## 2 FSW Experiments Considering Productivity
### Heat Transfer Analysis Using the Local Thermomechanical Model  
A heat transfer analysis was performed to calculate the maximum temperature and the temperature gradient in the vertical direction of the welding line during welding, which affect the inherent strain value. First, we used the equivalent heat source equation by [PERSON] et al., which considers the bottom of the tool shoulder, lateral of the tool pin, and the bottom of the tool pin, to analyze the heat transfer, as shown in Equation (3) below [22]. We assumed that the bottom surface of the shoulder was flat and the tool pin had a cylindrical shape, in order to simplify the heat source calculation in the analysis. \[ \begin{split}& Q_{t}=Q_{\text{Shoulder\_bottom}}+Q_{\text{Pin\_lateral}}+Q_{\text{Pin\_bottom}}\\ &=\eta\cdot[2\pi\omega\tau(R_{s}^{3}-R_{p}^{3})/3+2\pi\omega\tau R _{p}^{3}/3+2\pi\omega R_{p}^{3}H_{p}]\end{split}  \tag{3}\]  
where \(\eta\) is the welding efficiency, \(\omega\) is the rotation speed, \(\tau\) is the shear stress, \(R_{s}\) is the radius of the shoulder, \(R_{p}\) is the radius of the pin, and \(H_{p}\) is the height of the pin. Under the full sliding condition, the shear stress on the surface of the workpiece is expressed as  
\[\tau=\mu P=\mu F_{N}/(\pi\,R_{s}^{2}) \tag{4}\]  
where \(\mu\) is the friction coefficient, \(P\) is the normal pressure, and \(F_{N}\) is the downward force. The welding efficiency and the friction coefficient in Equations (3) and (4) are calculated through the actual experiment. The welding efficiency can be defined as a single value according to the process, but the friction coefficient cannot be expressed as a single value because it changes according to temperature [5]. This study performed a heat transfer analysis under the welding conditions of a 2000 RPM rotation speed and a 1000 mm/min traveling speed, which were derived as the optimum conditions from the previous experiment. In addition, the welding efficiency and friction coefficient values were determined, after correction, based on the temperature data collected through the experiment. In order to analyze the FSW heat transfer, we prepared a calculation flow chart, as shown in Figure 8, to calculate the temperature distribution during welding. This process is necessary to calculate the maximum temperature and the temperature gradient in the vertical direction of the welding line in order to obtain the inherent strain value. Figure 8: Calculation flow chart for heat transfer analysis. The local thermomechanical model on simplified geometry, from which it extracts the inherent strain to be used in the subsequent FE model, is shown in Figure 9. Provided that the temperature difference between the advancing side and the retreating side is about 10% in the results of the conventional heat flow analysis that considers bilateral asymmetry, we simplified the local thermomechanical model by assuming bilateral symmetry for the analysis. Since the size of the actual structure is large, it is reasonable to perform the analysis using the results of the advancing side. In addition, we used the values in Figure 10 as the density, specific heat, and thermal conductivity, which are temperature-dependent material properties for heat transfer analysis. Figure 11 compares the experimental results with the numerical results. Figure 11: Temperature distribution result: (**a**) numerical results when the tool is located at the center of the welding line; (**b**) comparison between experimental and numerical results. Figure 9: Finite element (FE) model for heat transfer analysis: (**a**) top view; (**b**) isotropic view. Figure 11a shows the temperature distribution when the heat transfer analysis is located in the center of the test piece. Figure 11b shows the temperature distribution in the vertical direction of the welding line in the FE model, which is compared with the experimental results. The experiment was performed once for 25 welding process conditions and the box marking in Figure 11b shows the experimental results.