## 3 Effect of Coil Width during Forming
### Forming Capacity of a Wider Coil  
The previous results show that increasing the coil width can produce a larger curvature. However, a wider coil could be unfavorable to produce shapes with smaller curvatures. In this study, the coil input power is changed to calculate and investigate the curvature coverage of a wider coil. The calculation is based on the coil used in Case 3. The plate deformation and curvature distribution under heating conditions with different input powers \(P\) are calculated, and the results are shown in Figures 15 and 16. Figure 16: Transversal curvatures for different input powers. Figure 14: Effect of coil width on transversal curvature. Figure 15: Bending deflection of the \(S_{B1}\)-\(S_{B1}\) section for different input powers. Considering the interval between the heating processes in Case 5, i.e., when the plate is heated for a second time, the residual temperature could affect the final plate deformation shape. This also makes it difficult to compare the heating deformation time for Case 5 with that of Case 3. For parallel heating, different intervals are applied to the two heating lines for calculation; i.e., after the first heating line is completed, different intervals are applied before the second heating. Figure 20 shows the final deflection at the plate \(B\) direction center for two heating lines subjected to parallel heating with different intervals. It shows that in parallel heating, the interval between the heating lines has an insignificant impact on the plate heating deformation. Hence, compared with heating completion time for Case 3, the parallel heating interval for Case 5 is zero in theory. This means that the processing time for Case 5 is twice that for Case 3. When the single-pass heating for Case 3 and the two-pass heating for Case 5 have the same travel speed and the same maximum temperature, the calculation results are as shown in Figures 21 and 22. Figure 19: Parallel heating diagram (\(L_{C}\)/\(B\) = 0.10). Figure 20: Maximum bending deflection of the \(S_{B1}\)-\(S_{B1}\) section for various intervals. Figures 21 and 22 show comparisons of the deformation shapes at the plate transversal and longitudinal flexure lines of center sections. For the transversal and longitudinal deformation shapes of the plate, Case 5 requires two-pass heating to achieve the same plate deformation shape as single-pass heating for Case 3, which means a higher forming processing efficiency for Case 3. Based on the above calculation results, a moderate increase in coil width essentially increases the plate heating range and the local contraction force, which is favorable to increasing the deformation level of the processed plate. During heating, when the coil travel speed is fixed and for a specific plate shape, a wider coil requires less heating time than a narrower coil does. This means that a wider coil has a higher forming efficiency than a narrower one. Additionally, as the maximum temperature cannot increase infinitely, for a wider coil, the input power can be reduced to cover a narrower coil to produce a small deformation or small curvature. However, because an increase in power input results in a further increase in temperature, when the maximum temperature is constrained, it is difficult for a narrower coil to achieve a large deformation or a large curvature produced by a wider coil by increasing the input power of a narrower coil. It is worth noting that an excessively wide coil could change the localized heating condition and reduce the local deformation of the heated plate. Therefore, the coil dimension selection should be optimized. Figure 21: \(S_{B1}\)-\(S_{B1}\) section flexure lines for different heating conditions. Figure 22: \(S_{L1}\)-\(S_{L1}\) section flexure lines for different heating conditions. As a fundamental study, the calculations in this paper are focused on single-pass or two-pass heating lines. However, multiple heating lines, heating lines in different directions or different plate deformation shapes will not change the previous conclusions.