# Railway Track Stress-Strain Analysis Using High-Precision Accelerometers
## 6 Experiments  
The presented results were produced on the testing ground of the Kuibyshev branch of Russian Railways, the Samara track distance, using the set of high-precision accelerometers. The sensors were installed according to the diagram presented above. As a result of measurements, vibration (acceleration) data were obtained from the results of the passage of two passenger trains and two freight trains. According to the simulation, the distance between the sensors for two passenger trains and the first freight train was set to 1.5 m. For the second freight train, the distance between the sensors was increased to 5 m, to test the hypothesis about the influence of the wheel sets of one car on the wheel set of the other. The distance between the wheel sets for all types of cars was on average 10.23 m.  
The data on the impact of freight and passenger trains on the railway track are presented in Figures 11 and 12. The figures present the acceleration data obtained from sensors installed on the rail under the dynamic impacts of freight and passenger trains on the railway track, based on the first sensor. The maximum amplitude of the track acceleration of freight trains was 41 m/s\({}^{2}\) on the first sensor on the vertical (\(z\)-axis), and that of passenger trains was 23 m/s\({}^{2}\), which corresponds to the actual condition, since the mass of freight train cars is higher than that of passenger trains. This parameter characterizes the vertical forces acting on the track under the influence of the mass of the wheel set acting on the axle. The maximum amplitude of the lateral acceleration of freight trains on the rail (\(x\)-axis) was 21 m/s\({}^{2}\), and that of passenger trains was 9 m/s\({}^{2}\), which characterizes the lateral effect of the wheel set on the rail under the action of forces arising from irregularities in the track and centrifugal forces on the turning sections of the track. The longitudinal maximum rail acceleration (\(y\)-axis) of freight trains is 10 m/s\({}^{2}\), and that of passenger trains is 7 m/s\({}^{2}\), which characterizes the action of forces arising from the rolling of the wheel onto the rail and depends on the speed and mass of the train. The obtained acceleration results correspond to the real state, since the mass of freight train cars is higher than that of passenger trains. To check the linear relationship between the sensors, the correlation coefficients were calculated for each axis separately (see Tables 3-5). The analysis of the coefficients of cross-correlation between the sensors did not reveal a linear relationship between them. The influence of the design features of the cars on the acceleration was not found. Figure 11: Acceleration of the track along the axes under the action of a freight train on the first sensor. From the obtained data, using double integration, a dynamic deviation from the equilibrium position was obtained at the first sensor (see Figures 13 and 14), showing that the rail subsidence under the influence of vertical forces (\(z\)-axis) of the freight train was within 6 mm, when the amplitude of the rail oscillation was within 9 mm. In this case, the subsidence under the passenger train was within 1.8 mm, and the vibration amplitude did not exceed 4.5 mm, which is within the values obtained using the modeling process. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Vertical Wheel Force, kN** & **Lateral Force, kN** & **Inner Side Edge** & **Outer Sole Edge** & **Rail Movement** & **Subgrade** \\ \hline \(1\) & \(0.092505\) & \(0.030213\) & \(0.040231\) & \(0.041666\) & \(-0.01078\) \\ \(1\) & \(0.048245\) & \(-0.00705\) & \(0.014493\) & \(-0.0382\) \\  & & \(1\) & \(-0.34413\) & \(0.083251\) & \(-0.09929\) \\  & & & \(1\) & \(-0.04389\) & \(-0.00759\) \\  & & & & \(1\) & \(0.27666\) \\  & & & & \(1\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Matrix of correlation coefficients between sensors’ axis Y.