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Top1. Introduction
Over the past decade, Single Point Incremental Forming SPIF has interested researchers as a metal forming process that requires no dedicated die, and hence saves time and effort. Basically, the SPIF depends on forming a specific feature on a blank by moving a special tool along a path, previously designed to suit the geometry and size of the required feature (Kopac & Kampus, 2005). Technically, there are similarities between the SPIF and the spinning process, and it is often said that SPIF has evolved from it (Jeswiet et al., 2005). In addition, SPIF originally descends from the incremental sheet forming ISF. The ISF processes are divided into two main categories, the negative incremental forming such as the SPIF, and the positive incremental forming such as the two Point Incremental Forming TPIF. The main difference between both types is that SPIF is completely die-less forming, while the TPIF uses a partial die (Tisza, 2012). The SPIF is preferred for its relatively high forming limit, which is the maximum deformation achieved before reaching failure. Many researches have proved that the strains incurred by the material in the SPIF process are much higher than other forming processes (Nimbalkar & Nandedkar, 2013). Moreover, SPIF also has contributions in many fields such as aerospace, automotive, and biomedical industries. In the biomedical field, Eksteen and Van Der Merwe (2012) have produced plate implants for minimal invasive surgical procedures by employing the characteristics of Titanium. In fact, there are many parameters involved in the SPIF process such as the incremental step, the feed rate, the forming tool diameter, the blank thickness, and the forming angle. Therefore, investigating the influence of various process parameters has been a basic research line since the SPIF has been raised. In this context, an experimental assessment of the factors affecting the SPIF has been carried out by Al-Obaidi & Hamdan (2016). The surface roughness and thinning have been experimentally studied to investigate how much they are influenced by the incremental depth, feed rate, and spindle speed. They have concluded that the surface roughness is highly affected by the incremental depth in the first place, followed by the feed rate, while the thinning is proved to be mainly dependent on the spindle speed.
This multiplicity of the parameters affecting the SPIF process render it difficult to depend on the experimental method to introduce an informative study for the effect of each parameter, let alone performing an optimization analysis (Hrairi & Echrif, 2011). Therefore, attention has been directed towards exploring the potentials of numerical simulations. One of the valuable works in this field is that introduced by Popp, Rusu, Racz, & Popp (2019). Their work has focused on manufacturing the cranial implants using SPIF, and the finite element analysis (FEA) has been employed to predict the thickness and forces exerted while manufacturing.
One of the essential studying areas in the field of metal forming processes in general is applying various optimization techniques to find out the optimum conditions of the metal forming process that fulfils a specific objective function. Wang, Ye, Chen, and Li (2017) have introduced a detailed state-of-the-art that is considered a useful guide for the researchers who are interested in this field. In this context, many studies have been conducted to obtain an optimum tool path for a specific feature. For example, Azaouzi & Lebaal (2012) have employed the response surface method (RSM) to obtain an optimum tool path that reduces the manufacturing time, and simultaneously, homogenizes the thickness distribution. Besides, a methodology has been introduced by Suresh, Khan, and Regalla (2013) to generate the tool path in the SPIF by defining specific strategies that suit the desired feature. Moreover, Suresh and Regalla (2014) have introduced an optimization study for the parameters affecting the surface roughness in the SPIF. The study has considered three optimization different techniques namely, Artificial Neural Networks (ANN), Support Vector Regression (SVR), and Genetic Programming (GP). The results obtained by the optimization analyses have been validated to experimental results, and minor deviation within 10% only has been detected.