# Railway Track Stress-Strain Analysis Using High-Precision Accelerometers
## 7 Discussion  
Verification of the developed model was carried out using the methodology for assessing the impact of rolling stock on the track according to the conditions for ensuring reliability, approved by order of JSC Russian Railways Number 2706r, dated 22 December, 2017. The initial data include the characteristics of the stiffness of the rail base and the rail, the elasticity of the rail base, and the equivalent load determined with regard to them. These parameters consider the maximum forces transmitted from the wheel to the rail, taking into account the elastic deflection of the rail in the places where the vertical forces from the adjacent wheels are concentrated. The assessment of the vertical deflection of the rail during the passage of various types of rolling stock is presented in Table 6. In the first approximation, the value of the force transmitted from the wheel is taken to be equal to the static load. The modulus of elasticity of the rail base for a railway track with R65 rails on reinforced concrete sleepers with a diagram of 1840 sp./Km is about 150 MPa. Therefore, the results of finite element modeling and the experiments correspond to the calculated values of deflection, taking into account the idealization and simplification of the theoretical solution of loading a railway track. In fact, the vertical displacements exceed the calculated values due to dynamic impacts of wheels with sliders on the rails, and the presence of an unconsolidated ballast layer under the sleepers, which is clearly seen in the graphs of the results of experimental studies. Experimental rail deviations under the action of a freight train with 122.6 kN axle force allowed calculating the lateral forces (see Figure 15). As it can be seen from the figure, they are coincident with the presented results of modeling and approximation. With the help of the developed system, it is possible to control both static and dynamic rail inclination during the passage of the rolling stock by determining the angle of inclination of the rail base by the expression:  
\[\alpha=arctg\bigg{(}\frac{A_{x}}{A_{z}}\bigg{)}, \tag{1}\]  
where \(A_{x}\) and \(A_{z}\) are the values of static acceleration along the \(x\) and \(z\) axes. The proposed approach of high-precision accelerometers installation on the basis of the railway track line stress-strain analysis makes it possible to determine the load of the track; and knowing the movement of the rail, it becomes possible to calculate the stress in the elements of the railway track, to constantly monitor the parameters of the slope and rail subsidence. Determination of rail displacements with discreteness of at least tenths of a millimeter, in tandem with the use of a digital model of the deformation of the railway track, makes it possible to estimate the final mechanical stresses arising in the process of interacting with rolling stock with a high degree of reliability. In addition to that, the proposed method of \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Rolling Stock**} & **Number of** & **Force Transmitted** & **Distance between** & \multirow{2}{*}{**Equivalent Load, kN**} & **Vertical Rail** \\  & **Axles in** & & & **from the Wheel to** & **the Axles of the** & **Deification, mm** \\  & **the Bogie** & & **the Rail, kN** & **Wheels, m** & \\ \hline Passenger & & & & & \\ locomotive & 3 & 105.5 & 2.90 & 104.00 & 0.53 \\ Passenger coach & 2 & 78.5 & 2.40 & 75.80 & 0.39 \\ Freight locomotive & 2 & 112.8 & 3.00 & 111.56 & 0.57 \\ Freight car & 2 & 122.6 & 1.84 & 117.95 & 0.60 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Theoretical parameters of rail deflections. monitoring of the railway track's vertical and side deviations enables identification of a ground failure or a malfunction of a large number of rail fasteners in a short period of time. The concept of the Internet of Things potentially allows increasing the efficiency of railway infrastructure monitoring for track defects diagnostics.