# Simulation Study of Thermal-Mechanical Coupling Fretting Wear of Ti-6 Al-4V Alloy
## 4 Results and Discussion
### Effect of Cyclic Normal Load on Wear and Temperature Rise  
Fretting damage involves loads in several different directions, and the normal load affects the contact stress distribution. In order to demonstrate the effect of normal load on fretting wear, three different forms of normal load are applied in the model. Namely, the constant normal load, the sin normal load, and the triangle normal load in Figure 4.  
Figure 13a shows the contact pressure distribution under different normal loads. At the edge of the contact area, the contact pressure for variable normal loads (sin and triangle normal loads) is almost the same as that for constant normal loads. Near the contact center, the contact pressure for variable normal load varies more. If the peak of the curve is removed, the contact pressure value of the variable normal load is smaller in the left area and just the opposite in the right area. The reason for the above phenomenon is that the variable normal load has the same phase as the tangential displacement. The amplitude of the variable normal load increases when the upper specimen slides to the right (positive direction). On the contrary, the amplitude of the variable normal load decreases when the upper specimen slides to the left (negative direction). The amplitude of the variable normal load is close to the constant normal load when the upper specimen is close to both edges. Moreover, there is a difference between the two curves of the variable normal load, but the location of the contact pressure change is the same. This is because despite having different rates of change (loading forms), the two variable normal loads have the same maximum amplitude and phase values. The wear depth distributions under the three loads are shown in Figure 13b. From the analysis of the contact pressure, it can be seen that the variable normal load has a small value of contact pressure to the left of the contact center. It can be inferred that the shear stress of the variable normal load is also smaller on the left side of the contact center. Thus, the wear depth of the variable normal load to the left of the contact center is necessarily less than the wear depth of the constant normal load. Similarly, the wear depth of the variable normal load is greater to the right of the contact center than the wear depth of the constant normal load. The figure also exemplifies that the wear depth curve for a constant normal load has only one abrupt change, while the wear depth curve for a variable normal load has multiple abrupt change points. This is also the reason for the large variation in contact pressure for variable normal load. The temperature distribution on the contact surface under different normal loads is shown in Figure 14. The temperature of the variable normal load is higher than the temperature of the constant normal load throughout the contact surface. When the normal load is variable, the contact surface is depressed due to wear. In this case, frictional heat generation exists not only in the horizontal direction, but also in the vertical direction. Therefore, the temperature of variable normal load is higher. However, the increase in heat  
Figure 13: Variation of contact pressure and wear depth with normal load. (**a**) Contact pressure; (**b**) wear depth. is small due to the smaller amount of wear and the small variation in the variable normal load. For the temperature distribution of the variable normal load, near the center of the contact, the temperature of the triangle normal load is slightly greater than the \(\sin\) normal load. On both sides of the contact area and in the non-contact area, the temperature of the \(\sin\) normal load is higher since the rate of change of the triangle normal load is constant and the rate of change of the \(\sin\) normal load is variable. The rate of change of \(\sin\) normal load is large at the beginning, middle, and end of the cycle.