# Effect of Plate Curvature on Heat Source Distribution in Induction Line Heating for Plate Forming
## 3 Experimental Test  
To verify the accuracy of the finite element method, an induction heating test was designed. Figure 5 shows the experimental platform, electromagnetic inductor, and laser scanner. The coil was installed on a frame with trolley wheels which are in contact with the plate. In order to ensure that the coil adapted to the plate deformation, we used a cardan joint to connect the frame and the experimental platform. The platform controls the position of the coil, and the precision of the platform position is 1 mm. After the host computer has planned the path, the path data are transmitted to the lower computer to control the inductor movement.  
The FARO 3D focus scanner was used to measure the shape of the formed plate. The scanner uses phase difference laser ranging technology [19]. Phase difference laser ranging is also called continuous wave (CW) laser ranging. When the laser emits a CW laser, it is modulated by an amplitude modulator and then transmitted to the target to be tested. The echo signal returned from the target enters the receiving system. The distance can be obtained by measuring the phase difference between the transmitted signal and the received signal. The measurement accuracy of the FARO 3D focus scanner is 2 mm.  
After the origin points cloud was obtained, the Random Sample Consensus (RANSAC) algorithm was employed to distinguish the plate [20]. The RANSAC is a general parameter estimation approach and can be used efficiently for point cloud detection.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Temperature**} & **Young’s** & **Poisson** & **Heat Expansion** & **Yield** & **Density** & **Specific** & **Heat Conductivity** \\  & **Modulus** & **Ratio** & **Coefficient** & **Strength** & **Heat** & **Coefficient** \\ \hline
**(C)** & **(GPa)** & & & **x10\({}^{-5}\)(1/C)** & **(MPa)** & **(kg/m\({}^{3}\))** & **(J/(kg\({}^{-5}\)C)** & **(W/(m\({}^{-5}\)C))** \\ \hline
0 & 206 & 0.267 & 1.2 & 235 & 7842 & 450.36 & 66.97 \\
50 & 196 & 0.29 & 1.25 & - & - & 464.6 & 65.21 \\
200 & 196 & 0.322 & 1.4 & 163 & 7822 & 498.1 & 57.38 \\
250 & 186 & 0.296 & 1.43 & - & - & 502.26 & 54.91 \\
300 & 186 & 0.262 & 1.47 & - & - & 514.82 & 53 \\
400 & 166 & 0.24 & 1.54 & 130 & 7802 & 537.42 & 47.92 \\
450 & 157 & 0.229 & 1.57 & - & - & 623.64 & 45.83 \\
500 & 157 & 0.223 & 1.59 & - & - & 707.35 & 43.53 \\
600 & 135 & 0.223 & 1.64 & 119 & 7782 & 812 & 39.3 \\
650 & 117 & 0.223 & 1.66 & - & - & 904.07 & 36.37 \\
700 & 112 & 0.223 & 1.67 & - & - & 967.69 & 34.74 \\
800 & 113 & 0.223 & 1.69 & 109 & 7761 & 1026.32 & 31.02 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Material properties of the plate.  
Figure 4: FEM model for the mechanical and heat transfer calculation.  
The heat line is along the symmetry axis of the plate from one side to another, and the heat source moves at a velocity of 5 mm/s (see Figure 6). The test plate undergoes three cycles of heating, cooling, and measurement in the same line. The input power of the inductor is 65 kW, and the frequency is 12.7 kHz.  
The points cloud of the experimentally measured results is shown in Figure 7. We chose a section in the X direction \(S_{L}-S_{L}\) and a section in the Y direction \(S_{B}-S_{B}\) to compare the results of the FEM calculation and experimental measurement. Figure 8 shows the deflection variation in the Z direction after the first, second, and third processes of line heating. The results of the FEM calculations are in good agreement with the experimental results, and the FEM is verified.  
Figure 5: Experimental platform.  
Figure 6: Heating line, moving direction, and view sections.