Influence of additional tensile force on the stress and deformation of numerically controlled tube bending

According to the working way of the numerically controlled (NC) tube bender and taking the additional tensile force into account, the formulas are derived to calculate the average principal stress in different directions of the bending tube surface, the equivalent stress, the variation of wall thickness, and the ratio of the minor axis to the original radius of outer contour and validated by the experiments. The corresponding experiments and simulation analysis are performed to compare with the calculated results, and it is revealed that the equivalent stress of the bending tube surface is non-uniform and the maximum equivalent stress is localized in smaller deformation field around the bending terminating end. The consideration of the additional tensile force makes the equivalent stress in the outer convex portion of tube remarkably greater than that in the inner concave portion of tube, accelerating the thinning of the tube’s wall and the ovalization of tube’s outer contour. The approximate calculation formulae of additional tensile force is also derived and based on the deformation analysis; the proper adjustment of the additional tensile force could improve the quality of the NC bending tube.