### An Analytical study of Optimal Die Design of Elliptic Tube

#### Abstract

In this study, die profile of the elliptic tube extrusion is analysis to predict the optimum die design by using upper bound theory. Developed manner in determining the relative extrusion power by dividing the extrusion die for different sector and calculate the relative deformation power of each sector under different condition which are reduction of area, friction factor and relative die length. The study predicts a new equation for determining the optimum die length with taking in the count the effects of those variables. The surface of the die is generated by an envelope of straight lines drawn from the points on the perimeter at the entry section to corresponding points at exist of the die. An upper bound technique based on the kinematically admissible velocity field is used to determine the forming stress. A complex program built in Visual Fortran V5.0 used to calculate relative extrusion power with variable friction factor (relative optimum extrusion power for values of reduction area are changed from 52.6% at area reduction equals to 0.15 to 82.8% at area reduction equals to 0.4). ANSYS program is used to compare the behavior and values of relative extrusion stress for optimum relative die length at constant reduction of area (R.A.=25%). The results are compared with other papers theoretical and experimental results are found to be in a very good agreement.

#### Keywords

extrusion, upper bound theory, reduction of area, friction factor, kinematically admissible velocity field#### Metrics