## 4 Analysis of Matching Parameters  
### Non-Modelled Parameters  
The non-modelled matching parameters summarised by this article are inherent properties of carbon-ceramic brake discs, which maintain a static value during train braking. There is no better fitting model for such parameters; it is appropriate to use a method of comparative conformity check for analysis. The comparative conformity check process is divided into two phases: Firstly, values of the carbon-ceramic brake discs' parameters were checked with the range of values offered by standard documents; secondly, numerical comparison between carbon-ceramic discs and well-matched cast-steel discs' parameters were carried out after the preceding checking work was finished. Parameters with different values were filtered as the second phase, and a matching analysis was carried out based on the objective of improving the overall braking efficiency of the high-speed train. The study took the axle-mounted carbon-ceramic and cast-steel brake discs for examples to reproduce the process of the comparative conformity check, and the parameters' data comes from Hunan Shixin New Materials Co., Ltd, Zhuzhou, China, and the literature [12], respectively. Non-modelled matching parameters for these two brake discs meet the requirements of \"Brakes-Disc brakes and their application--General conditions for the approval of brake pads\" [13] and \"Brake disc rolling stock\" [14]. The specific comparative analysis of the non-modelled parameters is shown in Table 3.  
Comparing the parameters with the different values in Table 1, we can find that: \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Category**} & \multirow{2}{*}{**Parameters**} & \multicolumn{2}{c}{**Value**} \\ \cline{3-4}  & & **Carbon-Ceramic** & **Cast-Steel Brake Disc** \\ \hline \multirow{8}{*}{\begin{tabular}{c} Assembly \\ interface \\ \end{tabular} } & \multirow{2}{*}{Size} & Outer diameter/mm & 670 & 640 \\ \cline{3-4}  & & Inner diameter/mm & 350 & 350 \\ \cline{3-4}  & & Thickness/mm & 80 & 80 \\ \cline{3-4}  & & Bolts’ diameter/mm & 18 & 18 \\ \cline{2-4}  & & Density/(g/cm\({}^{3}\)) & 1.95–2.10 & 7.8 \\ \cline{2-4}  & & & & \\ \cline{3-4}  & & Construction & & \\ \cline{3-4}  & & & & \\ \hline \hline \multirow{8}{*}{\begin{tabular}{c} Physical \\ characteristics \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} Elastodynamic \\ parameters \\ \end{tabular} } & \multicolumn{2}{c}{Modulus of elasticity/Gpa} & 151 & 215 \\ \cline{3-4}  & & Yield strength/Mpa & 348.5 & 1054 \\ \cline{3-4}  & & Hardness/HB & 172 & 220 \\ \cline{3-4}  & & Specific heat & 900 & 457 \\ \cline{3-4}  & & \begin{tabular}{c} Thermodynamic \\ parameters \\ \end{tabular} } & \multicolumn{2}{c}{Thermal} & 56.4 & 19.5 \\ \cline{3-4}  & & \
\begin{tabular}{c} Linear expansion \\ coefficient/(\(\mu\)/K) \\ \end{tabular} & \(1.2\times 10^{-6}\) & \(1.04\times 10^{-5}\) \\ \cline{3-4}  & &
\begin{tabular}{c} Friction coefficient \\ \end{tabular} & Average-friction coefficient & 0.36 & 0.338 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparative conformity check on non-modelled matching parameters. (a) The outer diameter of the carbon-ceramic brake disc is 30 mm larger than that of the cast-steel brake disc; therefore, the train bogies need to be equipped with more space during the assembly process of the carbon-ceramic brake discs. In other words, the clamp-axle distance must be greater than the outer diameter of the brake discs. In Figure 1, the axle of high-speed trains (type CR400 AF) is shown in the top diagram and the clamp-axle distance is shown in the bottom diagram; it has a value of 400 mm, which is larger than the outer radius of the carbon-ceramic brake disc, indicating that carbon-ceramic brake disks are well matched in the parameters of size. (b) The density of carbon-ceramic brake discs is one-fourth of that cast-steel discs, and the weight of carbon-ceramic is about two-sevenths that of cast-steel discs.