# Development of a New Vertical Dynamic Model of a Rail Vehicle for the Analysis of Ride Comfort
## 5 Conclusions and Recommendations  
In this study, a passenger rail vehicle is modelled with rigid and flexible bodies using the OOM software Dymola. The main purpose is to build a dynamic model that allows for a good insight into the vertical ride comfort of a given passenger vehicle configuration in the design phase. For these reasons, simulation results from the developed models are compared with the outcomes of Vampire software (which is capable of conducting complex analysis on rail vehicle dynamics) in terms of computational efficiency and accuracy. Accuracy is ensured by the fact that the \(a^{worms}\) values and general vibration trends in the Dymola model are in good agreement with the Vampire model. The multi-body mechanics library of Dymola is used for the vehicle models. Linear suspension components are used in the vehicle models. Also, the calculations in Vampire are performed with a three-dimensional configuration. The car body flexibility is modeled by dividing the car body into two equal \begin{table}
\begin{tabular}{l l l l} \hline \hline
**Speed** & \(a^{worms}\) **of Dymola (m/s\({}^{2}\))** & \(a^{worms}\) **of Vampire (m/s\({}^{2}\))** & **Difference in \%** \\ \hline
145 km/h & 0.225 & 0.191 & 17.801 \\
200 km/h & 0.293 & 0.269 & 8.191 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of \(a^{worms}\) values of flexible rail vehicles in Dymola and Vampire. Figure 11: Left: Car body middle acceleration of flexible vehicles at 200 km/h, right: zoom view of 1 s interval. parts in Dymola. The car body halves are connected with a torsional spring to obtain an approximate vertical bending mode behavior similar to the Vampire model. The results of the study have shown that modeling a rigid car body for the ride comfort analysis yields underestimated results, which is consistent with previous studies. In general, there is a strong correlation between the track irregularity and vibration trends in both models, indicating the accuracy of the models. Peak amplitudes and zoom views indicate that the rigid and flexible models in Dymola generally show good agreement with the Vampire results. However, there are differences between the weighted-root mean square of accelerations that may result from variances in modeling approach. Specifically, the Vampire model is three-dimensional, while Dymola is two-dimensional. Also, the car body in Dymola is divided into two parts, which may lead to a somewhat oversimplification for the car body behavior. However, the flexible Dymola model is simple, fast and represents the main aspects of a more complex rail vehicle model for the vertical ride comfort analysis. Furthermore, using the methodology in this study (object-oriented approach and flexible body modeling), parametric analysis and optimization studies focusing on ride comfort are possible. Using Dymola or Modelica, which is open-source (white box) software, along with their various libraries (especially optimization) we can enhance the design processes for improving system-level performance. Some recommendations can be given to improve the accuracy of the model according to the results of the study, as follows:  
* The frequency response analysis of the model can provide valuable information about the body flexibility in Dymola. This paves the way for simulating car bodies with different bending frequencies, which could be a critical advancement for this study. Apart from that, the damping ratio can be adjusted with the help of frequency response analysis, which could be carried out in Dymola. * The car body can be divided into more parts to obtain a more realistic view of the behavior of the car body. * A three-dimensional model for the analysis of vertical-lateral movements can be developed in Dymola.