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<p>Metal forming processes have been widely applied in many industries. With the severe competition in the market, a reliable and robust metal forming process becomes crucial for the manufacturer to reduce product development time and cost. For the purpose of supplying engineers with an effective tool for a reliable and robust design of metal forming process, this research investigates the application of traditional reliability theory and robust design methods in metal forming processes for the ultimate goal of increasing quality and reducing cost in manufacturing.</p> <p> A method to assess the probability of failure of the process based on traditional reliability theory and the forming limit diagram (FLD) is presented. The forming limit of a material is chosen as the failure criteria for analysis of reliability.</p> <p> A study of prediction of forming limit diagrams using finite element simulation without pre-defined geometrical imperfection or material imperfection is presented. A 3D model of the dome test is used to predict the FLD for AA 5182-0. The FE predicted forming limit diagram is in good agreement with the experimental one. The uncertainty sources for the scatter of forming limits are categorized and investigated to see their effects on the shape of FLD.</p> <p>A novel method of improving the reliability of a forming process using the Taguchi method at the design stage is presented. The thickness-thinning ratio is chosen as the failure criteria for the reliability analysis of the process. A Taguchi orthogonal array is constructed to evaluate the effects of design parameters on the thinning ratio. A series of finite element simulations is conducted according to the established orthogonal array. Based on the simulation results, Taguchi S/N analysis and ANOVA analysis are applied to identify the optimal combination of design parameters for minimum thinning ratio, minimum variance of thinning ratio, and maximum expected process reliability.</p> <p> A multi-objective optimization approach is presented, which simultaneously maximizes the bulge ratio and minimizes the thinning ratio for a tube hydroforming process. Taguchi method and finite element simulations are used to eliminate the parameters insignificant to the process quality performance. The significant parameters are then optimized to achieve the multiple optimization objectives. The optimization problem is solved by using a goal attainment method. An illustrative case study shows the practicability of this approach and ease of use by product designers and process engineers.</p> / Thesis / Doctor of Philosophy (PhD)

<p>In sheet metal forming processes, friction has decisive effects on the strain distribution in the deformed sheets and the quality of the final product due to the large surface/thickness ratio of the blank sheets. It is well known that friction in sheet forming operations is dependent on local contact conditions such as surface roughness, contact pressure and sliding velocity. Adding complexity to this frictional behavior, some rolled sheets have oriented surface roughness and show considerable frictional anisotropy. A constant friction model without consideration of these relevant phenomena is regarded as the reason why sheet metal forming simulations often fail to produce satisfying results despite the well developed material models. </p> <p>To develop a friction model which considers both of the varying conditions of local contact and the frictional anisotropy was the aim of this thesis. For this purpose, the analysis method of the friction test (draw-bend test) had to be examined for the capability to evaluate these parameters independently. Through careful study using finite element simulations, it was found that the conventional method has shortcomings in addressing pressure dependent friction due to the pressure non-uniformity existing in the test. Therefore, a new analysis method, which can evaluate pressure dependency of a friction coefficient, was developed. In the new method, contact pressure maps obtained from simulations were included in the analysis of test data.</p> <p>The new analysis method was applied to friction measurement of aluminum sheets with known anisotropic mill finish, and friction coefficients were obtained as functions of contact pressure, sliding velocity and sliding direction. In the obtained friction model, a friction coefficient is a continuous surface over the domain of contact pressure and sliding velocity. Lastly, the new friction model was implemented into a finite element code and the model was validated through circular cup drawing experiments and simulations. The comparisons showed good agreements in the aspects of punch force, cup size and failure location. Thus, the newly developed model can accurately predict the effects of anisotropic friction in sheet metal forming processes. </p> / Thesis / Doctor of Philosophy (PhD)

O atrito na interface entre a peça e a ferramenta tem considerável importância em operações de estampagem de chapas, são necessários conhecimentos precisos sobre processos de conformação de chapas para a análise e projeto de novas peças e ferramentas, assim como para validação de uma simulação numérica. Este trabalho usa o método de determinação do coeficiente de atrito em estampagem através do ensaio de dobramento sob tensão e avalia sua precisão com o uso do software de elementos finitos LS-DYNAFORM, específico para esse processo de fabricação. Como existem seis equações que calculam o coeficiente de atrito para o mesmo ensaio de dobramento sob tensão, foram testadas todas as equações com o objetivo de verificar se existe variação entre os resultados. O material de estudo foi o alumínio comercialmente puro, liga AA1100. Os resultados indicam que há certa variação para cada equação usada, principalmente para aquelas que consideram o torque no pino. É observada também uma tendência do software a se distanciar dos resultados práticos por considerar o atrito como uma constante ao longo do processo. A pressão de contato entre o pino e a chapa no ensaio de dobramento sob tensão também foi avaliada através de um filme que tem a capacidade de registrar a pressão aplicada juntamente com a medição da força vertical aplicada ao pino. Os resultados indicam que a força vertical é mais precisa para se definir a pressão de contato ao uso de equações pré-estabelecidas e que a área de atuação da chapa no pino é sempre menor que a área calculada geometricamente. Por fim, para se saber qual é o comportamento do atrito para altas pressões, o ensaio de dobramento sob tensão foi feito com força variável e constatou-se que o atrito diminui com o aumento das pressões. No entanto, os valores iniciais da curva de atrito versus pressão de contato não foram obtidos pois nesse caso seria necessário usar uma máquina diferente da usada nesse estudo, ou seja, que não use pressão de óleo para acionamento e movimentação da chapa. / Friction at the interface of workpiece and tooling has a considerably importance in sheet metal forming operations. It is necessary an accurate knowledge for the analysis and design of new workpieces and tooling, as well as for the validation of a numeric simulation. This work uses the bending under tension test to determining the friction coefficient in sheet metal forming and evaluates its accuracy using the finite element software LS-DYNAFORM, specific to this manufacturing process. Since there are six equations that calculate the coefficient of friction for the same bending under tension test, all equations were tested in order to verify if there is much variation between the results. The material used in these work was pure commercial aluminum alloy AA1100. The results indicate that there is some variation for each equation used, especially for those that consider the torque on the pin. It was also observed a tendency for software to distance themselves from practical results considering friction as a constant throughout the process. It is also observed a tendency for the software to generate curves away from the tests as the friction increases. The contact pressure between the pin and the sheet in the bending under tension test was also evaluated through a film that has the ability to measure the pressure applied, together with the measurement of the vertical force applied to the pin. The results indicate that the vertical force is more accurate to define the contact pressure than equations previously established for this and that the contact area between the sheet and the pin is always smaller than the area calculated geometrically. Finally, to know the behavior of the friction at high pressures, the bending under tension test was done with variable forces and it was found that the friction decreases with increasing the pressure, which is in full agreement with the theory.

O atrito na interface entre a peça e a ferramenta tem considerável importância em operações de estampagem de chapas, são necessários conhecimentos precisos sobre processos de conformação de chapas para a análise e projeto de novas peças e ferramentas, assim como para validação de uma simulação numérica. Este trabalho usa o método de determinação do coeficiente de atrito em estampagem através do ensaio de dobramento sob tensão e avalia sua precisão com o uso do software de elementos finitos LS-DYNAFORM, específico para esse processo de fabricação. Como existem seis equações que calculam o coeficiente de atrito para o mesmo ensaio de dobramento sob tensão, foram testadas todas as equações com o objetivo de verificar se existe variação entre os resultados. O material de estudo foi o alumínio comercialmente puro, liga AA1100. Os resultados indicam que há certa variação para cada equação usada, principalmente para aquelas que consideram o torque no pino. É observada também uma tendência do software a se distanciar dos resultados práticos por considerar o atrito como uma constante ao longo do processo. A pressão de contato entre o pino e a chapa no ensaio de dobramento sob tensão também foi avaliada através de um filme que tem a capacidade de registrar a pressão aplicada juntamente com a medição da força vertical aplicada ao pino. Os resultados indicam que a força vertical é mais precisa para se definir a pressão de contato ao uso de equações pré-estabelecidas e que a área de atuação da chapa no pino é sempre menor que a área calculada geometricamente. Por fim, para se saber qual é o comportamento do atrito para altas pressões, o ensaio de dobramento sob tensão foi feito com força variável e constatou-se que o atrito diminui com o aumento das pressões. No entanto, os valores iniciais da curva de atrito versus pressão de contato não foram obtidos pois nesse caso seria necessário usar uma máquina diferente da usada nesse estudo, ou seja, que não use pressão de óleo para acionamento e movimentação da chapa. / Friction at the interface of workpiece and tooling has a considerably importance in sheet metal forming operations. It is necessary an accurate knowledge for the analysis and design of new workpieces and tooling, as well as for the validation of a numeric simulation. This work uses the bending under tension test to determining the friction coefficient in sheet metal forming and evaluates its accuracy using the finite element software LS-DYNAFORM, specific to this manufacturing process. Since there are six equations that calculate the coefficient of friction for the same bending under tension test, all equations were tested in order to verify if there is much variation between the results. The material used in these work was pure commercial aluminum alloy AA1100. The results indicate that there is some variation for each equation used, especially for those that consider the torque on the pin. It was also observed a tendency for software to distance themselves from practical results considering friction as a constant throughout the process. It is also observed a tendency for the software to generate curves away from the tests as the friction increases. The contact pressure between the pin and the sheet in the bending under tension test was also evaluated through a film that has the ability to measure the pressure applied, together with the measurement of the vertical force applied to the pin. The results indicate that the vertical force is more accurate to define the contact pressure than equations previously established for this and that the contact area between the sheet and the pin is always smaller than the area calculated geometrically. Finally, to know the behavior of the friction at high pressures, the bending under tension test was done with variable forces and it was found that the friction decreases with increasing the pressure, which is in full agreement with the theory.

O atrito na interface entre a peça e a ferramenta tem considerável importância em operações de estampagem de chapas, são necessários conhecimentos precisos sobre processos de conformação de chapas para a análise e projeto de novas peças e ferramentas, assim como para validação de uma simulação numérica. Este trabalho usa o método de determinação do coeficiente de atrito em estampagem através do ensaio de dobramento sob tensão e avalia sua precisão com o uso do software de elementos finitos LS-DYNAFORM, específico para esse processo de fabricação. Como existem seis equações que calculam o coeficiente de atrito para o mesmo ensaio de dobramento sob tensão, foram testadas todas as equações com o objetivo de verificar se existe variação entre os resultados. O material de estudo foi o alumínio comercialmente puro, liga AA1100. Os resultados indicam que há certa variação para cada equação usada, principalmente para aquelas que consideram o torque no pino. É observada também uma tendência do software a se distanciar dos resultados práticos por considerar o atrito como uma constante ao longo do processo. A pressão de contato entre o pino e a chapa no ensaio de dobramento sob tensão também foi avaliada através de um filme que tem a capacidade de registrar a pressão aplicada juntamente com a medição da força vertical aplicada ao pino. Os resultados indicam que a força vertical é mais precisa para se definir a pressão de contato ao uso de equações pré-estabelecidas e que a área de atuação da chapa no pino é sempre menor que a área calculada geometricamente. Por fim, para se saber qual é o comportamento do atrito para altas pressões, o ensaio de dobramento sob tensão foi feito com força variável e constatou-se que o atrito diminui com o aumento das pressões. No entanto, os valores iniciais da curva de atrito versus pressão de contato não foram obtidos pois nesse caso seria necessário usar uma máquina diferente da usada nesse estudo, ou seja, que não use pressão de óleo para acionamento e movimentação da chapa. / Friction at the interface of workpiece and tooling has a considerably importance in sheet metal forming operations. It is necessary an accurate knowledge for the analysis and design of new workpieces and tooling, as well as for the validation of a numeric simulation. This work uses the bending under tension test to determining the friction coefficient in sheet metal forming and evaluates its accuracy using the finite element software LS-DYNAFORM, specific to this manufacturing process. Since there are six equations that calculate the coefficient of friction for the same bending under tension test, all equations were tested in order to verify if there is much variation between the results. The material used in these work was pure commercial aluminum alloy AA1100. The results indicate that there is some variation for each equation used, especially for those that consider the torque on the pin. It was also observed a tendency for software to distance themselves from practical results considering friction as a constant throughout the process. It is also observed a tendency for the software to generate curves away from the tests as the friction increases. The contact pressure between the pin and the sheet in the bending under tension test was also evaluated through a film that has the ability to measure the pressure applied, together with the measurement of the vertical force applied to the pin. The results indicate that the vertical force is more accurate to define the contact pressure than equations previously established for this and that the contact area between the sheet and the pin is always smaller than the area calculated geometrically. Finally, to know the behavior of the friction at high pressures, the bending under tension test was done with variable forces and it was found that the friction decreases with increasing the pressure, which is in full agreement with the theory.

<p dir="ltr">This study investigated the effects of single-stage and multi-stage (two, three, or four) mandrel cold-forming processes on stainless steel U-shaped, thin-walled profiles, with a particular focus on their impact on stress. These profiles, commonly used as metal expansion joints (also known as compensators or bellows), are essential components in industries such as aerospace, energy, and piping systems. The need for these joints to absorb thermal expansion and mechanical movement while maintaining structural integrity makes precise forming processes critical. In particular, the investigation examined the effects of incrementally increasing the number of forming stages, from one to four, on profile geometry, with particular emphasis on thickness variation, consistency, and stress distribution. Profile geometry and thickness were assessed using three-dimensional scanning, a coordinate measuring machine, and ultrasonic thickness measuring techniques. While these methods have limitations, they provide valuable insights into the formed profiles. Increasing the number of forming stages up to four reduced thickness variation by up to 5%, producing profiles that were more closely aligned with the theoretical design specifications. Stress, a crucial factor in the long-term performance of metal expansion joints, was also reduced by increasing the number of forming stages by up to 6% with four stages. Further reductions in stress and thickness variation could be achieved with more than four stages, though the improvements became less significant. A formula was developed to determine the minimum number of forming stages (N_min) required for thin-walled U-profiles. Depending on the application, additional stages beyond N_min improved profile accuracy and further reduced stress, offering manufacturers flexibility in meeting performance requirements.</p>