Analysis of the energy vanished by friction in tube drawing processes with a fixed conical inner plug by the upper bound method

In this work, an analysis of the energy vanished by friction of thin-walled tube drawing processes in conical converging dies with a fixed conical inner plug has been conducted. The method used for analysis is the upper bound method (UBM), and the plastic deformation zone has been modelled by three triangular rigid zones (TRZ). The tube inner diameter is considered constant during the process, and therefore, a state of plane strain can be assumed. In addition, the existent friction between the external surface of the tube and the die (material-die), as well as that between the inner surface of the tube and the plug (material-plug) has been modeled by Coulomb friction (mu(1) and mu(2), respectively). Some significant findings emerged from this study are: the establishment of explicit expressions for evaluating the non-dimensional energy vanished by friction in the die and in the plug, the ability to select the plug that enables the process to be performed with a lower requirement of energy under defined conditions, and the detection of coupled effects between the friction coefficients define above.