Die shape optimisation for net-shape accuracy in metal forming using direct search and localised response surface methods

In this paper, three direct search algorithms, i.e. a modified simplex, random direction search and enhanced Powell’s methods together with a new localised response surface method are presented and applied to solve die shape optimisation problems for achieving net-shape accuracy in metal forming processes. The main motivation is to develop efficient and easy to implement optimisation algorithms in metal forming simulations which often involve complex tool and workpiece interaction and coupled thermal and mechanical analysis. Three case studies are presented including a simple upsetting, a 2D blade forging and a forward extrusion problem. In all cases, the objective was to achieve net-shape accuracy of the formed parts, one important criterion for precision forming. C+ + programs were developed to implement these algorithms and to automatically integrate optimisation computation and forging simulation. The optimisation results from the three case problems show that direct search based methods especially the modified simplex and the localised response surface methods are computationally efficient and robust for net-shape forging and extrusion optimisation problems. It is also suggested that these methods can be used in more complex forging problems where die shape design and optimisation are essential for achieving net-shape accuracy.