## 4 Results
### Effect of Deep Rolling Speed  
Figure 15a illustrates the effect of deep rolling speed on the material surface using both a vector plot (top side) and a time-based velocity variation graph (bottom side). The analysis compares the deep rolling speed from the experiment (1800 mm/min or 30 mm/s) with the simulated speed from FEA of 1796.52 mm/min (29.942 mm/s). The close approximation between the experimental and simulated speeds allows us to analyze the material's behavior under consistent conditions. The color-coded vector plot represents the velocity field on the material surface during the deep rolling process, with arrows indicating the direction and magnitude of movement  
regions with slower material movement. These areas are still affected by the rolling process but experience less displacement compared to the zones directly under the tool. The displacement vectors here are smaller, indicating that the material deformation decreases as the distance from the tool increases. The arrows in the vector plot indicate the direction and magnitude of material movement. Larger arrows with warm colors represent higher velocities, while smaller arrows in cooler colors (blue and green) represent slower material movement. This variation reflects how the rolling speed directly affects the surface's displacement, with the greatest impact being in the immediate contact area. The graph on the bottom shows the velocity variation over time, corresponding to the tool's movement across the material at 29.942 mm/s (simulated) compared to the experimental speed of 30 mm/s. The horizontal axis represents time, measured in seconds over a period of 7 milliseconds. This represents the duration of the deep rolling process being analyzed. The vertical axis shows the velocity in mm/s, with different colored lines representing the velocity variations at specific points on the material's surface. The velocity graph shows periodic fluctuations, where the tool's movement causes the material to experience peaks and valleys in velocity. Each peak indicates a moment where the tool moves across a particular point on the surface, causing maximum displacement. The valleys represent moments of lower velocity, likely when the tool moves to different points or changes direction slightly. Despite the fluctuations, the overall velocity remains close to 30 mm/s throughout the process, as indicated by the peaks. This consistency between the  
Figure 15: (a) Velocity vector plot on the material surface during deep rolling. (b) Time-based velocity variation during the deep rolling process. experimental speed and FEA simulation demonstrates that the tool maintains a relatively stable speed, ensuring even pressure application and uniform stress distribution across the material. The deep rolling speed has a direct impact on how the tool interacts with the material and the resulting residual stress distribution at 1800 mm/min (30 mm/s), the rolling tool moves quickly over the surface, applying pressure dynamically across different points. While the speed ensures rapid treatment of the material, it also results in periodic velocity fluctuations, as seen in the graph. These fluctuations may cause slight variations in the stress distribution, but the overall impact remains consistent due to the stable speed. The high velocity of the rolling tool leads to significant surface deformation, particularly in the regions directly under the tool (yellow and orange zones in the vector plot). This deformation induces compressive residual stresses, which enhance the material's resistance to fatigue and cracking. The displacement vectors show how the material moves in response to the tool's speed, contributing to the overall effectiveness of the deep rolling process. The deep rolling speed of 1800 mm/min (30 mm/s) from the experiment and 1796.52 mm/min (29.942 mm/s) from the FEA simulation demonstrate similar effects on the material surface.