A general formulation for hydroforming of arbitrarily-shaped boxes and its application to hydroforming of an elliptic-circular box

A general kinematically admissible velocity field is suggested for the upper-bound solution of hydroforming of arbitrarily-shaped boxes. The suggested formulation is then applied to hydroforming of an elliptic-circular box. From the proposed velocity field, the fluid pressure vs. punch stroke relationship to render uniform thickness and the deformed configuration are determined by minimizing the total power consumption with respect to some chosen parameters. Experiments are carried out in the hydroforming press according to the computed pressure vs. punch stroke curve. The assumption of uniform wall thickness is confirmed by measuring the thickness variation. The effects of various process parameters including blank size, work-hardening exponent and frictional coefficient on the pressure curve are analyzed and discussed. It is thus shown that the proposed method of analysis in the present study can be effectively used for hydroforming of arbitrarily-shaped boxes.