Skip to main content
SpringerLink
Log in

To the theory of analysis of a two-layer cylindrical bearing

  • Published:
Mechanics of Solids Aims and scope Submit manuscript

Abstract

We consider the plane contact problem of elasticity concerning the interaction between an absolutely rigid cylinder and the internal cylindrical surface of the cylindrical base, which consists of two circular cylindrical layers with different elastic constants. The base external surface is fixed, the layers are rigidly connected with each other, and the friction forces are absent in the contact region. Such problems sufficiently well model the operation of a composite cylindrical slider bearing, especially in the case of loads for which the angular dimension of the contact site is commensurable with the bearing width and the moduli of the insert liner and of the support are different and significantly less than the modulus of elasticity of the other details of the bearing.

For the above-stated problem of elasticity, we first construct integral equations, which are solved by the direct collocation method [1, 2] and by the asymptotic method [3, 4].

In contrast to the similar problems considered earlier (e.g., see [3, 4]) for a single-layer cylinder, the collocation method used here permits studying the problem practically for any parameter values. The asymptotic approach gives an efficient solution in the case of relatively thin layers in simple analytic form. We also compare the two solutions numerically and determine the scope of the asymptotic method.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. V. V. Voronin and V. A. Tsetsokho, “Numerical Solution, by Interpolation and Collocation, of Integral Equations of the 1st Kind with a Logarithmic Singularity,” Zh. Vychisl. Mat. Mat. Fiz. 21(1), 40–53 (1981) [[U.S.S.R. Comput. Math. Math. Phys. (Engl. Transl.) 21 (1), 38–52 (1981)]].

    MATH  MathSciNet  Google Scholar 

  2. P. G. Ivanochkin, V. I. Kolesnikov, B. N. Flek, and M. I. Chebakov, “Contact Strength of a Two-Layer Covering under Friction Forces in the Contact Region,” Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 1, 183–192 (2007) [Mech. Solids (Engl. Transl.) 42 (1), 157–165 (2007)].

  3. V. M. Alexandrov and M. I. Chebakov, Analytical Methods in Contact Problems in Theory of Elasticity (Fizmatlit, Moscow, 2004) [in Russian].

    Google Scholar 

  4. V. M. Alexandrov and M. I. Chebakov, “On the Theory of Cylindrical Bearing Design,” Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 1, 22–30 (2004) [Mech. Solids (Engl. Transl.) 39 (1), 14–20 (2004)].

  5. I. I. Vorovich, V. M. Alexandrov, and V. A. Babeshko, Nonclassical Mixed Problems of Elasticity (Nauka, Moscow, 1974) [in Russian].

    Google Scholar 

  6. I. S. Gradshtein and I. M. Ryzhik, Tables of Integrals, Sums, Series, and Products (Nauka, Moscow, 1971) [in Russian].

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Vorovich Research Institute of Mechanics and Applied Mathematics, South Federal University, pr-t Stachki 200/1, Rostov-on-Don, 344090, Russia

    M. I. Chebakov

Authors
  1. M. I. Chebakov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. I. Chebakov.

Additional information

Original Russian Text © M.I. Chebakov, 2009, published in Izvestiya Akademii Nauk. Mekhanika Tverdogo Tela, 2009, No. 3, pp. 163–170.

About this article

Cite this article

Chebakov, M.I. To the theory of analysis of a two-layer cylindrical bearing. Mech. Solids 44, 473–479 (2009). https://doi.org/10.3103/S0025654409030169

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S0025654409030169

Keywords

Search

Navigation