## 1 Introduction  
Tube forming in a closed die is a shaping method aimed at limiting highly unstable tube forming that produces folding defects in workpieces. This method of forming from a tubular workpiece has many advantages such as conservation of material, minimization of manufacturing labor, and, especially, the creation of metal fibers in parts that promote the mechanical properties of the product [1]. However, this method faces several challenges; while the level of deformation of the parts is not large, managing tube instability in the forming process is much more difficult than deforming with a normal workpiece. Instability in the forming process causes internal defects such as concave, groove, and fold defects. Several studies on tube deformation, which mainly report on hot deformation using numerical simulation methods, have been presented [2; 3; 4]. The forming devices are chiefly specialized horizontal machines with a die-integrated induction heating system on the machine [5]. Other studies on tube forming techniques such as gas-forming have been presented by [PERSON] et al. [6; 7]. The authors carried out an experimental and numerical investigation on the influence of pulsating pressure on hot tube gas forming heating by an oscillating heating mechanism [6]. The influences of the internal pressure and axial feeding on the expansion and wall-thickness distribution during hot tube gas forming were also investigated. The authors proposed that this method is effective for forming aluminum alloy tubes, and that the axial feeding is a vital parameter to prevent reductions in wall thickness [7]. Numerical simulations have been widely applied to technical problem-solving, as they can reduce the number of experimental trials, thereby reducing time and cost in the product development cycle. In 2012, [PERSON] et al. presented a review on finite element simulations in metal forming. The authors showed the advantages of simulations in comparison with practical tests [8]. For example, the concept of a forming limit diagram was proposed by [PERSON] et al. for the cold upsetting-extruding process of a tube flange based on finite element method (FEM) simulations [9]. In an analysis and numerical simulation of the upsetting process of a metal pipe, by [PERSON] et al., they authors suggested that there are similarities between experiment and simulation results [10]. Numerical simulations have also been used to predict defects in metal-forming processes [4; 11; 12]. From there, it is possible to adjust the shape parameters and friction conditions, to avoid defects during forming [4]. In 2019, [PERSON] et al. presented current trends in both experimental and numerical studies of metal forming for several common products in the field [13]. Moreover, [PERSON] presented a review of modeling in metal forming where the author proposed that the finite element method is the most preferred, after comparison with other modeling techniques, such as the slab and slip-line field methods [14]. In 2007, [PERSON] proposed a finite element analysis of the uncertainty in sheet- and tube-metal-forming processes, to estimate the variance of the material's properties that addresses the difficulties during the design phase [15]. [PERSON] presented the new development in both applied materials and innovative forming processes, concerning the automotive industry [16]. In addition, an elastomer material used for tube forming was also investigated through finite element analyses and experiments to find feasible parameters for the forming process [17; 18]. [PERSON] et al. presented an experimental and numerical investigation of metal tube forming with a new reconfigurable hydroforming die. The authors stated that the forming process was valuable to the small batch production of tubes due to the low cost of this new die. Moreover, the effects of pin diameter and polyurethane layer thickness on the characteristics of products were also demonstrated through numerical simulations [19].