# Dynamical Effects of the Increase of the Axle Load on European Freight Railway Vehicles
## 2 Vehicle Model
### Model Architecture  
The vehicle model consists of 16 rigid bodies, in particular, the vehicle frame which is divided into two half-structures, two bogie frames, four wheelsets, and eight axle-boxes. The inertial characteristics of the bodies are indicated in Table 1. These data are relative to the standard Y25L bogie. The position of the center of gravity has been established on the basis of a simplified three-dimensional geometric model of each body (see Figure 1 where these geometries have been applied to the Multibody model). The reference system for the vehicle has been taken considering the x axis parallel to the track axis and towards the vehicle forward motion, the y-axis parallel to the wheelset axis, and the z-axis along the gravitational acceleration. The center of gravity of the payload has been supposed to be unchanged for all the loaded configurations. This simplifying assumption is required to compare the different solutions in similar conditions; of course, in a real case, the center of gravity may significantly vary depending on the type of goods being carried. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Body** & **Mass** & **Ixx** & **Iyy** & **Izz** \\  & [**kg**] & [**kg m\({}^{2}\)**] & [**kg m\({}^{2}\)**] & [**kg m\({}^{2}\)**] \\ \hline Half-body frame (tare) 1  & 12,980 & 12,826 & 131,467 & 128,261 \\ Half-body frame (22.5 ton/axle) 1  & 40,710 & 59,188 & 721,517 & 726,122 \\ Half-body frame (25 ton/axle) & 45,557 & 66,235 & 807,422 & 812,575 \\ Half-body frame (27.5 ton/axle) & 50,413 & 73,295 & 893,487 & 899,189 \\ Half-body frame (30 ton/axle) & 55,278 & 80,368 & 979,711 & 985,963 \\ Half-body frame (32.5 ton/axle) & 60,151 & 87,453 & 1,066,076 & 1,072,880 \\ Half-body frame (35 ton/axle) & 65,029 & 94,545 & 1,152,531 & 1,159,887 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Inertial properties of the vehicle bodies. The values indicated for the half-body frame refer to a vehicle in different load conditions (tare to 35 tonnes) since the model was used to simulate different load conditions. The corresponding values of moments of inertia were obtained by scaling them with respect to the mass at 22.5 tonnes/axle, which was the reference value for loaded conditions. In addition, the masses of wheelsets, axle-boxes, and bogie frames were increased as axle load increased to take into account that stronger mechanical components are necessary. The masses of wheelsets, axle-boxes, and bogies were increased in order to take into account that heavier structures are required when greater axle load are considered. The axle-boxes are connected to their wheelsets using rigid kinematical joints allowing only the rotation along the axis of the wheelset (revolute joints); therefore, each axle-box has only one degree of freedom. For all the other bodies, only elastic connecting elements are used, even if the two half-body frames are connected to each other by means of an elastic element with very high stiffness in all directions, except for the roll rotation. Therefore, it can be assumed that also the two half-body frames have only one degree of freedom. The suspension elements are divided into two stages: the primary suspension, which connects each axle-box to the bogie frame, and the secondary suspension, which connects the bogie frame to the corresponding half-body frame.