceleration of the lubricant fluid imposed on the movement of the mechanism. The dynamic response is studied for different sets of parameters of clearance and rotational speed of the crank. Moreover, a simplified model of the generation of the pressure curve for a typical internal combustion engine was included in the system. It was observed that the present lubrication model does not guarantee the support of the pin-piston system for hydrodynamic lubrication in the present simulations. Therefore, it is necessary to develop a more realistic model of hydrodynamic lubrication and elastohydrodynamic lubrication that is capable of reproducing the behavior of the piston-pin contact / Mestrado / Mecanica dos Sólidos e Projeto Mecanico / Mestre em Engenharia Mecânica

Orientadores: Paulo Sollero, Eder Lima de Albuquerque / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica / Made available in DSpace on 2018-08-28T12:08:28Z (GMT). No. of bitstreams: 1 Shaterzadeh-Yazdi_MohammadHossein_M.pdf: 5411191 bytes, checksum: 83da697ff892a31af99059f3e88bd338 (MD5) Previous issue date: 2015 / Resumo: Em problemas de contato mecânico entre dois corpos elásticos, o cálculo de tensões e deformações dos componentes é de grande importância. Em casos particulares os corpos estão sujeitos a cargas normal e tangencial na presença de atrito, o qual aumenta a complexidade do problema. O estudo do fenômeno e a modelagem do problema, empregando o método dos elementos de contorno (MEC), é apresentado neste trabalho. Devido à presença de atrito e restrições de contato, esse problema torna-se um caso não linear. A não linearidade do problema foi contornada com a aplicação incremental de carga e o uso de um método de resolução de sistemas não lineares. A zona de contato é uma das variáveis do problema e pode conter estados de adesão e escorregamento, simultaneamente. Esses estados dependem dos esforços normais e tangenciais no componente e podem variar durante o processo de aplicação de carga. Dessa forma, cada incremento de carga pode perturbar em relação ao estado anterior. Portanto, o cálculo de variáveis e a atualização do sistema de equações em cada iteração é indispensável. Por este motivo, um algoritmo robusto para definição dos estados de contato é proposto. Como o sistema de equações obtido é não linear, o uso de um método numérico adequado é exigido. Para a solução deste sistema, o método de Newton foi aplicado, o qual permite a verificação do estado de contato em cada incremento. A análise é feita com o uso de elementos quadráticos contínuos, apresentando resultados contínuos e sem oscilação. A comparação dos resultados com as soluções analíticas de Hertz e Mindlin-Cattaneo mostram boa concordância / Abstract: The computation of stresses and strains on the components is of great importance, when the contact mechanics problems between two elastic bodies are analyzed. In particular cases, bodies are subjected to normal and shear loading in the presence of friction, which increases the complexity of the problem. The study of the phenomenon and modeling of the problem, using the boundary element method (BEM), are presented in this work. Due to the presence of friction and natural restrictions, this problem becomes non-linear. The non-linearity of the problem was solved with an incremental applied load and with the use of solvers to non linear systems. The contact zone can contain stick and slip states, simultaneously. These states are dependent on the normal and shear forces on the component and can vary during the application load process. Thus, each load increment can violate the previous state and therefore, the evaluation of variables and the updating of the system of equations after each iteration is indispensable For this reason, a robust algorithm for contact state definition is suggested. Since a non linear system of equations is obtained, an appropriate numerical method is required. To solve this system, Newton¿s method is applied, which allows the verification of the state of contact at each increment. The analysis is done with the use of quadratic continuous elements and provides continuous and non-oscillatory results. Comparisons of the results with the analytical solutions of Hertz and Mindlin-Cattaneo show good agreement / Mestrado / Mecanica dos Sólidos e Projeto Mecanico / Mestre em Engenharia Mecânica

Nowadays, high demands are made on filling materials in modern dentistry: Durability, Reliability &Aesthetic Requirements Thus, a group of physicists and an independent practicing dentist investigated 11 different teeth fillings (composite materials) as used in modern dental practices according to their stability and ability to withstand contact loadings.

During life of railway vehicles, shape irregularities develop on wheels and rails because of wear. The shape irregularities then affect forces in wheel-rail contact and cause further damage of contact surfaces, vibrations and noise and increase risk of derailment. A numerical simulation of railway vehicle motion with more details on contact surfaces geometry was created to investigate dynamic contact loads in wheel-rail contact. A variety of methods can be used to evaluate forces in rolling contact, the method chosen for this study was algorithm CONTACT based on boundary element method. Four studies are presented in this papers: contact loads from a wheel with a flat and with a wavy tread pattern, loads on wavy rail and load in a curve. The first three studies investigated effects of existing wear patterns, the last one looked for cause of common wear pattern developing on rails. Results of the studies with worn components used showed that the worst kind of shape irregularities is a flat present on wheel. This type of shape cause loss of contact and following impacts. The study of ride in curve showed that cause of high wear in curves, especially those with small radii, is caused by vibration of wheelset. This vibration is then caused by different length of inner and outer rail and wheels travelling along a different path.

No description available.

No description available.

Rolling contacts are utilized in many technical applications, both in bearings and in the contact between gear teeth. These components are often highly loaded, which makes them susceptible to suffer from rolling contact fatigue. This work focuses on the rolling contact fatigue mechanism of pitting. In order to attain a better understanding of why pitting initiates and grows, detailed simulations of rolling contacts have been performed. In particular the contact between two gears in a truck retarder was here used as a case study. The investigated contact experienced elastohydrodynamic lubrication conditions since the load was high enough to causes the surfaces in contact to deform and the viscosity of the lubricant to increase significantly. In Paper A it was investigated if surface irregularities in the size of the surface roughness are large enough to cause surface initiated fatigue. The investigation focused on the pitch line since small surface initiated pits were found here even though there was no slip present. Since there were pits present at the pitch line, it is important that the theories of pitting can explain the development of pits also in the absence of slip. The conclusion of the work was that surface irregularities of the size of normal surface roughness are enough to cause surface initiated fatigue at the pitch line. In Paper B it was investigated why pits are more likely to initiate in the dedendum of pinion gears than in the addendum. In both areas slip is present but in different directions. In the dedendum the friction from slip is against the rolling direction which enhances the risk for pitting. The investigation was performed by studying the effect of the temperature rise in the contact caused by the slip. The conclusion drawn was that the temperature rise in the contact explained why pitting was more common in the dedendum than in the addendum. / Rullande kontakter förekommer i många applikationer, till exempel i lager och mellan kugghjulständer. Både lager och kugghjul utsätts ofta för höga laster vilket gör att dess ytor löper stor risk att utmattas, vilket kallas rullande kontaktutmattning. Denna studie fokuserar på pitting, även kallat spalling, vilket är en typ av rullande kontaktutmattning där en utmattninsspricka växer fram som får delar av ytan att ramla av. För att få en bättre förståelse varför pittingskador uppkommer har noggranna simuleringar utförts av rullande kontakter. Kontakten mellan två tänder på kugghjul i en lastbilsretarder har används som underlag då många pittingskador påträffats på dem.  För att minska friktionen och nötningen i kontakten mellan kuggtänderna användes smörjmedel. De höga lasterna lastbilsretardern utsattes för deformerade kuggarnas ytor elastiskt samtidigt de kraftigt ökade viskositeten hos smörjmedlet. Dessa förhållanden gör att kontakten kallas för elastohydrodynamiskt smord, vilket på engelska förkortas till EHL. I Artikel A undersöktes om små ytojämnheter kan orsaka ytinitierade pittingskador. Eftersom skadan påträffats i friktionslösa kontakter, så som vid rullcirkeln på de undersökta kugghjulen, är det viktigt att teorierna som förklarar uppkomsten inte är beroende av friktion. Undersökningen fokuserade därför på förhållandena vid rullcirkeln.  Slutsatsen från arbetet var att små ytojämnheter, av samma storleksordning som ytojämnheterna på de undersökta kugghjulen, är tillräckligt stora för att orsaka utmattningsskador. I Artikel B undersöktes varför det är vanligare att pitts initieras i dedendum än addendum på drivande kugghjul. Kontakten på båda sidorna om rullcirkeln slirar svagt åt olika håll. Att kontakten slirar skapar friktion som är motriktad rullriktningen i dedendum vilket ökar risken för pittingskador. För att undersöka varför dessa förhållanden ökar risken för skador fördjupades analysen av kontakten genom att inkludera temperaturfältet. Simuleringarna visade att temperaturen ökar genom kontakten vilket orsakar en asymmetrisk spänningsfördelning. Denna asymmetriska spänningsfördelning gör att ytojämnheter i dedendum är troligare att orsaka skador än ytojämnheter i addendum. / <p>QC 20180213</p>

This research investigates the modeling of randomly distributed surface-breaking microcracks and their effects on higher harmonic generation in Rayleigh surface waves. The modeling is based on micromechanical considerations of rough surface contact. The nonlinear behavior of a single microcrack is described by a hyperelastic effective stress-strain relationship. Finite element simulations of nonlinear wave propagation in a solid with distributed microcracks are performed. The evolution of fundamental and second harmonic amplitudes along the propagation distance is studied and the acoustic nonlinearity parameter is calculated. The results show that the nonlinearity parameter increases with crack density and root mean square roughness of the crack faces. While, for a dilute concentration of microcracks, the increase in acoustic nonlinearity is proportional to the crack density, this is not valid for higher crack densities, as the microcracks start to interact. Finally, it is shown that odd higher harmonic generation in Rayleigh surface waves due to sliding crack faces introduces a friction nonlinearity.

Cette thèse propose trois nouveaux développements de la méthode des bases réduites (RB) et de la méthode d'interpolation empirique (EIM) pour des problèmes non-linéaires. La première contribution est une nouvelle méthodologie, la méthode progressive RB-EIM (PREIM) dont l'objectif est de réduire le coût de la phase de construction du modèle réduit tout en maintenant une bonne approximation RB finale. L'idée est d'enrichir progressivement l'approximation EIM et l'espace RB, contrairement à l'approche standard où leurs constructions sont disjointes. La deuxième contribution concerne la RB pour les inéquations variationnelles avec contraintes non-linéaires. Nous proposons une combinaison RB-EIM pour traiter la contrainte. En outre, nous construisons une base réduite pour les multiplicateurs de Lagrange via un algorithme hiérarchique qui conserve la positivité des vecteurs cette base. Nous appliquons cette stratégie aux problèmes de contact élastique sans frottement pour les maillages non-coïncidents. La troisième contribution concerne la réduction de modèles avec assimilation de données. Une méthode dédiée a été introduite dans la littérature pour combiner un modèle numérique avec des mesures expérimentales. Nous élargissons son cadre d'application aux problèmes instationnaires en exploitant la méthode POD-greedy afin de construire des espaces réduits pour tout le transitoire temporel. Enfin, nous proposons un nouvel algorithme qui produit des espaces réduits plus représentatifs de la solution recherchée tout en minimisant le nombre de mesures nécessaires pour le problème réduit final / This thesis introduces three new developments of the reduced basis method (RB) and the empirical interpolation method (EIM) for nonlinear problems. The first contribution is a new methodology, the Progressive RB-EIM (PREIM) which aims at reducing the cost of the phase during which the reduced model is constructed without compromising the accuracy of the final RB approximation. The idea is to gradually enrich the EIM approximation and the RB space, in contrast to the standard approach where both constructions are separate. The second contribution is related to the RB for variational inequalities with nonlinear constraints. We employ an RB-EIM combination to treat the nonlinear constraint. Also, we build a reduced basis for the Lagrange multipliers via a hierarchical algorithm that preserves the non-negativity of the basis vectors. We apply this strategy to elastic frictionless contact for non-matching meshes. Finally, the third contribution focuses on model reduction with data assimilation. A dedicated method has been introduced in the literature so as to combine numerical models with experimental measurements. We extend the method to a time-dependent framework using a POD-greedy algorithm in order to build accurate reduced spaces for all the time steps. Besides, we devise a new algorithm that produces better reduced spaces while minimizing the number of measurements required for the final reduced problem