Central Composite Design Optimisation in Single Point Incremental Forming of Truncated Cones from Commercially Pure Titanium Grade 2 Sheet Metals

Abstract

Single point incremental forming (SPIF) is an emerging process that is well-known to be suited for fabrication in small series production. The aim of this paper was to determine the optimal input parameters of the process in order to minimise the maximum of both the axial and the in-plane components of the forming force achieved during SPIF and the surface roughness of the internal surface of truncated-cone drawpieces. Grade 2 pure titanium sheets with a thickness of 0.4 mm were used as the test material. The central composite design and response surface method was used to determine the number of experiments required to study the responses through building a second-order quadratic model. Two directions of rotation of the forming tool were also considered. The input parameters were spindle speed, tool feed rate, and step size. The mathematical relations were defined using the response surfaces to predict the surface roughness of the drawpieces and the components of the forming force. It was found that feed rate has an insignificant role in both axial and in-plane forming forces, but step size is a major factor affecting axial and radial forming forces. However, step size directly affects the surface roughness on the inner surfaces of the drawpieces. Overall, the spindle speed −579 rpm (clockwise direction), tool feed 2000 mm/min, and step size 0.5 mm assure a minimisation of both force components and the surface roughness of drawpieces.