# Simulation of the Thermal Behavior of Cast Iron Brake Block during Braking Maneuvers
## 5 Results  
The FE model only considers a single brake block. Therefore, the portion of the total heat flow entering the block, calculated with Equation (7), must be determined prior to the simulation. The heat flow entering the block \(\Phi_{b}\) is calculated introducing a partitioning factor \(\alpha\), depending on the geometry of wheel and shoe and on the thermal effusivity of the contacting bodies, see Equations (8)-(10), in which \(S\) is the contact surface, \(k\) is the thermal conductivity, \(\rho\) is the density, \(c\) is the mass specific heat, and finally, subscripts \(s\) and \(w\) relate to the shoe and wheel, respectively. \[\Phi_{b}=(1-\alpha)\Phi_{th}, \tag{8}\]  
\[\alpha= \frac{\beta_{w}S_{w}}{\beta_{w}S_{w}+\beta_{s}S_{s}}, \tag{9}\]  
\[\beta_{w/s}=\sqrt{k_{w/s}\rho_{w/s}c_{w/s}}. \tag{10}\]  
The wheel and shoe contact surfaces are calculated according to Equations (11) and (12), in which \(R_{w}\) is the wheel radius, \(H_{b}\) is the block axial width, \(L_{b}\) is the block length and \(N_{bw}\) is the number of blocks per wheel as suggested by [PERSON] and [PERSON] [41]. \[S_{w} =2\pi R_{w}H_{b}, \tag{11}\]  
\[S_{r}=L_{b}H_{b}N_{bw}. \tag{12}\]  
Figures 4 and 5 show the results of the simulation of braking operation A, considering two different time steps. In fact, Figure 4 shows the brake block temperature field when the braking action ends, while Figure 5 shows the distribution of temperatures on the brake block when the maximum temperature is reached at the position where the temperature sensor is installed. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Braking** & **Braking** & **Initial Speed** & **Final Speed** & **Initial Block** & **Mean** & **Braking** & **Time Elapsed from** \\
**Maneuver** & **Distance [m]** & **Speed** & **[km/h]** & **Temperature** & **Pressure of the Brake** & **Duration [s]** & **Braking Maximum Temperature [s]** \\ \hline A & 786 & 95 & 33 & 23 & 1.12 & 47 & 271 \\ \hline B & 713 & 93 & 23 & 37 & 1.20 & 46 & 220 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Input data for the finite element (FE) model. Figure 3: Mesh of the brake pad obtained in Ansys ADPL. Figure 6 shows the altitude and speed of the vehicle, measured by the GPS sensor, the pressure on the brake cylinder, and the temperature of the brake block. The data were recorded during on track tests and are relative to braking operation A. The last plot of Figure 6 compares the trend of the brake block temperature obtained during the experimental test with the one obtained from the numerical model, and it shows a great agreement between the experimental records and the numerical predictions. In particular, the numerical model is able to correctly predict the trend of the temperature increase on the brake block due to the braking maneuver. Moreover, braking type A and B being very similar, the maximum temperature increases on the brake block at the end of the braking maneuver are very close to each other. Figures 7-9 show similar results for braking maneuver B, and even in this scenario the simulation results fit well with the trend of the real temperature of the cast iron brake block. Analyzing Figures 4 and 7 it is evident the thermal gradient on the brake block due to the thermal inertia of the material. In fact, the block surface in contact with the wheel reaches much higher temperatures. Figures 5 and 8 show the temperature of the brake block after the braking operation has been over for a significant amount of time; in fact, the material thermal inertia requires a certain amount of time to heat up the material block at the location where the thermal sensor is installed. Results show that the central part of the block reaches lower temperatures with respect to the edges, and this effect can be related to the prominence used to connect the block to the holder, which has a high thermal inertia. Figure 4: Braking maneuver A—Temperature of the brake block at the end of the brake maneuver.