## 4 Simulation
### ANSYS Simulation for Flying Touch  
The gap between the two rollers in the flying touch simulation can only be controlled by the upper roller (the lower roller is fixed); hence, the simulation in this research is implemented according to the velocity profiles of the upper roller only.  
Two types of tests were simultaneously performed in the roller gap control simulation. The first test was conducted to determine the effect of the descending velocity of the roller on the impact force exerted on the steel plate. The second test compared the cases in which the roller descended at a constant speed with the case in which the roller gradually decelerated. In these simulations, the roller velocity was assumed to be well-synchronized with the steel plate velocity to evaluate the effects of the descending velocity of the roller only.  
Figure 9 shows the simulation results of the change in stress when the descending velocities of the roller are constant at 20 and 40 mm/s. The simulation results indicate that, immediately after the initiation of rolling, the stress caused by the descending velocity of 40 mm/s was seemingly greater than that due to the stress caused by a descending velocity of 20 mm/s. Although the difference between the two descending speeds did not have a significant effect on the stress during the continuous rolling period after the roller collided with the steel plate, the downward motion of the roller with a low descending velocity, to the extent feasible to reduce stress at the instant of collision, was confirmed to be better.  
Figure 8: Distribution of stress according to velocity difference between roller and steel plate.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Properties** & **Values** \\ \hline Thickness of the steel plate (half size) & 200 mm \\ Diameter of the upper roller & 630 mm \\ Transfer velocity of the steel plate & 500 mm/s \\ Rolled thickness of the steel plate & 12 mm \\ Initial gap between the upper roller and the steel plate & 20 mm \\ Simulation duration & 10 s \\ \hline \hline \end{tabular}
\end{table}
Table 1: Properties of stress analysis simulation.  
In the second test, the roller is given a trajectory that followed a curved velocity profile to descend smoothly. For comparison with the first test, the instantaneous velocities when the roller collides with the steel plate are assumed to be 20 and 40 mm/s. The experimental results are shown in Figure 10, where the area marked with a red circle in the graph indicates the moment of impact. The stress graph shows that the stress increases starting from the time of impact.  
The results of the experiment shown in Figures 9 and 10 are summarized in Table 2. The stress when the descending roller was gradually decelerated until the moment of collision appeared to be less than that when the roller had a constant velocity. Furthermore,  
Figure 10: Stress distribution when roller descends according to curved velocity profile. Graphs of velocity profile of upper roller and steel plate stress when descending velocities are (**a**) 40 mm/s and (**b**) 20 mm/s at moment of impact.  
Figure 9: Stress distribution when roller descends at constant velocities (20 and 40 mm/s).  
it was confirmed that the change in the amount of stress at the moment of impact when applying the proposed flying touch velocity profile (Figure 10) was considerably smaller than that when a constant velocity was applied. This phenomenon intensifies in the case of actual hot rolling because of the disturbance and vibration present in the real environment. The positional trajectory of the third-order equation was created based on the decelerated descending profile (20 mm/s) to apply the curved descending velocity trajectory to the vertical motion of motor of the upper roller.