Modeling the process of radial-direct extrusion with expansion using a triangular kinematic module

It has been proposed to use the developed triangular kinematic module 2a with a curvilinear sloping boundary as an axial one, making it possible to describe the character of metal flow in the reversal zone to radial extrusion. Based on the energy method, we have derived the magnitudes of deformation force power inside the built kinematic module 2a, the power of friction forces at the border of the contact between a blank and a tool, and the power of cut forces with adjacent kinematic modules. The result is the obtained analytical expression of the reduced pressure for the deformation of the axial triangular kinematic module 2a with a sloping boundary, whose shape depends on the parameter α. We have analyzed the possibilities of optimizing the reduced deformation pressure for the parameter α under different ratios of geometric parameters of the module and friction conditions. Taking into consideration the shape of the adjacent kinematic module 3a, it has been proposed to use the resulting reduced pressure dependences to calculate the power modes of the combined sequential radial-longitudinal extrusion processes with the developed radial component of metal flow. A comparative analysis has been performed of the estimation schemes EM-2a with the developed axial triangular kinematic module 2a and EM-2 with the use of the axial rectangular kinematic module 2 and experimental data from modeling the process of combined radial-direct extrusion with expansion. The data on a deformation effort derived from the EM-2a scheme (with the developed triangular module with a curvilinear boundary 2a) and EM-2 exceed those experimentally obtained by 12‒15 % and 15‒20 %, respectively. This confirms the rationality of using the developed axial kinematic module 2a with a curvilinear boundary instead of an axial rectangular kinematic module when modeling processes of the sequential radial-direct extrusion with the developed radial component of metal flow. The resulting dependences of the reduced pressure of the module 2a deformation can be built into other estimation schemes of successive radial-longitudinal extrusion processes. As a result, the decrease in the obtained power parameters of the process could amount to 7‒10 % relative to the schemes involving the axial rectangular kinematic module 2