# Research on Wheel Flat Recognition Based on Wayside Wheel-Rail Force
## 7 Conclusions  
Based on the impact mechanism of wheel flats and the detection principle of the wayside wheel-rail force detection system (TODS), this study investigates the fault conditions of wheel flats in heavy-haul railway freight cars, establishes a rigid-flexible coupling dynamics model of freight cars and flexible tracks, and simulates and validates the reliability of TODS' wheel-rail force concatenation method. Through simulation, the mapping relationships between wheel flats and wheel-rail impacts under both full-load and empty-load conditions are obtained. Finally, field data was measured. Combining theoretical derivation, simulation, and field measurements, the following conclusions are drawn:  
1. The wayside wheel-rail force acquisition system (TODS) is theoretically and simulation-verified. A detection section spanning 14 rail spans (covering an 840 mm wheel surface) ensures full circumferential coverage of wheel profiles. 2. Wheel flats induce periodic wheel-rail impacts. At low speeds (\(\leq\)80 km/h), the magnitude of impact first increases with speed and then decreases. Heavier vehicle loads lower the critical speed at which maximum wheel-rail impact occurs. 3. A mapping relationship is established between wheel-rail impact parameters (e.g., peak force, impact equivalent) and wheel flat characteristics (length) across different \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Number** & **Date** & **Time** & **Type** & **Vehicle Number** & **Fault Location** & **Alarm Classification** \\ \hline
1 & 17 October & 16:34 & C80 & 0018149 & Right of the 2 nd wheelset & Warning \\
2 & 18 October & 09:06 & C80 & 0024047 & Right of the 3 rd wheelset & Warning \\
3 & 19 October & 07:26 & C80 & 0018149 & Right of the 2 nd wheelset & Warning \\
4 & 23 October & 16:52 & C80 & 0026293 & Right of the 3 rd wheelset & Warning \\
5 & 23 October & 12:53 & C80 & 0028830 & Left of the 1 st wheelset & Warning \\
6 & 24 October & 15:34 & C80 & 0039023 & Right of the 2 nd wheelset & Warning \\
7 & 24 October & 13:33 & C80 & 0014170 & Left of the 1 st wheelset & Warning \\
8 & 24 October & 17:05 & C64K & 0415827 & Left of the 3 rd wheelset & Warning \\
9 & 24 October & 17:24 & C80 & 0024160 & Left of the 3 rd wheelset & Warning \\
10 & 24 October & 14:33 & C80 & 0016461 & Left of the 3 rd wheelset & Warning \\
11 & 24 October & 17:05 & C64K & 0354058 & Right of the 4 th wheelset & Warning \\
12 & 26 October & 18:02 & C80 & 0027758 & Left of the 1 st wheelset & Warning \\
13 & 26 October & 12:20 & C80 & 0017694 & Left of the 4 th wheelset & Warning \\
14 & 26 October & 13:34 & C70A & 0030607 & Left of the 3 rd wheelset & Warning \\
15 & 27 October & 15:29 & C80 & 0024851 & Left of the 4 th wheelset & Warning \\
16 & 27 October & 11:50 & C80 & 0024146 & Left of the 2 nd wheelset & Warning \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Alarm forecast of wayside detection system (data from 17 October to 27 October 2022). speeds. By detecting impact equivalents, key flat parameters (e.g., length) can be inversely calculated through these relationships. 4. The TODS and the flat length deduction method have been applied to the operational railway line. Through a period of operation, good effects in monitoring wheel flats have been achieved. Indirect comparison with the detection results of the TPDS system has indirectly verified the effectiveness of the system. These findings provide theoretical and data-driven support for wheel flat identification and real-time fault monitoring. X.P. : Conceptualization, Validation, Formal analysis, Writing--original draft. J.Z. : Supervision, Funding acquisition, Writing--review and editing. L.Y. : Validation, Writing--review and editing. Q.W. : Validation. Y.S. : Validation. L.Z. : Software, C.M. : Validation. All authors have read and agreed to the published version of the manuscript. This project is supported by National Natural Science Foundation of China (Grant No. 52102441), and Sichuan Provincial Natural Science Fundation (Grant No.