Multi-objective optimization of 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 objective of this paper is to develop a method for the analysis of the effects of variation of initial residual stress of a part formed by the sequential brakeforming process. Although the primary concern of process control is to achieve a desired curvature profile in the formed part, an equally important objective is to minimize variation in the obtained curvature. The process is modeled as a series of overlapping three-point bends. With an empirical characterization, variation of the initial residual stresses in the part is shown to have a potential influence on the curvature output variation, and therefore on the effective precision and sensitivity of the process. The trade-off between the objectives of minimizing the shape error and the curvature variation is obtained as the Pareto solutions. In the case of two bends, an interesting study is made to compare two methods of adjacent bending and reverse bending. A multi-objective optimization approach is proposed for simultaneously minimizing curvature error and curvature variation. The optimization problem is solved using the ε-constraint method. The trade-off information and decision-making ability represents one of the potential uses of the multi-objective optimization study.