# Application of Digital Twin in the Industry of Axial Hollow-Wall Pipes
## 3 Establish a Digital Twin of the Pipe End-Forming Process
### Pre-Production Test
production test, six different heating times were set: 40 s, 50 s, 60 s, 70 s, 80 s, and 90 s. To mitigate performance variations among different pipe materials and to reduce the influence of random factors on the experimental results, each test involved one length of axial hollow pipe (6 m) divided into six 1 m segments, which were randomly assigned to six groups. The experiments were repeated five times, and the results were averaged. \[\text{Q}=\text{C}\,\text{M}\,(\text{T}-\text{T}_{0})=\text{C}\,\text{V}\,\rho \,(\text{T}-\text{T}_{0}) \tag{1}\]  
Q: Quantity of heat, C: Specific heat capacity, M: Mass, V: Volume, \(\rho\): Density, T: Final temperature, T_0: Initial temperature. To prevent rapid cooling and its impact on the forming quality of the heated pipes upon contact with the stamping equipment, preheating is required for the stamping equipment. In the case of solid-wall pipes, the preheating temperature for the stamping equipment is generally around 90 \({}^{\circ}\)C. However, for hollow pipes, the preheating temperature for the stamping equipment can be appropriately reduced. On the other hand, excessive residual temperature stress can be induced in the pipes, due to a high residual temperature after the flaring process. Therefore, it is necessary to control the temperature at the moment of cooling and detachment of the pipes after the flaring process. After the heating process, temperature measurements were conducted at intervals of 50 mm within a 400 mm range from the pipe opening, as depicted in Figure 6. The horizontal axis, X, represents the distance from the measurement point to the pipe opening. The results depicted in Figure 6 demonstrate that, in the heating section (0-200 mm), the average temperature of the pipe gradually increased as the heating duration progressed. This temperature variation pattern aligned with Equation (1) mentioned earlier. Additionally, due to the non-enclosed structure of the oven, the temperature decreased as the position in the pipe segment moved closer to the oven outlet. However, the overall temperature remained within an appropriate range. In the non-heating section (200-400 mm), the cooling effect of the surrounding air led to a rapid temperature drop from 73-144 \({}^{\circ}\)C to 20-40 \({}^{\circ}\)C within the pipe segment. Beyond the 400 mm point, the pipe temperature approached room temperature, and the influence of temperature became negligible. The pipe end heating process is illustrated in Figure 7, wherein the pipe is fed into the oven using a fixture and heated using internal and external radiation heating tubes. In the heating process, the fixture rotates the pipe to ensure uniform heating of the pipe walls at all locations. The expanded mouth forming process is carried out on the heated pipe. The schematic diagram of the end-forming process is illustrated in Figure 7. After heating, the pipe is swiftly moved to the end-forming process area. Firstly, the sealing ring is placed inside the groove of the punching head. Then, the pipe is pushed forward, and the punching head is utilized to expand the pipe diameter. During the end-forming process, the pneumatic pressure loading device on the outer slide rail of the punching head applies air pressure to ensure tight contact between the pipe wall and the punching head; thus, preventing any gaps between the pipe wall and punching head. Figure 8 visually presents different  
Figure 5: Schematic diagram of the cross-section of the pipe. types of defects that were observed during this process. The experimental observations are summarized below:  
In the 40 s heating group, the pipe material exhibited whitening on the inner wall diameter changed area of the socket end and small cracks appeared at the expanded section. This was due to insufficient heating of the pipe material, resulting in low elongation at fracture. Consequently, excessive plastic deformation (whitening), and even cracking, occurred during the flaring process, as illustrated in Figure 8(1,2).