# Prediction of Damage to the Vehicle Underbody due to Stone Chipping
## 3 Results  
### Numerical Simulation for Impact Prediction with the Kinetic Energy  
In this numerical simulation based on the Equations (12)-(18), we calculated the estimation model of the random stone chipping for different combinations of variables; three vehicle speeds (60, 80, 110 kph), ten masses of stone (1, 2,..., 9, 10 g), five tire pressures (70, 75, 80, 85, 90 kPa), and four underground heights (0.25R, 0.5R, 0.75R, _R_). For each simulation, the stone chipping area is obtained as the code angle of the tire belt changes from \(-\)5\({}^{\circ}\) to 20\({}^{\circ}\) with the fifty-one cases (\(-\)5, \(-\)4.5, \(-\)4,... 19, 19.5, 20\({}^{\circ}\)). Figure 4(a)-c shows the predicted stone chipping zone for different vehicle speeds (60, 80, 110 kph) at the range from 70 kPa to 90 kPa of tire pressure. Figure 4(a)-c indicates that the tangential angle of the stone depends on the tire pressure. In other words, at low tire pressure, stone chipping occurs around the front-axle because the linear velocity of the stone is low and then the tangential angle of the stone is high. However, at high tire pressure, stones hit the area around the rear-axle because of higher linear velocity and then lower tangential angle. Figure 4(d)-f shows the effect of tire pressure on stone chipping zone for different stone masses (1, 5, 10 g) at the vehicle speed of 110 kph. When the vehicle speed is constant, the stone chipping tends to progress in the direction of the rear-axle according to the mass of the stone. In addition, there is a variation in the stone chipping area depending on the mass of the stone. At low tire pressure, the  
effect of stone mass on the stone chipping area around the underbody is small. Moreover, the radial distribution and shape of the stone chipping zone are much the same. The ground clearance (ride height), which is the underbody height to the ground, of a driving vehicle varies due to road condition, tire pressure and additional passengers. Figure 6a-d displays the stone chipping zone for the four cases of ground clearance (0.25R, 0.5R, 0.75R, \(R\)). For each case, the stone chipping area is plotted together in one color for five tire pressures (70, 75, 80, 85, 90 kPa). At the ground clearance of 25%, the stone chipping zone is formed around the front-axle, as shown in Figure 6a. Whereas, the stones hit the area around the rear-axle at the ground clearance of 50% in Figure 6b, therefore, the stone chipping zone has a radial distribution around the rear-axle at higher ground clearance. In general, the ground clearance has a range between 0.75\(R\) and 1\(R\), as normal driving conditions are maintained. Figure 6c,d shows that the radially distributed critical zone is formed around the back of the rear-axle for the standard road clearance (75-100%) and high tire pressure. The predicted zone displays the area where stones may collide with the vehicle after passing below the tire contact surface identified by applying Equations (12)-(17). Furthermore, the zone obtained substituting the 3D space matrix for \(t\) in Equation (18) can be observed in Figures 5 and 6, considering the effect of the gravitational force on the stones; this demonstrates that the stones have radial directions, depending on the tire belt code angle. These results confirm that stone chipping occurs most frequently at the rear-axle, where the fuel tanks and mufflers of vehicles, in general, or the batteries and fuel cells of EVs are located. Figure 7a-c shows the predicted stone chipping zone, plotted together for all the cases (5 tire pressures, 4 ground clearances, 10 stone masses) for different vehicle speeds (60, 80, 110 kph). Figure 5: Predicted stone chipping zones for various vehicle speeds, tire pressures and stone masses. (**a–c**): The effect of tire pressure on stone chipping zone for different vehicle speeds; (**a**) 60 kph; (**b**) 80 kph; and (**c**) 110 kph at the range (1–10 g) of the stone mass.