## 3 Results
In the areas of interaction between the centre sill and the bolster beam, the maximum stresses are 308 MPa (Figure 13). Moreover, these stresses are concentrated in the area of the centre sill, which is located closer to the striker. In the area of interaction between the centre sill and the bolster beam, which is located on the opposite side, these stresses amount to 304.8 MPa. It should be noted that the maximum stresses do not exceed the permissible values, which, for design mode I, are taken to be 0.9\(\sigma_{\rm y}\)[27], where \(\sigma_{\rm y}\) is the yield strength of the material (\(\sigma_{\rm y}\) = 345 MPa). This distribution of stresses can be explained by the fastening diagram selected. The maximum displacements occur in the upper parts of the arches located behind the centre of the wagon body and are about 4.8 mm (Figure 14). Figure 12: Stress state of the wagon body. Figure 13: Stress state of the wagon body in the area of interaction between the bolster beam and the centre sill. The safety of the wagon movement is assessed by the first natural frequency of oscillations in accordance with the regulatory document [27]; it should be at least 8 Hz. In the case under study, it is 14.801 Hz. Therefore, in terms of the modal analysis, the safety of the wagon movement is ensured. Also, this study includes the determination of the dynamics of the proposed wagon design. Taking into account the results of the calculations, the indicators of the wagon dynamics were obtained. They were used to estimate the wagon motion: acceleration in the centre of mass and the coefficient of vertical dynamics. Figures 16 and 17 show the results of the calculation for the movement of the unloaded wagon. The maximum acceleration acting in the centre of mass when the wagon moves over a rail joint is 4.3 m/s\({}^{2}\) (0.43 g). This acceleration occurs when the wagon passes a joint irregularity. Further, the acceleration value decreases and amounts to about 3.5 m/s\({}^{2}\) (0.35 g). This acceleration corresponds to 'excellent' motion in accordance with [27], since it does not exceed a value of 0.5 g. The coefficient of vertical dynamics of the wagon is 0.49. At the moment when the first bogie facing the engine passes a joint irregularity, this coefficient is positive, and it is negative for the second bogie. This coefficient has a maximum value when the bogie passes an irregularity; after, that it decreases slightly and amounts to about 0.48. This value also corresponds to 'excellent' motion, since it does not exceed 0.5. Therefore, the motion of the unloaded wagon is assessed as 'excellent'. If the wagon is loaded, the maximum acceleration acting in its centre of mass is about 1.5 m/s\({}^{2}\) (0.15 g), (Figure 18) and the vertical dynamics coefficient is 0.19 (Figure 19). It should be noted that the accelerations in the centre of mass of the loaded wagon are lower than for an unloaded wagon since the body has a greater mass. Therefore, the coefficient of vertical dynamics is lower. wagon body and amount to about 4.8 mm (Figure 14). This is due to the fact that the body is secured at the centre sills. That is, their middle parts are not fastened. This is accompanied by the largest displacements. The study also includes a modal analysis of the wagon body for assessing the safety of the wagon operation in terms of frequency analysis. It is found that the first natural oscillation frequency of the body is higher than 8 Hz (Table 4). This demonstrates that, according to this criterion, the safety of the wagon operation is ensured. Also, this study includes an assessment of the wagon moving over a joint irregularity using mathematical modelling of its oscillations in the vertical plane (Figure 9). The calculations show that the motion of the unloaded wagon can be assessed as 'excellent' (Figures 16 and 17). The same result is obtained for the loaded wagon (Figures 18 and 19). However, the authors believe that this study has certain advantages over the known ones.