Thermoelastic contact of a shroud ring and a cylinder under unsteady friction-induced heat release

Mathematical formulation is performed and a solution is found for a quasi-static thermoelastic problem of contact interaction of an elastic shroud ring and a hollow circular cylinder inserted into this ring, which are compressed by a load varied along the axis of the system, under the condition of an unloaded contact over the ring surface or over the circumference contour. The radial displacements of the contact surface of the shroud ring are approximated by displacements of the surface of a long circular hollow cylinder. Unsteady friction-induced heat release caused by the action of friction forces owing to shroud ring rotation over the cylinder with a time-dependent low angular velocity is taken into account. The problem is reduced to a system of integral equations whose structure is determined by the form of thermophysical contact conditions. A numerical algorithm of the solution is proposed, and the influence of the problem parameters on the contact pressure and temperature distributions is considered. Based on an analysis of results, a conclusion is made that the character of axial variation of the compressing load has a significant effect on the distribution of contact pressure in describing the kinematic condition of interaction of bodies in accordance with Hertz’s theory.