# Numerical Simulation Study on Welding Process of Upper Frame of Hydropower Unit
## 3 Simulation Analysis of T-Joint Welding Based on TEPM  
### Finite Element Modeling  
According to the size of typical welded T-joint samples, 1:1 modeling and meshing were carried out, and transitional meshing was adopted to balance the computational efficiency and simulation accuracy [22]. The mesh in the weld- and heat-affected zones, which have large temperature gradients, was finely divided, while the mesh size became progressively coarser away from the weld zone. The grid type used throughout was the eight-node hexahedral grid, with each grid node ensured to be connected. The results of the grid division are depicted in Figure 5. The model comprises a total of 149,800 elements and 161,118 nodes. In the simulation process, the chewing gum method was employed to simulate the filling process of the weld material [23]. The material used in this study is Q345 alloy steel, which is chemically and mechanically similar to S355J2G3, as named by the European standard and available in the simulation software's material library. S355J2G3 was selected as the base material for the simulation. Since the performance of the welding wire is similar to that of the base metal, the weld material was also assumed to be S355J2G3. The  
Figure 4: Stress detection point position. (**a**) Schematic diagram; (**b**) physical diagram. Figure 3: Thermocouple temperature measurement point arrangement (**a**) schematic diagram; (**b**) physical diagram. simulation took into account the variation in the material's thermal physical and mechanical properties with temperature during the welding process. Heat radiation and heat convection phenomena exist between the weldment and the outside world during the welding process. Two-dimensional elements on the surface of the finite element model were extracted and set as boundary conditions for heat exchange, following [PERSON]'s law of cooling and the Stefan-Boltzmann law [24]. The temperature of the external environment was set to 20 \({}^{\circ}\)C, based on the actual indoor temperature during welding. Heat dissipation was considered throughout the entire welding process, with the process duration set from 0 to 3600 s.  
During the welding test, no additional external constraints were imposed on the sample. Therefore, only the three nodes of the finite element model's bottom plate were constrained during the welding simulation. During the subsequent cooling stage, these constraints were removed to allow free deformation. The heat dissipation and displacement boundary conditions applied are depicted in Figure 6.  
According to the design of the typical T-joint welding test scheme, the welding mode was selected as MAG welding in the simulation software, and the corresponding welding parameters were set. The heat source model, a mathematical function expression describing the heat input density distribution during welding, significantly influences the temperature and stress field calculations in welding simulations [25]. Based on the heat input characteristics of the welding method used in this paper, the double ellipsoid model was chosen for the simulation. The double ellipsoid heat source model is divided into front and back parts bounded by the center of the arc, which are characterized by two 1/4 ellipsoids, and its heat source density distribution is shown in Figure 7.  
Figure 5: Finite element mesh model. Figure 6: (**a**) Heat dissipation boundary; (**b**) displacement boundary.