Springback prediction model and its compensation method for the variable curvature metal tube bending forming

Metal tube (MT) is widely used in aerospace, marine, and vehicle fields. Springback problems on MTs during bending forming would seriously affect the forming accuracy while the springback prediction and compensation method can effectively improve the accuracy. This paper proposes a springback prediction model for variable curvature tube, which is based on the theoretical formula of the springback angle prediction of the fixed curvature tube. The curvature radius of any point on the tube central axis curve after springback can be calculated through this model. Combined with the curve Frenet formula, the functional relationship, which is between the springback of the variable curvature tube and the original parameter equation of its central axis, is established. Based on the springback prediction model, the bending compensation amount of the variable curvature tube can be obtained through the reverse process. The tube curve equation containing the compensation amount is obtained as well, which is used to compensate for the springback error of the metal tube bending forming to improve the bending forming precision. To verify the correctness of the proposed model, experiments for both fixed curvature MT and variable curvature MT were carried out. The results showed that the proposed method was good at variable curvature MT springback prediction.