## 5 Conclusions  
A thorough analysis of the 412W gondola car used in Poland (also by Polish State Railways) in terms of its nonlinear features revealed the existence of several such features. On the other hand, the only unfavourable nonlinear features closely related to the car's real conditions of exploitation were its stability features. It appeared that unfavourable features of this type concern the studied gondola car in its fully loaded state. The same vehicle in an empty state possesses satisfactory stability properties for the real conditions of its exploitation. The stability map in Figure 5, for the empty car, represents its uniform character for all curve radii \(R\), including on an ST (\(R=\infty\)). Most importantly, the nonlinear critical velocities \(v_{n}\) for all these \(R\) values are above the maximum admissible exploitation velocity \(v_{nd}\), equal to 33.3 m/s (120 km/h). The smallest \(v_{n}=37.2\) m/s exists for an ST. This means that the empty car avoids (is protected against) hunting motion, which is certainly desirable. In the case of the stability map for the fully loaded gondola in Figure 6, the stability features are not as uniform as those of the empty gondola. One can see uniform solutions starting at \(R=3000\) m and going down to \(R=1200\) m. On an ST at \(R=6000\) m, additional, untypical, and, to some extent, unfavourable bifurcations of the solutions from stable periodic solutions to stable stationary solutions exist above the critical velocity \(v_{n}\). Moreover, the \(v_{n}\) values for \(R=\infty\), 6000 m, and 3000 m are smaller than or relatively close to the maximum admissible exploitation velocity \(v_{nd}\). \(v_{n}\) equals 30.8, 45.5, and 33.0 m/s, respectively. So, formally, an ST and \(R=3000\) m appeared to need correction from the viewpoint of the exploitation velocities. Consequently, the corresponding measures were determined successfully. The analysis of a gondola freight car with Y25-type bogies shows there is potential to improve its motion properties through minor corrections to the suspension parameter values. From the point of view of the tested vehicle model's properties, it is possible to increase the car's critical velocity in the laden state by reducing the lateral stiffness in the primary suspension \(k_{zy}\) by a dozen percent or so relative to the nominal value. Reducing \(k_{zy}\) to 80% of its nominal value is indicated as a recommendation by the authors. In addition  
Figure 13: Influence of lateral stiffness \(k_{zy}\) on the first wheelset of an empty car. \(k_{zy}=389*10^{5}\) N/m—nominal value (black line), \(k_{zy}=35*10^{5}\) N/m \(\cong 90\%\) of nominal value (red line), \(k_{zy}=31*10^{5}\) N/m \(\cong 80\%\) of nominal value (blue line). Motion on a CC with \(R=3000\) m: (a) maximum absolute value of lateral displacement; (b) peak-to-peak value of wheelset’s lateral displacement. to the higher critical velocity value on an ST (\(v_{n}\) = 136.1 m/s), the critical velocities on CCs increased favourably for all \(R\) values, too. They were \(v_{n}\) = 107.1 and 103.6 m/s for \(R\) = 6000 and 3000 m, respectively. Furthermore, a reduction in \(k_{xy}\) causes the disappearance of periodic solutions with very small peak-to-peak values on CCs. This could mean an improvement in the quality of real gondola cars of the studied type to negotiate curved tracks. One should notice that reducing \(k_{xy}\) to just 90% of its nominal value could also be counted as a successful measure for improving the gondola's nonlinear features. Then, \(v_{n}\) for an ST, at \(R\) = 6000 m, and at \(R\) = 3000 m equal 36.9, 102.1, and 34.6 m/s, respectively. All of these values are greater than 33.3 m/s. On the other hand, two of them are quite close to \(v_{ad}\). In particular, the value for \(R\) = 3000 m resulted in a safety margin that was too small. One should also remember here that the accuracy of determining \(v_{n}\) is limited.