Modeling and optimization of the sequential brakeforming processes

The sequential bending process is often used to produce parts with simple curvatures (such as stringers and wing spars in airplane structures). The process involves a series of three-point bends, often overlapping, to produce the desired curvature profile along the arc-length of the part. The objective of this work is to develop a bending model and an optimization method for obtaining the “best” sequence of multiple bends. The goal is to improve dimensional accuracy and to substantially reduce the rework iterations. In the analytical beam model developed, the part state is represented by its curvature and stress distribution. The model accounts for curved initial geometry, residual stresses and strain-hardening of the material. Results of multiple bends for parts with symmetric cross-sections are presented. The synthesis of optimal bends was formulated as an optimal control problem that minimizes the curvature errors at specified points along the part. Results are presented for the forming of parts with constant curvature as an example.