Experimental and computational investigation of the roll forming process

One of the first questions to consider when designing a new roll forming line is the number of forming steps required to produce a profile. The number depends on material properties, the cross-section geometry and tolerance requirements, but the tool designer also wants to minimize the number of forming steps in order to reduce the investment costs for the customer. There are several computer aided engineering systems on the market that can assist the tool designing process. These include more or less simple formulas to predict deformation during forming as well as the number of forming steps. In recent years it has also become possible to use finite element analysis for the design of roll forming processes. The objective of the work presented in this thesis was to answer the following question: How should the roll forming process be designed for complex geometries and/or high strength steels? The work approach included both literature studies as well as experimental and modelling work. The experimental part gave direct insight into the process and was also used to develop and validate models of the process. Starting with simple geometries and standard steels the work progressed to more complex profiles of variable depth and width, made of high strength steels. The results obtained are published in seven papers appended to this thesis. In the first study (see paper 1) a finite element model for investigating the roll forming of a U-profile was built. It was used to investigate the effect on longitudinal peak membrane strain and deformation length when yield strength increases, see paper 2 and 3. The simulations showed that the peak strain decreases whereas the deformation length increases when the yield strength increases. The studies described in paper 4 and 5 measured roll load, roll torque, springback and strain history during the U-profile forming process. The measurement results were used to validate the finite element model in paper 1. The results presented in paper 6 shows that the formability of stainless steel (e.g. AISI 301), that in the cold rolled condition has a large martensite fraction, can be substantially increased by heating the bending zone. The heated area will then become austenitic and ductile before the roll forming. Thanks to the phenomenon of strain induced martensite formation, the steel will regain the martensite content and its strength during the subsequent plastic straining. Finally, a new tooling concept for profiles with variable cross-sections is presented in paper 7. The overall conclusions of the present work are that today, it is possible to successfully develop profiles of complex geometries (3D roll forming) in high strength steels and that finite element simulation can be a useful tool in the design of the roll forming process.

Acoustic emission study on corona discharge using FDTD model

This paper attempts to study the propagating characteristics of acoustic signals emitted from the breakdown of air using time domain numerical model. Acoustic emissions are produced by high voltage faults such as partial discharge and surface discharge. Study of such emissions has become popular among researchers because of the promising correlation between partial and surface discharges and its byproduct, acoustic signal emission. In this paper, propagation characteristics of acoustic signals are studied using finite difference time domain (FDTD) method. Multiple monitoring points are placed within a designated computation space at different distance away from a source.

Determination of lower-bound ductility for AZ31 magnesium alloy by use of the bulge specimens

Despite the high demand for industrial applications of magnesium, the forming technology for wrought magnesium alloys is not fully developed due to the limited ductility and high sensitivity to the processing parameters. The processing window for magnesium alloys could be significantly widened if the lower-bound ductility (LBD) for a range of stresses, temperature, and strain rates was known. LBD is the critical strain at the moment of fracture as a function of stress state and temperature. Measurements of LBD are normally performed by testing in a hyperbaric chamber, which is highly specialized, complex, and rare equipment. In this paper an alternative approach to determine LBD is demonstrated using wrought magnesium alloy AZ31 as an example. A series of compression tests of bulge specimens combined with finite element simulation of the tests were performed. The LBD diagram was then deduced by backward calculation.

Crushing modes of aluminium tubes under axial compression

A numerical study of the crushing of circular aluminium tubes with and without aluminium foam fillers has been carried out to investigate their buckling behaviours under axial compression. A crushing mode classification chart has been established for empty tubes. The influence of boundary conditions on crushing mode has also been investigated. The effect of foam filler on the crushing mode of tubes filled with foam was then examined. The predicted results would assist the design of crashworthy tube components with the preferred crushing mode with the maximum energy absorption.

Cracking and blowout in an aluminium high-pressure die casting die

Die cracking and metal blowout have been identified as problems in production of the structural sump, a high pressure die cast aluminium part, at Ford's Geelong manufacturing plant. Visual inspection, thermography and strain measurements have been performed and results are consistent with the view that cracking and blowout are caused by excessive stresses and deflections, respectively, generated by bending of the sliding cores. Models are being developed for finite element simulation of the stresses and deflections in the die during production, with a view to eliminating the aforementioned problems.

Casting yield improvement in graphite iron castings

A well designed runner and feeding system should produce castings with minimal defects and low pour weight. This thesis investigates how the filling regime and solidification of the mould influences defects in the castings produced from that mould. Design guidelines to reduce such defects are proposed and tested. An existing shrinkage fault in a Grey Iron disc brake casting is simulated using a commercial finite-difference computer program. Three criteria are used to predict the defect and the effect of changes to the feeder geometry. Critical Fraction Solidification analysis is used to determine whether the feeder remains in liquid contact with the casting during solidification and this approach is shown to correctly predict the presence or absence of porosity* The feeder block is extended below the ingate of the casting to improve liquid contact between the casting and feeder without significantly increasing the feeder mass. Plant trials confirm the change to the feeder eliminates the porosity defect. The runner system and mould venting for a thin walled Ductile Iron casting are investigated. Trials show that by setting the total mould vent area to be greater than the net ingate area of the castings, the cold-shut frequency is halved. A method for runner system design based on peak linear flow velocity in the runner during mould filling is proposed. A new pressurised runner system produces castings with significantly fewer defects and reduced pour weight when runner areas are designed to maintain peak velocity below 1 m/s. Peak velocity and magnesium levels are demonstrated to be critical factors in the elimination of cold-shut defects. A pressurised runner system is also shown to isolate inclusion defects from castings more effectively than an unpressurised system. From this work, a technique is proposed which allows the yield of an existing runner and feeder system for iron castings to be improved with confidence in the results.

Comparisons of seismic rock slope stability assessments between the Hoek-Brown and Mohr-Coulomb failure criteria

Current investigations have shown that earthquakes can trigger significant damages of equipment, property infrastructure and environment. This is a persistent cause of economic loss for any country, especially for the loss of life. The conventional method for slope stability design is to utilize limit equilibrium method (LEM) in conjunction with the pseudo-static (PS) approach. However, the LEM has a significant drawback which is to determine the slip surface before factor of safety calculation. The numerical upper and lower bound limit analysis method employed in this paper can avoid this limitation. In this study, the presented slope stability evaluations considering earthquake effects based on the finite difference method will be discussed and compared with the results from the numerical limit analysis methods.

A case study of ground response due to diaphragm wall installation

The purpose of this research is to investigate the ground response due to diaphragm wall construction using three-dimensional numerical modelling. In this study, the commercial finite difference method software, FLAC3D, and the finite element upper and lower bound limit analysis methods are employed. In addition, a range of factors are investigated. They include the dimensions of the single panel, overconsolidation ration (OCR), soil stiffness (E/su), and the height of the bentonite slurry. The solutions from the numerical upper bound limit analysis method are used for comparison purposes. The results obtained indicate that the above factors do have influence on ground response in terms of its stability and displacements. The discussion in the paper can be utilised as the reference for practical designs.

Design and analysis of a low actuation voltage electrowetting-on-dielectric device

This paper presents an Electrowetting-on-Dielectric (EWOD) device with optimized insulating layers operated by low actuation voltage. The device consists of an electrode array on a silicon substrate, covered by a dielectric layer and a hydrophobic layer. To characterize the performance of the device, simulations are performed for the dielectric layer of Sio₂ and the hydrophobic layer of Sio₂, Su-8 and Parylene C at different voltages. The volume finite difference approach of the Coventorware software was used to carry out the simulations. Two different molar of di-ionized water droplet were considered in the simulations. It was observed that the device having the Sio₂ dielectric layer and the Parylene C hydrophobic layer moved the 1M KCL (potassium chloride) droplet at the actuation voltage of 25V.

Using the solid-shell element to model the roll forming of large radii profiles

Roll forming is an incremental bending process for forming metal sheet, strip or coiled stock. Although Finite Element Analysis (FEA) is a standard tool for metal forming simulation, it is only now being increasingly used for the analysis of the roll forming process. This is because of the excessive computational time due to the long strip length and the multiple numbers of stands that have to be modelled. Typically a single solid element is used through the thickness of the sheet for roll forming simulations. Recent investigations have shown that residual stresses introduced during steel processing may affect the roll forming process and therefore need to be included in roll forming simulations. These residual stresses vary in intensity through the thickness and this cannot be accounted for by using only one solid element through the material thickness, in this work a solid-shell element with an arbitrary number of integration points has been used to simulate the roll forming process. The system modelled is that of roll forming a V-channel with dual phase DP780 sheet steel. In addition, the influence of other modelling parameters, such as friction, on CPU time is further investigated. The numerical results are compared to experimental data and a good correlation has been observed. Additionally the numerical results show that the CPU time is reduced in the model without friction and that considering friction does not have a significant effect on springback prediction in the numerical analysis of the roll forming process.

An application of the flexible multibody approach used to estimate human skeleton loading

Skeletal loading can be estimated using several approaches. The most common approach is based on utilizing mechanical principles and ground reaction forces as predictors for skeletal loading. This method can be considered as a relatively simple approach since it cannot account for muscle forces. Flexible multibody approach allows for estimating skeletal loading and strains within the bones; once bone flexibility, muscle forces, ground reaction forces and the natural motion of a subject have been accounted for. This paper presents a summary that describes how deformable bodies can be introduced to the standard multibody formulation and explains the benefits and drawbacks. As an example of application, models used to assess tibial strains among two subjects are presented. The results of the multibody simulations are compared to in vivo studies, showing acceptable correlation and method performance.

Análise dinâmica de vigas assimétricas em curva com parede fina e aberta submetidas a ação de carga móveis

Fundamentalmente, o presente trabalho faz uma análise elástica linear de pontes ou vigas curvas assimétricas de seção transversal aberta e de parede fina, com propriedades físicas, geométricas e raio de curvatura constantes ao longo do eixo baricêntrico. Para tanto, utilizaram-se as equações diferenciais de VLASOV considerando o acoplamento entre as deformações nas direções vertical, transversal, axial de torcão nal. Na solução do sistema de quatro equações com derivadas parciais foi utilizado um apropriado método numérico de integração (Diferenças Finitas Centrais). A análise divide-se, basicamente, em dois tipos: análise DINÂMICA e ESTATICA. Ambas são utilizadas também na determinação do coeficiente de impacto (C.M.D.). A primeira refere-se tanto na determinação das características dinâmicas básicas (frequências naturais e respectivos modos de vibração), como também na determinação da resposta dinâmica da viga, em tensões e deformações, para cargas móveis arbitrárias. Vigas com qualquer combinação das condições de contorno, incluindo bordos rotulados e engastados nas três direções de flexão e na torção, são consideradas. 0s resultados da análise teórica, obtidos pela aplicação de programas computacionais implementados em microcomputador (análise estática) e no computador B-6700 (análise dinâmica), são comparados tanto com os da bibliografia técnica como também com resultados experimentais, apresentando boa correlação.

Avaliação de métodos numéricos para precificação de derivativos: aplicação ao mercado brasileiro

Os objetivos deste trabalho foram (i) rever métodos numéricos para precificação de derivativos; e (ii) comparar os métodos assumindo que os preços de mercado refletem àqueles obtidos pela fórmula de Black Scholes para precificação de opções do tipo européia. Aplicamos estes métodos para precificar opções de compra da ações Telebrás. Os critérios de acurácia e de custo computacional foram utilizados para comparar os seguintes modelos binomial, Monte Carlo, e diferenças finitas. Os resultados indicam que o modelo binomial possui boa acurácia e custo baixo, seguido pelo Monte Carlo e diferenças finitas. Entretanto, o método Monte Carlo poderia ser usado quando o derivativo depende de mais de dois ativos-objetos. É recomendável usar o método de diferenças finitas quando se obtém uma equação diferencial parcial cuja solução é o valor do derivativo.