# Development of a New Vertical Dynamic Model of a Rail Vehicle for the Analysis of Ride Comfort
## 4 Simulation Results and Discussion  
The selected track had the maximum service speed of 200 km/h and the data of vertical irregularities taken from VAMPIRE are shown in Figure 7. Journeys of rigid and flexible vehicles were simulated over a 1000 m section of straight track at speeds of 145 km/h and 200 km/h. The vertical accelerations were recorded in the middle of the car body. Dymola uses the DASSL algorithm (differential/algebraic system solver) for the mechanical system analysis. The tolerance of the integration in Dymola is 0.0001, which was proven to be optimal. The integration algorithm used in VAMPIRE is the Euler-Cromer method, with a time step of 0.001. The Euler-Cromer method was chosen because it is a method proposed by VAMPIRE for this type of analysis, which is a transient response analysis (time domain response of a vehicle to track irregularities). The effect of body flexibility is considered in the transient response analysis. Figure 7: Measured track irregularity data for 1000 m section of a track. \begin{table}
\begin{tabular}{l l} \hline \hline \(a^{\text{\tiny{warms}}}(\text{m/s}^{2})\) & **Ride Comfort** \\ \hline \(a^{\text{\tiny{warms}}}<0.2\) & Very comfortable \\ \(0.2\leq a^{\text{\tiny{warms}}}<0.3\) & Comfortable \\ \(0.3\leq a^{\text{\tiny{warms}}}<0.4\) & Medium \\ \(0.4\leq a^{\text{\tiny{warms}}}<0.6\) & Little comfortable \\ \(0.6\leq a^{\text{\tiny{warms}}}\) & Fairly comfortable \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Ride comfort levels according to ISO 2631. The output time step was chosen as 0.02, to enhance computational efficiency and facilitate a reasonable comparison between the results of the two software. The stiffness of the track (including the rail) does not play a significant role in simulations when investigating ride comfort and frequency range of interest [7]; therefore, the track was chosen to be rigid. Other assumptions for the analysis are as follows:  
* Wheels maintain contact with the rails, transferring track irregularities directly to the bogies. * The vehicle speed is constant during travel. The results of the simulations of the Dymola and Vampire models were compared at speeds of 145 km/h and 200 km/h; in total, the following eight simulation cases were executed:  
* Dymola rigid vehicle--Vampire rigid vehicle (145 km/h)
* Dymola flexible vehicle--Vampire flexible vehicle (145 km/h)
* Dymola rigid vehicle--Vampire rigid vehicle (200 km/h)
* Dymola flexible vehicle--Vampire flexible vehicle (200 km/h)  
In addition, zoom plots for 1 s intervals were provided for each comparison case. The results are shown in the following Figures. Firstly, the results of rigid vehicles with a velocity of 145 km/h are shown and it can be seen from Figure 8 that the acceleration curves of the two models agreed well. However, the Dymola model had slightly higher acceleration values. There was a highest peak at about 4 s of simulation, creating the largest difference between the models in this region in Figure 8 (left). This was an indication of the behavior of a low stiffness structure to a sudden dynamic excitation. Subsequently, Figure 9 shows the results of flexible vehicles at a speed of 145 km/h. Again, there was good agreement in terms of vibration tendencies, but the Dymola model had higher acceleration values. Figure 8: Left: Car body middle acceleration of rigid vehicles at 145 km/h, right: zoom view of 1 s interval. The travel at a velocity of 200 km/h was simulated for rigid vehicles and the accelerations are shown in Figure 10. The results were in satisfactorily good agreement. However, the Dymola model could not capture some of the peaks (especially between 2-4 s), but the vibration trends of both models seemed to be similar in general. Another observation is that there were higher oscillations in the 200 km/h rigid case than in the 145 km/h rigid vehicle case, which was caused by the higher speed, as expected. Finally, flexible vehicles were simulated at 200 km/h (see Figure 11).