## 3 Numerical Simulations
### Multi-Field Coupled Temperature Field Analysis  
Figure 4 illustrates the temperature distribution cloud maps of the fluid domain within the internal cavities of the upper heating plate, guide ring and lower heating plate filled with 180 \({}^{\circ}\)C steam. The figure reveals minor temperature fluctuations in localized regions of the upper and lower heating plate, attributed to irregular cavity geometries (non-uniform cross-sectional flow channels) that induce small-scale reflux in specific areas. From an overall trend perspective, the temperature reduction across the three fluid domains from the inlet to the outlet is extremely minor, with the entire fluid domain remaining above 179.99 \({}^{\circ}\)C. This uniformity ensures favorable thermal conditions for efficient heat transfer from the fluid to the mold [16]. Incorporating fluid temperature field analysis enhances the fidelity to actual production processes, thereby improving the accuracy of subsequent mold-wide temperature field evaluations. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Component**} & \multirow{2}{*}{**Material**} & \multirow{2}{*}{**Density (kg/m\({}^{3}\))**} & \multicolumn{2}{c}{**Thermal Expansion Coefficient (/K)**} & \multirow{2}{*}{**Elastic Modulus (GPa)**} & \multirow{2}{*}{**Poisson’s Ratio**} \\ \hline Guide Ring/Upper & & & & & \\ Side Plate/Lower & 35\# Steel & 7850 & \(1.2\times 10^{-5}\) & 203 & 0.3 \\ Side Plate & & & & & \\ \hline Mounting & & & & & \\ Ring/Lower & 45\# Steel & 7850 & \(1.2\times 10^{-5}\) & 210 & 0.27 \\ Base/Upper Cover & & & & & \\ \hline Guide Strip/Slide & & & & & \\ Block/Upper Slide & 40 Cr Steel & 7850 & \(1.2\times 10^{-5}\) & 195 & 0.3 \\ Block & & & & & \\ \hline Tread Segment & A514 Steel & 7850 & \(1.2\times 10^{-5}\) & 60 & 0.32 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The material selection and parameters of key mold components. Figure 3: Schematic diagram of loads and supports for the segmented tire mold. The three heat sources (heating plates and guide ring) transfer heat inward from the external components of the mold, and the final temperature distribution is reflected in the upper side plate, tread segment and lower side plate. Figure 5 presents the internal temperature distribution cloud maps, showing heat propagation from the upper heating plate, guide ring and lower heating plate through the upper cover slide block, slide block and lower base to the upper side plate, tread segment and lower side plate. Seven measurement points on the forming components were selected to visualize their heating trends (locations shown in Figure 6). Figure 7 displays the heating curves of these seven internal measurement points. Notably, the lower side plate exhibits the fastest temperature rise, followed by the upper side plate, while the tread segment, particularly measurement point #6 at its center, shows the slowest heating rate. This discrepancy arises from variations in component thickness between the measurement points and heat sources, leading to differences in heat transfer rates. Figure 4: The temperature distribution cloud map of the fluid domain: (**a**) Upper Heating Plate (**b**) Lower Heating Plate (**c**) Guide Ring. Figure 5: Temperature distribution cloud maps of the mold interior at different time points: (**a**) 1000 s (**b**) 4000 s (**c**) 9000 s (**d**) 14,400 s.  
During the mold heating process (raising the mold temperature to the level required for tire production), a significant temperature increase is observed within the first 4000 s, followed by a gradual slowdown in heating. After 9000 s, the temperatures of all components stabilize above 178 \({}^{\circ}\)C. Once the mold is fully heated, the local minimum temperature reaches 179.77 \({}^{\circ}\)C, meeting the requirements for rubber tire formation. The global temperature difference is controlled within 0.13%, demonstrating excellent temperature uniformity  
Figure 6: Schematic diagram of temperature measurement points inside the mold.