# Research on Wheel Flat Recognition Based on Wayside Wheel-Rail Force
## 4 Wheel Flat Shock Effect and Its Mapping Relationship  
Figure 8 presents wheel-rail force simulation results for a 30 mm flat at 50 km/h. The vehicle traverses the elastic track segment between 0.7 and 1.7 s, revealing distinct wheel-rail force characteristics between elastic and non-elastic rail sections. The wheel flat induces periodic impact forces: when the flat length is 30 mm and speed reaches 80 km/h, the peak wheel-rail force reaches 150 kN--approximately six times the static wheel-rail force (\(\approx\)25 kN). Under higher vehicle loads or speeds, these impacts could theoretically exceed current magnitudes. Continuous periodic impact is a defining characteristic of wheel flat faults. Figure 8 illustrates continuous wheel-rail force profiles under a flat condition, but the TODS measures discrete wheel-rail forces. The model's displacement sensor outputs mimic vehicle passage signals (as an alternative to the proximity switch in the simulation model), as shown in Figure 9. To align with real-world wayside detection data, discrete wheel-rail forces from the simulation model are processed, as depicted in Figure 10.  
Figure 8: Continuous wheel–rail force data. Figure 9: A single vehicle passing a signal in simulation (by using a displacement sensor). The top of Figure 10 shows the continuous wheel-rail force signal measured by the on-board wheel-rail force testing unit in SIMPACK. By combining the time when the vehicle enters/leaves the valid sections (such as the signal shown in Figure 9), the continuous wheel-rail force signal can be segmented according to the time of the effective testing interval, resulting in the discrete wheel-rail force signal shown in the middle of Figure 10. Finally, the discontinuous, discrete wheel-rail force signals in Figure 10 are connected in the same time domain, yielding the simulated concatenation wheel-rail force signal at the bottom of Figure 10, which is consistent with TODS. The bottom plot demonstrates that while TODS cannot provide continuous impact profiles like onboard systems, its full-circumference coverage ensures at least one impact signal per wheel rotation. This allows for identifying wheel damage and estimating flat length via detected impact signatures. By analyzing the wheel-rail impact-flat parameter mapping through this wayside force simulation model, the reliability of subsequent wheel fault identification in wayside detection systems is fundamentally ensured. By extracting peak wheel-rail forces for all wheel flat conditions under empty vehicle operation, a force-speed relationship curve is generated (Figure 11). As previously discussed, wheel-rail impact forces decrease proportionally once the vehicle exceeds the critical speed, whereas forces increase with speed below this threshold. Notably, a near-linear relationship exists between impact force magnitude and wheel flat length. The force-speed curve in Figure 11 is fitted using polynomial regression to quantify this relationship. Figure 10: Simulation of continuous wheel–rail force connection process based on the wayside detection system. In practical scenarios, wheel flat impacts on the track are most pronounced and damaging under loaded conditions. Therefore, analyzing flat-induced forces in heavy-load scenarios is critical. Under heavy load, the vehicle dynamics model undergoes parameter adjustments compared to the empty state, primarily in carbody mass, center of gravity (CG) position, and bolster CG position (Table 2). The elastic wheelset and track models are retained, with other dynamics parameters remaining consistent with the empty vehicle model. Figure 12 presents wheel-rail force simulation results for a 50 mm wheel flat under heavy-load conditions at 30 km/h. Correspondingly, the vehicle traverses the elastic track region between 0.6 and 1.7 s. Under heavy load, a 50 mm flat at 30 km/h generates a peak wheel-rail impact force of 596 kN--4.768 times the static wheel-rail force and 3.97 times the impact force under empty-load conditions.