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Incremental sheet forming (ISF) is a novel metal shaping technology that is economically viable for low-volume manufacturing, customisation and rapid-prototyping. It uses a small tool that is controlled by a computer-numerically controlled sequence and the path taken by this tool over the sheet defines the product geometry. Little is currently known about how to design the tool-path to minimise geometric errors in the formed part. The work here addresses this problem by developing a model based tool-path optimisation scheme for ISF. The key issue is how to generate an efficient model for ISF to use within a path optimisation routine, since current simulation methods are too slow. A proportion of this thesis is dedicated to evaluating the applicability of the rigid plastic assumption for this purpose. Three numerical models have been produced: one based on small strain deformation, one based on limit analysis theory and another that approximates the sheet to a network of rods. All three models are formulated and solved as second-order cone programs (SOCP) and the limit analysis based model is the first demonstration of an upper-bound shell finite element (FE) problem solved as an SOCP. The models are significantly faster than commercially available FE software and simulations are compared with experimental and numerical data, from which it is shown the rigid plastic assumption is suitable for modelling deformation in ISF. The numerical models are still too slow for the path optimisation scheme, so a novel linearised model based on the concept of spatial impulse responses is also formulated and used in an optimal control based tool-path optimisation scheme for producing axisymmetric products with ISF. Off-line and on-line versions of the scheme are implemented on an ISF machine and it is shown that geometric errors are significantly reduced when using the proposed method. This work provides a new structured framework for tool-path design in ISF and it is also a novel use of feedback to compensate for geometrical errors in ISF.

COMPUTER AIDED MODELING OF WRINKLING AND ITS PREVENTION PiSKiN, Mehmet Ali M.S., Department of Mechanical Engineering Supervisor: Prof. Dr. Bilgin KAFTANOgLU September 2005, 111 Pages Deep-drawing operations are performed widely in industrial applications. It is very important for efficiency to achieve parts with no defects. Wrinkling is a kind of defect caused by stresses in the flange part of the blank during metal forming operations. It is required that the flange of a workpiece in deep drawing operation should deform in its plane without wrinkling otherwise it will impair the quality of the product. To avoid wrinkling appropriate blank-holder force or drawbead can be applied. In this work, finite element method is used to obtain the wrinkling behavior. A four nodded five degree of freedom shell element is formulated. Isotropic elasto-plastic material model with Von Mises yield criterion is used. By using this shell element, the developed code can predict the bending behavior of workpiece besides membrane behavior. Simulations are carried out with four different element sizes and two different shapes (circular and rectangular). The thickness strain and nodal displacement values obtained are compared with results of a commercial finite element program and results of previously conducted experiments.

Sheet metal forming is used in a wide range of industrial processes ranging from tube manufacturing to automobile and aviation industry. It includes processes like stamping, bending, stretching, drawing and wheeling. In the past few years materials for sheet metal forming and, technology have improved a lot. The improved materials have higher strength and more ductility than conventional sheet steel and therefore they have to be worked differently. For such steels conventional methods can not be applied totally. So there is a need for constant improvement in technology. Trial and error method currently in use increases lead time and is not economic also. To overcome the problems, use of simulation software in metal forming processes has increased significantly. The rapid development of software technology accompanied with lower cost computer hardware have enabled many manufacturing operations to be modeled cost-effectively that only a few years ago would have been considered impractical. However there are some difficulties in simulation of sheet metal forming process. For example it is never an easy task to select the correct software for a particular process. Various authors ascribe different causes for the difficulties. Among them the prominent ones are lacunae in elasto-plastic modeling, material behaviour, involved complexities and a lack of good elements. Apart from that the demands of sheet metal processes are increasing both with respect to the tolerance requirements of the finished part and with regard to geometric complexity of the part to be formed. A few years ago finite elements have been developed using Papcovitch-Neuber solutions of the Navier equation for the displacement function. Among these elements PN5X1 has the abilities to predict both displacements and stresses accurately. And recently the element is extended to include material nonlinearity and is working well for the small deformation range. To use this element for sheet metal forming it is necessary that the element should predict correct results for large deformations. In the present work we have further extended this element for large displacements and large rotation. In the literature there are various algorithms recommended for use with large deformation. Among them we have selected a suitable algorithm and verified its usefulness. First we have taken a simple truss and applied loads to cause large deflection. We observe adequate convergence with the chosen algorithm and then we extend it to PN5X1. in large deformation analysis, equilibrium is computed about the deformed shape. In the chosen algorithm we apply incremental loading and within each load step loop we iterate for equilibrium. We ensure error free solution (equilibrium) before additional loading is introduced. With the help of flowchart these processes have been depicted. A computer program in C, based on the above incremental method and equilibrium check has been written. For the purpose of verification of the program, we have solved some benchmark tests. We start with linear cases and then attempt a number of geometric nonlinear problems like- cantilever subjected to end shear, pinched cylinder with open end etc. We have also included the classical benchmark problem of the cantilever subjected to end moment. The present algorithm gives solutions which are in excellent agreement with those reported in the literature. Finally, we look at some aspects of the problem which require further investigation.

<p>Abstract</p><p>Today sheet metal forming is used to make a variety of mass production because it has a high production rate. One of the biggest concerns in sheet metal forming is wear of the tool in form of galling. Galling in sheet metal forming is characterised by an increased tool surface roughness, unstable friction in the forming process and undesirable scratches on the final products.</p><p>Several ways of ranking materials resistance to galling exist today but only ASM G98 is standardised. Nevertheless, some different methods developed for ranking tool materials’ tendency to galling have also been developed.</p><p>The aim of this thesis is to develop and improve the Uddeholm Tooling Tribo Test rig located at Uddeholm Tooling AB. The rig, which is a variation of cylinder-on-cylinder test equipment, was improved with a new tool holder, a utilization of the real sheet material counter face and a new data acquisition system and software. The galling was detected using scratches on the sheet, metallographic analysis of the material adhered on the tool specimen, monitoring of coefficient of friction and the standard deviation of the coefficient of friction.</p><p>The obtained results show difficulties with ranking of tool materials in terms of galling resistance under non-lubricated conditions. The tool steels tested were SVERKER21 and UNIMAX. AISI304-10, DC04 and DOCOL1000DP sheets were used. Additionally a low friction coating of BalinitC on SVERKER21 was also included. All specimens of the tool steels showed signs of galling on every run, only the low friction coating showed a transition in behaviour of friction coefficient corresponding to galling initiation. The standard deviation of the coefficient of friction increased at low loads. A decrease of the test loads led to stability loss of the system detected by an increase in the standard deviation of the coefficient of friction. This might happen because the Kistler platform is originally designed for larger loads. Although, the test rig does not work properly in its present state, the concept looks promising.</p>

Os Aços Avançados de Alta Resistência ou AHSS (do inglês Advanced High Strength Steels) apresentam muitas vantagens mecânicas em relação aos aços convencionais. Seu uso crescente na indústria automotiva deve-se principalmente à sua capacidade de possibilitar a redução de peso e, ao mesmo tempo, o aumento da segurança aos ocupantes do veículo em caso de colisões. No entanto, apresentam maiores dificuldades no que se refere à conformabilidade (maiores níveis de solicitação e desgaste das ferramentas, menor deformabilidade plástica, etc). Assim, alguns testes para avaliar a conformabilidade destes materiais ganham maior importância. É o caso do Teste de Expansão de Furos, cuja propriedade medida é a Razão de Expansão de Furos (REF). Neste trabalho investiga-se o processo de expansão de furos para o aço avançado de alta resistência (AHSS) martensítico DOCOL 190M, sob as seguintes condições de processo: duas formas de obtenção do furo (jato d’água e usinagem); duas geometrias distintas de punções (cônico de 60º e elíptico); diversos diâmetros do furo inicial; com e sem o uso de lubrificante; com acabamento diferenciado da borda do furo; e expansão com deslocamento do punção em etapas. Os experimentos demonstram que a expansão de furos possui uma estreita relação com a geometria do punção utilizado para a expansão, bem como com o diâmetro do furo inicial, acabamento da borda e condições de lubrificação. A partir dos resultados experimentais de expansão de furos foi possível realizar a calibração de um software de simulação computacional em relação ao dano crítico do material no momento da fatura na borda do furo. / Advanced High Strength Steels (AHSS) offer many mechanical advantages over conventional steels. Its increasing use in the automotive industry is mainly due to its ability to reduce weight and, at the same time, increase occupant safety in the event of collisions. However, they present greater difficulties with respect to the formability (higher levels of solicitation and wear of the tools, lower plastic formability, etc). Thus, some tests to evaluate the formability of these materials come to have greater importance. This is the case of the Hole Expansion Test, whose measured property is the Hole Expansion Ratio (REF). This work investigates the hole expansion process for a martensitic advanced high-strength steel (AHSS), DOCOL 190M, under the following process conditions: two ways of obtaining the hole (water jet and machining); two different geometries of punctures (conical of 60º and elliptical); various diameters of the initial hole; with and without the use of lubricant; with differentiated finishing of the hole edge; and expansion with punch displacement in steps. The experiments demonstrate that the hole expansion has a close relationship with the geometry of the punch used for the expansion, as well as the initial hole diameter, edge finish and lubrication conditions. From the experimental hole expansion results it was possible to carry out the calibration of a computational simulation software in relation to the critical damage of the material at the moment of hole edge rupture.

O presente trabalho tem por finalidade apresentar e discutir os resultados encontrados para o coeficiente de atrito de três tipos de diferentes chapas utilizadas em processos de estampagem na indústria automotiva. O método adotado para determinação do coeficiente de atrito foi o dobramento sob tensão, método este que tem por finalidade simular as condições de uma operação de embutimento. Os resultados apresentados demonstram que diferentes chapas em aço NBR 5915 EM e EMS ME 1508 EM, com ou sem proteção galvânica, apresentam diferentes condições tribológicas determinadas através do ensaio. Coeficientes de atrito que variam desde 0,103 até 0,151 foram determinados, considerando condições de lubrificação e de ferramenta constantes. A influência do coeficiente de atrito no processo é exemplificada através do cálculo da força máxima de estampagem, sendo que para as mesmas condições de propriedades mecânicas a variação do coeficiente de atrito provocou um aumento de 7,6% na força máxima. Através do cálculo determinou-se também a influência do coeficiente de atrito nas forças de atrito do processo. Para as condições apresentadas, a influência do coeficiente de atrito no prensa chapas na força máxima de estampagem é 20x menor em relação à influência do coeficiente de atrito no raio da matriz. / This research aims to show and discuss the friction coefficient of three different kinds of sheet metal used in sheet metal forming processes of automotive industry. The methodology for the determination of the coefficient of friction was the bending under tension, that purpose to simulate the deep drawing conditions. The results show different kinds of sheets metals, as NBR 5915 EM and EMS ME 1508 EM, with or not galvanized protection, show different tribological conditions by the tests. Friction coefficients from 0,103 to 0,151 were founded, considering invariable lubrication and tool conditions. The influence of friction coefficient in the stamping process is exemplified by the maximum stamping strength. For these tests conditions, the coefficient of friction caused an increase of 7.6% in the maximum stamping strength. The influence of the friction coefficient on the friction strengths of the process was determined. For these conditions, the influence of the friction coefficient in the friction strength of the blank holder is 20x smaller than in the friction strength of die's radius.

Este trabalho apresenta um estudo sobre o processo de Estampagem Incremental de Chapas, em Latão C-268 de diferentes espessuras (s0: 0.50, 0.70 e 1.00 mm), motivado pela inobservância de pesquisas desta matéria prima neste processo de conformação de chapas. Atualmente, este material tem grande aplicação na confecção de utensílios domésticos (baixelas, travessas, etc) e ferragens para construção civil (espelhos, cubas, etc), instrumentos musicais de sopro e núcleos de radiadores automotivos, tendo assim, um amplo campo de aplicação industrial, e potencial para as aplicações do processo de Estampagem Incremental de Chapas. A pesquisa está pautada na caracterização das matérias primas, para a obtenção de dados como as Curvas de Escoamento, Índices de Anisotropia (r), Curvas Limite de Conformação (CLC) e em experimentos de Estampagem Incremental de Chapas, realizados em uma máquina dedicada a este processo de conformação. Para a realização dos experimentos, foram utilizados Incrementos Verticais com diferentes valores (∆Z: 0.10, 0.50 e 1.00 mm), assim como duas ferramentas de estampagem (DT: Ø10 e Ø15 mm). Foram aplicadas duas formas geométricas diferentes: Tronco de Cone e Tronco de Pirâmide, ambos com perfil radial das paredes verticais. Ao todo, foram realizados 15 experimentos diferentes na modalidade SPIF. Os experimentos foram realizados em uma máquina dedicada ao processo, capaz da aquisição dos valores de Força (FX, FY e FZ) durante a realização dos testes. Com a realização dos experimentos SPIF, foi possível a elaboração da Linha Limite de Fratura – LFC da chapa latão C-268 nas três espessuras investigadas, onde os resultados apontam para valores maiores de deformação verdadeira (1 vs 2), quando comparados aos valores da CLC. Adicionalmente, a LFC das três espessuras de chapas analisadas, apontam os valores das maiores deformações verdadeiras (1) muito próximos, evidenciando neste caso que a diminuição do Incremento Vertical (∆Z) é mais relevante para a estampagem do que o aumento da espessura da chapa. As geometrias Tronco de Cone e Tronco de Pirâmide apresentaram discrepâncias geométricas toleráveis em relação ao perfil projetado, mas diferentes entre si, influenciados pelo retorno elástico diferente de cada geometria. Entretanto, suas fraturas apresentaram o mesmo comportamento, propagação no sentido meridional. Os experimentos SPIF realizados com a ferramenta de estampagem com Ø10mm proporcionaram as maiores profundidades. A medição da espessura final (s1) próximas as regiões fraturadas, comprovou os valores medidos não ultrapassaram os respectivos valores resultantes da expressão matemática Lei do Seno, e ainda, que quanto menor a espessura inicial (s0) da chapa, menor a variação dos valores medidos e calculados. A análise das Forças (FX, FY e FZ) resultantes do processo SPIF mostram que quanto maior o Incremento Vertical (∆Z), maior a espessura inicial (s0) da chapa, e maior do diâmetro (DT) da ferramenta de estampagem, maiores serão as Forças necessárias no SPIF. Adicionalmente, foi possível determinar os valores de Atrito (µ), obtidos em função das Forças (FX, FY e FZ) do processo SPIF. / This paper presents a study of the Incremental Sheet Forming process, in Brass C-268 of different thicknesses (s0: 0.50, 0.70 and 1.00 mm), motivated by non-observance of research of this raw material in this sheet forming process. Currently, this material has great application in the manufacture of household items (plates, platters, etc.) and hardware for building (locks, vats, etc.), wind musical instruments and automotive radiator cores, having thus, a large industrial application field, and potential for the applications of the Incremental Sheet Forming process. The research is based on the characterization of raw materials, to obtain data such as Flow Curves, Anisotropy Indices (r), Forming Limit Curve and in Incremental Sheet Forming experiments, performed on a machine dedicated to this forming process. For the realization of the experiments, Vertical Increments with different values were used (∆Z: 0.10, 0.50 e 1.00 mm), As well as two forming tools (DT: Ø10 e Ø15 mm). Two different geometric forms were applied: Cone Frustum and Pyramid Frustum, both with radial profile of vertical walls. In all, 15 different SPIF experiments were performed. The experiments were carried out in a machine dedicated to the process, able to acquire the values of Force (FX, FY e FZ) during the tests. With the realization of SPIF experiments, it was possible to elaborate the Fracture Forming Line – FFL of Brass C-268 sheet, In the three thicknesses investigated, Where the results indicate higher values of true strain (1 vs 2), when compared to the FLC values. Additionally, the FFL of the three sheet thicknesses analyzed, indicate the values of the highest true deformations (1) very close, evidencing in this case, that the decrease of Vertical Increment (∆Z) is more relevant for the forming than the increase in sheet thickness. The Cone Frustum and Pyramid Frustum geometries presented tolerable geometric discrepancies in relation to the projected profile, more different from each other, influenced by different springback of each geometry. However, their fractures presented the same behavior, meridional direction propagation. The SPIF experiments performed with the forming tool with Ø10mm provided the greatest depths. The final thickness (s1) measurement near the fractured regions, proved the measured values did not exceed the respective values resulting from the mathematical expression Sine Law, and also, that the lower the initial thickness (s0) of sheet, lower the variation of the measured and calculated values. Analysis of Forces (FX, FY e FZ) resulting from the SPIF process, show that the larger the Vertical Increment (∆Z), larger the initial thickness (s0) of the sheet, and larger diameter (DT) of the forming tool, larger will be the necessary forces in SPIF. In addition, it was possible to determine the values of Friction (µ), obtained in function of the SPIF Forces (FX, FY e FZ).

Este trabalho é definido a partir da elaboração de uma metodologia de cálculo para a determinação da evolução dos parâmetros de anisotropia em chapas metálicas e na definição de uma nova superfície de escoamento anisotrópica. A metodologia proposta é fundamentada nas relações incrementais entre tensão e deformação da teoria clássica da plasticidade utilizando-se do critério de escoamento de Hill e baseado em um estado particular de tensão-deformação comum em processos de conformação mecânica, principalmente em regiões da peça onde ocorram dobras. A nova superfície de escoamento é definida a partir da superfície de Hill original, porém ponderada por um fator de correção o qual contempla uma evolução anisotrópica do encruamento. Este fator de correção é definido em função dos parâmetros evolutivos de anisotropia determinados pela metodologia proposta e um conceito particular é então adotado para a complementação deste novo modelo de superfície de escoamento. A contribuição científica apresentada estabelece o desenvolvimento do conjunto de equações que permite determinar a evolução dos parâmetros de anisotropia com o carregamento plástico e adicionalmente permite avaliar a evolução de nova superfície servindo como indicativo da formabilidade do material. Os resultados teóricos são comparados e discutidos com evoluções obtidas via ensaio normalizado de anisotropia. Além disso é realizada a aplicação do procedimento proposto em conjunto com análises numéricas via método dos elementos finitos para dois casos de processos de conformação. Desta forma tem-se uma contribuição para a representação do fenômeno de anisotropia plástica dado por um modelo evolutivo, cuja aplicação tem interesse em aprimoramento de algoritmos computacionais bem como em aplicações de cunho experimental como validações, predições e aprimoramentos de processos de conformação e outros. / This work is aimed to the elaboration of a new approach for prediction of anisotropy parameters evolution in sheet metal as well as definition of a new anisotropic yield surface. This approach is based on incremental relation between stress and strain from classical plasticity theory by using the Hill-48 yield criteria. Also, it is based on a particular stress-strain state, common to bending regions found in several sheet forming processes. The new yield surface is derived from the original Hill criteria, which was modified by a correcting factor proposed to represent an anisotropic evolution of the continuing plastic loading. This factor is a strict function of the evolutive anisotropy parameters generated by the present methodology. From this point, is adopted a special concept in order to reach a complete definition of the new model for yield surfaces. The scientific contribution presents the development of a set of equations in order to predict the evolution of the anisotropy parameters as function of plastic loading, and additionally, it is taken this new yield surface as an evaluation of material formability degree. The theoretical results are discussed and compared with results obtained from standardized anisotropy tests. Besides, the proposed procedure is applied, aided by numerical analysis using the finite element method to simulate two cases of sheet forming processes. Therefore it is presented a contribution to the representation of plastic anisotropy phenomenon using an evolutive model. The main interests for practical application of this work range from improvement of computational algorithms as well as experimental tests investigations, which are related to validation of this model, prediction and improvement of sheet metal forming processes.

Nowadays FE-simulations for sheet metal forming process are used to reduce the tryout phase in automotive industries. But the complex forming simulation processes are very challenging. One of the challenges is to create an FE-model which can be used to analyze the effects of cushion motion on the forming process. This thesis is focused on creating an FE model for two dies single cushion sheet metal forming press which can be used to analyze the effects of cushion motion on the contact pressure between the stamping tools and blanks. Using LS-PrePost a model with rigid stamping tools and cushion was created where the two blanks were of different thicknesses. After the model creation LS-DYNA was used for the simulations. The results showed that the cushion is moving in all DOFs and due to this movements, uneven contact pressure distribution is seen on the blanks and stamping tools.