## 3 Research on the Influence of Track Structure Stiffness Change on the Stability of Vehicle  
### Vertical Stiffness under Rail  
According to the calculation results of the simulation conditions of different vertical stiffness under rail, the maximum values of vehicle body lateral acceleration, vehicle body vertical acceleration, wheel-rail vertical force, wheel-rail lateral force, derailment coefficient, and wheel load reduction rate are summarized in Table 4 and the changes are shown in Figure 6. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Influencing Coefficients** & **Ranges** & **Value for Non-Variable Coefficients** & **Increment** \\ \hline Vertical stiffness under rail & 80–240 & 160 & 20 \\ Lateral stiffness under rail & 80–240 & 160 & 20 \\ Vertical stiffness under block & 40–160 & 100 & 20 \\ Lateral stiffness under block & 80–240 & 160 & 20 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Optimal values of track structure stiffness (unit: kN/mm). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Comparison** & **References**[28; 29] & **Calculated Value in** & **Relative Difference (\%)** \\
**Coefficient** & & **This Article** & **Relative Difference (\%)** \\ \hline Wheel-rail vertical force & 201.1 & 193.2 & 4.19 \\ Wheel-rail lateral force & 52.1 & 48.3 & 7.87 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison and verification of wheel-rail force (unit: kN). Figure 6: _Cont_. The right graphs of Figure 6 are box diagrams drawn according to the change curve of each dynamic response coefficient. The box diagrams can be used to easily view the original distribution of discrete data. The upper and lower lines of the rectangular box represent the upper and lower quartile values of the data, the lateral line in the rectangular box represents the median of the data, and the upper and lower lateral lines, respectively, represent the maximum and minimum values calculated based on the quartile values, and the rest are marked as out-of-boundary numerical points. In order to ensure the safety of train operation, China's \"Railway vehicles-specification for evaluating the dynamic performance and accreditation test\", based on the vibration intensity of the train body, sets limits on the lateral and vertical acceleration of the vehicle  
Figure 6: Variations in the stability coefficient under different vertical stiffness under rail. (**a**) Vehicle body lateral acceleration change: left-time history waveform, right-maximum, (**b**) Vehicle body vertical acceleration change: left-time history waveform, right-maximum, (**c**) wheel-rail vertical force change: left-time history curve, right-statistical distribution, (**d**) wheel-rail lateral force change: left-time history curve, right-statistical distribution, (**e**) Deraliment coefficient change: left-time history curve, right-statistical distribution, (**f**) Wheel load shedding rate change: left-time history curve, right-statistical distribution and (**g**) Wear coefficient change: left-time history curve, right-statistical distribution. body, and requires the lateral and vertical acceleration of vehicle body, respectively, no more than 0.5 g, 0.7 g. The article uses these limits as the reference limits for the study [26]. According to the analysis of Table 4 and Figure 6, when the vertical support stiffness under rail changes within the range of 80-240 kN/mm, the lateral and vertical acceleration of vehicle body varies in the range of 1.397-1.702 m/s\({}^{2}\), 1.175-1.243 m/s\({}^{2}\); none of them exceed the limits of the lateral acceleration and vertical acceleration of the \"Railway vehicles-specification for evaluating the dynamic performance and accreditation test\".