Investigation to the torsion generation of spatial tubes in bending-twisting process

Bending-twisting process can be used for manufacturing complex spatial tube products. To describe the relationship between the torsion of tube axis and the twisting angle, torsion adjustment index is introduced in existing literatures. However, a puzzling problem is that the torsion adjustment index varies nonlinearly in a large range. Until now, this phenomenon has not been explained properly. In this paper, three loading models are introduced to investigate the springback behavior of tube element in bending-twisting deformation, including synchronous loading model, asynchronous loading model, and multiple loading model. Equations are established to describe the relationship between torsion and twisting angle for the three loading models separately. By comparison, it is found that the relationships among bending radii, twisting angles, residual radii, and residual angles are only a little different for the three loading models above, while a distinguished relationship between torsion and twisting angle exists obviously. The multiple loading model is better for describing the inconformity between twisting angle and torsion in bending-twisting process. The executed work shows that the inconformity between twisting angle and torsion occurs before springback. There exists twisting deformation in feeding phase, but no torsion is generated. Twisting deformation in feeding phase only influences the torsion during springback. The enhanced twisting angle in bending phase is a key factor in torsion generation. The enhanced twisting angle can be influenced by the mobile die position and torque on clamp. Finally, the springback is also a factor in torsion variation.