Det är viktigt att barn får en lustfylld och positiv syn på matematik. Därför är det viktigt att arbeta med matematik redan från tidig ålder så att den kunskapen följer med dem i deras fortsatta liv. Matematik innefattar mycket och därför har jag valt att fokusera på ett område som jag inte har mycket kunskap om. Syftet med min studie är att undersöka hur pedagoger stödjer barns matematiklärande utifrån Gelman och Gallistels fem principer. Deras principer är:  Ett till ett principen, parar ihop två föremål från olika mängder.  Principen om räkneordens ordning, vilken ordning siffrorna kommer i räkneramsan.  Antalsprincipen, den sista siffran man räknar är antalet.  Abstraktionsprincipen, att man vet att konkreta och abstrakta föremål går att räkna.  Principen om godtycklig ordning, att det går att börja räkna i vilken ordning som helst men att ett föremål bara räknas en gång. Metoden som användes var observation med ett löpande protokoll på en förskola. Resultatet från observationerna analyserades med hjälp av hermeneutiken och begreppen som är hållpunkten i Gelman och Gallisels samt begrepp utifrån den teoretiska utgångspunkten, det sociokulturella perspektivet. De slutsatser som kan dras från min undersökning är att pedagogerna använder olika arbetssätt när de stödjer barnens lärande i Gelman och Galistells fem principer. Pedagogerna kan stimulera barnen under alla sorters aktiviteter och beroende på hur länge aktiviteten håller på kan barnen få möjlighet att möta på fler principer. Att pedagogerna kan använda nästan vilket material som helst när de utmanar barnen i deras lärande i Gelman och Gallistels fem principer är också en slutsats som gick att dra från min undersökning. Min undersökning visar även att det är viktigt att pedagogerna använder ett varierande material och använder materialet på olika kreativa sätt för att stödja barnens lärande. Samt att talet är en viktig del i barnens matematiklärande.

This thesis deals with thermal optimization of electric machines. There are described the connections of finite element methods with optimizations algorithms. This connection is used for modifications of brushless motor construction. The main parts of this work are the complete thermal analysis of EC machine and modifications of cooling.

This document deals with the development of drilling tools by means of CAD and CAE technologies. At first, a brief overview of various design procedures of 3D drill models is presented, possibilities of measurement of force and moment loading during drilling are mentioned, a chip formation mechanism is briefly described and then a list of commonly used explicit (mesh) finite element methods used for cutting simulations is presented. A meshless SPH method have been selected for this work. Although it is able to handle the large deformations easily, it has been used for cutting simulations very rarely and only an orthogonal cutting simulations related information can be found in scientific databases. It has been demonstrated on the orthogonal cutting simulation of A2024-T351 alloy that was also the starting point for SPH simulation of drilling. The following is a decription of the design, simulation and prototyping of new drilling tools - drills with three and two cutting edges and an internal chip channel. This document is focused in detail on the variant with two cutting edges for which SPH drilling simulation has also been performed. Some drawbacks related to more precise chip simulation demands have been revealed, especially a rapid increase in number of SPH elements followed with prolongation of a computational time. Information related to the design of the drilling head with two cutting edges were then used to create the patent application.

Student Number :0008015M - MSc Dissertation - School of Electrical and Information Engineering - Faculty of Engineering and the Built Environment / Shaft voltages and currents are an unavoidable characteristic of rotating machines, though they are typically a nuisance this work shows that shaft signals can be used for fault diagnosis. This work focussed on shaft voltages present on synchronous generators. Measurements on a 4-pole generator found that the angular position of the shaft could be determined from the shaft voltage. An experimental 20 kVA 2-pole synchronous generator was designed and built which resembled a full-size 600 MVA turbo-generator. The effects of a static eccentricity on the shaft voltage were successfully determined firstly through FEM simulation and then verified with physical measurements. Shaft voltages can be used to diagnose static eccentricity, future work should investigate other faults. In addition, computer simulation was found to be effective and simulation and measurements of operating machines (such as turbo-generators) should be considered.

O estudo das forças de corte em usinagem tem várias aplicações, tais como definir a melhor geometria da ferramenta e sua interação com a peça. Este trabalho apresenta os resultados de simulações do processo de torneamento utilizando o método dos elementos finitos no corte ortogonal em aço AISI 4340 usando insertos de metal duro, comparando-os com resultados experimentais. As simulações foram realizadas no programa comercial Abaqus/Explicit TM considerando os efeitos térmicos do processo oriundos tanto da deformação do material quanto dos atritos nas interface peça-ferramenta-cavaco. As variáveis do processo estudadas foram a velocidade de corte e o avanço. Os resultados da força de corte simulada mostraram-se bem próximos daqueles obtidos experimentalmente, com erro médio em torno de 5%, enquanto que os da força de avanço apresentaram erro médio de cerca de 27%. / Cutting force is a very important parameter, which can be used to determine tool geometry and its interaction with the workpiece. This work presents some orthogonal cutting simulations using Abaqus/Explicit TM finite element methods code with carbide tool on an AISI 4340 hardened steel workpiece. Comparison with experimental results are also carried out. The simulation considers the thermal effect caused by material deforming and friction between tool, workpiece and chips. The main parameters changed during the simulations are the cutting speed and the feed rate. As results, the simulated cutting forces showed an error around 5% and the simulated feed forces about 27% when compared to the experimental values.

The ability to convert electrical energy into mechanical motion is of significant interest in many energy conversion technologies. For more than a decade Ionic polymer-metal composite (IPMC) as an electroactive smart polymer material has been extensively studied and has shown great potential as soft robotic actuators, artificial muscles and dynamic sensors in the micro-to-macro size range. IPMC consists of an ion exchange polymer membrane sandwiched between two noble metal electrodes on either side of the membrane. Under applied potential, the IPMC actuator results in bending deformation because of ion migration and redistribution across its surface due to the imposed voltage. Nafion are highly porous polymer materials which have been extensively studied as the ion exchange membrane in IPMC. Nafion has also been mixed with carbon nanotubes, graphene, and metallic nanoparticles to improve actuation and bending characteristics of electro-mechanical actuators. For the first time, liquid phase exfoliated Transition Metal Dichalcogenides (TMDs)-Nafion nanocomposite based electro-mechanical actuators has been studied and demonstrate the improvement in the electromechanical actuation performance. In this thesis, we create a 2D model of the TMD-Nafion based electromechanical actuator in COMSOL Multi-physics software. The behavior of the model is examined at different electric potentials, frequencies, and actuation lengths. The simulation results were compared with the experimental data for validation of the model. The data showed improvement in the actuation for TMD-Nafion actuator when compared with pure Nafion actuator. The improvement in the actuation was due to the increase in diffusivity of the TMD-Nafion actuator in comparison with pure Nafion actuator. This increase in the diffusivity as seen in the model is because of the new proton conducting pathways being established with the addition of TMDs. The model also shows an increase in the stress and strain values with the incorporation of TMDs. With the same length of the actuator we were able to obtain more stress and strain with the addition of TMDs. This helps in improving the performance of the actuator as it would be able to handle more stress cycles which also increases the life of the actuator.

Detta examensarbete behandlar analys, simulering och dimensionering en drivaxel till en baltransportör för returfiber vid SCA Munksund. Transportören drivs i dagsläget av två hydraulmotorer försedda med varsin 3-stegs planetväxellåda, en på varje sida av drivaxeln för transportbandet. Växellådorna skall bytas ut och en driftsäker, kostnadseffektiv ersättningslösning efterfrågas. I studien kartläggs dimensionerande belastningar och en belastningsmodell upprättas för kedjetransportören. Befintlig axel beräknas både analytiskt och simuleras i Solidworks Simulation. Axeln, inklusive monterade detaljer som rullager, kedjehjul och kilar utreds med avseende på hållfasthet i fyra lastfall: Enkeldrift och dubbeldrift, med nominell belastning respektive maximal belastning. Studien konstaterar att befintlig axel håller i nuvarande uppställning men bör inte modifieras för att passa en ny växellåda, stor risk för plasticering av axeln föreligger. Befintlig axel håller inte för enkeldrift, spänningar i axelns stål överskrider sträckgränsen i a xelförbandet mot v äxellådan och lagerläget för mittersta rullagret. Förslag på en ny axel har tagits fram. Beräkningsunderlag, simuleringar och tillverkningsritning redovisas. Den nya axeln tillverkas i SS2541 som har sträckgränsen 700 MPa och med förbättringar i hålkäler främst vid diameterändringar kan befintliga lagringar återanvändas. En kostnadsuppskattning bifogas för kostnader relaterade till axelbytet.

The automotive engineering process is characterized by a long and complex design process which starts with the first sketches in the preliminary design phase and proceeds to the final detailed CAD and physical models. In this process, every design phase includes different process steps and tasks which are closely interconnected with each other. Therefore the different design stages demand capable Computer Aided Design (CAD) systems which are able to handle the different kinds of design information created and manipulated in the process. Currently in automotive practice, parametric and associative (PA) CAD systems are widely applied in the product development process. Such systems allow design knowledge to be embedded in CAD models by means of rules and formulae. In addition, CAD parts and assemblies can be generated faster and easier by modification of design parameters and therefore there is a possibility to create different CAD model variants which are based on the same CAD model. The four key element of the following work are (a) to identify the problems during the design process with parametric and associative (PA) methods during a three year of study and also the analysis of the literature survey. Furthermore (b) in this study the author will develop and implement a newly developed PA design approach (PARAMASS) in a ―real‖ industrial context. Beside this the following work will (c) discuss the issues which are important during the implementation of the developed PA approach in an industrial surrounding. The last key element (d) is to develop an evaluation approach for the PARAMASS approach during the application in an industrial context. In this case the author will be able to do action research in the industry and get first hand information during the accomplishment of these key elements. This thesis presents the results of a research programme carried out using the design research methodology of Blessing and Chakrabarti, aimed at understanding the difficulties and challenges faced by designers in using PA CAD systems and then developing and evaluating an integrated approach to the creation of PA CAD models in an automotive power train design context. Firstly, this thesis presents a review of the state of the art in PA design methods and approaches and also reviews previous research on the development of methodologies for the construction of PA CAD models. It then presents results of a descriptive study of the use of PA CAD tools and methods in vehicle power train design in an automotive original equipment manufacturer and in companies in its supply chain using questionnaires, interviews, tests and other field studies with a number of practising engineers. This study identified a number of issues faced by designers in the use of PA CAD tools and allowed the requirements for improved methods for the use of PA CAD tools to be formulated and indicators identified for their evaluation. Based on the results of the descriptive study a new integrated parametric associative (PA) approach for the design process of power train components was created in a prescriptive study stage. The approach, called PARAMASS, allows designers to construct and modify models in a methodical way based on three main phases: a specification phase to prepare the relevant parameters and associative relationships, a structuring phase that allows part and assembly structures to be created and a modification phase in which the created parametric and associative information can be modified and changed. The method makes extensive use of predefined structures matrix approaches adapted from the Design Structure Matrix. The prescriptive study phase of the research was followed by a second descriptive study to evaluate and investigate in both a qualitative and quantitative way the changes achieved by the PARAMASS approach. The qualitative evaluation was based on the Goal Question Metric approach and showed that there are advantages related to the reusability aspects like learning, application and acceptance of the developed integrated approach. The quantitative evaluation was based on the Use Case approach and demonstrated good advantages in applying the developed approach, but dependent on the complexity of the created parts and assemblies.

Syftet med studien är att beskriva hur lärare i årskurs 6 anpassar sin matematikundervisning till olika elever samt vilket inflytande eleverna har över dessa anpassningar. För att undersöka detta samlades data in med hjälp av observationer av matematiklektioner och intervjuer med vederbörande lärare. Utifrån detta analyserades data med hjälp av Smith och Steins (2014) fem undervisningspraktiker. Resultatet visar att lärare gör olika anpassningar där läraren behöver en överblick av elevernas matematikkunskaper. Specifika anpassningar kan vara att anpassa läromedlet på olika sätt. Generella anpassningar kan vara hörselkåpor, stressbollar, skärmar och placeringen i klassrummet. Vid val som påverkar undervisningen tar lärarna hänsyn till både sociala och matematiska aspekter. Det kan vara vid val av vilken elev som ska redovisa sitt svar. Då reflekterar läraren utifrån elevens perspektiv men även de andra elevernas förståelse av innehållet. Att använda olika representationsformer kan underlätta för elever på olika sätt.  Studiens resultat visar också elevernas inflytande över olika anpassningar. Anpassningarna bestäms i samråd mellan elever och lärare. Eleverna får bland annat vara med och utforma lektionens innehåll inför matematikprov. Även vid placeringen i klassrummet ges det möjlighet till elevinflytande. Med hjälp av elevernas självreflektioner över vad som gynnar deras lärande bäst bestäms placering. Studien kan ge lärare förslag och fler sätt att tänka på gällande anpassningar i matematikundervisningen.

Os modelos existentes de propagação de ondas de ultra-som em meios líquidos e sólidos consideram a geração e recepção das ondas produzidas por transdutores simulados segundo o modelo do pistão plano ou com excitações cuja amplitude varia radialmente no pistão. Esses modelos são simplificados e não explicam completamente o comportamento real de transdutores de ultra-som interagindo com líquidos e sólidos. As verificações experimentais de propagação da onda de ultra-som em meios líquidos mostram que a onda de borda é diferente da onda plana. Observa-se também a existência de outras ondas não previstas nos modelos anteriores. Essas ondas são conhecidas como ondas head. A utilização do método dos elementos finitos (MEF) para a modelagem de propagação de ondas de ultra-som, incluindo o transdutor piezelétrico, permite a obtenção de resultados realísticos, conseguindo assim descrever com maior precisão o comportamento do transdutor e das ondas de ultra-som se propagando em diferentes meios e interagindo com defeitos que se comportam como refletores. Apesar disso, os resultados desses modelos dependem das características precisas dos materiais que compõem o transdutor. O transdutor de ultra-som é composto por uma cerâmica piezelétrica, por camadas de casamento e de retaguarda que geralmente são compósitos de epóxi com alumina e epóxi com tungstênio respectivamente, e pelo encapsulamento. Neste trabalho é analisada a resposta transiente de um transdutor circular de 2 MHz, com diâmetro de 12,7 mm, banda larga. O modelo do transdutor foi implementado com o método de elementos finitos. A análise transiente pelo MEF é implementada com o software ANSYS. Na primeira parte do trabalho o transdutor é analisado no modo de transmissão em água. Os resultados do modelo com MEF foram comparados com os resultados do modelo do pistão plano e com verificações experimentais obtidas em tanque de imersão com um hidrofone tipo agulha. Na segunda parte é realizada a análise do transdutor operando em modo pulso-eco radiando em peças de teste com e sem defeito, utilizando acoplamento direto e acoplamento por buffer de água. Os resultados do MEF apresentam boa concordância com os resultados obtidos experimentalmente. / Simple models for ultrasonic wave propagation in liquid and solid media consider the wave generation and reception by transducers that behave as plane pistons. These models are simplified and they do not explain completely the behavior of an ultrasonic transducer when interacting with other media. Experimental verifications of ultrasonic wave propagation in liquid show that the pressure amplitude of the edge wave is different from the plane wave. Also it is observed the existence of other types of waves not foreseen in these previous models. These waves are known as head waves. More realistic models for ultrasonic wave propagation are obtained using the finite element method (FEM). These models include the piezoelectric transducer, thus, describing with higher precision the behavior of the transducer and the ultrasonic waves propagating in different mediums and interacting with defects. The precision of the models depends on the accurate determination of the mechanical and electrical properties of the involved materials. The ultrasonic transducer is composed by a piezoelectric ceramic, a matching layer and a backing layer that are generally made by epoxy/alumina and epoxy/tungsten composites respectively. In this work it is analyzed the transient response of a circular transducer of 12.7 mm diameter and 2 MHz center frequency. The transducer model was implemented with the finite element method. The FEM transient analysis was executed in the ANSYS software. In the first part of the work the transducer is analyzed in transmission mode in water and the MEF results are compared with the plane piston model and with experimental verifications using a hydrophone. In the second part it is carried at the transducer analysis operating in pulse-echo mode radiating into test pieces with and without defects, using direct and water buffer coupling. The MEF results show good agreement with the results obtained experimentally in the laboratory.