## 4 The Presentation of the Main Content of the Study
The design service life of the flat wagon with the 18-100 and Y25 bogies was determined using the method presented in [21]:  
\[T_{n}=\frac{(\sigma_{-1L}/[n])^{m}N_{0}}{B\,f_{d}\sigma_{ac}^{m}}, \tag{13}\]  
where \(\sigma_{-1L}\)--average value of the endurance limit; \(n\)--allowable strength factor; \(m\)--fatigue curve exponent; \(N_{0}\)--test base; \(B\)--coefficient characterizing continuous work in seconds; \(f_{d}\)--efficient frequency of dynamic stresses; \(\sigma_{ac}\)--amplitude of equivalent dynamic stresses. The coefficient that characterizes the time of continuous operation of the wagon is determined by the formula:  
\[B=\frac{365\cdot 10^{3}L_{var}}{v_{var}(1+0.34)}\, \tag{14}\]  
where \(L_{var}\)--average daily wagon mileage, km (\(\approx\)250 km); \(v_{var}\)--average value of a wagon speed, m/s; 0.34--empty operating ratio. Figure 14: Accelerations of the flat wagon carrying structure in the bogie support areas: bogie Y25. \begin{table}
\begin{tabular}{l c c c} \hline \hline  & \multicolumn{4}{c}{**Bogie Type**} \\ \cline{2-4}
**Parameter** & **18–100** & **Y25** & **Parameter Improvement, \%** \\ \hline Bogie acceleration, m/s\({}^{2}\) & 3.72 & 2.21 & 40.6 \\ Bogie acceleration in areas of support on the bogie, m/s\({}^{2}\) & 9.75 & 3.62 & 62.8 \\ Force in the spring suspension of a bogie, kN & 33.6 & 18.5 & 45.1 \\ Dynamic coefficient of a bogie & 0.61 & 0.34 & 44.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Dynamic parameters of an empty flat wagon in motion. The effective frequency of dynamic loadings is determined by  
\[f_{e}=\frac{1.1}{2\pi}\sqrt{\frac{g}{y_{s}}}\, \tag{15}\]  
where \(y_{s}\)--static deflection of spring suspension, mm. The rest of the variables of Formula (13) are taken from the source [21]. The amplitude of equivalent dynamic stresses was determined by the formula:  
\[\sigma_{ae}=\sigma_{ul}(k_{dv}+\psi_{e^{\prime}}/K_{\sigma}), \tag{16}\]  
where \(\sigma_{ul}\)--stresses from the static weight load; \(k_{dv}\)--coefficient of vertical dynamics; \(\psi_{e^{\prime}}\)--sensitivity coefficient; \(K_{\sigma}\)--overall fatigue strength reduction coefficient. The determination of the amplitude of equivalent dynamic stresses included the side force coefficient equaled 1.1. The following input parameters were taken for the calculation: \(\sigma_{1L}\) = 245 MPa; \(n\) = 2; \(m\) = 8; \(N_{0}\) = 107; \(B\) = 3.07 \(\times\) 106 s; \(f_{d}\) = 2.7 Hz; \(\psi_{e^{\prime}}/K_{\sigma}\) = 0.2. To determine the stresses from the static weight load of the supporting structure of the flat wagon, a strength calculation was carried out using the finite element method in the SolidWorks simulation software package (CosmosWorks) [22; 23; 24; 25]. Spatial isoparametric tetrahedrons were taken as the finite elements. Based on the previous research work of the authors, this element type provides sufficient convergence with technical experiments. Therefore, this type of tetrahedron was also selected in this study. The optimal number of elements was calculated with the graphic analytical method [26; 27]. In this case, the mesh was created with respect to the curved surfaces of the supporting elements of the frame. In the areas of interfaces, as well as the interactions of structural elements with each other, the mesh was compacted using software options. The number of elements in a mesh was 368,732, and number of nodes 14,938. The maximum element size in a mesh was 235.62 mm, the minimum size--47.12 mm, the maximum element side ratio--332; the percentage of elements with the side ratio less than three--24.6, and more than ten--31.5. 09G2S steel was taken as the material for the carrying structure, the mechanical parameters of which are given in Table 4.  
The model was fixed in the areas of support on the bogies. The design diagram of the flat wagon is given in Figure 16. The study included the vertical load Pv, conditioned by the deadweight, on the carrying structure. Figure 15: Comparative study of the dynamic parameters for a flat wagon with the 18–100 and Y25 bogies.