Effect of the Heat Sensitivity of Materials on Temperature in the Course of Friction
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EFFECT OF THE HEAT SENSITIVITY OF MATERIALS ON TEMPERATURE IN THE COURSE OF FRICTION O. Evtushenko,1, 2 M. Kuciej,1 and E. Och1
UDC 536.12:621.891:539.3
We construct the numerical-analytic solution of the nonstationary thermal problem of friction for two half spaces with regard for the heat sensitivity of their materials. The corresponding boundary-value problem of heat conduction is linearized in two stages: First, we perform its partial linearization by means of the Kirchhoff substitution and then the final linearization is performed by the methods of spline-approximation and simple iteration. For the titanium–iron-alloy friction couple, we study the influence of temperature-dependent thermal conductivity on the temperature field of the tribosystem. Keywords: friction heating, thermal sensitivity, thermal contact.
The accuracy of estimation of the thermal conditions of operation of heavily loaded friction units of machines depends on taking into account in the corresponding mathematical model, namely, in the heat problem of friction, the maximum possible number of parameters exerting the decisive influence on the temperature distribution [1]. Among these factors, it is necessary to mention the heat sensitivity of materials of the frictional couple, i.e., the temperature dependence of their thermal and mechanical properties [2]. The materials whose thermal conductivity and specific heat capacity change as a function of temperature but thermal diffusivity remains constant belong to the class of materials with simple nonlinearity [3]. One can perform the complete linearization of the boundary-value problem of heat conduction for a friction couple made of these materials by means of the Kirchhoff substitution only in the case of heating of each element separately by the heat flow whose intensity is proportional to the specific power of friction [4, 5]. Therefore, the aim of the present work is to obtain the numerical-analytic solution of the heat problem of friction for the conjugation of nonstationary temperature fields of two semibounded bodies via the boundary conditions on the contact surface and to study, on this basis, the influence of heat sensitivity of the materials on the evolution and space distribution of temperature. The solution of this problem for the case of constant thermal properties of materials was obtained in [6]. Formulation of the Problem Consider two dissimilar half spaces compressed at infinity by forces of constant intensity p applied parallel to the Oz -axis (Fig. 1). At the initial time t = 0 , one of half spaces begins to move with a constant velocity V over the surface of the other half space in the positive direction of the Oy -axis. As a result of friction, heat is generated on the contact surface z = 0 and the contacting bodies are heated. 1 2
Politechnika Białostocka, Białystok, Poland.
Corresponding author; e-mail: [email protected].
Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 50, No. 1, pp. 117–122, January–February, 2014. Original article submitted June 2
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