# Speed Limit of Linear Induction Motor Subway Trains Running through 65 m Radius Curves on Yard Line
## 4 Derailment Safety and Speed Limit Analysis  
### Conventional Conditions  
As the yard line is often designed with an S-curve, we use the line shown in Figure 10, where the radius of the circular curve is 65 m. The radius of the curve turning to the right is defined as positive, while the opposite is negative. Because of the low speed of trains running on the yard line (usually below 25 km/h), the yard line usually is not set ultra-high. The wheel-rail contact exhibits the profile of a new wheel and new rail, with the US five-level spectrum excitation. When the train runs at a speed of 25 km/h on the yard line, the attack angle of the wheelset and derailment coefficient of the first wheelset of the first vehicle are calculated, as shown in Figure 11a,b, respectively. When the wheelset has a counter clockwise angle of rotation with respect to the track, the defined attack angle is positive, while a clockwise angle is negative, as shown in Figure 12.  
Figure 11a shows that when the wheelset passes the first curve of the S-shaped curve, the angle attack of the wheelset is positive, while the angle attack is negative when it passes the second curve. Figure 11b shows that, at this time, the wheelset derailment coefficient is seriously overrun, i.e., the wheelset has a tendency to climb the rail at this time so that it is necessary to strictly control the time when the derailment coefficient exceeds the limit to avoid a derailment. Thus, the duration of derailment coefficient overrun is chosen as a derailment criterion in this study. Figure 13 shows that the maximum static derailment coefficient of each car exceeds the static derailment limit of 0.8. The maximum value occurs when the vehicle passes through the straight point of the curve. Figure 10: Line setting. Figure 11: Attack angle and derailment coefficient: (**a**) attack angle of the wheelset; (**b**) derailment coefficient. Figure 12: Attack angle diagram. Figure 14 shows time-domain simulation results of the maximum value of the derailment coefficient for each car under these operation conditions and statistical results of the duration of derailment coefficient overrun. The duration of derailment coefficient overrun exceeds the safety limit (15 ms) for the 1 st axle of the 3 rd car and the 1 st axle of the 6 th car. Therefore, a climbing derailment occurs when the train runs on the entry line at a speed of 25 km/h. Statistical results of subway vehicle derailment accidents of subway vehicles on the yard line also demonstrated that the middle car of the train derails first (often the third car). To determine the speed safety limit of the train running on the yard line, Figure 15 shows statistical results of the derailment coefficient, axle lateral force, duration of derailment coefficient overrun, and wheel unloading rate for trains running through the yard line at speeds of 5 to 25 km/h. Figure 14: Statistical results of the duration of derailment coefficient overrun. Figure 13: Derailment coefficient time-domain diagram. As shown in Figure 15a, the changes in the derailment coefficient and axle lateral force with the decrease in the speed are small, but both seriously exceed the safety limits. Figure 15b shows that when the speed is below 20 km/h, the duration of derailment coefficient overrun decreases with the decrease in the speed, and is within the safety limit. In addition, the wheel unloading rate decreases with the decrease in the speed, and is within the safety limit when the speed is below 25 km/h. According to this criterion, when the train passes on the yard line at a speed below 20 km/h, there would be no wheel climb derailment and overturning derailment. To illustrate the reason for the overrun of the axle lateral force, Figure 16 shows the changes in the wheel/rail lateral force and axle lateral force of the 1 st axle of the 1 st car in the time domain when the train passes the yard line at a speed of 25 km/h.