The accurate shaping curve for forming inside small right-angle step using cross-wedge rolling

Cross-wedge rolling (CWR) die generally has three parts: a knifing section, a stretching section, and a finishing section. When forming an inside step, to avoid generating spiral steps, a new transitional section is introduced between the knifing and finishing sections, during which the surface is cut in the same shape as the inside step. The resulting surface is called the shaping surface, and its intersection with the base surface of the die is called the shaping curve. The rolling of the inside right-angle step has long been a key technology of CWR. The general formula and algorithm for the rolling alignment curve are not suitable for producing small right-angle steps. To solve this problem, we improve the geometric model and propose a new method for calculating the volume of the spiral cone of the small right-angle step. Based on the characteristics of the CWR process, the initial radius of the rolled product is compared with the radius of the corresponding auxiliary circle to preliminarily determine the conditions required for the small inside right-angle step. Based on the relationship between the radius of large section and the rotation angle, the shaping process is divided into three phases, the volume formulas for which are deduced by dividing the spiral cone into three regular volumes. Based on the volume fixedness theory, an accurate shaping curve of the small right-angle step is obtained by changing the rotation angle of the rolled piece. Finally, the finite element software Deform-3D is used to simulate the large diameter part within a certain area reduction range, the results of which verify the applicability of the proposed calculation method. The results of a comparative analysis also reveal that the stretching angle should be as small as possible when producing large-diameter shaft parts with small right-angle steps.