In this paper influence of temporal profile of the specific friction power (i.e. the product of the coefficient of friction, sliding velocity and contact pressure) on thermal stresses in a friction element during braking was investigated. Spatio-temporal distributions of thermal stresses were analytically determined for a subsurface layer of the friction element, based on the model of thermal bending of a thick plate with unfixed edges (Timoshenko and Goodier, 1970). To conduct calculations, the fields of dimensionless temperature were used. These fields were received in the article (Topczewska, 2017) as solutions to a one-dimensional boundary-value problem of heat conduction for a semi-space heated on its outer surface by fictional heat flux with three, different time profiles of the friction power.
In this paper analytical solutions of the thermal problems of friction were received. The appropriate boundary-value problems of heat conduction were formulated and solved for a homogeneous semi–space (a brake disc) heated on its free surface by frictional heat fluxes with different and time-dependent intensities. Solutions were obtained in dimensionless form using Duhamel's theorem. Based on received solutions, evolution and spatial distribution of the dimensionless temperature were analyzed using numerical methods. The numerical results allowed to determine influence of the time distribution of friction power on the spatio-temporal temperature distribution in brake disc.
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