# Application of Digital Twin in the Industry of Axial Hollow-Wall Pipes
## 3 Establish a Digital Twin of the Pipe End-Forming Process
### Establish a Digital Twin Model
This discrepancy arose from the simulation's assumption that this section of the pipe experiences heating at 225 \({}^{\circ}\)C and heat dissipation at an ambient temperature of 15 \({}^{\circ}\)C. However, during the actual experiment, the high-temperature operation of the oven caused the surrounding air temperature to exceed 15 \({}^{\circ}\)C, resulting in a slightly higher pipe temperature than predicted by the simulation. The slight deviation in the simulated temperature of the 200-300 mm section, compared to the experimental results, can also be attributed to the aforementioned variations in heat dissipation conditions. However, in the case of the 300-400 mm section, the simulated and experimental results demonstrated good agreement. Overall, the simulation error was negligible, with a value of less than 5%. This indicated that the model satisfactorily met the required criteria. In the second step, the simulation of the flaring process for the softened pipe segment was performed, as illustrated in Figure 12. The stamping equipment of the actual expansion device was modeled at a 1:1 scale. Figure 7 illustrates the structure of the expansion equipment used for the pipe. In this simulation, the sealing ring was represented by solid elements, while the punch head was considered to be an analytically rigid body. To analyze this process dynamically, a temperature-displacement coupling approach was employed. The contact between the stamping equipment surface and the inner wall of the pipe, as well as between the inner wall of the pipe and the sealing ring, was modeled as frictional contact. The coefficient of friction was determined according to the specifications outlined in GB/T 10006-2021, as depicted in Table 2.  
The punch was programmed to move at a constant speed, covering a forward distance of 220 mm within a time duration of 2.2 s. In the pipe's 0-220 mm section, a uniform pressure of 0.1 MPa was uniformly applied to the outer side of the pipe. This pressure served as a substitute for the pneumatic load used in the experimental setup. The mesh  
Figure 11: Comparison between experimental results and numerical simulation results: (**a**) Comparison of 40s–60s, (**b**) Comparison of 70s–90s. Figure 12: End-forming numerical simulation. configuration utilized temperature-displacement elements, maintaining the same number of elements as in the previous step. The simulation results are presented in Figure 13.  
Based on the combination of Figures 9 and 13, it can be observed that after 40 s of heating, the temperature in the expanded section of the pipe ranged from 73 \({}^{\circ}\)C to 90 \({}^{\circ}\)C. At this temperature, the yield strength of the pipe material was 35.348 MPa. The presence of small cracks on both the inner and outer walls at the sealing ring placement indicated the maximum strain at this location, with some elements exceeding the fracture elongation rate of the material at this temperature (70-87%). This conclusion aligned with the experimental results. Following 50 s of heating, the temperature in the expanded section of the pipe increased to 92-110 \({}^{\circ}\)C. The yield strength decreased to 26.386 MPa, while the fracture elongation rate increased to 94-181%. No cracks were observed in the pipe section at this point, and the quality of the end-forming met the requirements. After 60 s of heating, the temperature in the expanded section of the pipe reached 108-128 \({}^{\circ}\)C. The yield strength further decreased to 22.554 MPa, while the fracture elongation rate rapidly increased to 165-250%. The higher fracture elongation rate indicated excellent ductility of the pipe material. Within the temperature range of 73-122 \({}^{\circ}\)C, the fracture elongation rate of the pipe material increased with the temperature. Considering the temperature drop caused by air cooling during the actual expansion process, selecting a 60 s heating time could effectively prevent the cracking issues observed in the 40 s heating model.