# Development of a New Vertical Dynamic Model of a Rail Vehicle for the Analysis of Ride Comfort
## 2 Modeling of Rail Vehicles
### Modeling of Rail Vehicles in Dymola (Dynamic Modeling Laboratory)  
Schematic representations of rigid and flexible vehicle models are shown in Figure 2. The Dymola software (dynamic modeling laboratory) was used for OOM of the rail vehicle. A feature of Dymola (and also of the OOM approach) is that the models in the user interface of the software explicitly represent the physical description of the system, rather than a mathematical description, i.e., the equations of the system (see Figure 3 for the rigid vehicle model and bogie model). The main components in the figure, such as the car body mass, suspension and track irregularities, can be seen explicitly, and quick modifications/improvements are possible within this approach. The other main feature of Dymola is that it is based on Modelica, which is an open-source code for dynamical system modeling. Modelica (and Dymola) has several libraries, such as multi-body dynamics, hydraulics, optimization, etc. Also, these libraries can be used in combination, for example with control and/or optimization algorithms focusing on various investigations related to the rail vehicle dynamics, whereas this is not possible in Vampire. The individual objects are set-up with necessary variable assignments and then assembled to form a technical system [22]. The coordinate system was defined by the world component, and it is visible in top left of Figure 3. Gravity is in the direction of the negative \(y\)-axis. The \(x\)-axis is positive to the right presenting the longitudinal direction. Two logics of the vehicle were named as front and rear bogies.  
\begin{table}
\begin{tabular}{l l l} \hline \hline
**Parameter** & **Value** & **Unit** \\ \hline \(m_{c}\)—car body mass & 34,000 & kg \\ \(L\)—car body moment of inertia & \(1.7\times 10^{6}\) & kg\(\cdot\)m\({}^{2}\) \\ \(m_{b}\)—bogie mass & 3000 & kg \\ \(l_{b}\)—bogie moment of inertia & 2000 & kg\(\cdot\)m\({}^{2}\) \\ \(k_{g}\)—stiffness of the torsional spring & \(3.7\times 10^{5}\) & kN\(\cdot\)m/rad \\ \(k_{1}\)—stiffness of the primary suspension & 5000 & kN/m \\ \(c_{1}\)—damping of the primary suspension & 30,000 & kN\(\cdot\)s/m \\ \(k_{2}\)—stiffness of the secondary suspension & 750 & kN/m \\ \(c_{2}\)—damping of the secondary suspension & 70 & kN\(\cdot\)s/m \\ \(f_{bending}\)—bending frequency of the car body & 9.6 & Hz \\ \(bs\)—bogie semi space & 8.75 & m \\ \(ws\)—wheel semi space & 1.25 & m \\ —car body length & 24 & m \\ \hline \hline \end{tabular}
\end{table}
Table 1: Geometrical and physical parameters of the rail vehicle.  
The flexible rail vehicle was also modeled in the same way as the rigid rail vehicle, but the car body was divided into two bodies with the revolute joint and torsional spring-damper components, so that the flexibility of the car body was included in the model. A virtual absolute acceleration sensor was placed in the center of the car body (see Figure 4).  
Figure 3: Components of rigid Dymola model and bogie component of the model.  
Figure 2: Schematic representations of models. Top: rigid Dymola model, bottom: flexible Dymola model.  
The torsional spring and torsional damper coefficients connecting the half car bodies were calculated using the method explained in Section 2.3. Prismatic joints on both sides of the car body were used to limit movement in the horizontal direction.