Determination of limiting radii of the contact area in axi-symmetric contact problems with frictional heat generation

Yevtushenko, A.A.; Kulchytsky-Zhyhailo, Roman

doi:10.1016/0022-5096(94)00073-e

Cited by 24 publications

(9 citation statements)

References 6 publications

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“…By substituting the coefficients [3* and ~-i, i = 1, 2, specified by relations (21) and (7), respectively, in relation (24) It is easy to see that the established expression for the critical radius of the contact region coincides with the corresponding expression presented in [3] provided that 3. * = 0 or 51 = 52 .…”

Section: + ~T! Dt Tf(xg'___(x))'___~+2~i Dt I X2p(x)dxmentioning

confidence: 78%

“…(23) differs from the corresponding equation of the problem with thermal insulation of the free surfaces presented in [3] only by the coefficient [3*. Therefore, as in [3], in the case where the pressing force P infinitely increases, there exists a critical value of the radius of the contact region = (12] I/2 acr t, rc~* J "…”

Section: + ~T! Dt Tf(xg'___(x))'___~+2~i Dt I X2p(x)dxmentioning

confidence: 94%

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Convective cooling in contact problems of thermoelasticity with frictional heat generation

Kul’chyts’kyi-Zhyhailo¹,

Evtushenko²

1997

Mater Sci

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Contact problems with frictional heat generation are, as a rule, studied under idealized conditions of perfect thermal insulation of the surfaces of bodies outside the region of contact. We solve an axially symmetric contact problem of stationary thermoelasticity for semibounded bodies of revolution by taking into account the effect of convective cooling of the free surfaces. The problem is reduced to a system of Fredholm integral equations. An approximate solution of these equations is obtained in terms of simple analytic relations. We determine the conditions under which the influence of convective heat exchange on the level and distribution of contact stresses can be neglected.Contact problems of thermoelasticity with heat generation caused by the action of frictional forces are, as a rule, studied under the assumption of thermal insulation of the free surfaces of contacting bodies [1--4]. This hypothesis substantially simplifies the problems and their solutions but is far from the adequate description of the reality. The condition of convective cooling of the surfaces of contacting bodies by environments seems to be more realistic. Therefore, it is interesting to determine the conditions under which it is possible to neglect the effect of convective cooling in analyzing the characteristics of contact such as the area of contact, pressure, and temperature.A procedure that enables one to construct exact solutions of axially symmetric contact problems with convective heat exchange was suggested in [5]. The system of two integral equations is solved numerically. Unfortunately, due to a great number of the input parameters of the problem (more than 10), it is difficult to obtain a clear picture of the influence of the intensity of heat exchange between the bodies and environment within the framework of this approach.In the present work, we propose an approximate procedure that enables one to construct solutions of the problem in the form of simple engineering formulas convenient for practical applications with sufficiently high accuracy (the relative error never exceeds 5-8%). Statement of the ProblemConsider two semibounded bodies of revolution coming in contact under the action of a normal force P applied to a disk of radius a and rotating about their common axis of symmetry with a constant angular velocity co. Frictional forces acting in the region of contact generate heat and, hence, increase the temperature of the bodies. Outside the region of contact, the process of heat exchange between the surfaces of the bodies and an environment obeys the Newton law.The problem reduces to the solution of the well-known equations of thermoelasticity and heat conduction [6] with the following boundary conditions in the cylindrical coordinate system r, z: ql + q2 =f~ r < a, z = 0,Franko L'viv State University.

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Section: + ~T! Dt Tf(xg'___(x))'___~+2~i Dt I X2p(x)dxmentioning

confidence: 78%

Section: + ~T! Dt Tf(xg'___(x))'___~+2~i Dt I X2p(x)dxmentioning

confidence: 94%

Convective cooling in contact problems of thermoelasticity with frictional heat generation

Kul’chyts’kyi-Zhyhailo¹,

Evtushenko²

1997

Mater Sci

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“…Extensive studies on the thermoelastic contact problem of conventional homogeneous materials have been done [30][31][32][33][34][35]. Barber and his collaborators [36,37] have shown that, for a thermoelastic contact model, pronounced differences from an isothermal one can be found.…”

Section: Introductionmentioning

confidence: 99%

Thermo-contact mechanics of a rigid cylindrical punch sliding on a finite graded layer

Chen

Peng

2012

Acta Mech

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A steady-state thermo-contact model of a rigid insulated cylinder of radius R sliding on a finite graded elastic layer is studied, whose Young's modulus, thermal conductivity coefficient and thermal expansion coefficient vary exponentially in the thickness direction. The transfer matrix method and Fourier integral transform technique are used to obtain a Cauchy-type singular integral equation for the contact stresses. Numerical calculation yields the interface traction and temperature distributions below the rigid punch. It shows that crack damage in the finite graded layer due to the frictional sliding can be prevented by several alternative ways, such as decreasing the shear modulus ratio of the surface to the bottom, decreasing the friction coefficient, increasing the thickness of the finite graded layer, increasing the thermal conductivity coefficient ratio of the surface to the bottom or increasing the sliding velocity. The finding should be very useful for the design of novel graded materials with potential applications in aerospace, tribology, coatings, etc.

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“…An analogous contact problem for two rotating semi-in®nite bodies has been analysed in [4,5] and [6,7]. An axisymmetrical contact problem in which a rigid cylindrical¯at punch presses into an isotropic elastic half-space and rotates about the axis of symmetry at constant angular speed has been considered in [8].…”

Section: Introductionmentioning

confidence: 99%

“…Now we analyse the in¯uence of the heat generation by friction on the value of principal contact characteristics. It is known [3,6] that in the solution of the rotating spherical punch problem r 0 0, there is a critical value of the contact area radius at an unlimited increase of the total load P. This is…”

mentioning

confidence: 98%

Thermoelastic contact problem of two rotating bodies with frictional heat generation in annular region

Yevtushenko

Kultchytsky-Zhyhailo

1998

Archive of Applied Mechanics (Ingenieur Archiv)

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An axisymmetric contact problem with frictional heating is considered in which a parabolic annular punch is pressed into a plane surface and rotates about its axis of symmetry at constant speed. The problem is formulated in terms of one governing equation with unknown pressure. This equation is solved numerically. The change of the geometry of the contact region and pressure has been investigated. IntroductionThe steady temperature ®eld in the semi-space subject to rotating frictional heating was studied in [1]. The corresponding axisymmetric quasi-static problem of the thermoelasticity was solved in [2].An approximate solution with frictional heating for a rotating rigid sphere which is pressed into an elastic half-space has been obtained in [3]. An analogous contact problem for two rotating semi-in®nite bodies has been analysed in [4,5] and [6,7]. An axisymmetrical contact problem in which a rigid cylindrical¯at punch presses into an isotropic elastic half-space and rotates about the axis of symmetry at constant angular speed has been considered in [8].A simultaneous calculation of heating by friction and abrasive wear in rotating of an annular at punch of the surface of a rough half-space has been investigated in [9]. We study the contact problem with frictional heating for a rotating parabolic annular punch and a half-space. This friction system likely will ®nd wide applications in the modelling study of drilling tools and other seal-like mechanical con®gurations.A classi®cation of the isothermal frictionless contact problems for the annular region may be found in [10]. Governing equations and boundary conditionsLet an axisymmetric elastic annular punch be pressed into an elastic half-space by a normal load P. The force P is applied along the axis of symmetry of the punch which rotates about this axis at constant angular speed x. Let us assume that in the cylindrical coordinate system rY /Y z the contact region is de®ned by a r b. In these circumstances, the friction forces which submit to Amonton's law lead to the origin of heat sources distributed over the contact area. We assume that the temperatures of two bodies are equal at the interface in the contact region, and there is no heat¯ux across the surfaces in the separation region. In addition, it is assumed that the tangential stress r rz is equal to zero everywhere on the surface z 0, and heat is generated due to stresses r z/ , which are proportional to the normal stresses r z .Moreover, as the width of the contact area is small, the punch can be replaced by a half-space in the solution of the corresponding thermoelasticity problem [11].In such a statement, the problem is reduced to the determination of axisymmetric components u i r rY z, u i z rY z of the displacement vector and the temperature T i rY z i 1Y 2 in the half-spaces z ! 0 and z 0 from the displacement equations

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Determination of limiting radii of the contact area in axi-symmetric contact problems with frictional heat generation

Cited by 24 publications

References 6 publications

Convective cooling in contact problems of thermoelasticity with frictional heat generation

Convective cooling in contact problems of thermoelasticity with frictional heat generation

Thermo-contact mechanics of a rigid cylindrical punch sliding on a finite graded layer

Thermoelastic contact problem of two rotating bodies with frictional heat generation in annular region

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