# 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  
The data gathered from the pre-production experiments was imported into the digital twin system platform, which encompassed interfaces for various modeling and simulation software. This platform empowers researchers to deploy software tailored to their specific requirements. Utilizing the collected data and AutoCAD software, a 1:1 digital twin model of the pipe was generated. Figure 5 illustrates the schematic cross-section of the pipe, showcasing an outer diameter of 200 mm and a wall thickness of 7.5 mm. The outer wall thickness measured 1.5 mm, the inner wall thickness measured 2 mm, the hollow cavity layer thickness measured 4 mm, and the interlayer support thickness measured 2 mm. The pipe included a total of 60 evenly distributed hollow holes along its circumference. The end-forming process of the pipe was simulated using ABAQUS software, as illustrated in Figure 7, involving two steps. Firstly, the simulation focused on the heating and softening of the pipe material. The length of the pipe segment considered for the simulation was 400 mm, and solid elements were utilized. The material properties are depicted in Table 1.  
The variation in the tensile properties of the pipe material with temperature was determined based on the standards GB/T 8804-2003 and GB/T 1040.1-2018. The corresponding curve is depicted in Figure 9.  
The analysis included a heat transfer step, where the time was determined based on the requirements of each group. To meet the experimental conditions, the initial temperature of the pipe segment was set at 15 \({}^{\circ}\)C. The temperature propagated from the pipe mouth towards the far end, with a transfer temperature of 225 \({}^{\circ}\)C. Within the last 200 mm section of the pipe segment, surface heat exchange occurred, establishing contact with an ambient temperature of 15 \({}^{\circ}\)C. After the heating process was complete, the entire pipe segment underwent a 10 s heat exchange in an environment with a temperature of 15 \({}^{\circ}\)C (there was approximately a 10 s gap between the oven heating and the punching press process). The mesh was divided into hexahedral elements, utilizing standard heat transfer elements for the grid attributes. The total number of elements was 1.008 million. The simulation results are illustrated in Figure 10. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Specific heat capacity & 1.0465 \(\times\) 10\({}^{3}\) J/kg \(\cdot\) K \\ Thermal conductivity & 0.14651 J/s \(\cdot\) m \(\cdot\) K \\ Coefficient of thermal expansion & 7 \(\times\) 10\({}^{-5}\)/K \\ Density & 1500 kg/m\({}^{3}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Material properties. As illustrated in Figure 11, a comparison between the experimental and simulated temperature variations of the pipe demonstrated certain differences. In the simulated results, the temperature of the pipe in the 0-100 mm section was approximately 0-3 \({}^{\circ}\)C higher than the experimental results. This divergence could be attributed to the simulation's assumption of an ideal sealed heating condition for this section of the pipe. However, in reality, the non-sealed structure of the oven led to some heat dissipation, resulting in a slightly lower actual heating effect compared to the ideal temperature. Figure 10: Simulated cloud map of the heating process. Figure 9: Temperature\(-\)tensile properties of pipes: (**a**) Temperature\(-\)young’s modulus properties of pipes and Temperature\(-\)yield strength properties of pipes, (**b**) Temperature\(-\)elongation at break properties of pipes, (**c**) Stress\(-\)strain properties of pipes at different temperatures. Conversely, in the simulated results, the temperature of the pipe in the 100-200 mm section was approximately 0-6 \({}^{\circ}\)C lower than the experimental results.