# Dynamical Effects of the Increase of the Axle Load on European Freight Railway Vehicles
## 5 Simulations and Results  
In order to analyze the effect of an increase in axle load in relation to the vehicle speed, simulations were carried out at two different velocities, 80 and 120 km/h. The axle load of the vehicle was changed from 22.5 tonnes to 35 tonnes with a step of 2.5 tonnes. The results of the simulations were statistically analyzed according to the indications of the Fiche UIC 518 [33] and the EN14363 standard [34]. In particular, this work considers the dynamic vertical load Q on the track, the total forces acting on the wheelset in the lateral direction \(\Sigma\)Y, the derailment safety ratio for wheel running on the outer rail Y/Q (limit value of 0.8 according to both EN14363 and UIC 518), the lateral accelerations measured in the vehicle frame (limit value of 3 m/s\({}^{2}\) according to both EN14363 and UIC 518), and the vertical accelerations measured in the vehicle frame (limit value of 5 m/s\({}^{2}\) according to both EN14363 and UIC 518). As regards total forces acting on the wheelset \(\Sigma\)Y, the limit depends on the vehicle mass and it can be calculated according to Equation (26) (EN14363), where \(Q_{0}\) is the nominal wheel load in kN, or according to Equation (27) (UIC518), where \(P_{0}\) is the nominal axle load in kN. \[\Sigma\mathrm{Y}=0.85\cdot\left(10+\frac{2Q_{0}}{3}\right) \tag{26}\]  
\[\Sigma\mathrm{Y}=0.80\cdot\left(10+\frac{P_{0}}{3}\right) \tag{27}\]  
The limits considering an axle load of the vehicle of 22.5 t, 25 t and 35 t are, respectively, equal to 71, 78, and 106 kN according to EN14363, and equal to 67, 73, and 100 kN according to UIC 518. The data simulated numerically by the multibody model and sampled at 200 Hz, have been processed considering sections of 100 m in length, on each of which the percentiles of the quantities of interest have been calculated. The results obtained at 80 km/h are shown in graphical form (Figures 5-10) for two different axle loads (22.5 and 35). Figures 5 and 6 show the lateral forces acting between the wheelset and the track (for the leading wheelset) considering the two different axle loads. For each 100 m length section, the percentiles at 99.85% and 0.15% of the filtered value of the sum of the lateral forces on the wheelset are considered. The forces are filtered by means of a low-pass filter with a cut-off frequency of 20 Hz (Chebyshev 3 dB), and then by a moving average with a sampling interval of 0.5 m over a reference distance of 2 m.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \(\mathbf{P_{xale,Tare}}\) & \(\mathbf{P_{xale,Load}}\) & \(\mathbf{M_{wheel}}\) & \(\mathbf{P_{int}}\) & \(\mathbf{f_{int}}\) [Hz] & \(\mathbf{L_{0,Load}+}\) & \(\mathbf{Dl}\) [mm] & \begin{tabular}{c} \(\mathbf{l_{Max}}\) \\ **Tare** \\ **Design** \\ **Spring** \\ **[MPa]** \\ \end{tabular}  & \begin{tabular}{c} \(\mathbf{t_{Max}}\) \\ **Tare** \\ **Design** \\ **Spring** \\ **[MPa]** \\ \end{tabular}  & \begin{tabular}{c} \(\mathbf{t_{Max}}\) \\ **Ster Tare** \\ **Design** \\ **Spring** \\ **[MPa]** \\ \end{tabular}  & \ \begin{tabular}{c} \(\mathbf{t_{Max}}\) \\ **Ster Tare** \\ **Design** \\ **Spring** \\ **[MPa]** \\ \end{tabular}  & \begin{tabular}{c} \(\mathbf{Ster Load}\) \\ **Spring** \\ **Spring** \\ **[MPa]** \\ \end{tabular}  \\ \hline
5.18 & 25.00 & 1.47 & 6.42 & 4.83 & 61.4 & 28.4 & 542 & 595 & 1.92 & 1.75 \\ \hline
5.35 & 27.50 & 1.52 & 7.98 & 4.62 & 67.3 & 26.3 & 594 & 595 & 1.75 & 1.75 \\ \hline
5.50 & 30.00 & 1.56 & 9.60 & 4.36 & 73.6 & 25. Figure 5: Sum of lateral forces (\(\Sigma\)Y) on the first wheelset of the second bogie, 22.5 t/axle, speed 80 km/h. Figure 6: Sum of lateral forces (\(\Sigma\)Y), on the leading wheelset of the leading bogie, 35 t/axle, speed 80 km/h. Figure 7: Derailment safety ratio (Y/Q) of the right wheel of leading wheelset of first bogie, 22.5 t/axle, speed 80 Km/h. Figure 8: Derailment safety ratio (Y/Q) of the right wheel of leading wheelset of first bogie, 35 t/axle, speed 80 km/h.