Pass schedule design for flat-tool forging based on upper bound analysis

A pass schedule algorithm, which uses an improved upper bound method for metal flow analysis is proposed for multi-pass flat-tool forging. In the upper bound analysis, a set of kinematically admissible velocity fields is firstly constructed. The effects of billet-die frictions and rigid end constraints on metal flow are both taken into account. By using the calculated approximate velocity fields, changes in the billet dimensions in each forging pass are predicted. In order to verify effectiveness of the analysis, the predicted spread coefficients under different process conditions are compared with the cited experimental results. Based on the upper bound analysis, pass schedules are developed by iterative searches under the requirement of billet target dimensions. As an example, the proposed algorithm is applied to an alloy block forging process. The designed pass schedules are then selected and simulated by finite element method to get an optimal one. It is shown that the overall process design of multi-pass flat-tool forging could be achieved by the proposed algorithm and the subsequent finite element simulations.