Load prediction on metal forming process (tube sinking) using finite element method

Abstract

This study focuses on the Bubnov-Galerkin finite element model used to obtain the stresses and pressure fields set up at various cross-sections of a blank during the metal forming process. Four Lagrange quadratic elements were assembled to represent the various blanks. The governing equation adopted is a one-dimensional differential equation describing the pressures and stresses exerted on the forming process. In conducting the analysis, the various blanks are divided into a finite number of elements and further applying the Bubnov-Galerkin-weighted residual method to obtain the weighted integral form; the finite element model is obtained in a matrix form, from the weighted residual boundary conditions which are now applied to obtain the pressure distribution across the cross-section of the various blanks. Finite element results are obtained for a value of the coefficient of friction, die angle, length, and blank radius. Solution of the finite element method was compared with the exact solution, along with an experimental test known as press-fit analysis using Ansys Workbench, a program-controlled mesh of polar hexahedral elements which was utilized to further validate the result. Furthermore, the use of a computer-aided software assists in visualizing the solution of the tube sinking problem. The results were all presented in both tabular and graphical modes. This study shows that there are potentials for using this approach in engineering practices to ensure that the strength of materials be considered before usage in design and fabrication. These results are expected to improve advance knowledge in manufacturing processes.