## 3 Results and Discussion  
### Bogie Maintenance Influence  
The obtained wear function is the variation in the rate as a function of the flange thickness, with higher values for the new flange (32 mm). This effect can be explained by the smaller difference in the rolling radius of the new wheels in curves, as wheels with thicker flanges reduce the lateral displacement. This condition reduces the steering moment, an important force couple that promotes the curve inscription. It is noteworthy  
Figure 8: HFT 3D modeling. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Frequency** & **Mode** & **f\_[n](Hz)** \\ \hline
1 & Roll & 0.58 \\ \hline
2 & Pitch & 1.74 \\ \hline
3 & Bounce & 1.76 \\ \hline
4 & Upper center roll & 2.57 \\ \hline
5 & Yaw & 2.54 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Modal analysis results. Figure 7: HFT roll signal measured—maximum peak-to-peak of 0.11 rad/s. that this behavior justifies the use of wheels with a 32 mm flange instead of a 36 mm initial flange, which would make the wear rate even higher. The obtained wear function is not defined for flanges smaller than 26 mm due to the sampling that was used. The operation strategy removes wheels from circulation with a 24 mm flange thickness in the off-season. Thus, although the function is not linear, the average wear rate of the sample for all flange thicknesses was 2.5 \(\times\) 10\({}^{-5}\) mm/km. Considering this rate, it is possible to carry out the maintenance plan by contemplating the need to replace the wheels. Therefore, considering the three useful lives of the wheels, the expected lifespan of the wheel is approximately 9 years. Although there are differences in the hardness of each wheel's lifespan due to the heat treatment in the manufacturing process, which influences the wear behavior, this projection considers them to have the same performance. To identify bogies with a poor performance and wheel wear rate that is higher than average, the uneven wedge criterion was used. This provides the warp conditions of the bogie and the angle of attack, even on tangents, and consequently increases the wear rate. This criterion was chosen due to the analysis of the wedge conditions that presented this characteristic. In general, high wedges were not found above 39.7 mm. Among the sample of measured vehicles, a high wear rate was observed in bogies with an unevenness wedge greater than 16 mm on the same side of the bogie. One of these wedges was under the initial height of 17.5 mm. These wagons represented 4.6% of the measured sample, and the worst wheel wear rate was 6.42 \(\times\) 10\({}^{-5}\) mm/km. The wagons, on average, circulated close to 100,000 km per year, with the bogies with uneven wedges. These spent approximately 4 mm more flange thickness wear per year on wheels with the highest wear rate, representing a useful life expectancy of 4 years. Figure 9 illustrates the wear rate for the average bogie without retrofitting and for warp bogies with an unevenness greater than 16 mm. The wear rate values obtained for different bogie maintenance conditions were applied in the modeling developed in Item 3.1 of the methodology. Thus, considering the average costs of bogie correction, wheel replacement, and turning, it is possible to define the best maintenance strategy for minimal costs. The results of the integer linear programming indicated that if the initial wheel wear rate of a vehicle is 6.42 \(\times\) 10\({}^{-5}\) mm/km, the best strategy is to consider the bogie fixing in the first year, as the maintained bogie can consider two turning costs over a nine-year projection. Therefore, after adding the bogie maintenance cost and two turnings, the total cost will be BRL 3783.00. The costs of the modeling are the current values used in the VLI maintenance budget and are related to the Brazilian market. This result represents a gain in relation to what is currently practiced for this bogie condition, in which the total cost would be BRL 7898.00.