Abstract
We consider a one-dimensional model of friction contact of two layers of different nature. The lower surface of the first layer is elastically fixed and the second layer is pressed to the upper surface of the first layer and moves along this surface with variable velocity. As a result of friction, heat is produced on the contact surface according to the Amonton's law. For known boundary and initial conditions, we pose the problem of evaluation of the friction coefficient and the intensity of friction heat flux according to given values of the vertical displacements of the upper surface of the second layer. The posed problem is reduced to the inverse contact problem of thermoelasticity described by the Volterra integral equation of the first kind. The solution of the problem obtained by the method of averaging of functional corrections enables us to study the time behavior of the indicated quantities for the entire period of interaction of the bodies and establish the dependence of the friction coefficient on the basic parameters of the process (sliding velocity, contact pressure, and temperature of the contact surface). The solution of the direct contact problem of thermoelasticity is used to perform the numerical verification of the proposed method for the solution of the inverse problem.
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REFERENCES
É. D. Braun, Yu. A. Evdokimov, and A. V. Chichinadze, Simulation of Friction and Wear in Machines [in Russian], Mashinostroenie, Moscow (1982).
B. I. Kostetskii (editor), Surface Strength of Materials in Friction [in Russian], Tekhnika, Kiev (1976).
D. V. Hrylits'kyi, Thermoelastic Contact Problems in Tribology [in Ukrainian], Institute of Methodology of Teaching, Kiev (1996).
G. P. Cherepanov, “Inverse problems of the two-dimensional theory of elasticity,” Prikl. Mat. Mekh., 38, No. 6, 963–979 (1974).
V. G. Yakhno, Inverse Problems for Differential Equations of Elasticity [in Russian], Novosibirsk, Nauka (1990).
N. Noda, “Optimal heating problem for transient thermal stresses in a thick plate,” J. Thermal Stresses, 11, No. 2, 141–150 (1988).
B. L. Pelekh, A. V. Maksymuk, and I. N. Korovaichuk, Contact Problems for Layered Structural Elements and Bodies with Coatings [in Russian], Naukova Dumka, Kiev (1988).
V. V. Shirokov and O. V. Maksymuk, “Analytic methods for the evaluation of contact interaction of thin-walled structural elements,” Fiz.-Khim. Mekh. Mater., 38, No. 1, 51–61 (2002).
A. D. Kovalenko, Thermoelasticity [in Russian], Vyshcha Shkola, Kiev (1975).711
M. A. Lavrent'ev and B. V. Shabat, Methods of the Theory of Functions of Complex Variable [in Russian], Nauka, Moscow (1973).
A. V. Yasins'kyi, “Reconstruction of the temperature field and thermal stresses in layers with friction contact according to displacements,” Fiz.-Khim. Mekh. Mater., 38, No. 6, 43–50 (2002).
A. Yu. Luchka, Projection-Iterative Algorithms for the Solution of Differential and Integral Equations [in Russian], Naukova Dumka, Kiev (1980).
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Yasins'kyi, A.V. Inverse Problem of Evaluation of the Coefficient of Friction of Layers According to the Data of Measurements of the Surface Displacements. Materials Science 39, 704–711 (2003). https://doi.org/10.1023/B:MASC.0000023510.47497.0b
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DOI: https://doi.org/10.1023/B:MASC.0000023510.47497.0b