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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
181

Travel Log

Young, Pamela L. 01 January 2006 (has links)
Artists generally begin their craft by relating to what is most familiar to them. It is in this comfort zone that my journey into painting began. From my first painting of the Chrysler Building in New York City to the countryside in Tuscany, my work tells the story of my travels. When I began to create jewelry that contained elements of my paintings, I expanded on the concept of documenting my travels. Further experimentation with new materials used in jewelry making allowed me to create a visual correlation between my paintings and my wearable jewelry.
182

Experimental determination of prestressing wire bond and splitting propensity characteristics through tensioned pullout tests

Holste, Joseph Robert January 1900 (has links)
Doctor of Philosophy / Department of Civil Engineering / Robert J. Peterman / This dissertation describes a testing program to evaluate the bond and splitting propensity characteristics of 5.32-mm-diameter prestressing wires. Prestressing wire reinforcement is used primarily in the production of prestressed concrete railroad ties. Twelve different 5.32-mm-diameter wires were tested in this study in order to measure bonding characteristics of the reinforcement. Establishment of the bond-slip characteristics of these reinforcement at both transfer of prestress (transfer bond) and under flexural loading (flexural bond) is necessary to enable the accurate modeling of these ties using finite elements. Transfer bond and flexure bond of various indent patterns were tested using tensioned pullouts. Specimens of various sizes with single or multiple wires were tested to determine the effects of cover and wire number on bond. Indents were machined on smooth prestressing wires to accurately compare indent geometries. Lateral expansion was tested to determine which wires have higher propensity to cause cracking or splitting. Crossties were instrumented to compare resulting lateral expansion with results found in the laboratory. The results from the testing program showed that the tensioned pullout test was able to be used to predict the transfer length of prisms made with the same reinforcement. The results also showed that the indent geometries were able to be used to predict the splitting of specimens based on the amount of slip the wire had experienced. The testing also showed the importance of concrete cover with the relation to splitting potential.
183

Estudo do fenômeno da biestabilidade em cilindros finitos com média razão de aspecto

Woyciekoski, Marcos Leandro January 2018 (has links)
Este trabalho apresenta um estudo experimental a respeito do fenômeno da biestabilidade em cilindros finitos com média razão de aspecto. Na biestabilidade, há uma esteira estreita a jusante de um dos cilindros e uma esteira larga a jusante do outro. Pode estar presente em muitas situações práticas da engenharia dependendo da distância entre os cilindros. Em cilindros finitos ainda é pouco compreendida e explorada. Para compreender o mecanismo do desprendimento de vórtices, são estudados o escoamento em torno de um único cilindro finito, com cilindros de diâmetros entre 25 e 60 mm e razão de aspecto entre 1 e 4 e após, o escoamento em torno de dois cilindros finitos dispostos lado a lado, com cilindros de diâmetros entre 25 e 32 mm e razão de aspecto entre 3 e 4. A técnica experimental aplicada consiste na medição das flutuações de velocidade em canal aerodinâmico, utilizando a técnica de anemometria de fio quente e na visualização do escoamento no mesmo canal, mantendo os parâmetros, utilizando gelo seco e laser. Além disso, foi realizada a visualização do escoamento em canal hidráulico com as mesmas dimensões do canal aerodinâmico, utilizando injeção de tinta através de agulhas. Para o estudo foram utilizados Re=2,00×104 para um cilindro finito e 3,86×103 ≤ Re ≤ 4,81×104 para cilindros finitos dispostos lado a lado. Os dados medidos em canal aerodinâmico são tratados através de ferramentas estatísticas, espectrais e de ondaletas, e os resultados das visualizações do escoamento são apresentados por meio de imagens obtidas das filmagens realizadas com uma câmera digital. Além disso, os vídeos são tratados com softwares de edição de vídeo e com ferramentas estatísticas. Os resultados confirmam a existência do fenômeno da biestabilidade para dois cilindros finitos dispostos lado a lado, que é um dos objetivos do estudo, nas três posições estudadas. A técnica de visualização de escoamento reforça a interpretação dos resultados obtidos através da técnica de anemometria de fio quente. Neste trabalho é considerada a existência de três escoamentos concomitantes: o escoamento ascendente, caracterizado pela estrutura de vórtices na base; o escoamento descendente, caracterizado pela estrutura de vórtices no topo; e o aqui chamado escoamento principal, caracterizado pelo desprendimento de vórtices a meia altura dos cilindros. / This work presents an experimental study on the bistability phenomenon in finite cylinders with a mid-aspect ratio. In the bistability phenomenon the flow to form two wakes behind the cylinders, a large wake behind a cylinder and a narrow wake after another. It can be present in many practical engineering situations depending on the distance between the cylinders. In finite cylinders, it is still poorly understood and explored. To understand the vortex shedding mechanism are studied the flow in a single finite cylinder with diameters between 25 and 60 mm and aspect ratio between 1 and 4 is studied. After that, the flow of two finite cylinders placed side by side with cylinders of diameters between 25 and 32 mm and aspect ratio between 3 and 4 was studied. The experimental technique of hot wire anemometry in aerodynamic channel is applied in the measurement of velocity fluctuations of the flow. The flow visualization was performed on the same aerodynamic channel, keeping the parameters, through using dry ice and laser. In addition, flow visualization is performed on the hydraulic channel with the same dimensions of the aerodynamic channel using ink injection through needles. All images are captured with a camera digital. For the study, Re=2.00×104 for a finite cylinder and 3.86×103 ≤ Re ≤ 4.81×104 for finite cylinders arranged side by side were used. The data measured in aerodynamic channel are treated through statistics, spectral and wavelet tools and the videos are treated through video editing software and with statistical tools. The results show the existence of two different levels of mean velocity in time series, corresponding to two flow modes confirming the phenomenon of bistability for two finite cylinders placed side by side, which is one of the objectives of the study. The flow visualization technique strengthens the interpretation of the results obtained through the hot wire anemometer technique. In this work the existence of three concomitant flows is considered: the upwash flow, characterized by the vortex structure in the base; the downwash flow, characterized by the vortex structure at the top; and the so-called main flow, characterized by the vortex shedding at half height of the cylinders.
184

Desenvolvimento do arame galvanizado BWG 18 para aplicação na fabricação de telas / Development of galvanized wire BWG18 for application in the manufacture of wire mesh

Kalil, Sandro Aurélio Pereira January 2009 (has links)
O objetivo deste trabalho visa analisar criticamente o processo de fabricação do arame galvanizado, discutindo a influência de variáveis, tais como: composição química do aço, velocidade dos fios na linha de galvanização e temperaturas associadas ao tratamento térmico, garantindo com isto um produto aderente as novas necessidades apresentadas pelo setor da avicultura que emprega o arame galvanizado BWG 18 na confecção de telas. A metodologia adotada envolveu as etapas de revisão da literatura e procedimento experimental D.O.E. (Design of Experiments), com coleta de amostras sob diferentes empregos (matéria prima) e condições operacionais (alteração de velocidades na linha de galvanização) e posterior realização de ensaios e análises de laboratório nas amostras coletas. Na etapa final foi realizado a avaliação e discussão dos resultados obtidos, identificando o produto galvanizado que melhor atende as propriedades mecânicas exigidas na fabricação de telas para o setor de avicultura. / The objective of this work aims at critically analyze the process of manufacture of the galvanized wire, arguing the influence of variables, such as: chemical composition of the steel, wire speed in the galvanizing line and temperatures associates to the heat treatment, ensuring with this an adherent product the new necessities presented for the poultry keeping that uses galvanized wire BWG 18 in the manufacturing of wire mesh. The adopted methodology involved the stages of revision of literature and experimental procedure D.O.E. (Design of Experiments), with acquisition of samples under different jobs (raw material) and operational conditions (alteration of speeds in the galvanizing line) and later accomplishment of assays and analyses of laboratory in the samples collections. In the final stage it was carried through the evaluation and quarrel of the acquired results, identifying the galvanized product that better takes care of the demanded mechanical properties in the manufacture of wire mesh for the poultry keeping sector.
185

Heterogeneidades mecânicas e microestruturais durante o processo de trefilação combinada do aço SAE 1045

Ferlauto, Eduardo Möller January 2011 (has links)
Este trabalho estuda o processo de trefilação combinada do aço SAE 1045, que consiste nas etapas de pré-endireitamento com múltiplos rolos, jateamento, trefilação, corte e endireitamento por rolos, tendo como produto final barras acabadas trefiladas. Este produto final é empregado na fabricação de hastes de amortecedores para indústria automotiva. O Objetivo do estudo é de entender como são geradas e como se comportam as principais heterogeneidades mecânicas do material processado e a influência dos parâmetros do processo e das características do material na formação e modificação dessas heterogeneidades, buscando como resultado parâmetros otimizados para o processo. Foram variados no processo três parâmetros e avaliadas a interação existente entre eles. Os parâmetros modificados foram ângulo da ferramenta de trefilação (fieira), o ângulo de endireitamento e polimento por rolos cruzados (PERC) e a colocação de revestimento de carbo-nitreto de titânio (TiCN) no núcleo da ferramenta de trefilação (fieira). Foi realizada caracterização do aço, como microestrutura, composição química e microdureza. As tensões residuais superficiais das amostras foram caracterizadas utilizando o método de difração de raios-X. Após avaliação das tensões residuais superficiais, foi analisada a variação das tensões com a profundidade através do método do furo cego (hole-drilling), A classificação das inclusões foi de acordo com o método microscópico A (“piores campos”) da norma ASTM E45-97, feita através da maior severidade encontrada analisando o material aleatoriamente através de varredura com microscópio em sua superfície. Os resultados obtidos permitiram conhecer a combinação de ângulo de fieira e de endireitamento por rolos cruzados (PERC) mais favoráveis para gerar níveis baixos de tensões residuais. Além do ângulo, foi possível verificar que a geometria das zonas da ferramenta de trefilação (fieira) influência os níveis de tensões residuais após a trefilação. O núcleo da fieira com revestimento em todos os ensaios realizados apresentou menores níveis de tensões residuais, mostrando ser uma condição importante para a otimização do processo principalmente para a redução das tensões trativas após a trefilação. / This paper studies the process of cold drawing combined SAE 1045 steel, which consists of the steps with multiple pre-straightening rolls, sandblasting, drawing, cutting and straightening by rollers, with the final product finished extruded bars. This final product is used in the manufacture of rods of shock absorbers for the automotive industry. The objective of the study is to understand how they are generated and how they behave the main mechanical heterogeneities of the processed material and the influence of process parameters and material characteristics of the formation and modification of these heterogeneities, seeking as a result the optimized parameters for the process. We varied three parameters in the process and evaluated the interaction between them. The parameters were modified angle of wire drawing tool (spinneret), the angle of straightening and polishing rolls (PERC) and the placement of coating titanium carbo-nitride (TiCN) in the core of the wire drawing tool (spinneret). We performed characterization of steel, such as microstructure, chemical composition and microhardness. The surface residual stresses of the samples were characterized using the method of X-ray diffraction. After evaluation of surface residual stresses, we analyzed the variation of stress with depth by the method of blind hole (hole-drilling), Classification of inclusions was according to the microscopic method ("worst fields") of ASTM E45 -97, made more severe by analyzing the material found randomly through scanning with microscope on its surface. The results obtained allow us to know the combination of angle stringer and straightening by rollers (PERC) more favorable to generate low levels of residual stresses. In addition to the angle, we found that the geometry of the areas of wire drawing tool (spinneret) influence the levels of residual stress after wire drawing. The core of the spinneret clad in all tests had lower levels of residual stress, proving to be an important condition for the optimization of the process mainly to the reduction of tensile stress after wire drawing.
186

Orthopaedic surgical skills: examining how we train and measure performance in wire navigation tasks

Long, Steven A. 01 May 2019 (has links)
Until recently, the model for training new orthopaedic surgeons was referred to as “see one, do one, teach one”. Resident surgeons acquired their surgical skills by observing attending surgeons in the operating room and then attempted to replicate what they had observed on new patients, under the supervision of more experienced surgeons. Learning in the operating is an unideal environment to learn because it adds more time to surgical procedures and puts patients at an increased risk of having surgical errors occur during the procedure. Programs are slowly beginning to switch to a model that involves simulation-based training outside of the operating room. Wire navigation is one key skill in orthopaedics that has traditionally been difficult for programs to train on in a simulated environment. Our group has developed a radiation free wire navigation simulator to help train residents on this key skill. For simulation training to be fully adopted by the orthopaedic community, strong evidence that it is beneficial to a surgeon’s performance must first be established. The aim of this work is to examine how simulation training with the wire navigation simulator can be used to improve a resident’s wire navigation performance. The work also examines the metrics used to evaluate a resident’s performance in a simulated environment and in the operating room to understand which metrics best capture wire navigation performance. In the first study presented, simulation training is used to improve first year resident wire navigation performance in a mock operating room. The results of this study show that depending on how the training was implemented, residents were able to significantly reduce their tip-apex distance in comparison with a group that had received a simple didactic training. The study also showed that performance on the simulator was correlated with performance in this operating room. This study helps establish the transfer validity of the simulator, a key component in validating a simulation model. The second study presents a model for using the simulator as a platform on which a variety of wire navigation procedures could be developed. In this study, the simulator platform, originally intended for hip wire navigation, was extended and modified to train residents in placing a wire across the iliosacral joint. A pilot study was performed with six residents from the University of Iowa to show that this platform could be used for training the other applications and that it was accepted by the residents. The third study examined wire navigation performance in the operating room. In this study, a new metric of performance was developed that measures decision making errors made during a wire navigation procedure. This new metric was combined with the other metrics of wire navigation performance (tip-apex distance) into a composite score. The composite score was found to have a strong correlation (R squared = 0.79) with surgical experience. In the final study, the wire navigation simulator was taken to a national fracture course to collect data on a large sample of resident performance. Three groups were created in this study, a baseline group, a group that received training on the simulator, and a third group that observed the simulator training. The results of this study showed that the training could improve the overall score of the residents compared to the baseline group. The overall distribution from resident performance between groups also shows that a large portion of residents that did not receive training came in below what might be considered as competent performance. Further studies will evaluate how this training impacts performance in the operating room.
187

Developing and implementing a computer vision based surgical simulator for hip wire navigation

Long, Steven A. 01 May 2016 (has links)
Orthopaedic residency training is in the midst of a paradigm shift. Recent mandates from the Residency Review Committee (RRC) for Orthopaedic Surgery and the American Board of Orthopaedic Surgery (ABOS) are requiring that programs must provide structured motor skills training to first year residents. Although other surgical fields such as laparoscopic surgery have been using simulation tools to train incoming residents for over a decade, the orthopaedic field has lagged behind in developing these training tools. Given the need for orthopaedic training devices and the lack of currently available solutions to residency programs, this work has focused on developing a surgical simulator for the task of hip guide wire navigation. Hip wire navigation was targeted for this work because it is a core competency skill for surgical residents and few options currently exist for training residents on this task. Much of this work focuses on the development of the wire navigation simulator. The simulator has six main components; a single camera interfaced with a Raspberry Pi (a credit-card sized computer), a series of three mirrors, a surrogate femur, a guide wire driver, a laser etched guide wire, and a laptop. These components interact to create virtual radiograph images that the resident can use to place the guide wire inside the bone. The goal in developing this simulator is to provide a platform which enables residents to acquire the skill of hip wire navigation in a safe environment and eventually transfer that skill into the operating room. Assessment of the simulator has shown that the guide wire can be located in bone within 1.5mm of its true position and less than a degree of its true trajectory. This level of accuracy is sufficient for providing residents with a training tool to practice their technique on. In training with resident surgeons, initial trends show that practicing with the simulator can result in an improvement in one’s technique. Residents who have trained with the simulator show a decrease in both the amount of radiographic images required to complete the procedure and the amount of time required to perform the procedure in a pseudo operating room environment. While more work is needed to be done to show the significance of this trend, this work has achieved its goal of providing residents with a safe platform for practicing the task of hip guide wire navigation.
188

Experimental Studies of Magnetic Islands, Configurations and Plasma Confinement in the H-1NF Heliac

Kumar, Santhosh Tekke Athayil, santhosh.kumar@anu.edu.au 2008 May 1915 (has links)
Rational magnetic flux surfaces in fusion (toroidal plasma confinement) devices can break the magnetic field lines and reconnect them in the form of magnetic islands. Formation of these magnetic islands can have a serious impact on the plasma confinement properties of the device. Islands can in general degrade the confinement by mixing up different regions of the plasma. However there has been experimental evidence of confinement improvement by island induced transport barriers, under certain conditions. Even though there are a large number of theoretical and experimental works on magnetic islands to date, there is clearly a paucity of convincing experimental understanding on the nature of behaviour of islands in plasma. This thesis reports detailed experimental studies conducted on the H-1NF heliac stellarator, to gain an in-depth understanding of magnetic islands and their influence in plasma confinement.¶ Work reported in this thesis can be mainly divided into three parts: (a) high resolution imaging of vacuum magnetic islands and flux surfaces of H-1NF, (b) accurate computer modeling of H-1NF magnetic geometry and (c) detailed experiments on magnetic islands in plasma configurations.¶ Electron-beam wire-tomography in the H-1NF has been used for the high resolution mapping of vacuum magnetic flux surfaces and islands. Point-to-point comparison of the mapping results with computer tracing, in conjunction with an image warping technique, has enabled systematic exploration of magnetic islands and surfaces of interest. A fast mapping technique has been developed, which significantly reduced the mapping time and made this technique suitable for mapping at higher magnetic fields.¶ Flux surface mapping has been carried out at various magnetic configurations and field strengths. The extreme accuracy of this technique has been exploited to understand the nature of error fields, by point-by-point matching with computer tracing results. This has helped in developing a best-fit computer model for H-1NF magnetic configurations, which can predict rotational transform correct to three decimal places. Results from plasma experiments on magnetic configuration studies are best explained by the new model.¶ Experiments with low order magnetic islands in plasma configurations yielded some new results. It has been observed that the low order magnetic islands (m = 2) near the core of the plasma serve as pockets of improved confinement region under favourable conditions. This results in significant profile modifications including enhancement of the radial electric field near the core to a large positive value. The characteristics of islands are found to be dependent on the plasma collisionality and the island width.¶ Experiments with a magnetic configuration which exhibits no vacuum islands, but the core rotational transform very close to low order rational value, show a spontaneous transition of the radial electric field near the core to a large positive value (nearly 5 kV/m), with a strong electric field shear (nearly 700 kV/m2) and localised improvement in confinement, during the discharge. Evidence indicates that the transition is driven by the excitation of low order magnetic islands near the axis during the plasma discharge, due to the modification of rotational transform profile by toroidal plasma currents. The situation is similar to the Core Electron-Root Confinement (CERC) observed during high temperature ECH plasma discharges on other helical devices. This result provides an experimental evidence for the hypothesis that the threshold conditions for observing CERC can be reduced by exciting magnetic islands near the core of the plasma.
189

Utvärdering av MK F1500 testutrustning / Evaluation of MK F1500 Test Equipment

Croner, Len January 2010 (has links)
<p>SAAB Support and Services, som är servicecenter för flygplanskomponenter, utför idag huvuddelar av sina mätningar manuellt, mätningar som ibland kan ta upp till fyra dagar. För att höja noggrannheten samt öka effektiviteten köpte de år 2007 in ett automatiskt testkoncept från MK Test systems.</p><p>I examensarbetet har vi först undersökt den inköpta utrustningen.</p><p>Sedan har vi tagit fram rutiner för kalibrering av utrustningen som klarar SAAB:s krav. Därefter har vi arbetat fram kravspecifikationer och instruktioner för hur utrustningen ska användas. Under arbetets gång har vi samlat in information för att kunna göra en utvärdering av hur lämplig utrustningen är att använda för att testa flygplanskomponenter.</p><p>Arbetet resulterade huvudsakligen i tre st manualer som går igenom tre olika områden; kalibrering, kablagetest och ett standardtest för t.ex.</p><p>paneler och styrboxar.</p> / <p>SAAB Support & Services, a service centre for air plane components, perform most of their measurements manually. These measurements can sometimes take up to four days to perform. In 2007 an automatic concept for testing from MK Test systems was purchased in order to enhance the accuracy and increase the efficiency.</p><p>In our thesis we have initially examined the automatic concept for testing and then developed standards for how to calibrate this equipment, standards that meets SAAB:s requirements. Thereafter we have developed specifications and instructions on how to use the equipment. During our work we have gathered information for an evaluation of how fitting it is to use the F1500 for testing air plane components.</p><p>The main outcome of our work consists of three manuals for three different areas; calibration, harness test and a standard test for example panels and controller units.</p>
190

Improved Billet Shape Modeling in Optimization of the Hot Rod and Wire Rolling Process / Förbättrad geometrimodellering av heta och valsspår för optimering inom profilvalsningsprocessen

Betshammar, Jan January 2006 (has links)
<p>The hot rod and wire rolling process is widely used to produce rolled iron alloys in different shapes and dimensions. This industry has been under a constant development during the last decades. Today, complex geometries are produced at a high speed since it is possible to use several stands in each mill at the same time. A reason for the development is rising demands from customers. The most important demands are to save energy, to get better material properties and higher dimension accuracy. To meet these demands on speed and accuracy, a better control of how the material behaves in the process is needed. There is also a need to be able to quickly find a new setup of the mill in order to be able to produce other geometries.</p><p>The purpose with this Master Thesis is to model and simulate the hot rod and wire rolling process with the modeling language Modelica. The model is given the known inputs and the desired final result in order to compute the unknown inputs to the mill. To meet these goals, a model that depends on for example the gap between the rolls, the roll speeds and the tensions between different stands is needed. It should be possible to make simulations to find roll speeds or to calculate the tensions caused by known roll speeds.</p><p>With the help of models of the steps in the process, a model has been developed in Modelica. The model can be expanded to a mill with an arbitrary number of stands. In the search for the best way of modeling a hot rod and wire rolling mill, several algorithms have been simulated and analyzed in Modelica. The results from all simulations show that the billet and the groove should be described by different functions for the upper and the lower half. Furthermore, it is not a good solution to use only polynomials to describe the shapes in the process. A function with infinite derivative in the endpoints is needed to describe the billet in an acceptable way. The problem has also been solved using Matlab. In this work it is shown that the Modelica solution is preferred, compared to solving the optimization problems in Matlab. An advantage with the Modelica solution is that the model can be split into several easily connected sub models. Unfortunately it was even hard for Modelica to solve general problems. The describing functions made it hard to find the intersections and to keep the area constant during the rotation. The least square method could lead to bad approximations of the shapes.</p> / <p>Profilvalsning används idag globalt som en process för att tillverka metaller i olika former och har under de senaste årtiondena varit i en lång utvecklingsfas. Numera valsas komplicerade geometrier samtidigt som produktiviteten har ökat drastiskt tack vare möjligheten att valsa med flera valspar samtidigt. Under utvecklingsprocessen har även kraven från kunderna ökat, främst vad gäller energibesparing och noggrannhet på den slutgiltiga produktens dimensioner och materialegenskaper. För att kunna möta dessa krav på snabbhet och noggrannhet krävs större kontroll av hur materialet beter sig i valsningsprocessen och att det snabbt går att bestämma hur valsverket ska ställas in när en ny serie ska tillverkas.</p><p>Syftet med examensarbetet som redovisas i denna rapport är främst att modellera och simulera profilvalsningsprocessen med modelleringsspråket Modelica. Modellen ska sedan kunna användas för att utifrån givna indata till processen bestämma olika inparametrar till valsverket för att uppnå önskat slutresultat. För att nå dessa mål krävs en modell som bland annat beror på spelet mellan valsarna, valshastigheterna och dragen mellan olika valspar. Simuleringar ska kunna göras för att både bestämma önskade valshastigheter och för att beräkna vilka drag givna valshastigheter ger upphov till i valsverket.</p><p>Med hjälp av modeller och beskrivningar av de olika stegen i valsningsprocessen har en modell tagits fram i Modelica. Modellen har en given inprofil och kan sedan byggas ut till ett valsverk med önskat antal valspar. I Modelica har olika modeller och algoritmer simulerats och analyserats för att kunna svara på hur ett profilvalsverk modelleras på bästa sätt. Resultaten från de olika simuleringarna visar att heta och valsspår bör beskrivas med olika funktioner för den övre och för den undre delen av profilen. Det är ingen bra lösning att endast använda polynom för att beskriva de olika formerna. En basfunktion med oändlig derivata i ändpunkterna är nödvändig för att beskriva hetan på ett bra sätt. En fördel med Modelica är även att modellen enkelt kan delas upp i flera enkelt sammankopplade delmodeller. Tyvärr var det svårt även för Modelica att lösa generella problem. Funktionerna som användes för att beskriva de olika formerna gjorde det svårt att hitta skärningspunkter och att hålla arean konstant under rotationen. Minsta kvadratmetoden resulterade ibland i dåliga approximationer av de olika formerna.</p>

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