## 1 Introduction  
The strong development of automotive and machine industries over the past decades has required advanced manufacturing techniques, especially for thin-shell products. Therefore, a hydrostatic forming technology with outstanding characteristics for the production of high-quality sheet details has been researched and applied in industrial manufacturing [1, 2, 3, 4, 5, 6, 7]. The process of hydrostatic formation is fast and satisfies the forming requirements of thin-shell parts. The working principle of this technology is shown in Figure 1. Moreover, this technology can be suitable for the shaping of a wide variety of materials, from high deformability materials, such as carbon steel material, to low deformability materials, such as stainless steel or some alloys [1, 8, 9, 10, 11, 12].  
Figure 1: Hydrostatic formation process diagram.  
There are many impressive studies on forming technology. In this context, the main concerns are technological parameters such as the forming fluid pressure, closing pressure, shape of die, friction, workpiece material, etc. [3; 13; 14; 15; 16; 17; 18; 19]. Among them, a large amount of research on forming liquid pressure parameters has been published to determine their influence on the forming process and product quality [20; 21; 22; 23; 24]. Studies have been conducted with many methods, the most common of which have been simulation or experimentation, or a combination of both. The results of these studies were impressive, informative, and highly applicable. [PERSON], [PERSON] and [PERSON] [25] worked to obtain a mathematical model of the forming fluid pressure. Their study built a mathematical relationship between the working fluid pressure and the thickness of steel and aluminum in the hydrostatic forming process for pairs of welded sheets. [PERSON] and [PERSON] [26] also studied the control of forming pressure in hydraulic formation. [PERSON] et al. optimized the forming fluid pressure using the Taguchi method when forming an AA 5182 alloy material to shape squared-cup parts [27]. The influence of technological parameters on product quality was also studied in the work of [PERSON] et al. [12]. These authors demonstrated that the formability of high-strength cryo-rolled Al alloy sheets could be enhanced by hydroforming.  
[PERSON] et al. studied the influence of working pressure on the product quality in the hydrostatic formation of DC04 materials [28; 29]. A relationship between technological parameters (working pressure and blank holder pressure) and the die geometry has been proposed to optimize the forming process for the cylindrical cup. However, the majority of studies have been conducted with only one type of material, while very few authors have implemented different types of materials. Therefore, the comparison of the effects of forming pressure on products with different materials has been limited.  
This paper provides an analysis of the forming process of a typical cylindrical cup in hydrostatic forming with three types of materials--steel (DC04), copper (CDA260), and stainless steel (SUS 304) at different thicknesses (0.8 mm, 1.0 mm, 1.2 mm)--within the binder pressure range of 80-115 bar. For each experimental product with a defined shape and size, the forming pressure is measured. Based on the results of the experiments, the mathematical equation of forming pressure is formulated. The formula allows for the analysis of the influence of each input variable (binder pressure, thickness of material, and ratio of stress (ultimate strength per yield stress)) on forming pressure.