Forming characteristics of thin-walled tubes manufactured by free bending process-based nontangential rotation bending die

The free-bending process of a metal tube involves a geometric relationship between the eccentricity, the rotation angle of the bending die, the deformation zone length, and the bending radius. Ideally, during the forming process, the contact position between the bending die, and the outer bend of the tube remains tangent. However, due to factors such as the clearance of the bending die and material properties, the rotation angle can be adjusted within a specific range while still ensuring smooth tube formation. The tangential state is disrupted when the rotation angle changes, resulting in overbending or underbending. Thus, in this study, a new theoretical analysis of the free bending process, accounting for clearance, was developed to analyze the material flow and changes in the bending radius during the nontangential contact between the bending die and the tube. In addition, the reasons for achieving smooth tube bending even after adjusting the rotation angle were explained, and the deformation mechanism of the tube under the combined effects of additional tangential force from the bending die and axial propulsive force was analysed. Furthermore, the impact of the rotation angle on the bending radius and the displacement of the strain neutral layer (strain NL) was determined. Afterwards, finite element (FE) modeling and forming experiments were conducted to verify the proposed theoretical analysis under different deformation zone lengths and eccentricities conditions. Besides, the distribution of the inner and outer wall thicknesses of the tube under the nontangential rotation of the bending die was further analysed. The simulation and experimental results fit well with that obtained from theoretical analysis.