# Simulation of the Thermal Behavior of Cast Iron Brake Block during Braking Maneuvers
## 1 Introduction
[16] investigated the wear of different brake shoe materials at elevated temperature by means of a pin-on-disk. Modeling of the wheel-block thermo-mechanical interaction is of paramount importance to improving the performance of the braking systems and to reducing maintenance costs related to the replacement of brake blocks or to the re-turning of the wheel tread surface. In particular, an accurate modeling of the brake block temperature can be helpful to correlate on-board recorded data to the wheel-shoe contact temperature, which is difficult to measure directly. Several works in the railway literature deal with modeling of the block temperature, typically using FE software packages, thanks to the large computational efficiency and power of modern computers. [PERSON] [17] built a 2D plane strain FE model to investigate TEI phenomena and hot spot formations on the wheel tread for both cast iron and composite brake shoes, by superimposing an initial perturbation on the contact pressure. The author found that hot spots are produced when cast iron shoes are adopted; however, the experimental results were not in full accordance with the experimental observations [17], due to the limits of the model. [PERSON] [18] implemented a 2D FE model of wheel and block, modeling both bodies as circular sectors and applying convection boundary conditions on the free surfaces of the block and a heat flux boundary condition on the contact surface, with the repartition of the total friction heat calculated by introducing the thermal resistances of the block and the wheel, considered as proportional to the local normal contact pressure, whose distribution was assumed a priori. [PERSON] [19] developed a 2D FE model of an elastic block and a rigid wheel, solving the contact problem by superimposing [PERSON]'s conditions and considering also the block wear, using temperature-dependent laws for the calculation of the wheel-block friction and of the block Archard's wear coefficient. The author performed several simulations to find optimal values of different design properties of the system, including friction coefficient and thermal and mechanical properties of the block. [PERSON] and [PERSON] [20] carried out an experimental-numerical activity, first performing drag braking tests on a 1:4 scaled rig, measuring the temperatures of the block and wheel and the block wear, and then developing a 3D FE coupled thermo-mechanical model of the scaled system, considering the mutual influence between thermal stresses and contact pressure, as well as the dependency of the wear coefficient on temperature. To save the computational time, the wheel was modeled as a rigid body, and only half of the block was modeled, superimposinga symmetry condition with respect to a plane perpendicular to the wheel axis. The total friction heat was partitioned between the wheel and the block using a constant partitioning factor. [PERSON] and [PERSON] [21] used a 2D axisymmetric decoupled model and a 2D thermoelastic model of wheel and block to investigate the wear of different brake block materials in typical commuter train operations, and later the research group calibrated the second model using data collected on a Stockholm commuter train [22]. [PERSON] et al. [23] developed a 3D FE model of a brake block, meshed with a grid of hex-type elements, to study the temperature field in the block at different states of surface wear for three values of the pressing force, finding that with a worn surface the mean and peak temperatures increase, thus leading to a reduction of the friction coefficient. Modeling of the wheel-block thermo-mechanical behavior can help in designing new brake systems and brake shoe materials with desired properties and behaviors, to reduce the number of maintenance interventions and their corresponding costs. In addition to modeling, a continuous monitoring of the brake block temperature can be a useful strategy to detect possible faults as soon as they occur, with a big increase in the safety of the whole system.