# Evaluation of Dynamics of a Freight Wagon Model with Viscous Damping
## 4 Simulation Study
### Result of the Simulation Study
The percentage changes in the sum of the lateral forces are shown in Figure 19. In addition to the RMS values, percentile 0.15% was chosen for the analysis due to the fact that the extreme values of the sum of the lateral forces are negative. The use of viscous damping resulted in a reduction in the absolute value of the forces (percentile 0.15%), by up to 70% for the front wheelset and 44% for the rear wheelset when the laden wagon was running on the second track. This is particularly favorable given the greater impact of a laden vehicle on the track. A reduction in the extreme values of the sum of lateral forces occurred in all study scenarios. Considering the RMS value, it can generally be seen that viscous damping has a reducing effect on the averaged values of the sum of the lateral forces. Also in this case, a 70% reduction in values was achieved for the front wheelset of the laden wagon moving on the second track, but on the rear wheelset, the reduction in lateral forces was only 6%. The increase in RMS value relates only to the run of a laden wagon on the first track and is 24%. In order to explain the adverse increase in the sum of the guiding forces on the second wheelset during running of a laden wagon on the first track, the lateral displacements of the wheelsets can be investigated for this purpose (Figure 20), as well as their angles of attack (Figure 21). This allows for the alignment of the wheelsets with respect to the track to be clarified, which has a significant effect on the generat  
Figure 18: Vertical forces of a left and right wheel of the first wheelset: (**a**) Relative changes of the 99.85% percentile; (**b**) The RMS value. contact. The rear wheelset of the empty model follows the curvature of the track, regardless of the damping used (Figure 20a). The plot of angle of attack is qualitatively similar for the same model, indicating an incomplete radial alignment of the wheelset in the track (Figure 21a). As a result of the increased weight of the wagon, the wheelset of the friction damped wagon changes to the opposite lateral shift from about halfway through the first curve. Disregarding the straight section between the curves, the wheelset is displaced in the opposite direction to that of an empty wagon and opposite to that of a wagon with viscous damping (Figure 20b). With the exception of a short section of tangent track connecting the reverse curves, where the value of angles of attack reached as much as \(1.5^{\circ}\), for the remainder of the section, the angles of attack were smaller than for the empty wagon and for the wagon with viscous damping. The laden wagon with friction dampers ran at a near-zero angle of attack for certain sections of the track, thus reducing its interaction with the track. This phenomenon can explain the 24% increase in the RMS value of the sum of lateral forces on the wheelset of the laden wagon model with viscous damping. Figure 19: A sum of guiding forces: (**a**) Relative changes of the 99.85% percentile; (**b**) The RMS values. Figure 15:0 Lateral displacement of the second wheelset in the first simulation track: (**a**) The empty wagon; (**b**) The laden wagon. Qualitatively and quantitatively, the plots of angle of attack of the rear wheelset for the wagon with viscous damping without load and with load were similar. The vibration damping ability can be compared based on the power dissipated by individual dampers. The RMS values of the dissipated power for the wagon models tested on the first track are shown in Figures 22 and 23. For an empty wagon, the RMS value of the dissipated power is several times higher when viscous damping is used. This difference increased considerably in the case of a laden wagon--in an extreme instance, there was even a difference of more than 20 times in the value of the dissipated power (Figure 22a, 1R wheel). When the laden wagon passed on the second track, the difference was on average 10 times in favor of the wagon with viscous damping (Figure 23a).