# Performance Evaluation of Track Curvature Sensor for
## 2 Development of the Track Curvature Sensor
### Curvature Measurement Simulation  
In order to confirm the validity of the curvature measurement method described in the previous section, a multi-body dynamic analysis simulating running on a real track was performed. For the multi-body dynamic analysis of railway vehicles, VAMPIRE (Vehicle dynAmics Modelling Package In a Railway Environment), a program for analyzing the dynamics of railway vehicles, was used. The vehicle model is as shown in Figure 4. An electric railway vehicle with a high frequency of operation of the curved section was modeled. The vehicle model consists of a body, a front and bogies, and wheelsets and a suspension system. One-half of the distance between the center of the front bogie and the rear bogie (\(L\)) is 6.9 m, and lateral spacing between the curvature sensor and the bogie center (\(x\)) is 1050 mm. The track model for the vehicle running simulation was modeled as a 10 km section, which is a part of the operation section of a train. Figure 5 shows the curvature, cant, and the vertical and lateral irregularity of the track model. During analysis, the running speed of the vehicle model was set at the commercial operating speed condition (Case-1) passing through the track model section. In addition, in order to analyze the effect of driving speed on curvature measurement, the simulation was conducted by including the condition that decreased to 50% of the operating speed (Case-1) and the condition that increased by 50% of the operating speed (Case-3). Figures 6 and 7 show the results of the displacements of the curvature sensor of the front and rear bogie obtained through dynamic simulation. When running on a straight section, the displacement of the curvature sensor hardly appears, but when passing through the curved section, the bogie rotates with respect to the vehicle car body to adapt to the curve and the displacement of the curvature sensor is significantly detected. In general, when running on a curved track, the rotational resistance of the front bogie in the running direction is relatively increased compared to the rear bogie, and thus the bogie angle of the front bogie is relatively smaller than that of the rear bogie. Therefore, it is confirmed that the displacement of the front bogie's curvature sensor, which is the relative displacement between the vehicle car body and the front bogie, is relatively small compared to the displacement of the rear bogie's curvature sensor. When analyzing the displacement of the curvature sensor according to the running speed, it can be seen that the analysis result of Case-1, which is the operating speed condition, or the analysis result of Case-2 and Case-3, which change the speed, show almost similar results. Figure 4: Railway vehicle model. Figure 5: Track model for multibody dynamic simulation. Figure 6: Displacement of front curvature sensor from simulation. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & & \multicolumn{3}{c}{**Curvature (I/km)**} & & \multicolumn{3}{c}{**Deviation (\%)**} \\
**Curve** & **Track** & **Case-1** & **Case-2** & **Case-3** & **Case-1** & **Case-2** & **Case-3** \\  & **Data**  
Table 1 is the result of analyzing the mean curvature for the section corresponding to the circular curve among the curve sections and the absolute value of the deviation compared to the track inspection data. The deviation of the curvature simulation result of the commercial operating speed condition (Case-1) is only at minimum 0.5%, at maximum 2.4% and on average 1.7%, so the performance of the proposed curvature measurement method is expected to be good. In addition, to analyze the effect of speed, the analysis results of speed with a 50% reduction (Case-2) and speed with a 50% increase (Case-3) show that the average deviation is 1.8% and 1.9%, respectively, which tends to increase very slightly compared to the average deviation of 1.7% of the normal operating speed (Case-1).