Switched model predictive path control of incremental sheet forming for parts with varying wall angles

Abstract

As a promising rapid manufacturing technology, incremental sheet forming (ISF) has been tentatively applied in forming prototype parts in many industries, such as aerospace, automobile etc. One of the problems facing scientists and engineers is that geometric accuracies of the parts formed by typical open-loop ISF processes cannot meet dimensional requirements in industries. To address this problem, linear model predictive control (MPC) approaches have been developed that optimize the ISF tool paths to reduce geometric errors. However, in the ISF process, the geometric response of the formed part relative to the tool perturbation is highly non-linear. Due to model mismatch, existing linear MPC path control approaches have been successfully applied to simple geometries only. In contrast, this paper proposes a generic and systematic tool path control approach for forming parts with varying wall angles which have more complex geometric features. In particular, a Switched MPC framework based on linearizing the non-linear ISF geometry response with linear parameter-varying (LPV) state-space models is developed. Then, optimized tool paths to compensate geometric errors were determined by solving convex optimization problems. Experiments were conducted to validate the performance of the developed control approach. The results show that the developed Switched MPC was able to reduce the maximum geometric error by 72 %, 49 % and 80 % in the wall, conjunction and base zones of the formed “funnel”-shaped part respectively. Compared to the Conventional MPC, the Switched MPC improved the maximum geometric error in the wall zone by 0.21 mm. The Switched MPC control algorithm is then shown to be robust on two other complex shapes with varying wall angles.