The thesis deals with numerical analysis of delay differential equations. Particularly, the -method is applied to the pantograph equation considering equidistant and quasi-geometric mesh. Qualitative properties of the numerical methods are demonstrated on several special cases of the pantograph equation.

Der Kontakt Fahrdraht - Schleifleiste hat die Aufgabe, elektrischen Strom zwischen der Oberleitung und dem Stromabnehmer des Triebfahrzeuges mittels eines Gleitkontaktes zu übertragen. Das Kontaktverhalten und der dabei entstehende Verschleiß sind von einer Vielzahl von Parametern und Einflussfaktoren sowie deren Verknüpfungen abhängig. Der Verschleiß lässt sich in elektrischen und mechanischen Verschleiß unterteilen. Die vorliegende Arbeit beschreibt erstmals zusammenhängend und umfassend das Kontakt- und Verschleißverhalten von Fahrdraht und Schleifleiste. Daraus geht hervor, dass der Kontaktwiderstand eine herausragende Bedeutung für den elektrischen Verschleiß besitzt. Zur Berechnung des Kontaktwiderstandes existieren für einen stationären Kontakt mehrere Modelle, die jedoch auf einer Vielzahl von Annahmen und Vereinfachungen beruhen. Die Messung des Kontaktwiderstandes zwischen dem Fahrdraht und der Schleifleiste ist somit zwingend erforderlich. Dafür wurde an der TU Dresden ein Versuchsstand errichtet, mit dem der Kontaktwiderstand unter möglichst realen Bedingungen gemessen werden kann. Untersucht wurde die Kontaktpaarung Kupferfahrdraht und Kohlenstoffschleifleiste. Die durchgeführten Messungen des Kontaktwiderstandes und der Temperaturen von Fahrdraht und Schleifleiste im Stillstand und bei Fahrt werden beschrieben und ausgewertet. Dabei zeigt sich, dass die Kontaktkraft und der Kontaktstrom den größten Einfluss auf den Kontaktwiderstand besitzen. Der Kontaktwiderstand bzw. die Kontaktspannung bilden die Grundlage zur Berechnung der Erwärmung des Kontaktbereiches. Es wird ein Verfahren vorgestellt, mit welchem die maximalen Temperaturen in Fahrdraht und Schleifleiste ermittelt werden können. Die auf diese Weise ermittelten Temperaturen erlauben tendenzielle Aussagen zum elektrischen Verschleiß.

[pt] As estruturas ajustáveis ou dobráveis (deployable structures) consistem em um grupo de estruturas capazes de modificar sua forma e volume para atender a uma variedade de aplicações. Geralmente, são estruturas pré-fabricadas compostas por barras retas ou curvas unidas por meio de articulações que permitem que se movimentem para formar um arranjo compacto e se desdobrem em formas estruturais de grande porte. Essas estruturas atuam como mecanismos durante sua implantação e se tornam estruturas capazes de suportar cargas externas durante a fase de serviço. Além disso, elas devem ser leves e compactas a fim de serem facilmente transportadas e simples e rápidas de montar. Todas essas restrições dificultam a escolha dos melhores parâmetros que levem ao menor peso, maior rigidez e que permitam à estrutura desempenhar suas duas funcionalidades e garantir sua reutilização. Entre os tipos de estruturas dobráveis, os elementos pantográficos (tesouras) têm despertado grande interesse de engenheiros e arquitetos nos últimos anos. Este estudo avalia o comportamento não linear geométrico de arcos planos constituídos por dois tipos clássicos de elementos pantográficos: polar e translacional. Para isso, uma análise geométrica não linear detalhada é conduzida por meio de software de elemento finito elaborado com formulação corrotacional, a fim de avaliar a influência dos parâmetros geométricos da estrutura, como o tipo de elemento patográfico, o tipo de apoio e número de elementos no comportamento não linear e na estabilidade da estrutura. Os resultados obtidos por nossas análises revelam, na maioria dos casos, um comportamento eminentemente não linear característico de arcos esbeltos, com o caminho de equilíbrio exibindo vários pontos limites de carga e deslocamento, onde podem ocorrer saltos para configurações remotas e indesejáveis. Com base nestes resultadods, a influência dos parâmetros do sistema na capacidade de carga do arco é quantificada. / [en] Deployable structures consist of a group of structures capable of modifying their shape and volume in order to meet a range of conditions and needs. They are usually prefabricated structures consisting of straight or curved bars linked together in a compact bundle, which can then be unfolded into large-span, load bearing structural shapes. These structures have dual functionality since they act as mechanisms during its deployment and become immovable structures capable of supporting external loads during the service phase. In addition, they should be lightweight and compact to be easily transported and simple and quick to deploy. All these restrictions make it difficult to choose the best parameters regarding the shape and material of the structure, since many analyzes must be performed in order to find parameters that give lowest weight, highest stiffness, and that allow the structure to perform its two functions and ensure its reuse. Among the types of folding structure, those made of pantographic elements (scissors) have attracted great interest from engineers and architects in recent years. This study evaluates the geometric nonlinear behavior of plane arches constituted by two classic type of pantographic element, namely: polar and translational. For this, a detailed nonlinear geometrical analysis is conducted through tailored corotational finite element software in order to evaluate the influence of the structure s geometrical parameters, type of scissor units and supports on the nonlinear behavior and stability of the structure. The results obtained by our analyzes reveal, in most cases, a characteristic non-linear behavior of these structures with the nonlinear equilibrium path exhibiting several load and displacement limit points where jumps to remote and undesirable configurations may occur. Based on them, the influence of system parameters on the load carrying capacity of the arch is quantified.

Wear condition modelling is a research topic which lately has increased in popularitydue to its significance to the railway industry. Large sums are spent on maintenanceof the network every year, which has generated a demand for understanding and predictingwear mechanisms in a multitude of components within both railway vehiclesand infrastructure. To acquire this knowledge, using a simulation software to predictwear and maintenance needs, is a cheap and dependable option. This thesis sets outto create a wear modelling software for the catenary-pantograph interaction, which intheory could enlighten railway operators of the condition of their infrastructure. This research contains an extensive literature review on the subject of wear modelling,analysing different strategies and theories of the wear mechanism and desired modelproperties. Thereafter, an attempt to recreate a model for a representative Swedishcase was conducted; implementing parameters of a typical Swedish rail vehicle to awear rate formula, recreating a passage of a pantograph sliding along the catenary.The output was a wear rate as a function of time, a determination of life expectancyfor the infrastructure and a worn profile of the catenary wire after one year of operation. The model, named AWEAR, was deemed functional for determining wear mechanismtendencies and behaviour for a few cases of alternating parameters. However, sinceno validation could be performed due to a lack of resources, the validity of the outputvalues could not be confirmed - thus leaving calibration of the model to future work.In conclusion, AWEAR needs to be calibrated for future research but does contain amultitude of enhancement opportunities proposed in this thesis. While not completelyfunctional, the software was deemed a useful foundation for future projects and mightresult in a product that aids operators maintaining their infrastructure.Keywords: Wear modelling, catenary pantograph interaction, mechanism, / Slitagemodellering är ett forskningsområde som den senaste tiden har ökat i popularitetpå grund av dess betydelse till järnvägsindustrin. Stora summor spenderas på underhållav nätverket varje år, vilket har genererat en efterfågan på att förstå och förutspåslitage i en mängd olika komponenter inom både spårfordon och infrastruktur.För att uppnå vetskapen, är att använda simulering till att förutspå slitage och underhållsbehov, ett billigt och tillitsfullt alternativ. Detta arbete söker att skapa ett slitagemodelleringsprogram för interaktionen mellan pantograf och kontaktledning, vilket iteorin skulle kunna upplysa järnvägsoperatörer om skicket på deras infrastruktur. Denna forskning innehåller en genomgående litteraturstudie inom ämnet slitagemodellering, där det olika strategier och teorier analyseras om slitagemekanism och önskade modellegenskaper. Därefter görs ett försök på att återskapa en modell för ettrepresentativt svenskt fall; där parametrar för svenska järnvägsfordon och svensk infrastruktur implementeras i en ekvaktion för att simulera en passage av en pantografglidandes längst med en kontaktledning. Resultatet var en slitagenivå som funktionav tiden, ett fastställande av förväntad livslängd på infrastrukturen och en modelleradprofil av kontaktledningen efter ett år i tjänst. Modellen, döpt till AWEAR, ansågs funktionabel till att identifiera tendenser inomslitagemekanism och beteende för ett fåtal fall av alternerande parametrar. Då ingenjämförelse med resultat och data från riktiga scenarion genomfördes på grund utav enbrist på resurser, kunde resultaten från modellen inte bekräftas och därmed lämnadeskalibreringen åt framtida arbete. Sammanfattningsvis behöver AWEAR kalibrerasför framtida forskning men innehåller därtill en mängd olika förbättringsmöjligheterföreslagna i denna rapport. Även om modellen hitills inte är fullkomligt funktionabel,kan den skapade mjukvaran anses vara nyttigt grundmaterial för framtida projekt. Islutändan kan detta därmed

Foldable and deployable space structures refer to a broad category of pre-fabricated structures that can be transformed from a compact folded configuration to a predetermined expanded configuration. Such deployable structures are stable and can carry loads. These structures are also mechanisms with one degree of freedom in their entire transformation stages whether in the initial folded form or in the final expanded configuration. Usually, pantograph mechanisms or a scissor-like elements (SLEs) are part of such deployable structures. A new analysis tool to study kinematic and static analyses of foldable and deployable space structures /mechanisms, containing SLEs, has been developed in this thesis. The Cartesian coordinates are used to study the kinematics of large deployable structures. For many deployable structures the degree of freedom derived using the standard Grubler-Kutzback criteria, is found to be less than one even though the deployable structure /mechanism can clearly move. In this work the dimension of nullspace of the derivatives of the constraint equations are used to obtain the correct degrees of freedom of deployable structure. A numerical algorithm has been developed to identify the redundant joints /links in the deployable structure /mast which results in the incorrect degrees of freedom obtained by using the Grubler-Kutzback criteria. The effectiveness of the algorithm has been illustrated with several examples consisting of triangular, box shaped SLE mast and an eighteen-sided SLE ring with revolute joints. Further more the constraint Jacobian matrix is also used to evaluate the global degrees of freedom of deployable masts/structures. Closed-form kinematic solutions have been obtained for the triangular and box type masts and finally, as a generalization, extended to a general n-sided SLE based ring structure. The constraint Jacobian matrix based approach has also been extended to obtain the load carrying characteristics of deployable structures with SLEs in terms of deriving the stiffness matrix of the structure. The stiffness matrix has been obtained in the symbolic form and it matches results obtained from other commonly used techniques such as force and displacement methods. It is shown that the approach developed in this thesis is applicable for all types of practical masts with revolute joints where the revolute joint constraints are made to satisfy through the method of Lagrange multipliers and a penalty formulation. To demonstrate the effectiveness of the new method, the procedure is applied to solving (i) a simple hexagonal SLE mast, and (ii) a complex assembly of four hexagonal masts and the results are presented. In summary, a complete analysis tool to study masts with SLEs has been developed. It is shown that the new tool is effective in evaluating the redundant links /joints there by over coming the problems associated with the well –known Grubler-Kutzback criteria. Closed-form kinematic solutions of triangular and box SLE masts as well as a general n-sided SLE ring with revolute joints has been obtained. Finally, the constraint Jacobian based method is used to evaluate the stiffness matrix for the SLE masts. The theory and algorithms presented in this thesis can be extended to masts of different shapes and for the stacked masts.

This thesis presents the stability analysis of an Electric Road System (ERS), which is often abbreviated as eHighway, used for the electrification of the hybrid vehicle. The overall system modelling of the ERS, starting from the sub-station to the critical part of the Scania hybrid truck is performed in the MATLAB Simulink environment. The ERS consists of an overhead catenary line (OCL), where vehicles are electrified by using a pantograph mounted over the vehicle. The stability analysis of the power supply of the overhead line is done by taking into account several aspects of the system. The simulation results are validated with the real test track measurements and the deviations are shown. The frequency response of the system is considered to measure the stability margin. The resonance conditions are clarified and essential variable choke is proposed to damp them out. Also the harmonic components injected from the vehicle side, that are in the closer range of the resonance, are figured out and filtered. When multiple vehicles are electrified from the same catenary line, then there are interferences in between the vehicles. These disturbances both to the vehicles and the overhead power supply system are presented in the time domain. Finally, the results are shown to demonstrate the effectiveness of the variable choke to increase the stability margin in the overhead supply system. In the frequency domain results, it has shown that the resonance is shifted out of the system operating frequency. In the time domain results, it has shown that the high amplitude of the current and voltage signals are sufficiently damped out by variable choke implementation.

This thesis is about the design of the telescopic platform. which should be fasten on robot called Breach. Purpose of this platform is to carry another equipment like sensors, cameras or manipulator. The platform has to provide chiefly the high demands on load capacity. Another part of the thesis is design of mechanism placed on this telescopic platform, or just on the robot Breach. This mechanism has to load up small subject on the top part of the platform and then unload it on chosen place. Only thing defined for this subjekt is maximal weight of 2 kilograms, but other parameters aren´t specified. Construction is therefore focused on maximal versatility of this mechanism.