ORIGINAL ARTICLE Optimization of processing parameters and surface roughness of metallic sheets plastically deformed by incremental forming process Mariem Dakhli 1 & Atef Boulila 2 & Pierre-Yves Manach 3 & Zoubeir Tourki 1 Received: 7 September 2018 /Accepted: 26 December 2018 # Springer-Verlag London Ltd., part of Springer Nature 2019 Abstract Single point incremental sheet forming (SPIF) is a process of manufacturing parts that leads to low prices of manufactured parts and high productivity. However, surface finish and forming time are responses that still need to be optimized to get better surface quality and less forming time. In the present paper, two techniques, the Taguchi grey relational analysis (TG) and response surface methodology (RSM), are combined together in order to get an optimal combination of several process parameters, such as the step increment, the feed rate, the rotation speed, the lubricant, and the sheet material. The cost function takes into account the response parameters such as the forming time, the axial, and the radial force, as well as the surface roughness in the sheet plane. The obtained results of this combination of techniques predict the grey relational grade by an empirical model that could be used in further experiments. Furthermore, the analysis of variance (ANOVA) for the grey relational grade is conducted to obtain the best levels of input process parameters. Keywords SPIF . RSM . TG . DOE . ANOVA 1 Introduction The single point incremental sheet forming (SPIF) is a recent technology for manufacturing sheet parts considered as a rapid prototyping process. The principle of this pro- cess is to deform locally and successively a blank sheet using a hemispherical tool following a tool path which controlled by a 3-axis CNC machine. This process is used in many areas to manufacture parts for small series and prototypes, and it covers various fields such as biomedical, aeronautics and micromechanical applications. In previous studies [1–4], two classes of incremental sheet forming processes have been presented. SPIF has attracted the in- terest of several researchers worldwide [5–7]. Several authors have chosen this technique for its simplicity and rapidity for applications. It optimizes the forming compo- nents served to stamp sheets, which leads to cost reduc- tions [8, 9]. Some authors like Kim et al. [10] have studied the effect of tool geometries on formability and they have shown that the best formability is achieved by an optimal tool diameter of about 10 mm, which results in using a hemispherical tool in this work with a 10-mm diameter. In the above studies, many techniques have been used for multi-response optimization. The most commonly tak- en methods include the response surface methodology, the fuzzy logic, the relational analysis, and the artificial neural networks [11–13]. For the present work, the response sur- face methodology is chosen, which is applied to explore the relationships between the input variables and the re- sponses resulting from an experiment, i.e., to propose an analytical equation of responses taking into account uncer- tainty, hazards and error. It is used to study the interaction effect of input factors on response parameters. It deter- mines, as well, the optimal combination to get the best performance characteristic. For a different manufacturing process, the impact of various process parameters on sur- face roughness has been studied by a lot of authors [ 14–16]. However, it has not been treated well in the forming process. Among the small number of authors, * Atef Boulila atef.boulila@insat.rnu.tn 1 Mechanical Laboratory of Sousse, National Engineering School of Sousse, University of Sousse, BP 264, Sousse, Erriadh, Tunisia 2 National Institute of Applied Sciences and Technology, University of Carthage, Centre Urbain Nord BP 676, 1080 Tunis Cedex, Tunisia 3 Univ. Bretagne Sud, UMR CNRS 6027, IRDL, 56100 Lorient, France The International Journal of Advanced Manufacturing Technology https://doi.org/10.1007/s00170-018-03265-x