Operator learning-based springback behavior prediction for complex-shaped tube free-bending forming

Free-bending (FB) technology enables the efficient processing of spatially complex-shaped tubes. Springback causes variations in curvature and torsion of the tube axis during the FB process. The mapping relationship of bent tube curvature and torsion from ideal to actual values can be abstracted as nonlinear physical operators. This paper first proposes a novel six-axis FB processing method that can control geometric features of tube transition segments. Then, an operator learning-based springback behavior prediction (OL-SBP) framework is presented, which includes an OL module and an SBP module. A feature-information-enhanced deep operator network (FIE-DeepONet) is integrated into the first module to learn tube springback operators. The curvature and torsion predicted by the OL module are then fed into the SBP module to calculate the overall shape of the springback axis. This paper also introduces a set of similarity evaluation indicators that are independent of the curve’s spatial attitude. Planar and spatial bent tubes are selected as case studies. Results show that the framework yields more accurate predictions compared to the analytical model. The framework also exhibits excellent generalization performance. Once FIE-DeepONet has learned the springback operators, it can accurately predict the springback curvature and torsion, even for tube shapes not present during training.