“THIRD BODY” AS A MATHEMATICAL MODEL OF CONTACT THERMOELASTICITY

Abstract

The variety of factors affecting the thermal conditions of a frictional couple results in complexity of the simulation of this problem. Among these factors, thermophysical (thermal conductivity, specific heat, coefficient of linear expansion of bodies, etc.) and also mechanical ones (elasticity, hardness of contacting bodies, etc.) play an important role. The conditions of friction, wear and heat generation are also determined by the characteristics of the so-called “third body”, i.e., thin near-surface and intermediate layers, the physical and mechanical properties of which differ from those of the interacting bodies, and by the microgeometry of their surfaces in the contact zone. The method of determination of thermal contact conductance in mathematical modelling of contact interaction with considering friction and hear generation by “third body” is presented. Using of modified conditions of heat contact in mathematical model of contact thermoelasticity taking into account of friction and heat generation is proposed. After numerical analysis, the graphs of dependence of thermal contact conductance on the input parameters are constructed and substantial influence of some of them is detected. In the trybological problems a contact pressure in the different points is different, so contact thermal conductivity is not constant value for this different points. The one-dimensional non-stationary contact problem of thermoelasticity with heat generation of friction on the border of two half-spaces for finding of the influence of some physical and mechanical parameters on the temperature and heat fluxes in the contact bodies is investigated. This contact problem is equivalent to superposition of two one-dimensional contact problems of thermoelasticity. The three most typical different cases of given stresses are investigated. The solution of problems by Laplace integral transformation is constructed. The analytical expressions for distributions of temperature and heat fluxes is obtained. On the base of numerical analysis, the dependence of thermal conductivity on different input factors is investigated, corresponding graphs are built, essential or not substantive influence of certain factors is detected.