materials Article Central Composite Design Optimisation in Single Point Incremental Forming of Truncated Cones from Commercially Pure Titanium Grade 2 Sheet Metals Marcin Szpunar 1 , Robert Ostrowski 2 , Tomasz Trzepieci´ nski 2, * and L’uboš Kašˇ cák 3   Citation: Szpunar, M.; Ostrowski, R.; Trzepieci´ nski, T.; Kašˇ cák, L’. Central Composite Design Optimisation in Single Point Incremental Forming of Truncated Cones from Commercially Pure Titanium Grade 2 Sheet Metals. Materials 2021, 14, 3634. https:// doi.org/10.3390/ma14133634 Academic Editor: Alexander Hartmaier Received: 21 May 2021 Accepted: 26 June 2021 Published: 29 June 2021 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- iations. Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). 1 Doctoral School of Engineeringand Technical Sciences, Rzeszow University of Technology, al. Powst. Warszawy 12, 35-959 Rzeszów, Poland; d547@stud.prz.edu.pl 2 Department of Materials Forming and Processing, Faculty of Mechanical Engineering and Aeronautics, Rzeszow University of Technology, al. Powst. Warszawy 8, 35-959 Rzeszów, Poland; rostrows@prz.edu.pl 3 Institute of Technology and Material Engineering, Faculty of Mechanical Engineering, Technical University of Košice, Mäsiarska 74, 040 01 Košice, Slovakia; lubos.kascak@tuke.sk * Correspondence: tomtrz@prz.edu.pl 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. Keywords: ANOVA; incremental sheet forming; sheet metals; single point incremental forming; SPIF 1. Introduction Single point incremental forming (SPIF) is based on obtaining the desired shape of the drawpiece without special tooling [1]. A universal tool—a rotating pin which ends with a rounded tip—is used and this forms the desired shape from clamped sheet metal. The widespread use of CNC machines and robots in production enables SPIF to be applied in industry [2]. Incremental forming is justified in small batch production and enables the production of components that are impossible to form in a conventional deep-drawing process [3]. Compared with conventional sheet metal forming (SMF) methods, SPIF technology has many advantages, such as [4–7]: • Sheet metal components with higher elongation can be made; • Increased forming limits can be achieved; • SPIF technology is more environmentally friendly than SMF methods; • Surface quality and shape–dimensional accuracy are higher; • As a die-less technology, SPIF does not require expensive stamping machines; • It can replace SMF in small batch production. In the SPIF process, many parameters that determine the accuracy and quality of the treated surface are controllable [8,9]. Among these parameters, the most important are: Materials 2021, 14, 3634. https://doi.org/10.3390/ma14133634 https://www.mdpi.com/journal/materials