An analysis of the closed-die forging of a general non-axisymmetric shape by the upper-bound elemental technique

A kinematically admissible velocity field suitable for the closed-die forging of a general non-axisymmetric shape such as the forging of a cylindrical billet is proposed. By using the proposed velocity field, the upper-bound forging load and the velocity field for the closed-die forging of elliptic and trochoidal shapes by the forging of cylindrical billets are determined with respect to a chosen parameter. Experiments were carried out with commercially pure aluminum billets at room temperature. The forging loads between theory and experiment are shown to agree well, thus validating the proposed velocity field.