During closed-die forging, the billet is deformed through one or more intermediate shapes before achieving the final forged shape. Designers rely on handbooks and experience to choose a few of the limitless number of intermediate shapes that are possible. A finite element method and optimization- based design technique for tracing the deformation back from the final to the initial shape is developed. Because plastic deformation is an irreversible process, no unique path exists between the initial and final shapes. Unlike previous backward tracing methods, the backward deformation optimization method (BDOM) selects the optimum path based on constraints placed on the deformation of the workpiece. Minimization of the variation in effective strain rate within the workpiece is used to determine the sequence of workpiece nodes to be detached from the die. Examples of intermediate shapes for the forging of a disk and a ball-joint socket demonstrate this design technique.
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