# Speed Limit of Linear Induction Motor Subway Trains Running through 65 m Radius Curves on Yard Line
## 4 Derailment Safety and Speed Limit Analysis
### Wheel-Rail Extreme Wear Conditions  
As mentioned in the previous section, due to the limitation of the small radius of the curve, the wheel flange face contacts with the rail gauge face seriously in the circular curve section, which leads to a serious wheel-rail wear. The wheel-rail wear profile affects the wheel-rail contact relationship, thus affecting the traffic safety. Therefore, it is also necessary to study the traffic safety and speed limits of trains running through the yard line under the conditions of wheel rail wear.  
The worn rail profile used in this section is the actual measured profile of an overused rail on the yard line, as shown in Figure 17a. In the calculation analysis, the worn rail profile is used for the outer rail of the curve, and the new rail profile is used for the inner rail. The worn wheel profile is obtained from the worn wheel profile for running for 100,000 km after turning, as shown in Figure 17b.  
Figure 18 shows the statistics of the maximum values of the derailment coefficient, axle lateral force, duration of the derailment coefficient, and wheel unloading rate of the LIM trains running through the yard line at a speed of 25 to 5 km/h.  
Figure 18a shows that the changes in the derailment coefficient and axle lateral force with the decrease in the speed are small. At a speed of 5 to 25 km/h, the derailment coefficient is within the safety limit, while the lateral axle force exceeds the safety limit. Figure 18b shows that the duration of derailment coefficient overrun decreases with the decrease in the speed, and is within the safety limit. As the derailment coefficients are within the safety limit, the durations of derailment coefficient overrun are 0. Therefore, the LIM train does not derail when it passes through the yard line under this condition. When the wheel and rail are seriously worn, LIM trains can more easily run through the yard line, because the wheel diameter difference of the worn wheel-worn rail matching  
Figure 17: Wear profile: (**a**) worn rail profile; (**b**) worn wheel profile.  
is significantly larger than that of the new wheel-new rail matching. Figure 19 gives the wheel diameter difference comparison of the 1 st axle of the 1 st car of the worn wheel-worn rail matching and new wheel-new rail matching. The wheel diameter difference changes the alignment balance of the wheelsets. So, the larger wheel diameter difference results in a significant improvement in the train's curve passing performance.  
Further, we consider the operation safety of trains running through the yard line under conditions of a seriously worn track and new wheel matching. The derailment factor, axle lateral force, and wheel unloading rate were not significantly different (slightly improved) from the results of the new wheel-rail matching (Figure 15). Therefore, the results are not repeated here. The duration of derailment coefficient overrun under the conditions of worn rail-new wheel matching is presented in Figure 20.  
Figure 19: Wheel diameter difference.  
Figure 18: Operation safety indices vs. train running speed under extreme wear conditions: (**a**) derailment coefficient and axle lateral force; (**b**) duration of derailment coefficient overrun and wheel unloading rate.  
As shown in Figure 20, the derailment factor overrun time decreases with the decrease in the speed in the range of 5 to 25 km/h. When the speed is below 15 km/h, the derailment factor overrun time is within the safety limit. Thus, under this condition, there will be no wheel climb derailment. The comparison of Figures 15b and 20 shows that the worn rail reduces the safety when the train passes through the yard line.