Investigation on variation characteristics of bent tube axis and determination of bending die motion trajectory in free bending process

In free bending process, the axis shape of bent tube is determined by motion trajectory of bending die. The bent tubes with different bending radii and bending directions can be formed by continuously adjusting the position and posture of die. To accurately form the pre-designed bent tube, the formation mechanism of bending arc in free bending process was analyzed. The mathematical model between bending radius and deviation was established and the moving direction of bending die was also determined according to the plane space azimuth where the bending arc segment is located. The formation process of transition segments with variable curvature and variable bending direction is illustrated during the movement of bending die, and the influence of transition segment on the axis shape was also explored. By comparing the axis deviation of experimental and simulated bent tubes, the length of transition segment and the moving path of bending die can be optimized. Finally, the applicability of free bending forming technology in forming bent tubes with different axis features was verified by conducting free bending experiments on bent tubes with three typical shapes. Due to the high flexibility of free bending forming technology, the work in this paper could promote the engineering application of this technology in the precise control of axis shape of bent tube.