Approach Based on Response-Surface Method to Optimize Lining of Dies Used in 3D Free-Bending Forming Technology

Abstract In three-dimensional free-bending forming (3D-FBF), the tube is not overly constrained, and the plastic deformation behavior and forming quality of the bent tube are significantly affected by the critical structure of the forming die lining. However, the effects of die-lining structural parameters on the tube quality, and a method to determine the combination of die-lining structural parameters is yet to be devised. This study aims to propose a new framework that allows one to understand the effects of various die-lining structural parameters on tube quality and to propose the best combination of die-lining structural parameters. First, finite-element modeling is performed to simulate 3D-FBF and examine the effects of individual die-lining structures on the quality of tube formation. The simulation results show that the deformation-zone length and die gap are positively correlated with the tube-section distortion and wall-thickness variation, whereas it shows an opposite trend with respect to the bending radius. Additionally, the lining chamfer radius of the bending die and the guide lining chamfer radius minimally affect the tube forming quality. Subsequently, the optimal die-lining structure is obtained using the response-surface method. The tube cross-sectional distortion rate reduced from 2.73 to 2.53% after the die lining is optimized. Additionally, the average inner-wall thickness reduced to 1.06 mm, whereas the average outer-wall thickness increased to 0.97 mm. This paper proposes a method for optimizing the forming-die-lining mechanism and for improving the tube forming quality in 3D-FBF.