Comprehensive Modeling of Forming Forces in Three Directions for Incremental Sheet Forming Process Based on the Contact Area

Incremental sheet forming (ISF) is a promising sheet forming process for small batch production of complex 3D workpieces without time consuming set-up operation. However, the understanding of comprehensive effect of the contact area and stress on forming force is still insufficient, which is critical to the feedback control, process optimization and professional machine design, etc. Therefore, the present work aims to provide efficient mechanism-based prediction models for both the contact area, stress and the forming force. First, a universal predicted shape of the contact area between the forming tool and sheet in the ISF process was deduced and modeled based on typical experimental phenomena. In particular, the influence of parameters on the shape of contact area was clarified by defining contact angles β, α and α1. Then, stress components of the material within the contact area were derived after the theoretical analysis by adopting the cylindrical coordinate. In addition, an efficient forming force prediction model for ISF especially in three directions was established and verified, which combined the contact area model and calculated stress components. Finally, it is proved that sheet thickness has the most significant positive effect on forming force in three directions, since the rise of thickness not only increases the size for contact area but also leads to a large growth of equivalent thickness coefficient. Meanwhile, tool diameter has limited effect on forming fore, although it has the largest effect on the size of contact area. This study provides the fundamental understanding of the dynamic interrelation between contact area, stress-strain states and forming forces, which promotes the industrial transformation of ISF.