## 2 Materials and Methods
### Finite Element Analysis Conditions  
The braking system of a railway vehicle comprises a brake disc, brake pad, caliper, and additional components. To streamline the analysis and save time, the finite element (FE) model was limited to the brake disc and brake pad alone. The FE models for the brake disc and pad are depicted in Figure 3. Detailed specifications of the brake disc and friction block, including the outer/inner diameter and thickness, are outlined in Table 2. These FE  
\begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Description** & **Unit** & **Notation** & **Brake Disc** & **Brake Pad** \\ \hline Density & kg/m\({}^{3}\) & \(\rho_{d}\), \(\rho_{p}\) & 7850 & 5120 \\ Poisson’s ratio & - & \(\
u\) & 0.3 & 0.25 \\ Elastic modulus & GPa & \(E\) & 202 & 102 \\ Thermal conductivity & W/(m\(\cdot\)K) & \(k_{d}\), \(k_{p}\) & 45 & 24 \\ Specific heat & J/(kg\(\cdot\)K) & \(c_{d}\), \(c_{p}\) & 460 & 500 \\ Thermal expansion coefficient & \(1/\)K & \(\alpha\) & \(1.05\times 10^{-5}\) & \(1.67\times 10^{-5}\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Mechanical properties of the brake disc and brake pad [17].  
\begin{table}
\begin{tabular}{l c c c} \hline \hline
**Item** & **Unit** & **Notation** & **Spec.** \\ \hline Weight of the railway vehicle & kg & \(M\) & 49,060 \\ Max. velocity & km/h & \(V\) & 300 \\ Wheel diameter & mm & \(D_{w}\) & 920 \\ Outer diameter of the disc & mm & \(D_{d}\) & 640 \\ Inner diameter of the disc & mm & \(D_{i}\) & 350 \\ Thickness of disc & mm & \(t_{d}\) & 45 \\ Diameter of the friction block on pad & mm & \(D_{p}\) & 40 \\ Thickness of the friction block on pad & mm & \(t_{p}\) & 20 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Specifications of the railway vehicle.  
models consisted of 9592 nodes and 5832 elements, utilizing hexahedron solid elements (C3D8T) for the thermomechanical analysis.  
The analysis adhered to the international standard UIC 541-3 [22]. The initial velocity was set at 300 km/h, accompanied by a temperature of 60 \({}^{\circ}\)C. The braking process consisted of two stages: an initial deceleration from 300 km/h to 215 km/h, followed by a subsequent phase decelerating from 215 km/h to a complete halt at 0 km/h. Both commercial and emergency braking forces were accounted for and analyzed within the context of the finite element analysis (FEA). Figure 4 illustrates the progressive variation in the convective heat transfer coefficient during braking, showcasing a linear decline under constant deceleration for both laminar and turbulent flows. At the velocity of 300 km/h, the coefficient was measured at 273 W/(m\({}^{2}\cdot\)K). Utilizing Equation (3), the heat distribution rates were computed as 0.61 for the disc and 0.39 for the pad, respectively. Deceleration and friction coefficient values were derived based on the guidelines provided in UIC 541-3.  
To conduct the FEA, the ABAQUS/Explicit software was utilized, employing a coupled temperature-displacement analysis. Figure 3 visually represents the boundary conditions utilized for the braking analysis, encompassing definitions for contact, pressure, convection, velocity, and initial temperature.