“…Nagpal et al (1978) used the stream function to define a kinematically admissible velocity field for the analysis of the problems of the upset forging of rings, where the axial velocity is derived as a function of the axial and radial directions to account for the effect of material hardening and temperature on the forming process. Although most velocity fields mentioned in the foregoing have been demonstrated properly in predicting the bulge profile as well as the forming load of the upset ring, none of them can account for natural boundary conditions that, in a certain sense, physically reflect the effect of the interfacial frictional condition as observed experimentally (Lee and Altan, 1972;Nagpal et al, 1978;Yang and Kin, 1986;Liu, 1972;Male and Cockcroft, 1964;Saida et al, 1970;Male and Depierre, 1970;Pawelski et al, 1989;Hsiang and Huang, 1991;Moon and Van Tyne, 2000). Experimental results of upset forgings of rings and disks (Lee and Altan, 1972;Nagpal et al, 1978;Liu, 1972;Male and Depierre, 1970;Hsiang and Huang, 1991) show that various types of lubricants applied on the interface considerably influence the shape of the bulged profile and the forming load.…”