## 4 The Presentation of the Main Content of the Study
The input parameters of the model were the technical characteristics of the carrying structure with the design and actual parameters, the bogies (Figures 3 and 4), and the disturbing force (Table 1). The mass and the moment of inertia of the carrying structure of the flat wagon with the design parameters and with the actual parameters were determined through their spatial models in SolidWorks software [10, 11, 12] The mass of the carrying structure of the flat wagon with the design parameters was 15.6 tons, the moment of inertia 283.1 ton \(\times\) m\({}^{2}\), and those with the actual parameters 11.1 ton and 102 ton \(\times\) m\({}^{2}\), respectively (Figure 5). Differential Equations (1)-(6) were reduced to standard Cauchy problems and then they were integrated by the Runge-Kutta method [13, 14, 15, 16, 17, 18]. The initial displacements and \begin{table}
\begin{tabular}{|c|c|} \hline \multicolumn{1}{|c|}{**Track Parameter**} & \multicolumn{1}{c}{**Value**} \\ \hline damping coefficient, kN\(\cdot\)s/m & 200 \\ stiffness, kN/m & 100,000 \\ irregularity amplitude, m & 0.01 \\ irregularity length, m & 25 \\ \hline \end{tabular}
\end{table} 
Table 1: Parameters of the disturbing force. Figure 4: Y25 bogie and its main parameter. Figure 5: Spatial model of the carrying structure of the flat wagon. Figure 3: 18–100 bogie and its main parameter. The results obtained made it possible to conclude that the dynamic parameters were within the allowable values and the motion of the wagon can be estimated as excellent [19; 20]. A comparative study of the dynamic parameters of the flat wagon is given in Figure 10.  
The application of the Y25 bogie for a flat wagon can decrease the acceleration of the carrying structure in comparison to that with the 18-100 bogie by 34%. The other dynamic parameters were also improved (Figures 11 and 12). \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \multicolumn{3}{c}{**Bogie Type**} \\ \cline{2-4}
**Parameter** & **18–100** & **Y25** & **Parameter Improvement, \%** \\ \hline Bogie acceleration, m/s\({}^{2}\) & 2.96 & 1.95 & 34.1 \\ Bogie acceleration in areas of support on the bogie, m/s\({}^{2}\) & 5.53 & 3.16 & 42.9 \\ Force in the spring suspension of a bogie, kN & 38.5 & 21.53 & 44.2 \\ Dynamic coefficient of the bogie & 0.49 & 0.28 & 42.9 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Dynamic parameters of an empty flat wagon in motion. Figure 10: Comparative study of the dynamic parameters of the flat wagon with the 18–100 and Y25 bogies. Figure 9: Accelerations of the flat wagon carrying structure in the bogie support areas: bogie Y25. The next research stage included determination of the dynamic characteristics of the flat wagon with the actual parameters. The accelerations on the carrying structure of the flat wagon in the center of gravity are given in Figures 11 and 12 and the accelerations in the areas of support on the bogies in Figures 13 and 14. Figure 11: Accelerations of the carrying structure of the flat wagon in the center of gravity: bogie 18–100. Figure 12: Accelerations of the carrying structure of the flat wagon in the center of gravity: bogie Y25. The mathematical model (1)-(6) was also used for determination of other dynamic parameters of the flat wagon (Table 3). The calculation was made for a wagon speed of 80 kph. The results obtained made it possible to conclude that the dynamic parameters were within the allowable values and the motion of the wagon can be estimated as excellent [19; 20]. The comparative study of the dynamic parameters obtained for the flat wagon is given in Figure 15. It demonstrates improvements in percentage for certain dynamic parameters of the wagon with the Y25 bogie in comparison to those for a flat wagon with the 18-100 bogie. The application of the Y25 bogie for the flat wagon with the actual parameters can decrease the acceleration of the carrying structure in comparison to that with the 18-100 bogie by 41%. The other dynamic parameters were also improved (see Figure 15).