Impact of non-ideal rotation of bending dies on forming mechanism and quality of thin-walled tubes manufactured via free-bending forming technology

Manufacturing sound thin-walled metallic tubes via Free Bending Forming (FBF) technology depends on a geometric relationship involving the eccentricity of the bending die, rotation angle, deformation zone length, and bending radius. This accuracy of relationship relies ideally on the bending die rotating, maintaining tangency with the tube. Nevertheless, if the die deviates from this ideal rotation owing to material properties, the interaction between the die and tube occurs, leading to inaccuracies in the geometric relationship. Thus, investigating the influence of the non-ideal rotation of the bending die on thin-walled metallic tubes during the FBF process is essential. A new theoretical model is proposed to determine and study the forces acting on the tube during non-ideal die rotation, which is divided into bending outer and inner forces. The proposed model examines the force directions in three forms, over-rotation, under-rotation, and ideal rotation, to explain the changes in the internal forces within the cross-section and bending radius of tube. In addition, it determines the unit squeezing force on the tubes during non-ideal rotation. To validate the proposed theoretical model, Finite Element Modeling (FEM) and actual forming experiments were conducted to investigate the influence of forces acting on the tube during non-ideal die rotation and analyze the tube stresses under the three rotation forms. The FEM and experimental results strongly correlate with the theoretical analysis, confirming the accuracy of model in predicting tube behavior under varying bending die conditions.