The influence of the thermal sensitivity of a coefficient of friction and thermophysical properties of the pad and disk materials on the temperature distribution during single braking has been studied. For this purpose, the corresponding one-dimensional thermal problem of friction at braking has been formulated. The solution to such nonlinear problem has been made in two stages. First, the partial linearization was carried out using Kirchhoff's substitution, and then, the initial problem for a system of nonlinear ordinary differential equations was obtained by method of lines. Numerical solution to problem was received by Adams' method realized in the DIFSUB package. For a friction pair, disk (steel)-pad (retinax), an analysis of the evolution of sliding speed and temperature was carried out. The results obtained within the model that took into account the mutual influence between the speed and temperature were compared with those obtained without taking into account such effects.

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Analytical and numerical solution for transient thermal problems of friction were presented for semi limited bodies made from thermosensitive materials in which coefficient of thermal conductivity and specific heat arbitrarily depend on the temperature (materials with arbitrary non-linearity). With the constant power of friction assumption and imperfect thermal contact linearization of nonlinear problems formulated initial-boundary thermal conductivity, using Kirchhoff transformation is partial. In order to complete linearization, method of successive approximations was used. On the basis of obtained solutions a numerical analysis of two friction systems in which one element is constant (cermet FMC-845) and another is variable (grey iron ChNMKh or aluminum-based composite alloy AL MMC) was conducted

An analytical-numerical nonlinear model to investigate temperature fields and thermal stresses in a pad and a disk for a single braking with a constant deceleration has been proposed. For this purpose, the boundary-value heat conduction problem for a tribosystem strip-semi-space has been formulated, which takes into account the temperature dependence of the thermophysical properties of materials. The solution to this problem has been obtained by a partial linearization through the Kirchhoff substitution, and next with a subsequent use of the method of linearizing parameters. Knowing the distribution of temperature fields in the elements of a friction pair, the thermal stresses have been established within the theory of thermal bending of plates. In this case, the temperature dependence of the Young's modulus, Poisson's ratio, and linear thermal expansion of the pad and disk materials have been additionally taken into account. The numerical analysis has been performed for a friction pair consisting of a titanium alloy pad and a steel disk.

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