Two-directional toolpath correction in single-point incremental forming using model predictive control

Incremental sheet forming (ISF) is an emerging forming technology that promises high flexibility and formability. These properties make it suited for small-scale and customised production. However, the poor geometric accuracy of ISF limits the wide application of this flexible forming technology. This paper presents a two-directional toolpath correction approach to enhance ISF forming accuracy using a model predictive control (MPC) algorithm. A toolpath optimisation method for vertical toolpath correction has been validated in our previous work (Lu et al., Int J Adv Manuf Technol 72:1–14, 2015 ), and it helps to reduce errors in the base of the test shapes to a suitable level while its major limitation is that horizontal geometric errors are relatively large. This paper extends our previous work (Lu et al., Int J Adv Manuf Technol 72:1–14, 2015 ) by augmenting the vertical control module with a new control module for horizontal toolpath correction. The proposed control algorithm was experimentally validated in single-point incremental sheet forming (SPIF) using two forming case studies. In the first case study (a truncated pyramid), two control approaches with different assumptions for the horizontal springback distribution along the horizontal cross-sectional profile were tested and compared. Then, the developed MPC control algorithm was applied to form a more complex asymmetric shape. The results show that the developed strategy can reduce the forming errors in the wall and base of the formed shape compared to the existing works. The ISF process with MPC control leads to significant accuracy improvement in comparison with the typical ISF process that is without toolpath control.