Refinement issue of displaced volume at upsetting of cylindrical workpiece by radial dies

By analyzing the problem of upsetting of a workpiece by radial dies, an improved solution for determining the displaced volume was obtained. The value of the displaced volume is the basis for calculating such an important technological criterion as the engineering strain range of the workpiece during the upsetting. It is revealed that the main difficulty lies in calculating the volume that is placed between the contact surface and the end protuberances of the deformed workpiece, which requires the involvement of numerical or tabular integration methods that do not provide a complete solution