Adaptation of rectangular and trapezoidal time functions to simulate the rotational motion of the brake disc

Abstract

Numerical modeling of the rotational motion of the brake disc during frictional heating requires the use of specialized software. In this paper, an alternative approach was proposed consisting in the simulation of the displacement of the heating region contained within the boundaries of the friction surface of the brake pad relative to the stationary disc. The moving heat source effect was obtained using rectangular time functions generated based on the operating parameters and dimensions of the brake components. The first part of the article discusses the mathematical basis for the construction of time curves in relation to the solid brake disc combined with a pad in the shape of the angular section of a ring. Braking simulations were carried out using the finite element method (FEM) based software for 3D, 2D axisymmetric and 1D models of the disc. The calculated temperature filed changes were confronted with the results obtained using the 3D model developed based on standard methods. The temperature on the contact surface of the disc in the position of the mean radius at the end of braking, determined using the 2D axisymmetric and the 3D model with adaptation of rectangular time functions as well as the 3D reference model agreed well and were equal to 157.83 °C, 157.87 °C, and 157.90 °C, respectively. In the second part of the study, the 3D model of periodic heating was extended to the disc brake of a railway vehicle. The results of the calculations for the ventilated disc and segmented brake pad were compared with the experimental data obtained during testing on a full-scale dynamometer test stand. The maximum temperature values obtained on the basis of the 3D-pulse, 3D numerical models and measured on the test stand were equal to 73.3 °C, 74.4 °C and 75.6 °C, respectively. The insignificant temperature difference, i.e. below 3 %, obtained using the 3D-pulse heating model and measured using a thermocouple, confirms the correctness of the developed algorithm for simulating the rotational motion of the disc as well as the calculation methodology incorporating the heat partition coefficient (HPC).