The thermal problem of friction for a three-element tribosystem with composite strip (Q656749)

This article studies transient heat generation at friction for a three-element system with a composite strip. It is assumed that heat is generated during uniform sliding on the contact surface of the homogeneous top semi-space and a composite strip deposited on a semi-infinite foundation. The thermal contact of a top semi-space and a composite strip is imperfect, i.e., the jump of temperatures takes place on the contact surface. The analytical solution of a transient thermal problem of friction for such a tribosystem is found by means of the Laplace integral transform method. This exact solution for the temperature at any point of the system for an arbitrary time moment has the form of an integral on the semi-infinite interval with the integrand of a complicated structure. Therefore, the distribution of temperature in the system is analyzed by means of the numerical integration methods. For the two limiting cases of the input parameters of the problem, namely, at the perfect heat contact between the top semi-space and composite strip, and for the imperfect heat contact between these same elements, the obtained solution can be analytically integrated. For the first time for such a three-element system, the asymptotic solutions for small and large values of the time are obtained. All the obtained solutions are verified by limiting transitions to a homogeneous material of a strip. The use of such formulas for small and large values of the Fourier number requires no numerical integration and is easy to apply for engineering calculations. The numerical analysis of the problem allows to establish the dependencies of the temperature in a tribosystem on the dimensions of the periodic cells and thermal properties of materials of composite components. Moreover, the influence of properties of materials of the top semi-space and the foundation on the contact surface temperature are studied. The obtained solution at constant specific capacity of friction has not got an independent application only. It may also be used in investigations of processes of friction by means of the Duhamel formula, in which it is necessary to take the temporary structure of friction capacity into account, for example, in braking.