Tube bending is a widely used manufacturing process in the aerospace, automotive, and other industries. During tube bending, considerable in-plane distortion and thickness variation occurs. The thickness increases at the intrados (surface of tube in contact with the die) and it reduces at the extrados (outer surface of the tube). In some cases, when the bend die radius is small, wrinkling occurs at the intrados. In industry a mandrel is used to eliminate wrinkling and reduce distortion. However, in the case of a close bend die radius, use of a mandrel should be avoided as bending with the mandrel increases the thinning of the wall at the extrados, which is undesirable in the manufacturing operation. The present research focuses on additional loadings such as axial force and internal pressure which can be used to achieve better shape control and thickness distribution of the tube. Based on plasticity theories, an analytical model is developed to predict cross section distortion and thickness change of tubes under various loading conditions. Results from both the FEA and analytical model indicated that at the intrados the increase in thickness for bending with internal pressure and bending with combined axial pull and internal pressure was nearly the same. But in the case of bending with the combination of axial pull and internal pressure there was a significant reduction of thickness at the extrados. A parametric study was conducted for the case of bending with combined internal pressure and axial pull and it was seen that with proper selection of the pressure and axial pull wrinkling can be eliminated, thickness distribution around the tube can be optimized, and cross section distortion of the tube can be reduced. Predictions of the analytical model are in good agreement with finite element simulations and published experimental results. The model can be used to evaluate tooling and process design in tube bending.

Tube bending is a widely used manufacturing process in the aerospace, automotive, and other industries. During tube bending, considerable in-plane distortion and thickness variation occurs. The thickness increases at the intrados (surface of tube in contact with the die) and it reduces at the extrados (outer surface of the tube). In some cases, when the bend die radius is small, wrinkling occurs at the intrados. In industry a mandrel is used to eliminate wrinkling and reduce distortion. However, in the case of a close bend die radius, use of a mandrel should be avoided as bending with the mandrel increases the thinning of the wall at the extrados, which is undesirable in the manufacturing operation. The present research focuses on additional loadings such as axial force and internal pressure which can be used to achieve better shape control and thickness distribution of the tube. Based on plasticity theories, an analytical model is developed to predict cross section distortion and thickness change of tubes under various loading conditions. Results from both the FEA and analytical model indicated that at the intrados the increase in thickness for bending with internal pressure and bending with combined axial pull and internal pressure was nearly the same. But in the case of bending with the combination of axial pull and internal pressure there was a significant reduction of thickness at the extrados. A parametric study was conducted for the case of bending with combined internal pressure and axial pull and it was seen that with proper selection of the pressure and axial pull wrinkling can be eliminated, thickness distribution around the tube can be optimized, and cross section distortion of the tube can be reduced. Predictions of the analytical model are in good agreement with finite element simulations and published experimental results. The model can be used to evaluate tooling and process design in tube bending.

Cascas cilíndricas circulares com uma pequena variação de espessura ao longo de seu comprimento, quando submetidas à rotação, apresentam em alguns casos, deslocamentos elásticos de sua superfície externa, tendendo a uma forma de um oval. O objetivo deste trabalho é estabelecer a relação entre a variação de espessura das cascas cilíndricas com a sua deformação devida às forças centrífugas medida durante a rotação utilizando-se dois enfoques, um experimental e outro numérico, no caso o método de elementos finitos (MEF). As cascas cilíndricas estudadas tiveram sua espessura de parede medidas por meio de aparelho de ultra-som, mas por serem fabricadas em ferro fundido cinzento, as suas lamelas de grafita atuam como refletores, o que torna a medição imprecisa. Os resultados da análise numérica encontrados se relacionam bem com os experimentais de maneira qualitativa, mas divergem na forma quantitativa. Modelos de cascas com variação de espessura imposta também foram criados e analisados usando-se o método de elementos finitos de forma a se avaliar o comportamento da casca cilíndrica sob diversas configurações de distribuição da variação da espessura. Sugere-se a pesquisa de novas tecnologias para medições por ultra-som de peças fabricadas de ferro fundido com grafita lamelar. Neste trabalho, a medição da forma oval foi feita utilizando-se sensores de proximidade do tipo \"eddy-current\". / Circular cylindrical shells with small thickness variations along their body, when submitted to rotation, present, in some cases, elastic displacements of their outside surface induced by centrifugal forces leading to final oval like shapes. The main purpose of this study is to establish relationships between thickness variation of the cylindrical shells with their measured deformation during the rotation, due to centrifugal forces, using two approaches, one experimental and the other one numerical, in the latter case the finite element method (FEM). The studied cylindrical shells had their wall thickness measured by means of an ultrasound device. The used material is flake graphite cast iron (gray cast iron). The graphite flakes act as reflectors, what makes such measurements imprecise. The numerical results found are satisfactory in a qualitative way, but they disagree in the quantitative form. Shell models with theoretical imperfections also were created and analyzed using the finite element method in order to evaluate the behavior of the cylindrical shell under several configurations of distribution of the shell thickness variation. Further research is necessary on new technologies to measure the thickness of pieces manufactured of flake graphite cast iron. In this research, the oval shape measurements were done by means of eddy-current proximity sensors.

Over the past decade vehicle judder caused by Disc Thickness Variation (DTV) has become of major concern to automobile manufacturers worldwide. Judder is usually perceived by the driver as minor to severe vibrations transferred through the chassis during braking [1-9]. In this research, DTV is investigated via the use of a Smart Brake Pad (SBP). The SBP is a tool that will enable engineers to better understand the processes which occur in the harsh and confined environment that exists between the brake pad and disc whilst braking. It is also a tool that will enable engineers to better understand the causes of DTV and stick-slip the initiators of low and high frequency vibration in motor vehicle brakes. Furthermore, the technology can equally be used to solve many other still remaining mysteries in automotive, aerospace, rail or anywhere where two surfaces may come in contact. The SBP consists of sensors embedded into an automotive brake pad enabling it to measure pressure between the brake pad and disc whilst braking. The two sensor technologies investigated were Thick Film (TF) and Fibre Optic (FO) technologies. Each type was tested individually using a Material Testing System (MTS) at room and elevated temperatures. The chosen SBP was then successfully tested in simulated driving conditions. A preliminary mathematical model was developed and tested for the TF sensor and a novel Finite Element Analysis (FEA) model for the FO sensor. A new method called the Total Expected Error (TEE) method was also developed to simplify the sensor specification process to ensure consistent comparisons are made between sensors. Most importantly, our achievement will lead to improved comfort levels for the motorist.

Cascas cilíndricas circulares com uma pequena variação de espessura ao longo de seu comprimento, quando submetidas à rotação, apresentam em alguns casos, deslocamentos elásticos de sua superfície externa, tendendo a uma forma de um oval. O objetivo deste trabalho é estabelecer a relação entre a variação de espessura das cascas cilíndricas com a sua deformação devida às forças centrífugas medida durante a rotação utilizando-se dois enfoques, um experimental e outro numérico, no caso o método de elementos finitos (MEF). As cascas cilíndricas estudadas tiveram sua espessura de parede medidas por meio de aparelho de ultra-som, mas por serem fabricadas em ferro fundido cinzento, as suas lamelas de grafita atuam como refletores, o que torna a medição imprecisa. Os resultados da análise numérica encontrados se relacionam bem com os experimentais de maneira qualitativa, mas divergem na forma quantitativa. Modelos de cascas com variação de espessura imposta também foram criados e analisados usando-se o método de elementos finitos de forma a se avaliar o comportamento da casca cilíndrica sob diversas configurações de distribuição da variação da espessura. Sugere-se a pesquisa de novas tecnologias para medições por ultra-som de peças fabricadas de ferro fundido com grafita lamelar. Neste trabalho, a medição da forma oval foi feita utilizando-se sensores de proximidade do tipo \"eddy-current\". / Circular cylindrical shells with small thickness variations along their body, when submitted to rotation, present, in some cases, elastic displacements of their outside surface induced by centrifugal forces leading to final oval like shapes. The main purpose of this study is to establish relationships between thickness variation of the cylindrical shells with their measured deformation during the rotation, due to centrifugal forces, using two approaches, one experimental and the other one numerical, in the latter case the finite element method (FEM). The studied cylindrical shells had their wall thickness measured by means of an ultrasound device. The used material is flake graphite cast iron (gray cast iron). The graphite flakes act as reflectors, what makes such measurements imprecise. The numerical results found are satisfactory in a qualitative way, but they disagree in the quantitative form. Shell models with theoretical imperfections also were created and analyzed using the finite element method in order to evaluate the behavior of the cylindrical shell under several configurations of distribution of the shell thickness variation. Further research is necessary on new technologies to measure the thickness of pieces manufactured of flake graphite cast iron. In this research, the oval shape measurements were done by means of eddy-current proximity sensors.

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