A panel method free-wake code for aeroelastic rotor predictions

A panel method free-wake model to analyse the rotor flapping is presented. The aerodynamic model consists of a panel method, which takes into account the three-dimensional rotor geometry, and a free-wake model, to determine the wake shape. The main features of the model are the wake division into a near-wake sheet and a far wake represented by a single tip vortex, and the modification of the panel method formulation to take into account this particular wake description. The blades are considered rigid with a flap degree of freedom. The problem solution is approached using a relaxation method, which enforces periodic boundary conditions. Finally, several code validations against helicopter and wind turbine experimental data are performed, showing good agreement

Desarrollo de un Procedimiento Basado en Algoritmos de Optimización para el Dimensionado de Absorbedores Puntuales Aplicados a la Conversión de Energía Undimotriz

La energía transportada por el oleaje a través de los océanos (energía undimotriz) se enmarca dentro de las denominadas energías oceánicas. Su aprovechamiento para generar energía eléctrica (o ser aprovechada de alguna otra forma) es una idea reflejada ya hace más de dos siglos en una patente (1799). Desde entonces, y con especial intensidad desde los años 70, ha venido despertando el interés de instituciones ligadas al I+D+i y empresas del sector energético y tecnológico, debido principalmente a la magnitud del recurso disponible. Actualmente se puede considerar al sector en un estado precomercial, con un amplio rango de dispositivos y tecnologías en diferente grado de desarrollo en los que ninguno destaca sobre los otros (ni ha demostrado su viabilidad económica), y sin que se aprecie una tendencia a converger un único dispositivo (o un número reducido de ellos). El recurso energético que se está tratando de aprovechar, pese a compartir la característica de no-controlabilidad con otras fuentes de energía renovable como la eólica o la solar, presenta una variabilidad adicional. De esta manera, diferentes localizaciones, pese a poder presentar recursos de contenido energético similar, presentan oleajes de características muy diferentes en términos de alturas y periodos de oleaje, y en la dispersión estadística de estos valores. Esta variabilidad en el oleaje hace que cobre especial relevancia la adecuación de los dispositivos de aprovechamiento de energía undimotriz (WEC: Wave Energy Converter) a su localización, de cara a mejorar su viabilidad económica. Parece razonable suponer que, en un futuro, el proceso de diseño de un parque de generación undimotriz implique un rediseño (en base a una tecnología conocida) para cada proyecto de implantación en una nueva localización. El objetivo de esta tesis es plantear un procedimiento de dimensionado de una tecnología de aprovechamiento de la energía undimotriz concreta: los absorbedores puntuales. Dicha metodología de diseño se plantea como un problema de optimización matemático, el cual se resuelve utilizando un algoritmo de optimización bioinspirado: evolución diferencial. Este planteamiento permite automatizar la fase previa de dimensionado implementando la metodología en un código de programación. El proceso de diseño de un WEC es un problema de ingería complejo, por lo que no considera factible el planteamiento de un diseño completo mediante un único procedimiento de optimización matemático. En vez de eso, se platea el proceso de diseño en diferentes etapas, de manera que la metodología desarrollada en esta tesis se utilice para obtener las dimensiones básicas de una solución de referencia de WEC, la cual será utilizada como punto de partida para continuar con las etapas posteriores del proceso de diseño. La metodología de dimensionado previo presentada en esta tesis parte de unas condiciones de contorno de diseño definidas previamente, tales como: localización, características del sistema de generación de energía eléctrica (PTO: Power Take-Off), estrategia de extracción de energía eléctrica y concepto concreto de WEC). Utilizando un algoritmo de evolución diferencial multi-objetivo se obtiene un conjunto de soluciones factibles (de acuerdo con una ciertas restricciones técnicas y dimensionales) y óptimas (de acuerdo con una serie de funciones objetivo de pseudo-coste y pseudo-beneficio). Dicho conjunto de soluciones o dimensiones de WEC es utilizado como caso de referencia en las posteriores etapas de diseño. En el documento de la tesis se presentan dos versiones de dicha metodología con dos modelos diferentes de evaluación de las soluciones candidatas. Por un lado, se presenta un modelo en el dominio de la frecuencia que presenta importantes simplificaciones en cuanto al tratamiento del recurso del oleaje. Este procedimiento presenta una menor carga computacional pero una mayor incertidumbre en los resultados, la cual puede traducirse en trabajo adicional en las etapas posteriores del proceso de diseño. Sin embargo, el uso de esta metodología resulta conveniente para realizar análisis paramétricos previos de las condiciones de contorno, tales como la localización seleccionada. Por otro lado, la segunda metodología propuesta utiliza modelos en el domino estocástico, lo que aumenta la carga computacional, pero permite obtener resultados con menos incertidumbre e información estadística muy útil para el proceso de diseño. Por este motivo, esta metodología es más adecuada para su uso en un proceso de dimensionado completo de un WEC. La metodología desarrollada durante la tesis ha sido utilizada en un proyecto industrial de evaluación energética preliminar de una planta de energía undimotriz. En dicho proceso de evaluación, el método de dimensionado previo fue utilizado en una primera etapa, de cara a obtener un conjunto de soluciones factibles de acuerdo con una serie de restricciones técnicas básicas. La selección y refinamiento de la geometría de la solución geométrica de WEC propuesta fue realizada a posteriori (por otros participantes del proyecto) utilizando un modelo detallado en el dominio del tiempo y un modelo de evaluación económica del dispositivo. El uso de esta metodología puede ayudar a reducir las iteraciones manuales y a mejorar los resultados obtenidos en estas últimas etapas del proyecto. ABSTRACT The energy transported by ocean waves (wave energy) is framed within the so-called oceanic energies. Its use to generate electric energy (or desalinate ocean water, etc.) is an idea expressed first time in a patent two centuries ago (1799). Ever since, but specially since the 1970’s, this energy has become interesting for R&D institutions and companies related with the technological and energetic sectors mainly because of the magnitude of available energy. Nowadays the development of this technology can be considered to be in a pre-commercial stage, with a wide range of devices and technologies developed to different degrees but with none standing out nor economically viable. Nor do these technologies seem ready to converge to a single device (or a reduce number of devices). The energy resource to be exploited shares its non-controllability with other renewable energy sources such as wind and solar. However, wave energy presents an additional short-term variability due to its oscillatory nature. Thus, different locations may show waves with similar energy content but different characteristics such as wave height or wave period. This variability in ocean waves makes it very important that the devices for harnessing wave energy (WEC: Wave Energy Converter) fit closely to the characteristics of their location in order to improve their economic viability. It seems reasonable to assume that, in the future, the process of designing a wave power plant will involve a re-design (based on a well-known technology) for each implementation project in any new location. The objective of this PhD thesis is to propose a dimensioning method for a specific wave-energy-harnessing technology: point absorbers. This design methodology is presented as a mathematical optimization problem solved by using an optimization bio-inspired algorithm: differential evolution. This approach allows automating the preliminary dimensioning stage by implementing the methodology in programmed code. The design process of a WEC is a complex engineering problem, so the complete design is not feasible using a single mathematical optimization procedure. Instead, the design process is proposed in different stages, so the methodology developed in this thesis is used for the basic dimensions of a reference solution of the WEC, which would be used as a starting point for the later stages of the design process. The preliminary dimensioning methodology presented in this thesis starts from some previously defined boundary conditions such as: location, power take-off (PTO) characteristic, strategy of energy extraction and specific WEC technology. Using a differential multi-objective evolutionary algorithm produces a set of feasible solutions (according to certain technical and dimensional constraints) and optimal solutions (according to a set of pseudo-cost and pseudo-benefit objective functions). This set of solutions or WEC dimensions are used as a reference case in subsequent stages of design. In the document of this thesis, two versions of this methodology with two different models of evaluation of candidate solutions are presented. On the one hand, a model in the frequency domain that has significant simplifications in the treatment of the wave resource is presented. This method implies a lower computational load but increased uncertainty in the results, which may lead to additional work in the later stages of the design process. However, use of this methodology is useful in order to perform previous parametric analysis of boundary conditions such as the selected location. On the other hand, the second method uses stochastic models, increasing the computational load, but providing results with smaller uncertainty and very useful statistical information for the design process. Therefore, this method is more suitable to be used in a detail design process for full dimensioning of the WEC. The methodology developed throughout the thesis has been used in an industrial project for preliminary energetic assessment of a wave energy power plant. In this assessment process, the method of previous dimensioning was used in the first stage, in order to obtain a set of feasible solutions according to a set of basic technical constraints. The geometry of the WEC was refined and selected subsequently (by other project participants) using a detailed model in the time domain and a model of economic evaluation of the device. Using this methodology can help to reduce the number of design iterations and to improve the results obtained in the last stages of the project.

Reflexión y refracción de la luz en medios anisótropos

En este proyecto se pretende estudiar el comportamiento de la luz al atravesar medios de diversos materiales, tanto isótropos como anisótropos uniáxicos. Para ello se requiere realizar un estudio previo de las condiciones de contorno aplicables a las ecuaciones de Maxwell en la interfase de dos medios que pueden ser isótropos o anisótropos. En el caso de dos materiales isótropos, la solución del problema son los conocidos coeficientes de Fresnel de reflexión y transmisión. En este trabajo se pretende generalizar el estudio al caso del paso de la luz desde un medio isótropo a otro anisótropo uniáxico (con su eje óptico en orientación arbitraria) y viceversa y al caso de dos materiales anisótropos uniáxicos con ejes ópticos en orientaciones arbitrarias. Es de especial interés el caso de un mismo material uniáxico en el que las dos partes tienen el eje óptico con distinta orientación. Una vez planteadas las condiciones de contorno específicas en cada caso, se obtendrá un conjunto de ecuaciones algebraicas cuya resolución permitirá obtener los coeficientes de reflexión y transmisión buscados. Para plantear el sistema de ecuaciones adecuado, será necesario tener una descripción de las características ópticas de los materiales empleados, la orientación de los ejes ópticos en cada caso, y los posibles ángulos de incidencia. Se realizará un tratamiento matricial de modo que el paquete MatLab permite su inversión de manera inmediata. Se desarrollará una interfaz sencilla, realizada con MatLab, que permita al usuario introducir sin dificultad los datos correspondientes a los materiales de los medios incidente y transmitido, la orientación en espacial del o de los ejes ópticos, de la longitud de onda de trabajo y del ángulo de incidencia del haz de luz, con los que la aplicación realizará los cálculos. Los coeficientes de reflexión y refracción obtenidos serán representados gráficamente en función del ángulo de incidencia. Así mismo se representarán los ángulos transmitidos y reflejados en función del de incidencia. Todo ello de esta forma, que resulte sencilla la interpretación de los datos por parte del usuario. ABSTRACT. The reason for this project is to study the behavior of light when light crosses different media of different materials, isotropic materials and uniaxial anisotropic materials. For this, a previous study is necessary where the boundary conditions apply to Maxwell equations at the interface between two media which can be isotropic and anisotropic. If both materials are isotropic, the Fresnel ccoefficients of reflection and refraction are used to solve the problem. The aim of this work is to generalize a study when light crosses from an isotropic media to a uniaxial anisotropic media, where its axis have arbitrary directions, and vicecersa. The system consisting of two materials with axis in arbitrary directions are also being studied. Once the specific boundary conditions are known in each case, a set of algebraic equations are obtained whose solution allows obtaining the reflection coefficients and refraction coefficients. It is necessary to have a description of the optical characteristics of the materials used; of the directions axis in each case and the possible angle of incidence. A matrix is proposed for later treatment in Matlab that allows the immediate inversion. A simple interface will de developed, manufactured with Matlab, that allows the user to enter data easily corresponding to the incident media and transmission media of the different materials, the special axis directions, the wavelength and the angle of incidence of the light beam. This data is used by the application to perform the necessary calculations to solve the problem. When reflection coefficients and refraction coefficients are obtained, the application draws the graphics in function of the angle of incidence. Also transmitted and reflected angles depending on the incidence are represented. This is to perform a data representation which is a simple interpretation of the user data.

Application of the homogenization techniques to the determination of the effective flexure constants of plate structural systems

A Mindlin plate with periodically distributed ribs patterns is analyzed by using homogenization techniques based on asymptotic expansion methods. The stiffness matrix of the homogenized plate is found to be dependent on the geometrical characteristics of the periodical cell, i.e. its skewness, plan shape, thickness variation etc. and on the plate material elastic constants. The computation of this plate stiffness matrix is carried out by averaging over the cell domain some solutions of different periodical boundary value problems. These boundary value problems are defined in variational form by linear first order differential operators on the cell domain and the boundary conditions of the variational equation correspond to a periodic structural problem. The elements of the stiffness matrix of homogenized plate are obtained by linear combinations of the averaged solution functions of the above mentioned boundary value problems. Finally, an illustrative example of application of this homogenization technique to hollowed plates and plate structures with ribs patterns regularly arranged over its area is shown. The possibility of using in the profesional practice the present procedure to the actual analysis of floors of typical buildings is also emphasized.

Yeast chorismate mutase in the R state: Simulations of the active site

The isomerization of chorismate to prephenate by chorismate mutase in the biosynthetic pathway that forms Tyr and Phe involves C5—O (ether) bond cleavage and C1—C9 bond formation in a Claisen rearrangement. Development of negative charge on the ether oxygen, stabilized by Lys-168 and Glu-246, is inferred from the structure of a complex with a transition state analogue (TSA) and from the pH-rate profile of the enzyme and the E246Q mutant. These studies imply a protonated Glu-246 well above pH 7. Here, several 500-ps molecular dynamics simulations test the stability of enzyme–TSA complexes by using a solvated system with stochastic boundary conditions. The simulated systems are (i) protonated Glu-246 (stable), (ii) deprotonated Glu-246 (unstable), (iii) deprotonated Glu-246 plus one H2O between Glu-246 and the ether oxygen (unstable), (iv) the E246Q mutant (stable), and (v) addition of OH− between protonated Glu-246 and the ether oxygen. In (v), a local conformational change of Lys-168 displaced the OH− into the solvent region, suggesting a possible rate-determining step that precedes the catalytic step. In a 500-ps simulation of the enzyme complexed with the reactant chorismate or the product prephenate, no water molecule remained near the oxygen of the ligand. Calculations using the linearized Poisson–Boltzmann equation show that the effective pKa of Glu-246 is shifted from 5.8 to 8.1 as the negative charge on the ether oxygen of the TSA is changed from −0.56 electron to −0.9 electron. Altogether, these results support retention of a proton on Glu-246 to high pH and the absence of a water molecule in the catalytic steps.

A fast, high resolution, second-order central scheme for incompressible flows

A high resolution, second-order central difference method for incompressible flows is presented. The method is based on a recent second-order extension of the classic Lax–Friedrichs scheme introduced for hyperbolic conservation laws (Nessyahu H. & Tadmor E. (1990) J. Comp. Physics. 87, 408-463; Jiang G.-S. & Tadmor E. (1996) UCLA CAM Report 96-36, SIAM J. Sci. Comput., in press) and augmented by a new discrete Hodge projection. The projection is exact, yet the discrete Laplacian operator retains a compact stencil. The scheme is fast, easy to implement, and readily generalizable. Its performance was tested on the standard periodic double shear-layer problem; no spurious vorticity patterns appear when the flow is underresolved. A short discussion of numerical boundary conditions is also given, along with a numerical example.

Rock friction and its implications for earthquake prediction examined via models of Parkfield earthquakes.

The friction of rocks in the laboratory is a function of time, velocity of sliding, and displacement. Although the processes responsible for these dependencies are unknown, constitutive equations have been developed that do a reasonable job of describing the laboratory behavior. These constitutive laws have been used to create a model of earthquakes at Parkfield, CA, by using boundary conditions appropriate for the section of the fault that slips in magnitude 6 earthquakes every 20-30 years. The behavior of this model prior to the earthquakes is investigated to determine whether or not the model earthquakes could be predicted in the real world by using realistic instruments and instrument locations. Premonitory slip does occur in the model, but it is relatively restricted in time and space and detecting it from the surface may be difficult. The magnitude of the strain rate at the earth's surface due to this accelerating slip seems lower than the detectability limit of instruments in the presence of earth noise. Although not specifically modeled, microseismicity related to the accelerating creep and to creep events in the model should be detectable. In fact the logarithm of the moment rate on the hypocentral cell of the fault due to slip increases linearly with minus the logarithm of the time to the earthquake. This could conceivably be used to determine when the earthquake was going to occur. An unresolved question is whether this pattern of accelerating slip could be recognized from the microseismicity, given the discrete nature of seismic events. Nevertheless, the model results suggest that the most likely solution to earthquake prediction is to look for a pattern of acceleration in microseismicity and thereby identify the microearthquakes as foreshocks.

Numerical vorticity creation based on impulse conservation.

The problem of creating solenoidal vortex elements to satisfy no-slip boundary conditions in Lagrangian numerical vortex methods is solved through the use of impulse elements at walls and their subsequent conversion to vortex loops. The algorithm is not uniquely defined, due to the gauge freedom in the definition of impulse; the numerically optimal choice of gauge remains to be determined. Two different choices are discussed, and an application to flow past a sphere is sketched.

Equações de onda generalizadas e quantização funtorial para teorias de campo escalar livre

Nesta dissertação apresentamos um método de quantização matemática e conceitualmente rigoroso para o campo escalar livre de interações. Trazemos de início alguns aspéctos importantes da Teoria de Distribuições e colocamos alguns pontos de geometria Lorentziana. O restante do trabalho é dividido em duas partes: na primeira, estudamos equações de onda em variedades Lorentzianas globalmente hiperbólicas e apresentamos o conceito de soluções fundamentais no contexto de equações locais. Em seguida, progressivamente construímos soluções fundamentais para o operador de onda a partir da distribuição de Riesz. Uma vez estabelecida uma solução para a equação de onda em uma vizinhança de um ponto da variedade, tratamos de construir uma solução global a partir da extensão do problema de Cauchy a toda a variedade, donde as soluções fundamentais dão lugar aos operadores de Green a partir da introdução de uma condição de contorno. Na última parte do trabalho, apresentamos um mínimo da Teoria de Categorias e Funtores para utilizar esse formalismo na contrução de um funtor de segunda quantização entre a categoria de variedades Lorentzianas globalmente hiperbólicas e a categoria de redes de álgebras C* satisfazendo os axiomas de Haag-Kastler. Ao fim, retomamos o caso particular do campo escalar quântico livre.

Método da propagação de feixe de ângulo largo para análise de guias de ondas ópticos não-lineares

Este trabalho propõe uma extensão do método de propagação de feixe (BPM - Beam Propagation Method) para a análise de guias de ondas ópticos e acopladores baseados em materiais não-lineares do tipo Kerr. Este método se destina à investigação de estruturas onde a utilização da equação escalar de Helmholtz (EEH) em seu limite paraxial não mais se aplica. Os métodos desenvolvidos para este fim são denominados na literatura como métodos de propagação de feixe de ângulo largo. O formalismo aqui desenvolvido é baseado na técnica das diferenças finitas e nos esquemas de Crank-Nicholson (CN) e Douglas generalizado (GD). Estes esquemas apresentam como característica o fato de apresentarem um erro de truncamento em relação ao passo de discretização transversal, Δx, proporcional a O(Δx2) para o primeiro e O(Δx4). A convergência do método em ambos esquemas é otimizada pela utilização de um algoritmo interativo para a correção do campo no meio não-linear. O formalismo de ângulo largo é obtido pela expansão da EEH para os esquemas CN e GD em termos de polinômios aproximantes de Padé de ordem (1,0) e (1,1) para CN e GD, e (2,2) e (3,3) para CN. Os aproximantes de ordem superior a (1,1) apresentam sérios problemas de estabilidade. Este problema é eliminado pela rotação dos aproximantes no plano complexo. Duas condições de contorno nos extremos da janela computacional são também investigadas: 1) (TBC - Transparent Boundary Condition) e 2) condição de contorno absorvente (TAB - Transparent Absorbing Boundary). Estas condições de contorno possuem a facilidade de evitar que reflexões indesejáveis sejam transmitidas para dentro da janela computacional. Um estudo comparativo da influência destas condições de contorno na solução de guias de ondas ópticos não-lineares é também abordada neste trabalho.

Avaliação de métodos numéricos de análise linear de estabilidade para perfis de aço formados a frio.

Para o projeto de estruturas com perfis de aço formados a frio, é fundamental a compreensão dos fenômenos da instabilidade local e global, uma vez que estes apresentam alta esbeltez e baixa rigidez à torção. A determinação do carregamento crítico e a identificação do modo de instabilidade contribuem para o entendimento do comportamento dessas estruturas. Este trabalho avalia três metodologias para a análise linear de estabilidade de perfis de aço formados a frio isolados, com o objetivo de determinar os carregamentos críticos elásticos de bifurcação e os modos de instabilidade associados. Estritamente, analisa-se perfis de seção U enrijecido e Z enrijecido isolados, de diversos comprimentos e diferentes condições de vinculação e carregamento. Determinam-se os carregamentos críticos elásticos de bifurcação e os modos de instabilidade globais e locais por meio de: (i) análise com o Método das Faixas Finitas (MFF), através do uso do programa computacional CUFSM; (ii) análise com elementos finitos de barra baseados na Teoria Generalizada de Vigas (MEF-GBT), via uso do programa GBTUL; e (iii) análise com elementos finitos de casca (MEF-cascas) por meio do uso do programa ABAQUS. Algumas restrições e ressalvas com relação ao uso do MFF são apresentadas, assim como limitações da Teoria Generalizada de Viga e precauções a serem tomadas nos modelos de cascas. Analisa-se também a influência do grau de discretização da seção transversal. No entanto, não é feita avaliação em relação aos procedimentos normativos e tampouco análises não lineares, considerando as imperfeições geométricas iniciais, tensões residuais e o comportamento elastoplástico do material.

Modelo computacional para avaliação do desempenho hidrodinâmico de embarcações de planeio em águas calmas.

Em geral, uma embarcação de planeio é projetada para atingir elevados níveis de velocidade. Esse atributo de desempenho está diretamente relacionado ao porte da embarcação e à potência instalada em sua planta propulsiva. Tradicionalmente, durante o projeto de uma embarcação, as análises de desempenho são realizadas através de resultados de embarcações já existentes, retirados de séries sistemáticas ou de embarcações já desenvolvidas pelo estaleiro e/ou projetista. Além disso, a determinação dos atributos de desempenho pode ser feita através de métodos empíricos e/ou estatísticos, onde a embarcação é representada através de seus parâmetros geométricos principais; ou a partir de testes em modelos em escala reduzida ou protótipos. No caso específico de embarcações de planeio, o custo dos testes em escala reduzida é muito elevado em relação ao custo de projeto. Isso faz com que a maioria dos projetistas não opte por ensaios experimentais das novas embarcações em desenvolvimento. Ao longo dos últimos anos, o método de Savitsky foi largamente utilizado para se realizar estimativas de potência instalada de uma embarcação de planeio. Esse método utiliza um conjunto de equações semi-empíricas para determinar os esforços atuantes na embarcação, a partir dos quais é possível determinar a posição de equilíbrio de operação e a força propulsora necessária para navegar em uma dada velocidade. O método de Savitsky é muito utilizado nas fases iniciais de projeto, onde a geometria do casco ainda não foi totalmente definida, pois utiliza apenas as características geométricas principais da embarcação para realização das estimativas de esforços. À medida que se avança nas etapas de projeto, aumenta o detalhamento necessário das estimativas de desempenho. Para a realização, por exemplo, do projeto estrutural é necessária uma estimativa do campo de pressão atuante no fundo do casco, o qual não pode ser determinado pelo método de Savitsky. O método computacional implementado nesta dissertação, tem o objetivo de determinar as características do escoamento e o campo de pressão atuante no casco de uma embarcação de planeio navegando em águas calmas. O escoamento é determinado através de um problema de valor de contorno, no qual a superfície molhada no casco é considerada um corpo esbelto. Devido ao uso da teoria de corpo esbelto o problema pode ser tratado, separadamente, em cada seção, onde as condições de contorno são forçadamente respeitadas através de uma distribuição de vórtices.

On the development of advanced techniques for mixed-elastohydrodynamic lubrification modelling of journal and sliding bearing systems.

The present thesis is focused on the development of a thorough mathematical modelling and computational solution framework aimed at the numerical simulation of journal and sliding bearing systems operating under a wide range of lubrication regimes (mixed, elastohydrodynamic and full film lubrication regimes) and working conditions (static, quasi-static and transient conditions). The fluid flow effects have been considered in terms of the Isothermal Generalized Equation of the Mechanics of the Viscous Thin Films (Reynolds equation), along with the massconserving p-Ø Elrod-Adams cavitation model that accordingly ensures the so-called JFO complementary boundary conditions for fluid film rupture. The variation of the lubricant rheological properties due to the viscous-pressure (Barus and Roelands equations), viscous-shear-thinning (Eyring and Carreau-Yasuda equations) and density-pressure (Dowson-Higginson equation) relationships have also been taken into account in the overall modelling. Generic models have been derived for the aforementioned bearing components in order to enable their applications in general multibody dynamic systems (MDS), and by including the effects of angular misalignments, superficial geometric defects (form/waviness deviations, EHL deformations, etc.) and axial motion. The bearing exibility (conformal EHL) has been incorporated by means of FEM model reduction (or condensation) techniques. The macroscopic in fluence of the mixedlubrication phenomena have been included into the modelling by the stochastic Patir and Cheng average ow model and the Greenwood-Williamson/Greenwood-Tripp formulations for rough contacts. Furthermore, a deterministic mixed-lubrication model with inter-asperity cavitation has also been proposed for full-scale simulations in the microscopic (roughness) level. According to the extensive mathematical modelling background established, three significant contributions have been accomplished. Firstly, a general numerical solution for the Reynolds lubrication equation with the mass-conserving p - Ø cavitation model has been developed based on the hybridtype Element-Based Finite Volume Method (EbFVM). This new solution scheme allows solving lubrication problems with complex geometries to be discretized by unstructured grids. The numerical method was validated in agreement with several example cases from the literature, and further used in numerical experiments to explore its exibility in coping with irregular meshes for reducing the number of nodes required in the solution of textured sliding bearings. Secondly, novel robust partitioned techniques, namely: Fixed Point Gauss-Seidel Method (PGMF), Point Gauss-Seidel Method with Aitken Acceleration (PGMA) and Interface Quasi-Newton Method with Inverse Jacobian from Least-Squares approximation (IQN-ILS), commonly adopted for solving uid-structure interaction problems have been introduced in the context of tribological simulations, particularly for the coupled calculation of dynamic conformal EHL contacts. The performance of such partitioned methods was evaluated according to simulations of dynamically loaded connecting-rod big-end bearings of both heavy-duty and high-speed engines. Finally, the proposed deterministic mixed-lubrication modelling was applied to investigate the in fluence of the cylinder liner wear after a 100h dynamometer engine test on the hydrodynamic pressure generation and friction of Twin-Land Oil Control Rings.

Finite Element Analysis of Thermal Buckling in Auotmotive Clutch and Brake Discs

Thermal buckling behavior of automotive clutch and brake discs is studied by making the use of finite element method. It is found that the temperature distribution along the radius and the thickness affects the critical buckling load considerably. The results indicate that a monotonic temperature profile leads to a coning mode with the highest temperature located at the inner radius. Whereas a temperature profile with the maximum temperature located in the middle leads to a dominant non-axisymmetric buckling mode, which results in a much higher buckling temperature. A periodic variation of temperature cannot lead to buckling. The temperature along the thickness can be simplified by the mean temperature method in the single material model. The thermal buckling analysis of friction discs with friction material layer, cone angle geometry and fixed teeth boundary conditions are also studied in detail. The angular geometry and the fixed teeth can improve the buckling temperature significantly. Young’s Modulus has no effect when single material is applied in the free or restricted conditions. Several equations are derived to validate the result. Young’s modulus ratio is a useful factor when the clutch has several material layers. The research findings from this paper are useful for automotive clutch and brake discs design against structural instability induced by thermal buckling.

Dynamical Equations For The Period Vectors In A Periodic System Under Constant External Stress

The purpose of this paper is to derive the dynamical equations for the period vectors of a periodic system under constant external stress. The explicit starting point is Newton’s second law applied to halves of the system. Later statistics over indistinguishable translated states and forces associated with transport of momentum are applied to the resulting dynamical equations. In the final expressions, the period vectors are driven by the imbalance between internal and external stresses. The internal stress is shown to have both full interaction and kinetic-energy terms.