## 5 Matching Analysis of Modelled Parameters
### Parameters' Calculation and Analysis
#### 5.2.2 Braking Distance and Average Braking Deceleration
The average braking deceleration can be calculated from Equation (7) and the data in Table 6, and the results are shown in Table 7 and Figure 3.  
A considerable reduction of the average braking deceleration can be captured in the progress of high-speed braking (\(v_{0}\geq 300\) km/h) from Figure 3; however, the value of the carbon-ceramic group is still significantly higher than that of the cast-steel group in each braking mode. Figure 4 reflects the changing patterns of the average deceleration difference between the carbon-ceramic group and the cast-steel group under the same braking mode. The graph shows that the difference in all three modes peaks in the process of high-speed braking, and under the initial braking speed, the average braking deceleration of the carbon-ceramic group compared with the cast-steel group is increased by 0.225-0.325 m/s\({}^{2}\), which greatly improves the braking efficiency and safety of trains. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multicolumn{1}{c}{**Initial Speed**} & **160** & **200** & **250** & **300** & **350** & **380** & \begin{tabular}{c} **Average** \\ **Value** \\ \end{tabular} \\ \hline \multirow{4}{*}{Carbon-ceramic group} & Emergency braking & 1.104 & 1.129 & 1.156 & 1.151 & 1.099 & 0.918 & \\ \cline{2-9}  & \begin{tabular}{c} Segmented \\ emergency braking \\ \end{tabular} & 1.17 & 1.161 & 1.164 & 1.138 & 1.082 & 0.906 & 1.038 & \\ \cline{2-9}  & \begin{tabular}{c} Maximum common \\ braking \\ \end{tabular} & 0.975 & 0.998 & 1.022 & 0.991 & 0.866 & 0.657 & \\ \hline \multirow{4}{*}{Cast-steel group} & Emergency braking & 0.904 & 0.925 & 0.946 & 0.933 & 0.867 & 0.650 & \\ \cline{2-9}  & \
\begin{tabular}{c} Segmented \\ emergency braking \\ \end{tabular} & 0.944 & 0.962 & 0.983 & 0.930 & 0.769 & 0.606 & 0.799 & \\ \cline{2-9}  &
\begin{tabular}{c} Maximum common \\ braking \\ \end{tabular} & 0.776 & 0.764 & 0.689 & 0.621 & 0.571 & 0.548 & \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Average braking deceleration data for braking simulation. Figure 3: Average brake deceleration graph. The same statistical method as described in Section 5.2.2 was used to analyse the maximum temperature, and it was found that the maximum temperature data of both carbon-ceramic and cast-steel groups obeyed normal distributions. The hypothesis that under the confidence level of 0.05, the maximum temperature of the carbon-ceramic brake disc increased by 200 \({}^{\circ}\)C compared with the cast-steel brake disc, could be accepted. Where the calculated value U equals 0.883, it is less than \(\mu_{0.95}\), which equals 1.645. Figure 5 shows that the peak temperature of the disc surface is approximately linear with the initial braking speed for both carbon-ceramic discs and cast-steel discs, and the temperature changes more slowly in the process of low-speed braking (\(v_{0}\leq 200\) km/h) than that in high-speed braking. The effect of the maximum temperature on the disc surface, compared between the non-slope and +15% slope, is more pronounced in low-speed braking than that in high-speed braking, and there is almost no difference at the initial speed of 380 km/h.