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Analýza modálních vlastností vertikálního synchronního generátoru / Analysis of vertical synchronous generator modal propertiesKornherr, Milan January 2012 (has links)
This Master´s thesis deals with the analysis of modal characteristics of the vertical synchronous generator. The goal of this work is to determine influence of individual parts of the generator on modal characteristics. Another part of this thesis contains analysis of different variants for storaging the generator and also structural modifications, which lead to the improvement of the modal properties. For modelation was used cumputional modeling in ANSYS.
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Predição da intensidade de corrida em máxima fase estável de lactato a partir da velocidade de crítica em atletas fundistas de alto rendimento : relações com performances /D'Angelo, Ricardo Antonio. January 2008 (has links)
Orientador: Claudio Alexandre Gobatto / Banca: Denise Vaz de Macedo / Banca: Miguel de Arruda / Resumo: A corrida de longa distância é considerada um fenômeno sócio-esportivo recente e de grande impacto na vida moderna. No segmento dos atletas profissionais, a busca por índices confiáveis de avaliação aeróbia, bem como programas de treinamento eficazes e de fácil aplicabilidade é contínua. O tema central desse trabalho foi fornecer uma ferramenta adequada e precisa para se determinar o atual estado da forma do atleta de fundo de alto rendimento, bem como predizer intensidades de carga confiáveis para treinamento e competição. Para tanto, foi estabelecida uma relação matemática entre dois testes de avaliação aeróbia: Máxima Fase Estável de Lactato (MFEL) e Velocidade Crítica (Vcrit). Nove atletas fundistas de alto rendimento, que participaram de seleções nacionais em competições internacionais, tomaram parte no experimento. As melhores marcas pessoais desses atletas correspondem à média ± erro padrão de 91,54 ± 0,93 % da velocidade de corrida do recorde mundial (considerados até o ano de 2007) de sua prova específica. Os testes foram realizados na fase final do período de treinamento de preparação geral. Inicialmente foi aplicado o teste de Vcrit nas distâncias de 800m, 1500m, 3.000m e 5.000m, realizadas aleatoriamente e em dias subseqüentes. A seguir, foi aplicado o teste clássico de MFEL, com duração de 30 min de corrida contínua e coleta de amostras de sangue (25μL) a cada 5 min, para determinação das concentrações de lactato (YSI 1500 sport). Para oito atletas a MFEL ocorreu na intensidade correspondente a 98% da Vcrit, sendo o restante obtido a 90% da Vcrit. A Vcrit (19,1±0,1 km/h) superestimou (p=0,005) os valores de MFEL (18,7±0,2 km/h). Houve correlação significativa entre Vcrit e MFEL (p=0,002, r=0,88). A equação obtida pela regressão foi MFEL=0,9673*Vcrit+0,2061, com erro padrão da estimativa de 0,236...(Resumo completo, clicar acesso eletrônico abaixo) / Abstract: The purpose of this study was to establish a mathematical relationship between the MLSS and the critical speed (CS) in high performance distance runners. Nine male high performance athletes were tested (28±2years), with personal bests of their specific events corresponding a mean ± ESE of 91,54 ± 0,93 % of world record running speed (updated 2007). The athletes were submitted to the CS test, which is the linear regression of the distances (800, 1.500, 3.000 and 5.000m) and their respective time. The CS was determined by the angular coefficient of the linear regression. For all athletes, the regression coefficient (R2) was equal to 1,0. The predicted workloads for the MLSS determination were: 100, 98, 95 and 90% of the CS, randomized and in a continuous way in subsequent days. In this test, the athletes run for 30 min, and it was collected blood samples (25μL) at each 5 min, to determine the lactate concentration (YSI 1500 sport). It was determined stable the non lactate variation higher than 1,0 mmol/L between the 10th and 30th minute. The MLSS has occurred for 8 athletes on the 98% intensity of CS and for 1 athlete on the 90%. The CS (19,1±0,1 km/h) overestimated (p=0,005) the MLSS values (18,7±0,2 km/h). There was significant correlation between CS and MLSS (p=0,002, r=0,88). The regression equation was MLSS=0,9673*CS+0,2061, with estimated standard error of 0,236. There was excellent application of distances to determine the CS in elite distance runners, as well as the parameter accuracy to the "gold standard" intensity verified with the MLSS test. These responses, associated with the low standard estimated error, suggest safety at the MLSS determination through the predicted equation proposed. / Mestre
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Porovnání modálních vlastností oběžných kol parní turbíny s různými délkami lopatek / Comparison of modal properties of steam turbine impeller with blades of different lengthsHavlásek, Michal January 2015 (has links)
The presented master's thesis deals with the safety assessment of several variants of the impeller with different blades length. The motivation for creating this thesis is to find the solution of the problem situation which is characterized by the breakdown of the steam turbine impeller with blades length of 30mm. As confirmed in this thesis, the impeller with blades length of 30mm is operated in the resonance. Likewise, according to the technical standard ČSN EN ISO 10437 its operation is not safe. As the correction action for the problem situation solving is proposed the prolongation of the impeller's blades. The safety is detected for six variants of impeller with dierent blades length. For each variant, there is executed a modal analysis and its results are drawn up into the Campbell diagram. On the basis of this diagram, the safety of individual components is evaluated. The last part of the masters thesis concerns with the examination of the influence of blades length on the modal properties of the impeller.
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Analýza frekvenčního naladění lopatek oběžného kola parní turbíny / Frequency analysis of the blades of the steam turbine impellerKrejčí, Jaroslav January 2015 (has links)
The master thesis deals with modal analysis of the blade of the steam turbine impeller. This analysis is made to find the frequency response of the blade in order to predict the dangerous speeds of the steam turbine. At first the problem situation is described. Than follows the research study which is focused on steam turbines and especially on the rotor dynamic systems and the way to ascertain the modal parameters of the dynamic system by experiment. After that the solution of the problem is performed by computational modelling. The results of the computation are analyzed in detail for different variations of the blade length by Campbell diagram. A graph showing dependency between dangerous speeds of the turbine and the blade length is made out of the results. Then the results are verified by experiment and the coefficients of proportional damping are specified. In conclusion the optimal variation of the blade length for the given operational state is determined.
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A Numerical Model to Predict Train Induced Vibrations and Dynamic Overloads / Modélisation des effets vibratoires et des surcharges dynamiques du trafic ferroviaireFerrara, Riccardo 21 May 2013 (has links)
Durant les cinquante dernières années le développement technologique du train et des infrastructures ferroviaires ainsi que la rapide augmentation des vitesses en ligne ont provoqué une forte augmentation du besoin d'outils numériques pour la conception des infrastructures et des véhicules. Les principaux objectifs de mes travaux de recherche sont de deux ordres : d'une part contribuer à faire progresser les méthodes numériques en développant un outil rapide et simple, capable de simuler les principaux comportements physiques et d'autre par étudier, comprendre et décrire deux phénomènes particuliers: la vitesse critique et le tassement du ballast. La thèse est composée de deux parties. Dans la première partie on montre le modèle numérique adopté pour simuler le système véhicule/infrastructure. Les innovations fondamentales introduites dans cette partie de la thèse résident dans le modèle de liaison entre les attaches et le rail, et dans le nouvel algorithme proposé pour résoudre la non linéarité du problème. En effet, afin de rendre plus rapide la résolution, la méthode du point fixe a été couplée avec la méthode de Newton Raphson. La deuxième partie de la thèse est consacrée à la présentation des résultats numériques obtenus. Enfin, les résultats des simulations ont été utilisés pour la compréhension et la description de l'origine de la vitesse critique et des effets du train sur le tassement du ballast. La vitesse critique peut être définie comme une certaine valeur de vitesse qui provoque un fort incrément des vibrations et des déplacements verticaux et latéraux de l'infrastructure. Ce phénomène a été étudié par plusieurs équipes et a été attribué à un effet de résonance comparable au phénomène aérodynamique du mur du son: «Mach effect». Le train produit des vagues de déformation sur l'infrastructure; la vitesse de ces vagues, nommée «vitesse de Rayleigh», dépend principalement des caractéristiques du ballast et du sol. En effet même si l'effet «Mach» est physiquement plausible pour ces conditions, les trains n'atteignent pas, pour le moment, ces vitesses. Néanmoins des résultats expérimentaux ont permis l'observation du phénomène de la vitesse critique pour des trains roulant à la vitesse de 135 km/h (nombre Mach proche à 0.4). Donc, pour le moment, il n'y a ni estimation exacte ni explication physique de la vitesse critique dans l'intervalle inférieur à la vitesse de Rayleigh. Dans cette thèse une nouvelle explication a été proposée. La masse du train et les suspensions ont une influence non négligeable qui modifie la réponse du système véhicule/infrastructure en termes de modes de vibration. Pour cette raison, il est nécessaire de lier les fréquences d'excitation, et donc la vitesse du train, avec les modes de vibration du système couplé. Des comparaisons entre les analyses modales du système couplé et la déflexion de la traverse en fonction de la vitesse du train ont été menées. Lorsque la vitesse du train, qui excite le système suite aux passage des traverses, rejoint la valeur critique, un phénomène de résonance s'observe. La deuxième étude développée concerne les coûts des entretiens liés au tassement du ballast. Le but est de trouver une fonction de coûts liés aux caractéristiques et aux variables du véhicule, et de proposer une nouvelle méthode pour calculer la partie du péage ferroviaire lié au tassement du ballast (50 % environ du coût total). En calculant la déflection du ballast grâce au modèle présenté dans cette thèse, il est possible d'évaluer l'effet de chaque véhicule sur le tassement. Une fois calculé le coût total d'un certain type de ligne, lié à une certain seuil d'intervention (somme des intervention des bourrages plus la substitution total du ballast), il est possible d'évaluer le coût de chaque passage de train et de le lier à toutes le variables du modèle. / A numerical model to predict train induced vibrations is presented. The dynamic computation considers mutual interactions in vehicle/track coupled system by means of a finite and discrete elements method. The vehicle is modeled by 7 bi-dimensional rigid elements representing: the body, the two boogies and the four wheels. The railway is discretized as finite Timoshenko beam elements. Axial deformation is assumed insignificant. The substructure is made-up of: rail-pads, sleepers, ballast, and background. Rail-pads are modeled as spring/damper couples without mass and sleepers are modeled as rigid elements. The rail-sleeper contact is assumed extended to a connection-area, rather than a single point assumption. To model this area many spring/damper couples are disposed along the length of sleepers. The ballast is modeled as blocks of mass made-up of rigid elements, connected to sleeper by spring/damper couples. To allow the transmission of vibrations in longitudinal direction too, spring/damper couples connect ballast elements horizontally.The dynamic interaction between the wheel-sets and the rail is accomplished by using the non-linear Hertzian model with hysteresis damping. The rail defects and the case of out-of-round wheels are considered too.A modal analysis of supporting structure is done to validate the substructure model comparing it to experimental data.Comparisons between numerical results of our model, experimental data and numerical results of others literature models are done on contact-force, rail accelerations and sleepers accelerations to validate the coupled vehicle/track system.Moreover a modal analysis of the coupled vehicle/track system is done to analyze the relationship between resonance frequencies, train velocities and ballast displacements.A sensitivity analysis is done to evaluate the variables more affecting the maintenance costs. The parameters more conditioning the ballast maintenance costs are the ballast modulus and the train mass.The effects of train velocity on the ballast displacements are analyzed in relationship with substructure properties. A new formulation to evaluate the railway toll connected to ballast wear is introduced.A new interpretation of the critical velocity in the range 100-300 km/h is proposed.
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Optimalizace modálního tlumení lopatek vysokotlakých stupňů parních turbín / Optimization of Modal Damping of Blades in High Pressure Stages of Steam TurbineLošák, Petr January 2011 (has links)
Steam turbine rotor is a very complicated assembly, typically consists of several rotor rows. Due to design limitations and increasing demands on the efficiency of the steam turbines, it is practically impossible to avoid all of the resonant states. The significant vibrations can occur, for example, due to passing resonance state during turbine start up or run out. In the worst case the turbine operates state is close to the resonance state of the rotor row. This leads to the significant oscillation of the bladed disk, and may results in the blade (or blade to disk joints) high cycle fatigue. These parts are highly loaded components and any cracks are unacceptable. Therefore it is absolutely necessary to damp vibration by using, for example, passive damping elements. The damping element analyzed in this thesis is a strap with an isosceles trapezoidal cross section, which is placed in the circumferential dovetail groove in the blade segmental shrouding. The sliding between the contact surfaces leads to the dissipation of energy which causes decreasing of undesirable vibrations. The main aim is to design the optimal dimensions of the strap cross-section with a view to the most effective damping of vibration for a particular turbine operating state. Considered bladed disk has 54 blades which are coupled in 18 packets by segmental shrouding. The damping element is paced in circumferential dovetail groove created in the shrouding. This type of damping element is suitable especially for damping vibrations in the axial direction and only with the mode shape with the nodal diameters. The modal properties of the bladed disk are influenced by the sliding distance. Since the friction force depends on centrifugal force acting on the damping element and on the angle of the side walls of the strap and groove, the sliding distance can be influenced by the damping element dimensions. During the optimization process the best possible size of middle width, height and angle of damping element cross-section is searched. The strap weight, contact area size and flexural stiffness of damping element can be influenced by these parameters. Their change has also impact on the size of the contact pressure and thus on the size of relative motion as well. As stated previously, the damping efficiency is influenced by the relative motion between the damping element and shrouding. Numerical simulation in time domain is very time-consuming, especially for systems containing nonlinearities. In order to verify dynamic behavior of the computational model with the passive friction element in numerical simulations, the simplified model is created. The model is created in the ANSYS environment. The main requirement imposed on this model is to have as small number of degrees of freedom as possible, so the time needed to perform the simulation is reduced to a minimum. To satisfy this requirement the simplified model is a cantilever beam with rectangular cross section. The dovetail groove is created in this model in longitudinal direction. In this groove is damping element. In addition to damping element dimensions optimization, the influence of each design variable on model dynamic behavior is studied. The results are verified experimentally. Experiment also shows other interesting results that confirm the damping element influence on the modal characteristics. The gained knowledge is used to optimize the dimensions of the damping element in the model of the bladed disk.
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Numerical modeling of soil flow and pressure distribution on a simple tillage tool using computational fluid dynamicsKarmakar, Subrata 28 October 2005
<p>Soils, in general, undergo both elastic and plastic deformations upon loading. Strain dependant anisotropic elasto-plastic models are required for realistic modeling for soil-tool mechanics that will address issues like stress history and soil anisotropy. Although several such models have been proposed, the science of coupled poro-mechanical analysis of an unsaturated soil has not been fully addressed.</p><p>Tillage tool modeling is primarily concerned with the analysis of soil deformation patterns and development of force prediction models for design optimization. Most of the models are based on quasi-static soil failure patterns that cause difficulty in accurately predicting soil-tool behaviour and soil forces for high speed operation. In recent years efforts have been made to improve the conventional analytical and experimental models by numerical approaches. Numerical simulations of soil-tool interactions using finite element modeling (FEM) and discrete element method (DEM) were mostly based on a solid mechanics approach. Due to limitations of constitutive relations, predictions of these numerical models have not been able to address tillage dynamics with high shear rates. The contribution of this research was to study the dynamics of soil-tool interaction using computational fluid dynamics (CFD) from the perspective of soil visco-plastic behavior.</p><p>A motorised soil rheometer was developed for evaluating soil visco-plastic parameters for CFD simulations. The apparatus was used to determine soil yield stress and viscosity at different soil moisture and compaction levels.</p><p>Three-dimensional CFD analyses were carried out using a commercial software CFX 4.4 to observe soil failure patterns around a tool and the pressure distribution on and around the tool. Duct flow as well as free-surface flow simulations of visco-plastic soil as a non-Newtonian Bingham material indicated soil deformation comprising of plastic flow and plug flow patterns. The soil failure front advancement demonstrated a critical speed range of 4 to 6.5 m s-1 where advancement of the failure front did not increase with speed. Soil pressure on the tool surface increased with the tool operating speed. Pressure distribution on the tool surface and draft requirement agreed well with the published literature based on experimental results and FEM analysis. The CFD approach, in its first attempt to tillage process, demonstrated its greater potential for dynamic modeling of soil-tool interaction.</p>
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Numerical modeling of soil flow and pressure distribution on a simple tillage tool using computational fluid dynamicsKarmakar, Subrata 28 October 2005 (has links)
<p>Soils, in general, undergo both elastic and plastic deformations upon loading. Strain dependant anisotropic elasto-plastic models are required for realistic modeling for soil-tool mechanics that will address issues like stress history and soil anisotropy. Although several such models have been proposed, the science of coupled poro-mechanical analysis of an unsaturated soil has not been fully addressed.</p><p>Tillage tool modeling is primarily concerned with the analysis of soil deformation patterns and development of force prediction models for design optimization. Most of the models are based on quasi-static soil failure patterns that cause difficulty in accurately predicting soil-tool behaviour and soil forces for high speed operation. In recent years efforts have been made to improve the conventional analytical and experimental models by numerical approaches. Numerical simulations of soil-tool interactions using finite element modeling (FEM) and discrete element method (DEM) were mostly based on a solid mechanics approach. Due to limitations of constitutive relations, predictions of these numerical models have not been able to address tillage dynamics with high shear rates. The contribution of this research was to study the dynamics of soil-tool interaction using computational fluid dynamics (CFD) from the perspective of soil visco-plastic behavior.</p><p>A motorised soil rheometer was developed for evaluating soil visco-plastic parameters for CFD simulations. The apparatus was used to determine soil yield stress and viscosity at different soil moisture and compaction levels.</p><p>Three-dimensional CFD analyses were carried out using a commercial software CFX 4.4 to observe soil failure patterns around a tool and the pressure distribution on and around the tool. Duct flow as well as free-surface flow simulations of visco-plastic soil as a non-Newtonian Bingham material indicated soil deformation comprising of plastic flow and plug flow patterns. The soil failure front advancement demonstrated a critical speed range of 4 to 6.5 m s-1 where advancement of the failure front did not increase with speed. Soil pressure on the tool surface increased with the tool operating speed. Pressure distribution on the tool surface and draft requirement agreed well with the published literature based on experimental results and FEM analysis. The CFD approach, in its first attempt to tillage process, demonstrated its greater potential for dynamic modeling of soil-tool interaction.</p>
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Predição da intensidade de corrida em máxima fase estável de lactato a partir da velocidade de crítica em atletas fundistas de alto rendimento: relações com performancesD'Angelo, Ricardo Antonio [UNESP] 01 July 2008 (has links) (PDF)
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dangelo_ra_me_rcla.pdf: 444962 bytes, checksum: 9e4977bddba15cb8009dd5428d72ccc4 (MD5) / Universidade Estadual Paulista (UNESP) / A corrida de longa distância é considerada um fenômeno sócio-esportivo recente e de grande impacto na vida moderna. No segmento dos atletas profissionais, a busca por índices confiáveis de avaliação aeróbia, bem como programas de treinamento eficazes e de fácil aplicabilidade é contínua. O tema central desse trabalho foi fornecer uma ferramenta adequada e precisa para se determinar o atual estado da forma do atleta de fundo de alto rendimento, bem como predizer intensidades de carga confiáveis para treinamento e competição. Para tanto, foi estabelecida uma relação matemática entre dois testes de avaliação aeróbia: Máxima Fase Estável de Lactato (MFEL) e Velocidade Crítica (Vcrit). Nove atletas fundistas de alto rendimento, que participaram de seleções nacionais em competições internacionais, tomaram parte no experimento. As melhores marcas pessoais desses atletas correspondem à média ± erro padrão de 91,54 ± 0,93 % da velocidade de corrida do recorde mundial (considerados até o ano de 2007) de sua prova específica. Os testes foram realizados na fase final do período de treinamento de preparação geral. Inicialmente foi aplicado o teste de Vcrit nas distâncias de 800m, 1500m, 3.000m e 5.000m, realizadas aleatoriamente e em dias subseqüentes. A seguir, foi aplicado o teste clássico de MFEL, com duração de 30 min de corrida contínua e coleta de amostras de sangue (25μL) a cada 5 min, para determinação das concentrações de lactato (YSI 1500 sport). Para oito atletas a MFEL ocorreu na intensidade correspondente a 98% da Vcrit, sendo o restante obtido a 90% da Vcrit. A Vcrit (19,1±0,1 km/h) superestimou (p=0,005) os valores de MFEL (18,7±0,2 km/h). Houve correlação significativa entre Vcrit e MFEL (p=0,002, r=0,88). A equação obtida pela regressão foi MFEL=0,9673*Vcrit+0,2061, com erro padrão da estimativa de 0,236... / The purpose of this study was to establish a mathematical relationship between the MLSS and the critical speed (CS) in high performance distance runners. Nine male high performance athletes were tested (28±2years), with personal bests of their specific events corresponding a mean ± ESE of 91,54 ± 0,93 % of world record running speed (updated 2007). The athletes were submitted to the CS test, which is the linear regression of the distances (800, 1.500, 3.000 and 5.000m) and their respective time. The CS was determined by the angular coefficient of the linear regression. For all athletes, the regression coefficient (R2) was equal to 1,0. The predicted workloads for the MLSS determination were: 100, 98, 95 and 90% of the CS, randomized and in a continuous way in subsequent days. In this test, the athletes run for 30 min, and it was collected blood samples (25μL) at each 5 min, to determine the lactate concentration (YSI 1500 sport). It was determined stable the non lactate variation higher than 1,0 mmol/L between the 10th and 30th minute. The MLSS has occurred for 8 athletes on the 98% intensity of CS and for 1 athlete on the 90%. The CS (19,1±0,1 km/h) overestimated (p=0,005) the MLSS values (18,7±0,2 km/h). There was significant correlation between CS and MLSS (p=0,002, r=0,88). The regression equation was MLSS=0,9673*CS+0,2061, with estimated standard error of 0,236. There was excellent application of distances to determine the CS in elite distance runners, as well as the parameter accuracy to the “gold standard” intensity verified with the MLSS test. These responses, associated with the low standard estimated error, suggest safety at the MLSS determination through the predicted equation proposed.
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Modélisation numérique du contact roue-rail pour l’étude des paramètres influençant les coefficients de Kalker : Application à la dynamique ferroviaire / Numerical modeling of the wheel-rail contact for the study of the parameters influencing Kalker’s coefficients : Application to the railway dynamicsToumi, Moncef 13 December 2016 (has links)
Le calcul des efforts normaux et tangents est important pour la modélisation dynamique du système véhicule-voie en ferroviaire. Pour déterminer les forces tangentielles au contact roue-rail, les coefficients de Kalker sont utilisés dans la plupart des codes de dynamique ferroviaire, pour les différents modèles de contact. Ces coefficients ont été mesurés sur banc à plusieurs reprises dans les années 80. Une synthèse de ces travaux, réalisée par Hobbs, montre que certaines de ces mesures présentent une baisse pouvant atteindre 50% par rapport à la théorie de Kalker. L’objet de cette thèse est d’identifier d’abord les véritables causes de la dispersion constatée entre les différentes mesures, généralement attribuée à la contamination de la surface, puis de développer un modèle numérique capable d’en tenir compte.La démarche numérique proposée est sur deux volets. Dans le premier volet, une méthode itérative directe par éléments de frontière basée sur les intégrales de surface de Boussinesq-Cerruti est réécrite pour l’étude du contact normal et glissant entre deux corps élastiques, puis étendue pour la résolution du problème de contact roulant. Appliquée avec succès au contact roue-rail non-Hertzien, cette méthode est un outil prometteur pour l’étude des paramètres influençant les coefficients de Kalker qui allie à la fois la précision et la rapidité.Dans le deuxième volet, le problème du contact roue-rail élastique est résolu à l’aide de la méthode des éléments finis en utilisant les schémas d’intégration temporelle explicite et implicite. La solution élastique est comparée avec le logiciel de référence CONTACT. Le modèle par éléments finis 3D développé a permis de prendre en compte d’une part le comportement élasto-plastique des corps en contact et d’autre part l’existence d’une couche de troisième corps sur l’interface du contact roue-rail. Ainsi, en fin de cette étude, une correction aux coefficients de Kalker est estimée à partir d’un modèle qui prend mieux en compte la réalité physique du contact roue-rail.Afin d’évaluer l’influence de cette correction sur la vitesse critique du véhicule ferroviaire, une étude de stabilité est réalisée avec le code de dynamique ferroviaire VOCO dans lequel des facteurs de réduction des coefficients de Kalker ont été appliqués / The calculation of normal and tangential forces is important for the dynamic modeling of the railway vehicle-track interaction. To determine the tangential forces at the wheel-rail contact level, the Kalker’s coefficients of stiffness are used in most of computer codes for different contact models. These coefficients were measured on bench several times in the 80s. A survey of these works, conducted by Hobbs, shows a decrease of up to 50 % in value compared to Kalker’s theory. The aim of this thesis is first to identify the real causes of the dispersion observed between the various measurements, usually attributed to the surface contamination, then to develop a model taking into account some of them.The numerical modeling of the wheel-rail contact is presented in two parts. In the first part, a direct boundary element method based on Boussinesq-Cerruti solution is developed to study the normal and sliding contact between two elastic bodies, and then extended to the resolution of rolling contact problem. Successfully applied to the wheel-rail contact for non-Hertzian situation, this method is a promising tool for studying the parameters influencing Kalker’s coefficients which combines both precision and speed.In the second part, a finite element model for rolling contact between wheel and rail is developed to study the normal and the tangential contact problems using the explicit and the implicit integration schemes. The elastic solution is compared with the solution of the CONTACT software. The three-dimensional finite element model takes into account the elastoplastic behavior of the bodies in contact as well as the existence of a third body layer at the interface between the wheel and the rail. Finally, a correction of Kalker’s coefficients is estimated from the results of the numerical simulations.To study the impact of this correction on the critical speed of the vehicle, a stability analysis is performed using the multibody dynamics software VOCO in which the reduced factors of Kalker’s coefficients are considered
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