# Numerical Simulation Study on Welding Process of Upper Frame of Hydropower Unit
## 4 Simulation Analysis of Welding Deformation of Upper Frame Based on ISM
### Simulation of Welding Deformation for the Upper Frame of Hydropower Unit  
#### 4.2.1 Extraction and Verification of Inherent Strain  
On the basis of verifying the validity of the finite element model and obtaining the welding process that meets the requirements, the inherent strain extracted from the TEP calculation results is used. However, in the simulation software, the inherent strain value cannot be directly applied as the initial load to the weld and its vicinity. Instead, it must be indirectly applied by modifying the thermal expansion coefficient in the material database. When the inherent strain value of the weld is known, the thermal expansion coefficient of the material can be calculated using Equation (5), which relies on the difference between the melting point of the material and the room temperature [20; 26].  
\[\varepsilon^{*}=\alpha\cdot\Delta T \tag{5}\]  
where \(\varepsilon^{*}\) is the inherent strain value; \(\alpha\) is the thermal expansion coefficient; \(\Delta T\) is the difference between the melting temperature of the material and the environmental temperature, taken as 1280 \({}^{\circ}\)C.  
The inherent strain value of all weld joints was extracted and averaged. Figure 18 shows the change in the average inherent strain of a typical T-joint over time. After the welding process was completed, the average inherent strain in the weld area eventually tended to a fixed value of 0.0386. According to the formula, the thermal expansion coefficient should be set to 0.000030.  
In order to verify the accuracy of deformation calculation using the ISM, a shell element model with the same size as the TEP finite element model was established in the deformation prediction software based on inherent strain. The thickness of the flange plate and web was set at 20 mm, and the constraints remained unchanged. The shell element model and constraints are shown in Figure 19.  
The thermal expansion coefficient of the material was modified to 0.000027 to apply the inherent strain effect, and then elastic calculations were conducted. The comparison of the overall deformation between the two methods is shown in Figure 20. The welding deformation obtained by the ISM is very similar to that obtained by the TEP-FEM. The maximum deformation calculated by the TEP-FEM is 1.438 mm, while the maximum deformation calculated by the TEP-FEM is 1.4  
Figure 18: The curve of average inherent strain value.  
deformation calculated by the ISM is 1.426 mm, resulting in an absolute error of 0.012 mm and a relative error of 0.83%.  
The \(Z\)-direction deformation of the two methods and the \(Z\)-direction deformation of the bottom of the flange perpendicular to the center line in the welding direction are shown in Figure 21. The maximum deformation value calculated by both methods appears at the sides of the flange. The absolute value of the Z-directional displacement obtained by the TEP-FEM is 1.27 mm, while that obtained by the ISM is 1.20 mm, resulting in an absolute error of 0.07 mm and a relative error of 5.5%.  
Figure 19: Mesh division and constraint setting of shell element model.  
Figure 20: Simulation results of overall welding deformation: (**a**) TEP and (**b**) ISM.  
Comparative analysis shows that the ISM can obtain accurate post-welding deformation, and the calculation time is short, so it can be used to predict the overall welding deformation of the upper frame. The inherent strain is affected by groove form, material thickness, welding process, and other factors. The thickness of the oil tank bottom plate of the upper frame is 30 mm. Therefore, a finite element model with a flange thickness of 30 mm and a web thickness of 20 mm was established using the TERM, and the inherent strain value is 0.0361. In the subsequent deformation prediction, the thermal expansion coefficient of the T-veld material at the bottom of the oil tank was modified to 0.000028.