Abstract
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.
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REFERENCES
V. M. Aleksandrov, “Axisymmetric contact problem for an infinite elastic cylinder,” Izv. Akad. Nauk SSSR, Mekh. Mashinostr., No. 5, 91–94 (1962).
V. M. Aleksandrov and B. L. Romalis, Contact Problems in Mechanical Engineering [in Russian], Mashinostroenie, Moscow (1986).
N. Kh. Arutyunyan, “Contact interaction of an elastic ring with an elastic cylinder,” Izv. Ross. Akad. Nauk, Mekh. Tverd. Tela, No. 2, 204–206 (1994).
V. V. Panasyuk and M. I. Teplyi, Some Contact Problems of the Elasticity Theory [in Russian], Naukova Dumka, Kiev (1975).
Yu. N. Drozdov, D. V. Grilitskii, and V. P. Levitskii, “Contact of a pair of rotating circular cylinders with allowance for friction-induced heat formation,” Trenie Iznos, 12, No.6, 974–980 (1991).
D. V. Grilitskii and P. P. Krasnyuk, “Elastic contact of two cylinders,” Fiz.-Khim. Mekh. Mater., 33, No.3, 31–38 (1997).
P. P. Krasnyuk and R. B. Chapovskaya, “Thermoelastic contact of a shroud ring and a cylinder under conditions of friction-induced heat formation,” Fiz.-Khim. Mekh. Mater., 36, No.3, 42–52 (2000).
G. A. Korn and T. M. Korn, Mathematical Handbook for Scientists and Engineers, McGraw-Hill, New York (1961).
I. Ya. Shtaerman, Contact Problem of the Elasticity Theory [in Russian], Gostekhteoretizdat, Moscow (1949).
A. S. Galitsyn and A. N. Zhukovskii, Integral Transforms and Special Functions in Heat-Conduction Problems [in Russian], Naukova Dumka, Kiev (1976).
D. V. Grilitskii and P. P. Krasnyuk, “Thermoelastic contact of two cylinders with nonstationary frictional heat formation,” J. Appl. Mech. Tech. Phys., 38, No.3, 428–436 (1997).
M. Abramowitz and I. A. Stegun (eds.), Handbook on Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Dover, New York (1972).
P. P. Krasnyuk, “Separation of contacting surfaces in thermoelastic interaction of two cylinders with time-dependent heat release due to friction,” J. Appl. Mech. Tech. Phys., 45, No.5, 712–723 (2004).
C. J. Tranter, Integral Transforms in Mathematical Physics, Wiley, London-New York (1966).
I. P. Natanson, Structural Theory of Functions [in Russian], Gostekhteoretizdat, Moscow (1949).
G. Ya. Popov, Concentration of Elastic Stresses near Stamps, Cuts, Inclusions, and Reinforcement [in Russian], Nauka, Moscow (1982).
V. M. Aleksandrov and E. V. Kovalenko, Problems in Continuum Mechanics with Mixed Boundary Conditions [in Russian], Nauka, Moscow (1986).
I. I. Vorovich, V. M. Aleksandrov, and V. A. Babeshko, Nonclassical Mixed Problems of the Theory of Elasticity [in Russian], Nauka, Moscow (1974).
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 4, pp. 161–178, July– August, 2005.
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Krasnyuk, P.P. Thermoelastic Contact of a Shroud Ring and a Cylinder under Unsteady Friction-Induced Heat Release. J Appl Mech Tech Phys 46, 594–608 (2005). https://doi.org/10.1007/s10808-005-0113-6
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DOI: https://doi.org/10.1007/s10808-005-0113-6