The Determination of Stresses in Wire-Drawing Operation Using the Finite Element Model

Abstract

In this work, the Bubnov-Galerkin finite element model is used to get the
distribution of stresses and pressures set up at various cross-sections of a blank during metal forming process. Four Lagrange quadratic elements were assembled to represent the blank. The governing equation is a one dimensional differential equation describing the pressures and stresses exerted on the forming process. In conducting the analysis, the blank is divided into a finite number of elements and the Bubnov-Galerkin weighted residual scheme is applied to obtain the weighted integral form. The finite element model is obtained in a matrix form and then weighted residual boundary conditions are applied to obtained the pressure distribution across the cross section of the blank. Finite element results are obtained for a particular value of the coefficient of friction, die angle, length and blank radius and compared with the exact solution on a table.

Keywords: Metal forming process, Bubnov-Galerkin weighted residual, finite element method, Lagrange quadratic element.