# Dynamical Effects of the Increase of the Axle Load on European Freight Railway Vehicles
## 4 Design of the Primary Suspension for Higher Axle Load  
In order to be able to carry out analysis with higher axle load that is realistic, it is necessary to redesign the primary suspension of the vehicle. In particular, the stiffness of the primary springs is modified in such a way as to keep the vertical frequency of the vehicle constant as the axle load increases. The primary suspension consists of the tare stage which is placed in parallel to the load stage. The latter acts only after the tare stage has undergone a pre-set deflection. In accordance with the standards [32], it was decided to consider a tare frequency \(f_{\text{tare}}\) equal to 3.5 Hz and a full load frequency \(f_{\text{L}oul}\) equal to 2.5 Hz. The stiffnesses of the individual springs that compose the primary suspension are calculated using the Equations (14) and (15). \[K_{z,\text{Tare}}=\frac{1}{2}(2\pi f_{\text{Tare}})^{2}\cdot\left(\frac{P_{ \text{a}\text{T}e_{\text{T}e},\text{Tare}}-M_{\text{w}theiset}}{2}\right) \tag{14}\]  
\[K_{z,\text{L}oul}=\frac{1}{2}(2\pi f_{\text{Load}})^{2}\cdot\left(\frac{P_{ \text{a}\text{T}e_{\text{L}oul}}-M_{\text{w}theiset}}{2}\right)-K_{z,\text{T}e _{\text{T}e}} \tag{15}\] \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Section** & **Type** & **Length** & **P\({}_{\text{initial}}\)** & **P\({}_{\text{end}}\)** & **P\({}_{\text{Constant}}\)** \\
1 & Constant & 556.25 & - & - & 0.14 \\
2 & Circular & 50.6 & 0.14 & 5.20 & - \\
3 & Constant & 217.44 & - & - & 5.20 \\
4 & Circular & 21.5 & 5.20 & 4.77 & - \\
5 & Constant & 736.51 & - & - & 4.77 \\
6 & Circular & 112.9 & 4.77 & 8.00 & - \\
7 & Constant & 3472.95 & - & - & 8.00 \\
8 & Circular & 431.44 & 8 & \(-2.79\) & - \\
9 & Constant & 2692.27 & - & - & \(-2.79\) \\
10 & Circular & 276.3 & \(-2.79\) & \(-11.99\) & - \\
11 & Constant & 496.3 & - & - & \(-11.99\) \\
12 & Circular & 804.02 & \(-11.99\) & 4.08 & - \\
13 & Constant & 479.93 & - & - & 4.08 \\
14 & Circular & 592.8 & 4.082 & \(-7.78\) & - \\
15 & Constant & 433.85 & - & - & \(-7.78\) \\
16 & Circular & 413.38 & \(-7.77\) & 0.49 & - \\
17 & Constant & 817.7 & - & - & 0.49 \\
18 & Circular & 375.24 & 0.49 & 8 & - \\
19 & Constant & 2005.02 & - & - & 8 \\
20 & Circular & 618.14 & 8 & \(-4.37\) & - \\
21 & Constant & 111.37 & - & - & \(-4.37\) \\
22 & Circular & 222.8 & \(-4.37\) & 3.07 & - \\
23 & Constant & 463.61 & - & - & 3.07 \\
24 & Circular & 231.44 & 3.07 & \(-4.67\) & \(-4.67\) \\
25 & Constant & 532.13 & - & - & \(-4.67\) \\
26 & Circular & 8.42 & \(-4.67\) & \(-4.71\) & - \\
27 & Constant & 542.94 & - & - & \(-4.71\) \\
28 & Circular & 264.56 & \(-4.71\) & \(-11.88\) & - \\
29 & Constant & 857.3 & - & - & \(-11.88\) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Track altimetry. In order to carry out the structural analysis of the spring, it is necessary to calculate the force acting on the tare spring and on the load spring when the vehicle is in the full load condition. Since the action of the load spring takes place only after a certain deflection of the tare spring, it is first necessary to calculate the mass \(M_{int}\) which causes the action of the load spring; see Equation (17). \[M_{int}=\frac{K_{z,Tare}(L_{0,Tare}-L_{0,Load})}{g} \tag{17}\]  
The corresponding \(P_{int}\) axle load that causes the action of the load spring can be calculated using Equation (18). The multiplication factor four corresponds to the number of tare springs acting on each axle (two per axle-box). \[P_{int}=4M_{int} \tag{18}\]  
The vertical frequency of the vehicle when the load spring is involved can be calculated according to Equation (19). \[f_{int}=\frac{1}{2\pi}\Bigg{(}\sqrt{4\frac{K_{z,Tare}+K_{z,Load}}{P_{int}}}\Bigg{)} \tag{19}\]  
After the action of the full load spring, the tare and full load springs work in parallel and undergo the same deflection \(\Delta l\), which can be calculated using Equation (20).