## 3 Results and Discussion
### Bogie Retrofit Influence  
The multibody simulation results using the VAMPIRE software showed a significant decrease in the T\(\gamma\)/A indicator when comparing the original ride control bogie design with the proposed retrofit. The graph in Figure 10 illustrates the retrofitted bogie's results on the 300 m radius curve for the left-hand wheels. It should be noted that, because the curve considered in the modeling is directed to the right, there will be no flange touch of the inner wheels (right). The used value was the maximum value of all curves. Tables 4 and 5 present the comparative results of T\(\gamma\)/A for the current design conditions for empty and loaded HFTs with ride control bogies and the retrofit application according to curve type using different radius values. Examining the table that includes the simulation results and relating it to the Lewis laboratory tests, the wear rate is shown to be constant (55 ug/m/mm\({}^{2}\)) in the severe wear regime for T\(\gamma\)/A values between 10.4 and 77.2 N/mm\({}^{2}\). Thus, in curves with tighter radii that are smaller than 450 m for empty and 400 m for loaded HFT, there is no gain for the retrofitted bogie, even in conditions with lower wear indicator values. However, for curve radii between 450 and 500 m for empty conditions, the wear regime changes and is characterized as medium. In this regime, the wear rate is proportional to T\(\gamma\)/A, multiplied by a factor of 5.3. The reduction in the wear indicator is reflected in the wear rate, in which the retrofitted bogie presents a significant percentage gain, reducing the wear rate. For open curve radii greater than 500 m for empty and 400 m for loaded HFT, the retrofitted bogies present an even more favorable behavior to reduce wear. In these curves, which exist in greater quantities, the bogies no longer touch the flange, which directly reduces wear. Figure 10: T\(\gamma\)/A left side wheels. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c c} \hline \hline
**t1** & **r1** & **s1** & **t2** & **r2** & **s2** & **t3** & **r3** & **s3** & **t4** & **r4** & **s4** & **t5** & **r5** & **s5** & **t6** & **r6** & **s6** \\ \hline
1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ \hline
**t7** & **r7** & **s7** & **t8** & **r8** & **s8** & **t9** & **r9** & **s9** & **t10** & **r10** & **s10** & **t11** & **r11** & **s11** & **t12** & **r12** & **s12** \\ \hline
0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Integer programming results. It should be noted that the loaded conditions presented lower wheel wear indicator values than empty conditions for the retrofitted bogie. The relationship between the longitudinal force acting on the pad and the pad stiffness can explain this. This force was enough to compress the pad and use the gap between the adapter and the side frame pedestal, resulting in less angle of attack. To extrapolate the results obtained for curves with other radius values, linear regressions were performed, and the functions were found to correlate with the radius with T\(\gamma\)/A. The regressions showed a high R\({}^{2}\) value, indicating a good correlation between the variables; therefore, it is possible to use the linear function. Thus, using the permanent track record for the corridor curves, T\(\gamma\)/A values were obtained for all curves, considering the circular radius and distance. * (Empty HFT 1L without retrofit ): y = \(-\)0.054x + 36.03; R\({}^{2}\) = 0.9995;
* (Empty HFT 3L without retrofit): y = \(-\)0.0406x + 29.01; R\({}^{2}\) = 0.9988;
* (Empty HFT 1L with retrofit): y = \(-\)0.0612x + 35.9; R\({}^{2}\) = 0.9976;
* (Empty HFT 3L with retrofit): y = \(-\)0.0448x + 30.22; R\({}^{2}\) = 0.996. Considering the equations for empty HFT, the retrofit could decrease wheel wear by 33.6%. Considering the regressions for loaded vehicle conditions, the retrofit could reduce wheel wear by 47%.