Axisymmetric Finite Element Model for the Calculation of Temperature at Braking for Thermosensitive Materials of a Pad and a Disc

Abstract Formulation of temperature dependence of thermophysical properties of materials in the braking systems involves the difficulty of mathematical and numerical description of the problem, and is typically ignored assuming their constancy regardless of the magnitude of load and the working time. The purpose of this article is to study an effect of thermal sensitivity of a pad and disc materials on the temperature distributions during single braking. In the first stage, a boundary value axisymmetric problem of heat conduction with temperature-dependent thermal conductivity and specific heat was formulated. The analytical temperature dependence of these properties for four various materials of the pad and the disc were obtained by approximation of the corresponding experimental data. Taking account of these relations, the solution of the boundary value problem of heat conduction by using the finite element method was obtained. The determined values of temperature for thermosensitive materials were compared with the corresponding results for constant thermophysical properties of the same materials. In the vast majority of the types of used materials, an insignificant influence of the variations of their thermophysical properties on the temperature was revealed both in the pad and disc; an exception was the titanic pad. A possible explanation is very strongly associated, unlike other materials, with the temperature dependence of the thermal effusivity of titanium on the resulting temperature of the pad and disc. Acknowledgments This article was financially supported by the National Science Centre in Poland (research project no. 2011/01/B/ST8/07446).