A model predictive path control algorithm of single-point incremental forming for non-convex shapes

The geometrical error of the formed part is one of the most significant limitations that restricts the widespread application of incremental sheet forming (ISF) in aerospace industry. The geometry of ISF parts is dependent upon the tool path, so its correction can improve the part precision. Previous research has utilized model predictive control approach to achieve this, but the method was restricted to simple convex shapes. In this study, the tool path and the formed shape were parameterized and the analytical models of geometry responses relative to tool perturbations were proposed. Then, a model predictive control algorithm was developed, aiming at reducing the geometrical errors of the parts with complex non-convex shapes in the ISF process. Experimental validation of the developed control algorithm was carried out by forming a complex shape by single-point incremental forming. The results show that the developed control algorithm greatly reduced the geometrical error in the closed-loop process.