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Esta dissertação apresenta modelagem matemática e um método de solução numérica para problemas de conformação eletromagnética de chapas metálicas finas circulares utilizando uma bobina em espiral plana. O método foca especificamente o cálculo do campo eletromagnético gerado pela bobina e análise do circuito que modela o sistema de estampagem eletromagnética. A bobina plana é aproximada por círculos concêntricos carregando a corrente de descarga dos capacitores. Os cálculos das correntes induzidas e perfil da força eletromagnética na chapa e acoplamentos magnéticos entre a bobina e chapa metálica são realizados para o instante inicial, antes da deformação plástica da chapa. O método utiliza a lei de Biot-Savart, sendo que a solução das integrais obtidas para indução magnética é realizada através de métodos numéricos, considerando as simetrias do problema. Para verificação da modelagem matemática, da solução numérica e comprovação da viabilidade técnica deste processo, um dispositivo de estampagem eletromagnética foi desenvolvido e diversos experimentos foram realizados com chapas de alumínio. Os parâmetros investigados foram a espessura da chapa a ser deformada e a influência da presença de vácuo na cavidade da ferramenta. Os resultados experimentais demonstram concordância com os resultados da modelagem proposta. A presença de vácuo também demonstrou um incremento na deformação da chapa. A rotina desenvolvida no software Matlab fornece informações importantes para o processo e permite que se faça ajustes no dispositivo. / This dissertation presents a mathematical model and numerical method to solve the problems of electromagnetic forming of thin circular metal sheets by using a flat spiral coil. The method focuses specifically on the calculation of the electromagnetic field generated by the coil flat and circuit analysis modeling system electromagnetic forming. The flat coil is approximated by concentric circles carrying a discharge current of capacitors. The calculations of induced currents and profile of the electromagnetic force on the plate and magnetic coupling between the coil and sheet metal are made to the initial time, before the plastic deformation of the plate. The method uses the law of Biot-Savart, and the solution of the integral obtained for magnetic induction is performed by numerical methods, considering the symmetries of the problem. To verify the mathematical model, the numerical solution and proving the technical feasibility of this process, a electromagnetic forming device was developed and several experiments were made with aluminum plates. The parameters investigated were the thickness of the plate to be deformed and the influence of the vacuum in the cavity of the tool. The experimental results show agreement with the results of the proposed model. The presence of vacuum also showed an increase in the deformation of the plate. A routine developed in software Matlab provide important information for the process and allow to make adjustments on the device.

Esta dissertação apresenta modelagem matemática e um método de solução numérica para problemas de conformação eletromagnética de chapas metálicas finas circulares utilizando uma bobina em espiral plana. O método foca especificamente o cálculo do campo eletromagnético gerado pela bobina e análise do circuito que modela o sistema de estampagem eletromagnética. A bobina plana é aproximada por círculos concêntricos carregando a corrente de descarga dos capacitores. Os cálculos das correntes induzidas e perfil da força eletromagnética na chapa e acoplamentos magnéticos entre a bobina e chapa metálica são realizados para o instante inicial, antes da deformação plástica da chapa. O método utiliza a lei de Biot-Savart, sendo que a solução das integrais obtidas para indução magnética é realizada através de métodos numéricos, considerando as simetrias do problema. Para verificação da modelagem matemática, da solução numérica e comprovação da viabilidade técnica deste processo, um dispositivo de estampagem eletromagnética foi desenvolvido e diversos experimentos foram realizados com chapas de alumínio. Os parâmetros investigados foram a espessura da chapa a ser deformada e a influência da presença de vácuo na cavidade da ferramenta. Os resultados experimentais demonstram concordância com os resultados da modelagem proposta. A presença de vácuo também demonstrou um incremento na deformação da chapa. A rotina desenvolvida no software Matlab fornece informações importantes para o processo e permite que se faça ajustes no dispositivo. / This dissertation presents a mathematical model and numerical method to solve the problems of electromagnetic forming of thin circular metal sheets by using a flat spiral coil. The method focuses specifically on the calculation of the electromagnetic field generated by the coil flat and circuit analysis modeling system electromagnetic forming. The flat coil is approximated by concentric circles carrying a discharge current of capacitors. The calculations of induced currents and profile of the electromagnetic force on the plate and magnetic coupling between the coil and sheet metal are made to the initial time, before the plastic deformation of the plate. The method uses the law of Biot-Savart, and the solution of the integral obtained for magnetic induction is performed by numerical methods, considering the symmetries of the problem. To verify the mathematical model, the numerical solution and proving the technical feasibility of this process, a electromagnetic forming device was developed and several experiments were made with aluminum plates. The parameters investigated were the thickness of the plate to be deformed and the influence of the vacuum in the cavity of the tool. The experimental results show agreement with the results of the proposed model. The presence of vacuum also showed an increase in the deformation of the plate. A routine developed in software Matlab provide important information for the process and allow to make adjustments on the device.

Esta dissertação apresenta modelagem matemática e um método de solução numérica para problemas de conformação eletromagnética de chapas metálicas finas circulares utilizando uma bobina em espiral plana. O método foca especificamente o cálculo do campo eletromagnético gerado pela bobina e análise do circuito que modela o sistema de estampagem eletromagnética. A bobina plana é aproximada por círculos concêntricos carregando a corrente de descarga dos capacitores. Os cálculos das correntes induzidas e perfil da força eletromagnética na chapa e acoplamentos magnéticos entre a bobina e chapa metálica são realizados para o instante inicial, antes da deformação plástica da chapa. O método utiliza a lei de Biot-Savart, sendo que a solução das integrais obtidas para indução magnética é realizada através de métodos numéricos, considerando as simetrias do problema. Para verificação da modelagem matemática, da solução numérica e comprovação da viabilidade técnica deste processo, um dispositivo de estampagem eletromagnética foi desenvolvido e diversos experimentos foram realizados com chapas de alumínio. Os parâmetros investigados foram a espessura da chapa a ser deformada e a influência da presença de vácuo na cavidade da ferramenta. Os resultados experimentais demonstram concordância com os resultados da modelagem proposta. A presença de vácuo também demonstrou um incremento na deformação da chapa. A rotina desenvolvida no software Matlab fornece informações importantes para o processo e permite que se faça ajustes no dispositivo. / This dissertation presents a mathematical model and numerical method to solve the problems of electromagnetic forming of thin circular metal sheets by using a flat spiral coil. The method focuses specifically on the calculation of the electromagnetic field generated by the coil flat and circuit analysis modeling system electromagnetic forming. The flat coil is approximated by concentric circles carrying a discharge current of capacitors. The calculations of induced currents and profile of the electromagnetic force on the plate and magnetic coupling between the coil and sheet metal are made to the initial time, before the plastic deformation of the plate. The method uses the law of Biot-Savart, and the solution of the integral obtained for magnetic induction is performed by numerical methods, considering the symmetries of the problem. To verify the mathematical model, the numerical solution and proving the technical feasibility of this process, a electromagnetic forming device was developed and several experiments were made with aluminum plates. The parameters investigated were the thickness of the plate to be deformed and the influence of the vacuum in the cavity of the tool. The experimental results show agreement with the results of the proposed model. The presence of vacuum also showed an increase in the deformation of the plate. A routine developed in software Matlab provide important information for the process and allow to make adjustments on the device.

Drückwalzen als inkrementelles Umformverfahren ist aufgrund seiner Verfahrenscharakteristik mit sehr hohen Rechenzeiten bei der Finite-Elemente-Methode (FEM) verbunden. Die Modelle ModIni und FloSim sind zwei analytisch-elementare Ansätze, um dieser Prämisse entgegenzuwirken. Das für ModIni entwickelte Geometriemodell wird in der vorliegenden Arbeit weiterentwickelt, so dass eine werkstoffunabhängige Berechnung der Staugeometrie ermöglicht wird und ein deutlich größeres Anwendungsspektrum der Methode bereitsteht. Die Simulationsmethode FloSim basiert auf dem oberen Schrankenverfahren und ermöglicht somit eine Berechnung von Zylinderdrückwalzprozessen innerhalb weniger Minuten. Für die Optimierung der Methode FloSim wurden in der vorliegenden Arbeit die analytischen Grundlagen für die Berechnung der Bauteillänge sowie der Umformzonentemperatur während des Prozesses erarbeitet. Weiterhin wurde auf Basis von numerisch realisierten Parameteranalysen ein Ansatz für die analytische Berechnung des Vergleichsumformgrades von Drückwalzprozessen entwickelt. Diese drei Ansätze, zu Bauteillänge, Temperatur und Umformgrad wurden in die Simulationssoftware FloSim integriert und führen zu einer deutlichen Genauigkeitssteigerung der Methode. / Flow Forming as incremental forming process is connected with extreme long computation times for Finite-Element-Analyses. ModIni and FloSim are two analytical/elementary models to antagonize this situation. The geometry model, which was developed for ModIni, is improved within the presented work. The improvement enables the material independent computation of the pile-up geometry and permits a wider application scope of ModIni. The simulation method FloSim is based on the upper bound method, which enables the computation of cylindrical Flow Forming processes within minutes. For the optimization of the method FloSim, the basics for the analytical computation of the workpiece length during the process and the computation of the forming zone temperature were developed within this work. Fur-thermore, an analytical approach for the computation of the equivalent plastic strain of cylindrical Flow Forming processes was developed based on numerical parameter analyses. This tree approaches for computing the workpiece length, the temperature and the equivalent plastic strain were integrated in FloSim and lead to an increased accuracy.

Master`s thesis deals with unusual high-pressure-fluid forming technology – hydroforming. There are discussed factors, which are affecting forming process, and there are made conclusion of it for machine design process. There is also made an evaluation of tube hydroforming technology in nowadays. The objective of thesis is to design new forming machine for tube hydroforming and for use in bicycle frames design. The machine is to be determined for manufacturing series up to 1000 pieces. Based on calculations and discussion of hydroforming technology, the best design solution is chosen. Machine is designed as modular conception with pressure multiplication of forming fluid right in die cavity. There is no need to use high pressure pump for forming fluid, used in common machines for tube hydroforming. This leads to cost reduction and so the objective of thesis is accomplished.

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The underlying motives of the research undertaken here are twofold: to obtain a deeper understanding of the dewatering mechanisms at the forming section of a papermaking machine and to develop numerical models that describe the flow through forming fabrics. More comprehensive knowledge of dewatering in the forming section allows suggestions to be made for improvements that reduce the amount of energy used in the process without affecting the quality of the end product.   The objective of this thesis is to answer the following questions: How and why does rewetting occur at the high vacuum suction boxes? How does the structure of the forming fabric affect dewatering at the forming section? Is it possible to create accurate numerical models for forming fabrics, and can these be used to predict the dewatering behaviour of new types of fabrics?   Laboratory and pilot studies simulating high vacuum suction boxes were performed together with numerical modelling of the flow of air and water through both the forming fabric and the paper sheet.   The conclusion drawn from the pilot study is that rewetting significantly lowers the dryness of the paper sheet exiting the suction boxes. The phenomenon is extremely rapid and is most likely driven by capillary forces. The high speed at which this rewetting occurs makes it difficult to impede by placing the suction boxes closer to the couch pick-up: the solution is more likely to be the use of new and improved designs of the forming fabric. The structure of the forming fabric has been shown to affect the dewatering rate at certain conditions of vacuum dewatering, and can possibly be connected partly to the fact that fibres penetrate the surface of the fabric to varying degrees and partly to the flow resistance of the different fabric structures. Numerical models of high accuracy can be constructed and used to predetermine how new fabric designs would affect dewatering at the forming section.   This thesis quantifies aspects of dewatering such as rewetting and the influence of the forming fabric. Understanding these dewatering aspects further provides for the potential enhancement of energy efficiency in the forming section, and thereby the entire papermaking process. The forming fabric can play an important role in improving energy efficiency: rewetting after the high vacuum suction boxes occurs more rapidly than was previously known, so its design might be the only possible way of impeding it. The forming fabric can also improve the rate of dewatering: it is therefore likely that its design will be important in the next stage of developing energy efficiency and thereby play a part in achieving a more sustainable future. / This thesis quantifies aspects of dewatering such as rewetting and the influence of the forming fabric. Understanding these dewatering aspects further provides for the potential enhancement of energy efficiency in the forming section, and thereby the entire papermaking process. The forming fabric can play an important role in improving energy efficiency: rewetting after the high vacuum suction boxes occurs more rapidly than was previously known, so its design might be the only possible way of impeding it. The forming fabric can also improve the rate of dewatering: it is therefore likely that its design will be important in the next stage of developing energy efficiency and thereby play a part in achieving a more sustainable future.

Dissertation (PhD) -- Stellenbosch University, 2001 / ENGLISH ABSTRACT: Millisecond pulse forming networks (PFNs) as applicable to electro-thermal chemical (ETC) loads fall into the <1 MJ energy bracket. The energy requirements of these loads require specialised power sources involving staged energy conversion. For the <1MJ energy bracket, capacitive storage systems are usually employed. However, these systems exhibit low volume energy density and for volume sensitive applications; alternatives need to be considered. Inductive storage supplies form a sub-group of the static supplies that have theoretically superior volume energy density characteristics. This thesis documents the execution of a project concerned with the volumeoptimisation of an inductive storage supply. The system is composed of a three stage energy conversion chain. A prime power source (low power) charges an intermediate storage (IS) which is characterised by its medium power delivery capabilities. Energy is then transferred from the IS to the storage inductor which is characterised by its high power delivery capabilities. When sufficiently charged, the energy is then transferred to the load. Where pulse forming is required, the inductor storage must necessarily be modular. Switching elements to control the energy flow are also required. Work performed at Soreq, Israel, is used as the starting point. A topology variation of the XRAM topology presented by Soreq, original to this thesis, is presented and all its functioning modes are analysed. An existing volume model is analysed and expanded to incorporate heretofore unmodelled yet non-negligible considerations. The volume model generalises the effect of system modularity, subsystem technologies and allows for the incorporation of practical construction issues into the design process. The aim is to develop a 500 kJ, 80 kA, 20 kV system with a volume not exceeding lm3. This volume must include the IS, storage inductor and full switch volume. The optimisation algorithm and system topology developed in this thesis is validated through the construction and testing of a 1.2 kA, 2.5 kV 4 module prototype. A potential full ratings system, composed of contemporary device technologies and exhibiting a volume of just over 0.8m3, is proposed. / AFRIKAANSE OPSOMMING: Millisekonde pulsvormingsnetwerke, soos toegepas op elektrotermies-chemiese laste, val in die <1 MJ energievlak. Die energievereistes van hierdie tipe las vereis gespesialiseerde kragbronne wat die gestoorde energie in verskillende stadiums aan die las beskikbaar stel. Tans word kapasitiewe stelsels gewoonlik vir toepassings wat minder as 1 MJ energie benodig gebruik. ‘n Nadeel van hierdie stelsels is egter hulle relatiewe lae energiedigtheid. Vir toepassings waar lae volume van belang is, moet altematiewe metodes ondersoek word. Pulskragbronne wat van ‘n induktiewe energiestoor gebruik maak vorm ‘n deel van die klas van statiese kragbronne met hoe energiedigtheid. Hierdie tesis handel oor die optimering, in terme van volume, van ‘n induktiewe pulskragbron. Die stelsel bestaan uit drie stadiums, wat die energie van een vorm na ‘n ander omskakel en sodoende die vorm van die puls wat aan die las gelewer word, beheer. A lae-drywing primere kragbron laai ‘n medium-dry wing intermediere energiestoor. Energie word dan van die intermediere energiestoor na ‘n hoe-drywing stoorinduktor oorgedra. Nadat die induktor volgelaai is, word die energie aan die las oorgedra. Indien pulsvorming benodig word, kan van ‘n modulere induktor gebruik gemaak word. Vaste-toestand skakelelemente word gebruik om die energievloei te beheer. Navorsing wat by Soreq, in Israel, uitgevoer is, word as die vertrekpunt vir die studie gebruik. ‘n Verandering aan die XRAM topologie word voorgestel en die werking daarvan word in detail geanaliseer. ‘n Bestaande volume model word ondersoek en uitgebrei om ‘n aantal nie-weglaatbare verskynsels in aanmerking te neem. Die nuwe volume model maak voorsiening vir modulariteit, die effek van substelseltegnologie en ‘n aantal praktiese oorwegings wat in die ontwerp van die stelsel ‘n rol speel. Die finale doel is om ‘n 500 kJ, 80 kA, 20 kV stelsel in ‘n volume van 1 m3 in te pas. Hierdie volume van 1 m3 moet die intermediere energiestoor, die stoorinduktor, asook die skakelaars, bevat. Die optimeringsalgoritme en stelseltopologie wat ontwikkel is, word eksperimenteel deur middel van ‘n 1.2 kA, 2.5 kV, 4 module prototipe geverifieer. Laastens word aangetoon hoe ‘n finale stelsel, gebaseer op huidige skakelaartegnologie, met ‘n totale volume van 0.8 m3 moontlik in die toekoms ontwikkel kan word.

<p>The present work deals with some aspects of the fluidmechanics of paper-making,more specifically partial dewateringduring roll forming. The study is mainly experimental. Pressureand wire position measurements have been carried out in anexperimental facility, the KTH-Former,which models the rollforming zone of a paper machine.</p><p>Measurements are carried out with pure water for threedifferent wires (fabrics): A non-permeable,a semi-permeable anda conventional wire. Although not used in paper making,thenon-permeable wire is useful when trying to understand thefundamental mechanics of roll forming.The semi-permeable wirewith finite but low permeability is used to model the effectsof the fibre web on the drainage.</p><p>Tests have mainly been carried out for different wiretensions and different jet speeds. It is shown that the localcurvature of the wire is strongly correlated to the dewateringpressure.</p><p>The conventiona wire shows a single pressure peak causingcomplete de- watering in the first part of the dewateringzone.The pressure distributions for the non-and semi-permeablewires are found to show two consecutive pressure peaks followedby a suction peak where the wire is taken of the roll.Thisoscillating behaviour is due to capillary waves where the wiretension plays the role of surface tension on a free surface.Thewavy behaviour of the wire is recovered from an analyticalmodel and the effect is governed by a dimensionless Webernumber. The measured wave lengths correspond well to thosegiven by the theory.</p><p>When the wire tension is high,i.e.a high dewateringpressure,the flow in the impingement region collapses when thedynamic pressure of the headbox jet is about half of thedewatering pressure. It is shown experimentally that the localdrainage shows a correlation to the dewatering pressure andhence to the wire curvature.</p>