# Experimental and Mathematical Study of Flexible-Rigid Rail Vehicle Riding Comfort and Safety
## 6 Conclusions  
Flexible-rigid rail vehicles are characterized by a combination of rigid and flexible components which interact with each other to determine the vehicle's behaviors. An important aspect of experimental and numerical analysis is accurately modelling these interactions and identifying ways to improve them. This can involve analyzing the behaviors of flexible components, such as the car body and bogie, and their interaction with rigid components, such as the wheels and track. The dynamic response of a rail vehicle using experimental and simulation analysis on a multi-rigid-flex body model was investigated. A mathematical model is developed by keeping the bogie frame and wheelsets rigid, and the car body is used as a flexible and rigid body, respectively. ANSYS is used to build a finite element model for the car body, and substructure and modal analyses are performed. The mathematical model is validated through the experiment conducted by RDSO. Based on  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Speed (Km/h)**} & **Rigid-Flexible** & **Multi-Rigid** & \multirow{2}{*}{**Experimental (E)**} & **\% Error = \((\frac{E-RF}{E})*100\)** & **\% Error = \((\frac{E-MR}{E})*100\)** \\ \hline
30 & 0.124 & 0.121 & 0.129 & 3.876 & 6.202 \\ \hline
60 & 0.139 & 0.130 & 0.146 & 4.7  
the substructure analysis, it has been determined that the first vertical bending frequency of the system is 12.14 Hz, the first lateral bending frequency is 14.25 Hz, and the first torsion frequency is 19.87 Hz. Comparing the experimental and simulation results for the considered speed range of 30-180 km/h using the Sperling Ride Index has shown that the ride comfort, mean derailment coefficient, and mean wheel load reduction rate varies for both RF and MR simulations. The % error for the RF simulation in ride comfort varies from 4 to 14%, in mean derailment coefficient from 5 to 9%, and in mean wheel load reduction rate from 3 to 15%. The % error for the MR simulation in ride comfort varies from 0.4 to 6%, in mean derailment coefficient from 8 to 14%, and in mean wheel load reduction rate from 6 to 14%. Therefore, using a rigid-flexible coupling dynamic model provides more accurate results than the rigid body dynamics model in terms of mean derailment coefficient and mean wheel load reduction rate. The simulation result shows that the elastic vibration may not be ignored in the vehicle dynamics, because the rigid-flexible coupling model is marginally larger than the rigid-body model of ride comfort and safety compared with experimental results.  
[PERSON] and [PERSON] prepared the inspection system for the experiment and performed the experiments presented in this research. [PERSON] conceived the original idea. [PERSON] designed the methodology, gave guidance, and helped to improve the quality of the manuscript. [PERSON] wrote the original draft preparation in consultation with [PERSON], who reviewed and edited the final manuscript. All authors have read and agreed to the published version of the manuscript.  
This work was supported by a National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2019R1A5A8083201) and Korea Institute of Energy Technology Evaluation and Planning (KETEP) grant funded by the Korea government (MOTIE) (2021400000480, Development of R&D engineers for combined cycle power plant technologies), No. 2020 RIGIA1011142).  
Not applicable.  
The authors declare no conflict of interest.