## 4 Results and Discussion
The contact pressure of the wheel profile for which the wear and fatigue are optimized by the change in the wheel profile is between the contact pressures of the existing wheel and the wheel with optimized wear. Accordingly, the surface fatigue index of the design with optimized wear and fatigue is between the existing wheel design and the design with optimized fatigue. Figure 12 shows the comparison of the initial design wheel and the optimized wheel profile. Figure 10: Position of contact points on wheel and rail depending on lateral displacement of wheelset (surface fatigue-optimized wheel profile). As shown in Figure 12, the optimized wheel profile is shown to be similar to the worn profile in Figure 6:0 When a vehicle moves in a curved section, the contact point between a wheel and a rail is located approximately between dx 2 and dx 5 of Figure 6:1 The optimized flange inclination is less steep than that of the existing profile, and a bigger lateral displacement in a curved section aids smooth driving of the vehicle. As the existing wheel tread profile is maintained when a new wheel profile is designed, the optimized profile has the wear number same as that of the existing wheel profile in straight sections. In the case of a two-point contact, the wear number is calculated by adding wear numbers arising from the two contacts. A wheel flange contacts a rail gauge corner in curved sections. Figure 13 shows the wear numbers of the existing wheel and the optimized wheel profile. In the case of the wheel profile with optimized wear, since the jump between contact points is uniform when compared to that of the existing wheel, the wear number has decreased. In the case of the wheel profile with optimized fatigue, since the jump is  
Figure 6:2 Position of contact points on wheel and rail depending on lateral displacement of wheelset (wear and fatigue-optimized wheel profile). Figure 6:3 Comparison of wheel profiles (**Left**: overall shapes, **Right**: detailed shapes). considerably great at the gauge corner as shown in Figure 10, the wear number has increased. In the case of the profile with optimized wear and fatigue, the wheel shaft shifts by a lateral displacement of about 3 to 7 mm when driving in a curved section, at which point the contact points of the gauge are more uniformly distributed than in the case of the profile with optimized fatigue. In the case of the profile with optimized wear, the wear number on a sharp curve has decreased by approximately 4% when compared with that of the existing wheel profile, and the wear number of the profile with optimized fatigue has increased by approximately 17%, and that of the profile with optimized wear and fatigue has decreased by approximately 2%. The surface fatigue indexes of the wheel profiles are shown in Figure 6:4  
The optimized wheel of the wheel profile changes the location of the contact with the rail. In succession, this change at the contact point changes the contact area and with contact pressure. As the surface fatigue index is smaller than 0 in straight sections, no surface fatigue occurs. As the surface fatigue index is bigger than 0 in curved sections, fatigue cracks occur, and the bigger the surface fatigue index is, the bigger the possibility for fatigue cracks to occur. The contact pressures of the wheel profiles with optimized wear, optimized fatigue, and optimized wear and fatigue have decreased by 99%, 45%, and 58%, respectively, when compared with that of the existing wheel profile. The wheel with optimized fatigue has the lowest contact pressure, which is thought to have resulted from the occurrence of the two-point contact between the wheel and rail in the curved section. As contact takes place between the rail ball and the wheel tread and between the rail gauge and the wheel flange, respectively, in the case of two-point contact, the vertical force is applied and divided into two contact points.