# Evaluation of Dynamics of a Freight Wagon Model with Viscous Damping
## 4 Simulation Study
### Result of the Simulation Study  
The vertical forces on the left wheel of the first (front) wheelset, for the two loading conditions of the wagon, are shown in Figure 14 and in Figure 15 for the changes in the forces on the right wheel during running in the first track. An increase in the value of vertical forces depending on the load mass is an obvious, expected result. The effect of using viscous damping instead of dry friction damping is the reduction of the impact of the vehicle on the track in the vertical direction. Both the 99.85% percentile values and the standard deviation of the vertical force on wheels of the first wheelset are significantly lower. The same observations are also valid for the recorded forces in the right wheel contact of the first wheelset (Figure 15). The sum of the lateral forces is the quantity used to assess the running characteristics of rail vehicles in the acceptance process according to EN-14363 [39]. The values of the sum  
Figure 14: The vertical forces of the left wheel of the first wheelset: (**a**) The empty wagon; (**b**) The laden wagon. Figure 15: The vertical forces of the right wheel of the first wheelset: (**a**) The empty wagon; (**b**) The laden wagon. of lateral forces recorded in the first track for the first wheelset are shown in Figure 16, and for the second wheelset in Figure 17. Changes in the value of the sum of lateral forces are characterized by a greater spread of values when the damping is a dry friction force (larger standard deviation). The extreme values, defined by the percentiles, are more favorable for the model with viscous damping. These conclusions are also valid for the second wheel set and the empty wagon (Figure 17a). The additional load on the wagon causes an increase in the dispersion of the sum of the guiding forces (standard deviation), which, for the first (Figure 16b) and second wheelsets (Figure 17b), can be the result of a significant reduction in the sum of the forces on the track section connecting the reverse curves and on the final track section. In curves, however, the first wheelset sustained much smaller variations in force values when the damping was viscous, as well as smaller values of percentile 0.15%, indicating smaller, in absolute terms, lateral forces. On the other hand, the sum of the lateral forces of the second wheelset reached higher, in absolute terms, values of percentiles for the model with dry friction. The wagon model with viscous damping is characterized by qualitatively similar runs of the sum of the guiding forces on the first and second wheelsets, in contrast to the model with dry friction, whose sum of the transverse forces of the second wheelset in the loaded state differs from the other plots for dry friction dampers. In general, it can be  
Figure 16: Sum of lateral forces of the first wheelset: (**a**) The empty wagon; (**b**) The laden wagon. Figure 17: The sum of lateral forces of the second wheelset: (**a**) The empty wagon; (**b**) The laden wagon. concluded that the variation in the sum of the lateral forces is greater in the case of dry friction damping. In order to statistically capture the obtained results, percentage changes in the percentile values and RMS values of forces in contact with the rail wheel were calculated using Formula (16):  
\[\Delta=\frac{x_{viscous}-x_{Coulomb}}{x_{Coulomb}}\cdot 100\% \tag{16}\]  
Percentage changes in the values of vertical forces are shown in Figure 18. The percentile 99.85% values of the vertical forces of both wheels of the first wheelset were lower in each case analyzed for the wagon model with viscous damping--the reduction in values ranged from 15% to 31%. Conversely, the RMS values for only the laden vehicle running on the second track were only increased by 1% relative to dry friction damping. The percentage changes for the left and right wheels are equal. In general, it can be concluded that, for the adopted tracks and running speeds, the implementation of viscous damping can contribute to a reduced vertical impact on the track.