An algorithm is presented for the solution of mechanical contact problems using the displacement based Finite Element Method. The corrections are applied as forces at the global level, together with any corrections for other nonlinearities, without having to nominate either body as target or contactor. The technique requires statically reducing the global stiffness matrices to each degree of freedom involved in contact. Nodal concentrated force are redistributed as continuous tractions. These tractions are re-integrated over the element domains of the opposing body. This creates a set of virtual elements which are assembled to provide a convenient mesh of the properties of the opposing body no matter what its actual discretizaton into elements. Virtual nodal quantities are used to calculate corrective forces that are optimal to first order. The work also presents a derivation of refereritial strain tensors. This sheds new light on the updated Lagrangian formulation, gives a complete and correct incremental form for the Lagrangian strain tensor and illustrates the role of the reference configuration and what occurs when it is changed. / Thesis / Doctor of Philosophy (PhD)

An algorithm is presented for the solution of mechanical contact problems using the displacement based Finite Element Method. The corrections are applied as forces at the global level, together with any corrections for other nonlinearities, without having to nominate either body as target or contactor. The technique requires statically reducing the global stiffness matrices to each degree of freedom involved in contact. Nodal concentrated force are redistributed as continuous tractions. These tractions are re-integrated over the element domains of the opposing body. This creates a set of virtual elements which are assembled to provide a convenient mesh of the properties of the opposing body no matter what its actual discretizaton into elements. Virtual nodal quantities are used to calculate corrective forces that are optimal to first order. The work also presents a derivation of refereritial strain tensors. This sheds new light on the updated Lagrangian formulation, gives a complete and correct incremental form for the Lagrangian strain tensor and illustrates the role of the reference configuration and what occurs when it is changed. / Thesis / Doctor of Philosophy (PhD)

Orientador: Katia Lucchesi Cavalca Dedini / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecanica / Made available in DSpace on 2018-08-16T18:19:16Z (GMT). No. of bitstreams: 1 Carvalho_RafaelVischi_M.pdf: 7127919 bytes, checksum: 2c7a6895f35098e4e4f46ed38b158980 (MD5) Previous issue date: 2010 / Resumo: Rolamentos de esfera são elementos de máquinas de forma simples mas utilizados em aplicações envolvendo altas velocidades, altas temperaturas e diferentes carregamentos. O modelo para o carregamento é fundamental para análise dinâmica do mancal e por esse motivo é necessário definir com precisão o desempenho desses mecanismos usando métodos analíticos. O objetivo deste trabalho é analisar o rolamento de esferas baseando-se, em um primeiro momento, em referências bibliográficas de diversos autores para, em seguida, iniciar o equacionamento e simulação para analisar as influências do momento giroscópico, das velocidades geradas nos diversos componentes do rolamento e do carregamento nas esferas. A partir de um rolamento padrão, aplicou-se uma metodologia de testes por simulação numérica variando os principais fatores críticos de um rolamento do ponto de vista estático, cinemático e dinâmico. Conclui-se que a rotação e o ângulo de contato influem nas forças de atrito que resistem ao momento giroscópico e nas velocidades geradas na zona de contato entre esfera e pistas interna e externa. Em altas rotações, quanto maior os seus valores, maior a influência nos ângulos de precessão e de nutação, causando o efeito de escorregamento. Verificou-se, ainda, o valor do ângulo de nutação no qual a velocidade normal ao contato é nula, isto é, validou-se o efeito de outer raceway control. Assim, o modelo apresentou-se consistente com a aproximação para as velocidades e acelerações presentes no elemento rolante, fatores estes fortemente relacionados à condição de lubrificação de mancais de esferas / Abstract: Ball bearings are simple machine elements but largely used in several applications involving high velocities, high temperatures and different loads. The load model is fundamental for the ball bearing's dynamic and for this reason it is necessary to define with accuracy the mechanisms performance using analytical methods. The objective of this thesis is to analyze the ball bearings using, firstly, the most relevant books and papers from several authors as reference and then initiate the modeling and simulation to analyze the influences from the gyroscopic moment and from the velocities created due to the bearing's components and also to the load. Based on a basic bearing, a numeric simulation's test methodology was applied modifying the main critical factors from the bearing and considering the kinematical, dynamical and statical behaviors. The conclusion is that the rotation and the contact angle have influence at the friction forces that resist to the gyroscopic moment and to the velocities that are created at the contact zones between balls and inner and outer raceways. Under high rotations, as higher its value is, higher is the influence at the precession and nutation angles, causing sliding. It was also verified the nutation angle in which the normal velocity at contact is zero, validating the outer raceway control. The model presented itself very consistent with the approximation for the velocities and accelerations presented at rolling element, factors that are highly related to the lubrication condition from the ball bearings / Mestrado / Mecanica dos Sólidos e Projeto Mecanico / Mestre em Engenharia Mecânica

Orientador: Katia Lucchesi Cavalca Dedini / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica / Made available in DSpace on 2018-08-23T01:22:57Z (GMT). No. of bitstreams: 1 Nonato_Fabio_D.pdf: 15501749 bytes, checksum: e33de59a100f07bcab576880e3654db0 (MD5) Previous issue date: 2013 / Resumo: A representação dinâmica dos contatos mecânicos em modelos computacionais de mancais de elementos rolantes baseia-se comumente no clássico modelo de Hertz para o contato seco, mesmo sendo a presença de um meio lubrificante imperativa para evitar o desgaste prematuro destes componentes. Desta maneira, os efeitos dinâmicos da presença de um filme fluídico nas interfaces de contato são desconsiderados, quando tais mancais são lubrificados por óleo. Com o intuito de introduzir tais efeitos em um modelo de mancal de elementos rolantes de esferas, este trabalho propõe um método baseado na aproximação dinâmica das características de cada contato lubrificado por vínculos de rigidez não linear e amortecimento viscoso. Estes vínculos dinâmicos são caracterizados a partir da resposta dinâmica da simulação completa do contato elastohidrodinâmico (EHD) elíptico, através da implementação de um integrador temporal que utiliza o método de diferenças finitas em múltiplos níveis para solução da parcela hidrodinâmica do problema. Posteriormente, aplica-se a aproximação do contato EHD por vínculos não lineares a um modelo do mancal radial de esferas, de dois graus de liberdade, com o intuito de analisar vibrações transversais no mancal, em modelos computacionais de máquinas rotativas. A comparação entre os resultados obtidos pelo modelo proposto e os valores obtidos pelo equacionamento completo por diferenças finitas mostrou ser adequada à representação do comportamento estacionário e dinâmico do contato. Observa-se a presença do enrijecimento do mancal devido à presença do filme EHD, quando analisando a resposta do mancal linearizado, efeito observável anteriormente apenas em investigações experimentais. Por fim, a integração temporal de um modelo de elementos finitos de um rotor apoiado por mancais lubrificados representou adequadamente o comportamento em frequência de uma montagem experimental de rotor. Conclui-se, portanto, que o modelo não linear proposto para o mancal de elementos rolantes radiais de esfera, sob influência da lubrificação EHD, é promissor para descrever o comportamento destes componentes quando em aplicação / Abstract: The dynamic representation of mechanical contacts in computational models of rolling element bearings is commonly based on the classic Hertz's model for the dry contact, even though the presence of a lubricant medium being essential to avoid premature wear of such components. Thus, the dynamic effects of the fluid film on the contacting interfaces are overlooked when such bearings are under oil lubrication. With the intent of introducing such effects in a radial deep groove ball bearing model, this work proposes a method based on the dynamic approximation of each lubricated contact by dynamic links of non-linear stiffness and viscous damping. Such dynamic links are characterized from the response of a complete dynamic simulation of the elastohydrodynamic (EHD) elliptic contact, through an implementation of a numerical integrator, which uses the multi-level finite difference method for the solution of the hydrodynamic portion of the problem. Afterwards, the approximation of each contact by dynamic links is applied to a complete rolling element bearing model, with two degrees of freedom, with the intent of analyzing transverse vibrations on the bearings applied to rotating machinery computational models. The comparison between the results attained through the proposed model and the values simulated using the complete finite difference model showed an adequate representation of the stationary and dynamic behaviors of the contact. When evaluating the linearized bearing model, the presence of fluid stiffening is observed, which was previously only observed through experimental investigations. Lastly, the time integration of a finite element model of a rotor supported by lubricated bearings portrayed the frequency content of an experimental set-up of the rotor adequately. It is concluded that the proposed nonlinear model for the deep grove ball bearing, under the influence of the EHD lubrication, is promising to describe the behavior of such components when on application / Doutorado / Mecanica dos Sólidos e Projeto Mecanico / Doutor em Engenharia Mecânica

Il est communément admis aujourd'hui que le contact entre deux surfaces se compose en réalité d'une multitude de contact ponctuels entre des aspérités. Cette considération amène à une surface de contact réelle significativement différente de l'aire de contact parfaite supposée dans la théorie de Hertz.De même, elle implique également la présence d'un espace libre entre les deux surfaces en contact. Dans cette situation, l'objectif principal de ces travaux de thèse est de développer des approches numériques permettant l'analyse du contact mécanique entre surfaces rugueuses dans le but de qualifier/quantifier l'étanchéité de ce contact rugueux.Deux approches différentes sont étudiées. La première consiste à analyser le contact mécanique entre une surface rugueuse et un plan rigide au moyen de la méthode des éléments finis et d'un nouveau modèle numérique. La seconde concerne l'estimation de la transmissivité d'un contact rugueux en considérant des simulations de l'écoulement d'un fluide au sein du champ des ouvertures présent entre les deux surfaces en contact.La comparaison de ces estimations numériques avec les résultats expérimentaux révèlent des écarts importants. Dans le but de comprendre ces écarts, l'influence du modèle de comportement matériau dans de telles simulations est étudiée. La plasticité cristalline, mais également l'élévation de la température dégagée par déformation plastique seront considérés. La question de la représentativité de notre problème vis-à-vis de l'approche fluide sera également discutée. / It is now widely accepted that the contact between two surfaces is in fact a one-to-one contact between many asperities, depending on the roughness of the contact pair. This represents a strong deviation from the perfect contact assumed in engineering approaches, with the real contact area being significantly smaller than the apparent contact area.In addition, such an approach also implies the presence of a free space between surfaces in contact. Thus, the purpose of our study is the development of numerical tools to analyse the mechanical contact between rough surfaces and the tightness of such a contact.Two different approches are studied. The first one is devoted to the observation of the mechanical contact between a rough surface and a rigid plane by means of the finite element method and a new numerical model. The second approach is related to the estimation of the contact transmissivity by considering simulations of the fluid flow in the resulting free space between surfaces in contact.The comparison between experimental and numerical estimations of the resulting flow rate shows significant deviations.In order to understand these deviations, the influence of material models on contact simulations is studied. In particular, the effect of using crystal plasticity and the effect of including plasticity-driven temperature changes are considered. The question of problem representation in fluid flow approaches is also addressed.

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The following links contain the Documentation and Prototype of the software FilmDoctor with simple intrinsic stress module

Orientador: Auteliano Antunes dos Santos Junior / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica / Made available in DSpace on 2018-08-16T12:15:36Z (GMT). No. of bitstreams: 1 Baruffaldi_LeonardoBartalini_M.pdf: 4986344 bytes, checksum: 359223cc9295f5b392b883e2841d037a (MD5) Previous issue date: 2010 / Resumo: Por 150 anos, os truques de três peças têm sido a estrutura padrão para o suporte de eixos e suspensões de trens de carga em diversos países. Embora sua robustez e facilidade de manutenção tenham conservado, em linhas gerais, a disposição e projeto dos componentes, novos requerimentos de carga e velocidade dos trens vêm mudando a forma como os projetistas enxergam o truque. Especial atenção tem sido dada ao modelo matemático da cunha de atrito, a peça fundida que é responsável pelo amortecimento dos vagões. A cunha de atrito promove a dissipação da energia mecânica por meio de contato de atrito seco com outros componentes do vagão. Devido às altas forças normais desenvolvidas nas superfícies de contato com características não suaves e, em geral, não lineares de atrito, as equações que regem o movimento da suspensão tornam-se de resolução difícil e surgem fenômenos como o de adesão escorregamento e o comportamento caótico típico de osciladores auto excitados. O presente trabalho tem como objetivo propor o uso de algoritmos de solução de problemas de complementaridade linear para resolver as forças de contato entre os corpos, visando a aprofundar a discussão sobre os modelos adotados para a cunha de atrito. Os resultados obtidos mostram que é possível modelar as forças de contato desse sistema utilizando um problema de complementaridade linear e que essa abordagem é, sob certas condições, mais eficiente do que o método das penalidades, normalmente aplicado para a resolução de problemas de contato / Abstract: For about 150 years now, three-piece trucks have been the standard axis' and suspensions' subframe used in freight railroad cars. The toughness and low maintenance costs of this system worked to maintain its basic design almost unchanged, but new requirements for loads and speed for freight cars are changing the way designers see the three-piece truck. Among the many interesting components of the three-piece truck, the friction wedge is getting some attention. The friction wedge is the main damping element in three-piece trucks and acts to dissipate mechanical energy via highly stiff contacts with friction. Due to the non-smooth and non-linear nature of frictional efforts, the equations of motion of the three-piece trucks become very awkward to deal with. Interesting phenomena of stick-slip, bifurcations, and limit cycle, typical of friction oscillators appear to some extent under normal operation. This work's main objective is to propose a new approach based on complementarity problems, used to solve for contact forces, to further extend the discussion on wedge dampers models. Results show that it is possible to model the problem using the linear complementarity problem and that, in some situations, this can be even more computationally efficient than the usual approach to solve contact problems: the penalty method / Mestrado / Mecanica dos Sólidos e Projeto Mecanico / Mestre em Engenharia Mecânica

Grandes bague de roulement utilisés dans éolienne sont l'un des éléments de transmission de charge importantes de ces machines tournantes. Ces roulements fonctionnent grâce à des cycles de charge et de la fréquence et de l'expérience des défis complexes tribologiques sévères. Le coût de remplacement de ces paliers est très élevé et conduit aussi à quantité importante de temps d'arrêt. Il est donc important de comprendre certains des principaux problèmes de conception et tribologiques de ces roulements. Quatre points type de roulement de l'anneau de contact de rotation a été considéré comme une base de référence pour cette étude pour démontrer les questions de contact de troncature et d'échec de la cage pour les roulements de hauteur. Un palier de contact à deux points de remplacement est proposé d'éliminer le contact troncature et de réduire la force de la cage accumulation. Les méthodes de conception et d'analyse démontré dans cette étude peuvent être facilement étendus à lacet paliers ainsi que d'autres grands roulements utilisés dans l'industrie. / Large slewing ring bearings used in wind turbine are one of the important load transmitting elements of these rotating machines. These bearings operate through complex load and frequency cycles and experience severe tribological challenges. The cost of replacement of these bearings is very high and also leads to significant amount of down-time. It is therefore important to understand some of the major design and tribological issues in these bearings. Four-point contact slewing ring bearing type has been considered as a baseline for this study to demonstrate contact truncation and cage failure issues for pitch bearings. An alternate two-point contact bearing is proposed to eliminate contact truncation and reduce the cage force build-up. The design and analysis methods demonstrated in this study can be easily extended to yaw bearings as well as other large bearings used in the industry.

L'objectif de cette thèse est l'identification de couplages (nanoparticules / matrice de poly(methyl-methacrylate) PMMA) qui renforcent la rigidité de surface du PMMA tout en conservant le maximum de transparence. Le choix s'est porté sur trois type de nanoparticules carbonées : du graphène multicouches (FLG), de l'oxyde de graphène (GO) et des nanotubes de carbones (MWCNT). Une première décrit la préparation et la fonctionnalisation de ces trois types de nanoparticules pour assurer une meilleure dispersion dans la matrice. Deux méthodes ont été retenues pour réaliser ces matériaux composites : la polymérisation en masse et le mélange en solution. Une seconde partie présente la caractérisation des propriétés mécaniques de ces revêtements en trois étapes : en volume, en surface et sous forme de revêtement en couches minces (15-20µm). Les résultats majeurs montrent que les nano-composites réalisés retardent l'apparition de la plasticité comparé à un PMMA pur, même à faible pourcentage, et permettent ainsi de limiter les effets de rayures de surfaces. Le faible pourcentage de renfort permet de conserver la transparence et plus l'épaisseur diminue plus on peut augmenter ce taux de renfort sans dégrader les propriétés mécaniques du revêtement. Les nanoparticules choisies comme agents de renfort de la matrice polymère s'avèrent être également de très bons candidats pour la diminution du frottement comparée à un plastifiant type Erucamide / The goal of this thesis is the identification of couplings (nanoparticles / matrix poly (methyl methacrylate) PMMA) which ensure PMMA surface rigidity while maintaining maximum transparency. The choice fell on three types of carbonaceous nanoparticles: Few layer graphene (FLG), graphene oxide (GO) and carbon nanotubes (MWCNT). A first part describes the preparation and functionalization of these three types of nanoparticles to provide a better dispersion in the matrix. Two methods were used to prepare nanocomposite materials: bulk polymerization and solution blending. A second part presents the characterization of the mechanical properties of these coatings in three stages: volume, surface and thin layer coating (15-20μm). The main results show that nanocomposites made delay the onset of plasticity compared with pure PMMA, even at a low percentage, and help to limit the effects of surface scratches. The small percentage of reinforcement keeps the transparency and the more the thickness decreases the more the rate of reinforcement can increase without degrading the mechanical properties of the coating. Moreover, nanoparticles chosen as the polymer matrix of reinforcing agents prove to be very good candidates for reduction in friction compared to a plasticizer such Erucamide.