Optimal Design of the Shape of a Non-Ball Mandrel for Thin-Walled Tube Small Radius Cold Bending

Abstract

In the field of cold bending, it is necessary to use ball mandrels, especially to bend thin-walled tubes with a small radius. However, the bending process with a ball mandrel is complex and expensive, and it is easy to jam the core ball inside the tube. To solve these issues, we designed two kinds of hollow non-ball mandrel schemes with low stiffness that were suitable for the small radius bending of thin-walled tubes. We evaluated the forming quality of cold bending numerically and the influence of the hollow section length and thickness on the forming indices. Our results showed that the thickness of the hollow section has a greater influence on forming quality than the length. As the hollow section’s thickness increased, the wrinkling rate first declined by approximately 40% and then increased by above 50%. When the thickness was 11 mm in scheme 1 and 13 mm in scheme 2, the wrinkling rate reached minimum values of 1.32% and 1.50%, respectively. As the hollow section’s thickness increased, the flattening rate decreased by more than 60% and the thinning rate increased by about 40%. A multi-objective optimization of forming indices was carried out by ideal point method and grey wolf optimizer. By comparing the forming results before and after optimization, the feasibility of using the proposed hollow mandrel was proved, and the hollow mandrel scheme of standard cylinder is therefore recommended.