Forward extrusion through steadily rotating conical dies. Part II: theoretical analysis

The upper bound approach is utilized to analyze the forward extrusion of metals through a rotating conical die. A continuous spherical velocity field, compounded with a torsional velocity field constrained in a conical channel, is assumed. The circumferential slippage between the material and the tooling is analyzed by carrying out a minimization procedure on the expression derived for extrusion pressure. The length of material twisting inside the container is evaluated both using a slab method and an approach based on the balance of moments. This enables a complete upper bound estimate of extrusion pressure to be obtained. The reasonably simple model thus produced enables an analytical solution to be generated that agrees well with the experimental results.