On Kinematics in Sequential Three-Dimensional Stretch Bending: Analytical Springback Model

In profile bending, the geometrical defect that reduces dimensional quality is mainly due to springback. While predicting dimensions after bending is important for quality control, many factors during bending cause difficulty in springback prediction. Furthermore, complex three-dimensional (3D) shapes in bending can make springback prediction significantly more difficult. This work presents a springback prediction method for varying curvature 3D profile/tube bending. An advanced five-axis bending machine, with rotary semi-dies opposing each other, has been developed. As the geometry of the bend die constrains the workpiece in the bending region, a model for 3D stretch bending is established from the rotational motion of the bend die. The discretized curvature of a bent profile geometry is described by using the Frenet-Serret frames, and a model for springback prediction is further developed based on the kinematics analysis of the bending process. This generalized analytic approach and numerical simulation are applied to evaluate springback in both 2D and 3D stretch bending of a thin-walled aluminum profile with a rectangular cross section. The analytical and numerical results for springback prediction are validated with experiments, showing good agreement. The developed model is able to evaluate 3D springback of a profile with arbitrary cross section efficiently for product design and development.