Theoretical analysis of the possibility of manufacturing a metal sealing ring on the CNC machine tool. Selecting the most appropriate technology and manufacturing process analysis, involving selection of materials, tools and machining conditions.

The main purpose of this thesis is the modification of the original flange gasket of the VVER1000 pressurizer manhole. Then the construction and function of the pressurizer itself is described, together with detailed calculations of the original and new modified gasket to meet the ČSN EN 1591 standard together with a description of the legislation that has to be followed in the calculations. The comparisons of both gasket types together with main conclusions are placed in the last section of this thesis.

The dissertation consists of two parts. The first part (Chapter 1 to 4) is on some contributions to the development of a non-linear analysis on the quintessential fractal set Sierpinski gasket and its probabilistic interpretation. The second part (Chapter 5) is on the asymptotic tail decays for suprema of stochastic processes satisfying certain conditional increment controls. Chapters 1, 2 and 3 are devoted to the establishment of a theory of backward problems for non-linear stochastic differential equations on the gasket, and to derive a probabilistic representation to some parabolic type partial differential equations on the gasket. In Chapter 2, using the theory of Markov processes, we derive the existence and uniqueness of solutions to backward stochastic differential equations driven by Brownian motion on the Sierpinski gasket, for which the major technical difficulty is the exponential integrability of quadratic processes of martingale additive functionals. A Feynman-Kac type representation is obtained as an application. In Chapter 3, we study the stochastic optimal control problems for which the system uncertainties come from Brownian motion on the gasket, and derive a stochastic maximum principle. It turns out that the necessary condition for optimal control problems on the gasket consists of two equations, in contrast to the classical result on ℝ^d, where the necessary condition is given by a single equation. The materials in Chapter 2 are based on a joint work with Zhongmin Qian (referenced in Chapter 2). Chapter 4 is devoted to the analytic study of some parabolic PDEs on the gasket. Using a new type of Sobolev inequality which involves singular measures developed in Section 4.2, we establish the existence and uniqueness of solutions to these PDEs, and derive the space-time regularity for solutions. As an interesting application of the results in Chapter 4 and the probabilistic representation developed in Chapter 2, we further study Burgers equations on the gasket, to which the space-time regularity for solutions is deduced. The materials in Chapter 4 are based on a joint work with Zhongmin Qian (referenced in Chapter 4). In Chapter 5, we consider a class of continuous stochastic processes which satisfy the conditional increment control condition. Typical examples include continuous martingales, fractional Brownian motions, and diffusions governed by SDEs. For such processes, we establish a Doob type maximal inequality. Under additional assumptions on the tail decays of their marginal distributions, we derive an estimate for the tail decay of the suprema (Theorem 5.3.2), which states that the suprema decays in a manner similar to the margins of the processes. In Section 5.4, as an application of Theorem 5.3.2, we derive the existence of strong solutions to a class of SDEs. The materials in this chapter is based on the work [44] by the author (Section 5.2 and Section 5.3) and an ongoing joint project with Guangyu Xi (Section 5.4).

Cette étude s’inscrit dans le projet ANR Célajoas (ComposÉs LAmellaires pour les JOints en Applications Sévères) dont l’objectif est l’étude et l’optimisation de joints d’étanchéité à base de vermiculite exfoliée compactée (VEC). Ces joints d’étanchéité doivent se substituer aux joints à base de graphites pour des applications à hautes températures (800 °C) et à pressions élevées (200 bars). Des essais de mise en œuvre ont permis de mettre en évidence différents paramètres,tels que le type de vermiculite, la pression et la température de compaction sur les performances de ces joints. Les caractérisations expérimentales ont fournis des informations sur la microstructure et les propriétés de joints à base de la VEC. Ainsi, une étude par microscopie électronique à balayage, en compléments de résultats de porosimétrie mercure ont permis d’obtenir certaines caractéristiques du réseau poral. Des caractérisations expérimentales ont fournis les principales propriétés mécaniques anisotropes (modules élastiques, reprise élastique, contrainte à rupture) ainsi que la perméabilité de la VEC et donc le taux de fuite des joints à base de la VEC. Dans un souci de compréhension et d’optimisation des propriétés de ces joints, différents outils de prévisions des propriétés macroscopiques sont proposés. Tout d’abord, un modèle de prévision de la perméabilité,qui se scinde en deux étapes :a) Tout d’abord la construction du réseau poral simplifié en utilisant les résultats des caractérisations expérimentales, b) la résolution, par la méthode des éléments finis, du problème de l’écoulement du fluide à travers le milieu poreux. Les résultats numériques sont confrontés à ceux obtenus par des approches analytiques simples (du type Carman-Kozeny). L’effet de la micromorphologie et du taux de porosité sur la perméabilité sont ensuite examinés. Pour surmonter les difficultés liées à la résolution par la méthode des éléments finis, un modèle semi analytique est ensuite proposé. L’objectif de cette approche est de fournir un outil simple (type bureau d’étude) de prévision de la perméabilité de la VEC, sans avoir recours à un logiciel d’éléments finis. Enfin, pour dimensionner un joint d’étanchéité, il est indispensable de connaître les propriétés mécaniques (modules d’élasticité…) afin de déterminer, par exemple, la pression de serrage du joint. En raison des spécificités du matériau étudié (squelette isotrope transverse, taux de porosité de l’ordre de30 %), un modèle d’homogénéisation itératif, basé sur des approches analytiques classiques, est proposé pour évaluer l’influence de certains paramètres de la micro géométrie (rapport de forme des porosités, leur orientation…) sur les propriétés élastiques de la VEC. / This study deals with the study and optimization of gaskets made from compacted exfoliated vermiculite(VEC). It is a response to the need to replace gaskets made from graphite for high temperature (800 °C) and high pressure (200 bars) applications. In this work [in the aim of providing information on the microstructure and properties of VEC gaskets] experimental characterization have been conducted. The influence of different parameters such as the type of vermiculite, pressure and temperature of compaction on the performance of these gaskets has been studied. From scanning electron microscopy and mercury porosimetry results, some characteristics of the porous network have been identified. The anisotropic mechanical properties (elastic properties, elastic recovery, tensile stress), the permeability and the leakage rate of the VEC have also been characterized. Based on experimental data, a finite element (FE) predicting model for permeability evolution has been developed. This model is divided in two steps:a) using the results of the experimental characterization, the pore network is constructed; b) the problem of fluid flow through the porous media is solved by finite element method. The numerical results have been confronted with analytical models (Carman-Kozeny). The effect of micromorphology and porosity is discussed. Due to meshing problems, a semi-analytical model is also proposed. The aim of this approach is to provide a simple tool (type design office) for predict the permeability of VEC, without have recourse to finite element software. The mechanical properties are necessary to design a gasket. Eventually, thanks to specificities of the studied material (skeleton transverse isotropic, porosity of around 30%), a model of iterative homogenization is proposed to evaluate the influence of some parameters of the micro geometry (porosities ratio, orientation ...) on the elastic properties of the VEC. This work is supported by the French research national agency (ANR) through the Célajoas project (ComposÉs LAmellaires pour les JOints en Applications Sévères).

This diploma thesis is engaged in replacement of gasket ion filter used in the ion filter of continuous cleaning TC SV01 of rector coolant in nuclear power plants with VVER 440 reactor. Original nickel gasket is replaced by kammprofile gasket with expanded graphite. Calculation results are compared with each other and are described as suggestions for further calculation. The first part included a detailed description of the primary coolant water chemistry, along with a description of the function and structure of ion filter.

Examensarbetet har utförts på uppdrag av Kongsberg Automotive AB, en underleverantör inom fordonsindustrin som bland annat tillverkar växelspaksystem till både manuella och automatväxlade fordon. Fordonsbranschen kantas av ständig utveckling med innovativa lösningar, vilket under de senaste åren har resulterat i att elektroniken har fått en större roll i produkterna. Ifall elektroniken skadas kan det få förödande konsekvenser för produktens funktion. Det medför högre krav på säker inkapsling. För att motverka läckage och intrång av skadliga partiklar används ofta någon form av tätning.    Produkten som har studerats i detta examensarbete är en aktuator, vars funktion är att omvandla elektroniska signaler från växelspaken till mekaniska rörelser som interagerar med växellådan. Produkten innehåller tre tätningar som samverkar för att uppfylla inkapslingskraven under fordonets hela livstid. Dessa tre tätningar består av en statisk tätning av typen FIPG, en dynamisk o-ring och en ventil tätning av Gore-Tex membran.  Syftet med examensarbetet är att studera och utvärdera olika tätningskoncept som uppfyller de krav på inkapsling som ställs. Kongsberg önskar att utforska om det finns bättre alternativ till de tätningar som används i nuläget, särskilt vid en framtida ökad produktionsvolym. För att kunna utföra arbetet har en omfattande litteraturstudie genomförts. Den har bestått av faktainsamling, konkurrensanalys, intervjuer och observationer både på och utanför företaget. Detta mynnade ut i en Pughs matris där de olika tätningskoncepten ställdes mot den befintliga lösningen, FIPG och o-ring. Kriterier såsom kostnad, produktionsvänlighet, monteringsvänlighet, arbetsmiljö, processtid, livslängd samt behov av omkonstruktion har tagits fram till matrisen med hjälp av DFX-verktyg och intervjuer. En Pughs matris har utförts för både den statiska och dynamiska tätningen. Samma kriterier användes i båda fallen. Utifrån matrisen utnämndes lasersvetsning som den mest lämpliga metoden för den statiska tätningen. Anledningen till att den rekommenderas är bland annat dess låga kostnad vid höga volymer, den snabba processtiden samt dess långa livslängd. För den dynamiska tätningen rekommenderas Kongsberg Automotive att fortsätta med den befintliga lösningen, o-ringar. Detta på grund av dess låga kostnad för en tillräcklig livslängd. För att implementera den nya statiska tätningen krävs omkonstruktion av produkten. För en lyckad fogning ställs en del krav på flänsarna, bland annat en låg skevningstendens och en viss ytfinhet. Dessutom behöver flänsarna få en ny utformning som möjliggör fogning. Metoden bygger på att en del är lasertransparent och släpper igenom laserstrålen till den undre delen, som är laserabsorbent och smälter materialet vid fogen. Studien leder till ett grundligt underlag för Kongsberg Automotive, som kan underlätta vid beslut gällande tätningskonstruktionen. / This thesis is performed in association with Kongsberg Automotive AB, a subcontractor within the automotive industry who specializes in gear shifters for both manual and automatic transmission vehicles. The automotive industry is highly dynamic and constantly searching for innovative improvements. In recent years, this has led to an increase in the importance of electronics within a product. In case of an electronic failure, this can lead to devastating consequences for the function of a product. This leads to higher demands for safe encapsulation. Some sort of sealing is often used to reduce the risk of leakage and penetration of foreign particles. The product that has been studied in this project is an actuator. The function of an actuator is to convert electronic signals from the gear shifter to mechanical movements that interacts with the gearbox. The product consists of three sealing solutions that works together to meet the requirements for encapsulation during the vehicles lifetime. These solutions include a static gasket in form of a FIPG, a dynamic o-ring seal and a Gore-Tex vent membrane. The purpose of this thesis is to study and evaluate different sealing solutions that fulfills the demands of encapsulation according to the specification. Kongsberg Automotive wishes to explore if there are better sealing alternatives than the ones used today, particularly in regards to a potential increase in volume in the near future. In order to perform the project, an extensive literature study has been conducted. It was based on collection of facts, benchmarking, interviews and observations both within and outside of the company. This resulted in a Pugh matrix where the different sealing concepts where evaluated against the current solution, FIPG and dynamic o-rings. Criteria such as cost, production and assembly friendliness, work environment, processing time, life expectancy and the need of redesign were developed based on DFX-tools and interviews. The Pugh matrix were performed for both the static and the dynamic seal, using the same criteria in both cases. Based on the matrix, laser welding were chosen to be the most suitable seal for the static application. A few of the reasons were its low cost for high volume productions, the fast processing time and high function. For the dynamic seal, Kongsberg is recommended to continue using the current o-ring solution due to its low cost. To implement the recommended static sealing, redesign of the product is required. To achieve a successful joint, there are increased requirements for the flange surfaces, such as warpage and surface finish. In addition to this, the flanges needs a new design that enables joining. Laser welding is based on the material properties of the flanges. One part needs to be laser transparent to let the laser beam through, while the other part has to be laser absorbent to melt the material by the joint. This study results in a foundation for Kongsberg Automotive, to facilitate decision-making in regards to sealing design.

Essa tese tem o objetivo modelar um subconjunto de peças de um compressor hermético de refrigeração idealizado utilizando um programa de elementos finitos para estudar a pressão de contato na junta da placa de válvulas com e sem pressão de gás refrigerante. Nessa pesquisa também se faz a modelagem dinâmica da bomba de um compressor acadêmico com vistas a estudar a vibração gerada durante seu funcionamento. No estudo da junta de vedação se faz um modelo geométrico do conjunto cabeçote e juntas com um programa CAD. A partir da geometria do subconjunto um modelo físico é construído no ANSYS®, que leva em consideração as diferentes propriedades dos materiais do conjunto cabeçote e juntas, inclusive a não linearidade do material da junta. São feitas simulações aplicando diferentes valores de força normal nos parafusos do cabeçote. No estudo de vibração do compressor faz-se o modelo de CAD da bomba de onde se obtém seu peso e propriedades de inércia. A matriz de rigidez do sistema de suspensão da bomba é calculada e se faz a análise modal da bomba. Os resultados das análises de pressão de contato foram mostrados através de gráficos da normal closure e da normal pressure da junta. Eles indicam de forma clara as regiões de baixa pressão de contato aplicada pelas peças que estão ou deveriam estar comprimindo a junta de vedação, que seriam regiões de falhas. Na análise dinâmica da bomba do compressor, é calculada a matriz de rigidez total do sistema com as molas de suspensão, levando em consideração a rigidez compressiva, de flexão e cisalhante das molas. Com a solução do modelo dinâmico criado, calcula-se a matriz dinâmica, a matriz modal normalizada, a matriz de frequências características, o deslocamento <span style=\"font-style:italic\">X <span style=\"position: relative; bottom: 1.3ex; letter-spacing: -1.2ex; right: 1.2ex\">&#8594; da bomba e também as energias cinética e potencial da bomba devido às forças de agitação. O modelo de elementos finitos da junta da placa de válvulas tem resultados coerentes e o modelo dinâmico da bomba fornece vários resultados para a análise de vibração de compressores. / This thesis has as objective to model a subset of parts of an idealized hermetic compressor for refrigeration using a program of finite elements intended to study the contact pressure on the valve plate gasket with and without pressure from the refrigerant gas. In this research a dynamic modelling of an academic compressor pump is also made with the aim of studying the vibration generated during its functioning. In the study of the sealing gasket, a geometric model of the cylinder head and gasket assembly is made by using a CAD program. From the geometric of the subset a physical model is built on the ANSYS®, which takes into account the different properties of the cylinder head and gasket assembly materials, including the non-linearity of the gasket material. Simulations are made by applying different normal force values on the cylinder head screws. In the compressor vibration study, a CAD pump model is made, thus obtaining its weight and inertia properties. The stiffness matrix of the pump suspension system is calculated and a modal analysis of the pump is made. The results from the contact pressure analyses were shown through \"normal closure\" and \"normal pressure\" charts of the gasket. They show in clear form the low contact pressure regions applied by the parts that are or should be compressing the sealing gasket, which would the regions of failures. In the dynamic analysis of the compressor pump, the total stiffness matrix of the system is calculated with the suspension springs, taking into account the compressive, flexural and shearing rigidities of the springs. With the solution of the dynamic model created, the following are calculated: the dynamic matrix, the normalized modal matrix, the characteristics frequency matrix, the <span style=\"font-style:italic\">X <span style=\"position: relative; bottom: 1.3ex; letter-spacing: -1.2ex; right: 1.2ex\">&#8594; displacement from the pump, as well as the kinetic and potential energy of the pump due to shaking forces. The finite elements model of the valve plate gasket has coherent results and the dynamic model of the pump provides various results for the analysis of the compressor vibration.

<p>In 1989 Jun Kigami made an analytic construction of a Laplacian on the Sierpiński gasket, a construction that he extended to post critically finite fractals. Since then, this field has evolved into a proper theory of analysis on fractals. The new results obtained in this thesis are all in the setting of Kigami's theory. They are presented in three papers.</p><p>Strichartz recently showed that there are first order linear differential equations, based on the Laplacian, that are not solvable on the Sierpiński gasket. In the first paper we give a characterization on the polynomial p so that the differential equation p(Δ)u=f is solvable on any open subset of the Sierpiński gasket for any f continuous on that subset. For general p we find the open subsets on which p(Δ)u=f is solvable for any continuous f.</p><p>In the second paper we describe the infinitesimal geometric behavior of a large class of smooth functions on the Sierpiński gasket in terms of the limit distribution of their local eccentricity, a generalized direction of gradient. The distribution of eccentricities is codified as an infinite dimensional perturbation problem for a suitable iterated function system, which has the limit distribution as an invariant measure. We extend results for harmonic functions found by Öberg, Strichartz and Yingst to larger classes of functions.</p><p>In the third paper we define and study intrinsic first order derivatives on post critically finite fractals and prove differentiability almost everywhere for certain classes of fractals and functions. We apply our results to extend the geography is destiny principle, and also obtain results on the pointwise behavior of local eccentricities. Our main tool is the Furstenberg-Kesten theory of products of random matrices.</p>

In 1989 Jun Kigami made an analytic construction of a Laplacian on the Sierpiński gasket, a construction that he extended to post critically finite fractals. Since then, this field has evolved into a proper theory of analysis on fractals. The new results obtained in this thesis are all in the setting of Kigami's theory. They are presented in three papers. Strichartz recently showed that there are first order linear differential equations, based on the Laplacian, that are not solvable on the Sierpiński gasket. In the first paper we give a characterization on the polynomial p so that the differential equation p(Δ)u=f is solvable on any open subset of the Sierpiński gasket for any f continuous on that subset. For general p we find the open subsets on which p(Δ)u=f is solvable for any continuous f. In the second paper we describe the infinitesimal geometric behavior of a large class of smooth functions on the Sierpiński gasket in terms of the limit distribution of their local eccentricity, a generalized direction of gradient. The distribution of eccentricities is codified as an infinite dimensional perturbation problem for a suitable iterated function system, which has the limit distribution as an invariant measure. We extend results for harmonic functions found by Öberg, Strichartz and Yingst to larger classes of functions. In the third paper we define and study intrinsic first order derivatives on post critically finite fractals and prove differentiability almost everywhere for certain classes of fractals and functions. We apply our results to extend the geography is destiny principle, and also obtain results on the pointwise behavior of local eccentricities. Our main tool is the Furstenberg-Kesten theory of products of random matrices.

Essa tese tem o objetivo modelar um subconjunto de peças de um compressor hermético de refrigeração idealizado utilizando um programa de elementos finitos para estudar a pressão de contato na junta da placa de válvulas com e sem pressão de gás refrigerante. Nessa pesquisa também se faz a modelagem dinâmica da bomba de um compressor acadêmico com vistas a estudar a vibração gerada durante seu funcionamento. No estudo da junta de vedação se faz um modelo geométrico do conjunto cabeçote e juntas com um programa CAD. A partir da geometria do subconjunto um modelo físico é construído no ANSYS®, que leva em consideração as diferentes propriedades dos materiais do conjunto cabeçote e juntas, inclusive a não linearidade do material da junta. São feitas simulações aplicando diferentes valores de força normal nos parafusos do cabeçote. No estudo de vibração do compressor faz-se o modelo de CAD da bomba de onde se obtém seu peso e propriedades de inércia. A matriz de rigidez do sistema de suspensão da bomba é calculada e se faz a análise modal da bomba. Os resultados das análises de pressão de contato foram mostrados através de gráficos da normal closure e da normal pressure da junta. Eles indicam de forma clara as regiões de baixa pressão de contato aplicada pelas peças que estão ou deveriam estar comprimindo a junta de vedação, que seriam regiões de falhas. Na análise dinâmica da bomba do compressor, é calculada a matriz de rigidez total do sistema com as molas de suspensão, levando em consideração a rigidez compressiva, de flexão e cisalhante das molas. Com a solução do modelo dinâmico criado, calcula-se a matriz dinâmica, a matriz modal normalizada, a matriz de frequências características, o deslocamento <span style=\"font-style:italic\">X <span style=\"position: relative; bottom: 1.3ex; letter-spacing: -1.2ex; right: 1.2ex\">&#8594; da bomba e também as energias cinética e potencial da bomba devido às forças de agitação. O modelo de elementos finitos da junta da placa de válvulas tem resultados coerentes e o modelo dinâmico da bomba fornece vários resultados para a análise de vibração de compressores. / This thesis has as objective to model a subset of parts of an idealized hermetic compressor for refrigeration using a program of finite elements intended to study the contact pressure on the valve plate gasket with and without pressure from the refrigerant gas. In this research a dynamic modelling of an academic compressor pump is also made with the aim of studying the vibration generated during its functioning. In the study of the sealing gasket, a geometric model of the cylinder head and gasket assembly is made by using a CAD program. From the geometric of the subset a physical model is built on the ANSYS®, which takes into account the different properties of the cylinder head and gasket assembly materials, including the non-linearity of the gasket material. Simulations are made by applying different normal force values on the cylinder head screws. In the compressor vibration study, a CAD pump model is made, thus obtaining its weight and inertia properties. The stiffness matrix of the pump suspension system is calculated and a modal analysis of the pump is made. The results from the contact pressure analyses were shown through \"normal closure\" and \"normal pressure\" charts of the gasket. They show in clear form the low contact pressure regions applied by the parts that are or should be compressing the sealing gasket, which would the regions of failures. In the dynamic analysis of the compressor pump, the total stiffness matrix of the system is calculated with the suspension springs, taking into account the compressive, flexural and shearing rigidities of the springs. With the solution of the dynamic model created, the following are calculated: the dynamic matrix, the normalized modal matrix, the characteristics frequency matrix, the <span style=\"font-style:italic\">X <span style=\"position: relative; bottom: 1.3ex; letter-spacing: -1.2ex; right: 1.2ex\">&#8594; displacement from the pump, as well as the kinetic and potential energy of the pump due to shaking forces. The finite elements model of the valve plate gasket has coherent results and the dynamic model of the pump provides various results for the analysis of the compressor vibration.