Orthogonal stress superposition for bending springback control in multi-bending thin-walled structures

Springback remains a persistent challenge in sheet metal forming. Among the various control strategies, the stress superposition method is notable for its cost-effectiveness and mechanical efficiency. However, its application to complex multi-bending components is limited because the conventional approach of superimposing stress along the bending axis often fails to impose the required stress field effectively. To overcome this limitation, this study proposes a paradigm shift in stress superposition theory: the orthogonal stress superposition method (OSSM). Extending beyond the conventional uniaxial stress superposition, this method suppresses springback by imposing a stress field orthogonal to the bending axis, thereby establishing a new theoretical framework for springback control. The physical basis of OSSM is a newly discovered counterintuitive phenomenon in bellows hydroforming, in which axial springback decreases with increasing tube length. Analysis shows that this phenomenon is governed by a transition to a “material-excessive” deformation mode, in which accumulated material induces circumferential compression in the trough region. This orthogonal compressive stress reduces the bending moment by homogenising the axial stress distribution, thereby forming the basis of OSSM. A mathematical model quantifies the OSSM effect by capturing the nonlinear decay of the bending moment. For the present geometry, the model identifies a critical orthogonal compressive strain of 3% required to achieve a 90% reduction in bending moment. Furthermore, a coupled springback model for the bellows reveals a theoretical suppression limit of 62.6% for axial springback, because the moment reduction is confined to the localised trough region. To demonstrate industrial feasibility, a novel die-based strategy termed tooling-induced shrinkage sizing (TISS) is developed. By modifying the die geometry, TISS achieves an 86.7% reduction in bending moment and a 49.3% suppression in axial springback, offering a practical solution for high-precision forming. This work thereby establishes and validates OSSM as a general theoretical framework for springback control, extending the stress superposition strategy and offering a new perspective for the precision forming of complex thin-walled structures.