## 4 Results and Discussion
### Parametric Studies
#### 4.2.4 Effects of Unsprung Masses  
The effective masses in the wheel-rail interaction are the unsprung (wheel) masses [6]. The effects of different unsprung masses are considered in the parametric study. The effects of the unsprung masses on both contact forces and the dynamic factor are presented in Figure 16. The dynamic factor corresponding to different wheel loads reveals an unexpected phenomenon. The reason is the definition of the dynamic factor, the maximum force (impact force) over static force. It could be inferred from the figure, that the impact forces increase with higher wheel masses and reach a horizontal asymptote. In other words, the impact forces become gradually less sensitive to higher wheel masses; in the meantime, static force always increases with wheel mass. As a consequence, the dynamic factor first shows a rise followed by a fall, which is consistent with the findings presented in [36]. Regarding Figure 16a, it can be concluded that the effect of unsprung masses on the dynamic factor is limited. By contrast, the heavier wheels have a significant effect and produce higher wheel-rail contact force fluctuations (Figure 16b) that are important for the fatigue behavior.  
Figure 15: Bending moment distributions of specific sleepers with reference to different sleeper types: (**a**) sleeper at the entrance; (**b**) sleeper under the switch blades; (**c**) sleeper at the closure panel; (**d**) sleeper under the crossing nose; (**e**) the longest sleeper; (**f**) the shortest sleeper.  
In Figure 17, the longitudinal bending moment distributions of the maximum positive and negative bending moments are highlighted for different wheel masses. Heavier wheels result in higher bending moments but interestingly, seem to affect the sleepers at the closure panel rather than those under the crossing nose in terms of maximum positive bending moments. This is due to a correlation between bending moments and contact forces.  
As can be seen from Figure 16b, the contact force ratio of the heaviest wheel over the lightest wheel at the closure panel is higher than at the crossing panel. Accordingly, the maximum positive bending moments of the sleepers at the closure panel have higher deviations. The deviation in the maximum positive bending moment at the closure panel is around 8 kNm whereas it is only 2.5 kNm at the sleeper under the crossing nose. In contrast, maximum negative bending moments do not have such a character. There is no clear trend for the deviation in maximum negative bending moments. The only clear observation is that the location of the maximum negative bending moment shifts from the sleepers under the crossing nose to the sleeper at the closure panel. Finally, heavier wheel masses cause the recognizable fluctuations in the bending moment distributions for both negative and positive bending moments.  
The bending moment distributions along specific sleepers under different wheel loads demonstrate no distinct behavior for most of the sleepers in Figure 18. This appears to be due to the irregularities applied in the simulation, which have been explained in the earlier section. A clear projection of the  
Figure 16: Effect of mass: (**a**) variations in dynamic factor which correspond to different wheel masses; (**b**) contact forces for minimum and maximum modulus of elasticity.  
Figure 17: Longitudinal bending moment distribution with reference to different wheel loads.  
effect of the increased load can be seen from the figures, showing the distribution for the sleepers at the closure panel and under the crossing nose. It is obvious that higher wheel masses cause higher positive and negative bending moments along the sleepers at closure panel and under the crossing nose.