Metal forming process is a widely used manufacturing process especially in high volume metal production system. In this paper, the main objective is using Bubnov-Galerkin finite element model to derive the pressure field set up at various cross-sections of a metal blank during a forging process, and the four Lagrange quadratic elements were assembled to represent the various metal blank. The governing equation adopted for this paper is a one-dimensional differential equation describing the pressures exerted on the forging process. During the analysis, the various metal blanks are divided into a finite number of elements and the weighted integral form for each element were formed after applying the Bubnov-Galerkin weighted residual method. A matrix form under certain boundary conditions from the weighted residual method were used to obtain the pressure distribution across the cross-section of the various metal blanks. Finite element results are obtained for a value of a circular disc diameter, thickness, coefficient of friction, principal stress, length, and radius of a circular material. Finite element method and the Exact solution approach are used to achieve and compare both results. Furthermore, the combination of both methods shows that there are potentials for using this approach towards the optimization of metal forming in manufacturing processes and some engineering practices.
Keywords: Forging; LaGrange Interpolation Function; Bubnov-Galerkin Weighted Residual Method; Finite Element Method.
Effects of Vibrations on Metal Forming Process: Analytical Approach and Finite Element Simulations
