 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12804 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4760 |
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| P. G. Ivanochkin, V. I. Kolesnikov, B. M. Flek, and M. I. Chebakov, "Contact strength of a two-layer covering under friction forces in the contact region," Mech. Solids. 42 (1), 157-165 (2007) |
| Year |
2007 |
Volume |
42 |
Number |
1 |
Pages |
157-165 |
| Title |
Contact strength of a two-layer covering under friction forces in the contact region |
| Author(s) |
P. G. Ivanochkin (Rostov State University of Communications, pl. Narodnogo Opolcheniya 2, Rostov-on-Don, 344038, Russia, prKomivan@rgups.ru)
V. I. Kolesnikov (Rostov State University of Communications, pl. Narodnogo Opolcheniya 2, Rostov-on-Don, 344038, Russia, reK@rgups.ru)
B. M. Flek (Vorovich Research Institute of Mechanics and Applied Mathematics, Rostov State University, pr-t Stachki 200/1, Rostov-on-Don, 344090, Russia, admin@vertolexpo.ru)
M. I. Chebakov (Rostov State University of Communications, pl. Narodnogo Opolcheniya 2, Rostov-on-Don, 344038, Russia, chebakov@math.rsu.ru) |
| Abstract |
Friction and antifriction composite materials of multilayer structure [1] have recently become very popular in the engineering industry. Antifriction materials are widely used in sliding bearings, and friction materials are widely used in brakes. In the first case, the friction forces between the contacting surfaces are negligible, but in the second case, they are rather large.
We use two examples of two plane problems from the theory of elasticity concerning the interaction between a die and a base formed by two elastic layers with different mechanical properties, which are rigidly connected with each other and with an undeformable support, to study how the geometric and mechanical parameters of the problem affect the stress-strain state of such a base, both on its surface and at its internal points, and to find the optimal parameters ensuring the required operation resources of the friction units thus modeled.
We assume that the die foot is parabola-shaped or plane, the normal and tangential stresses in the contact region are related to each other by the Coulomb law, and the die is subjected to normal and tangential forces. In this case, the die-two-layer base is in the limit equilibtrium, and the die does not rotate in the process of deformation of the layer.
In this setting, the problems were studied in [2] by solving the integral equations (IE) by the asymptotic method of large λ (see [3–7], etc.), which permits finding the effective solution only for relatively large thicknesses of layers compared with the dimensions of the contact region. But in real friction units mentioned above, the layers can have rather small relative thicknesses, and the large λ method cannot be used. We note that the other asymptotic methods (e.g., see [3]) efficient in the case of relatively small thicknesses of layers cannot yet be adapted to the case of friction forces in the contact region.
In the present paper, we propose to use the collocation method following the scheme given in [8] to solve the corresponding integral equation of the first kind with logarithmic kernel. This method allows one to obtain sufficiently exact solutions practically for all values of the parameters of the problem with relatively small expenditure of the computer time for modern computers.
The contact problem for a two-layer base was used in [9] for a close statement of the problem without friction forces in the contact region. |
| References |
| 1. | V. I. Kolesnikov,
Thermal Processes in Metallic-Polymer Tribosystems
(Nauka, Moscow, 2003)
[in Russian]. |
| 2. | M. I. Chebakov,
"Interaction between the Die and Two-Layer Basement
with Friction Forces in the Contact Region,"
Ekolog. Vestnik Nauch. Tsentrov ChES,
No. 1, 60-66 (2006). |
| 3. | V. M. Alexandrov,
"On Plane Contact Problem of the Theory of Elasticity
with Adhesion and Friction Forces,"
Prikl. Mat. Mekh.
34 (2), 246-257 (1970)
[J. Appl. Math. Mech. (Engl. Transl.)]. |
| 4. | V. M. Alexandrov and M. I. Chebakov,
Analytical Methods in Contact Problems in Theory of Elasticity
(Fizmatlit, Moscow, 2004)
[in Russian]. |
| 5. | I. I. Vorovich, V. M. Alexandrov, and V. A. Babeshko,
Nonclassical Mixed Problems of Theory of Elasticity
(Nauka, Moscow, 1974)
[in Russian]. |
| 6. | M. I. Chebakov,
"Asymptotic Solution of Contact Problems for an Elastic Layer
of Relatively Large Thickness with Friction Forces in the Contact Region,"
Prikl. Mat. Mekh.
69 (2), 324-333 (2005)
[J. Appl. Math. Mech. (Engl. Transl.)]. |
| 7. | M. I. Chebakov,
"On Several Characteristics of the Contact Interaction
Between a Die and an Elastic Layer with Friction Forces
in the Contact Region,"
Ekolog. Vestnik Nauch. Tsentrov ChES,
No. 3, 23-28 (2004). |
| 8. | V. V. Voronin and V. A. Chechekho, "Numerical Solution of Integral
Equation of the First Kind with Logarithmic Singularity by the
Interpolation and Collocation Method," Zh. Vychisl. Mat. i Mat. Fiz.
21 (1), 40-53 (1981) [U.S.S.R. Comput. Math. and Math. Phys.]. |
| 9. | V. M. Alexandrov and V. V. Klindukhov,
"Contact Region for Two-Layer Basement with Nonideal Mechanical Connection
Between the Layers,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 3, 84-92 (2000)
[Mech. Solids (Engl. Transl.)]. |
| 10. | V. M. Alexandrov and M. I. Chebakov,
Introduction to Mechanics of Contact Interaction
(TsVVR, Rostov-na-Donu, 2005)
[in Russian]. |
|
| Received |
10 July 2006 |
| Link to Fulltext |
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