Skip to main content
SpringerLink
Log in

Solution of a plane contact problem of the theory of elasticity on the basis of an elastic half-space model

  • Reliability, Durability, and Wear Resistance of Machines and Constructions
  • Published:
Journal of Machinery Manufacture and Reliability Aims and scope Submit manuscript

Abstract

A theoretical solution of a plane contact problem of the theory of elasticity based on a method of determination of the convergence of elastic bodies using an elastic half-space model is presented, and the contact deformation (diameter change) of circular cylinders with parallel axes is deter-mined on its basis. The possibility of obtaining a precise solution for the problem, using an elastic half-space model based on the Hertz theory, is demonstrated for the first time. It is shown that the known Kovalskii solution for contact deformation of circular cylinders with parallel axes is a rough approximation of a more precise solution of the problem. It is found that the obtained result agrees well with the Dinnik’s experimental data.

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.

Institutional subscriptions

Similar content being viewed by others

References

  1. Hertz, H., Uber die Beruchtung fester elastischen Korper, Leipzig, 1895, vol. 1, pp. 155–174.

    Google Scholar 

  2. Dinnik, A.N., Izbrannye trudy (Selected Works), Kiev: AN USSR, 1952, vol. 1.

    Google Scholar 

  3. Belyaev, N.M., Trudy po teorii uprugosti i plastichnosti (Works on Plasticity and Elasticity Theory), Moscow: Gostekhteorizdat, 1957.

    Google Scholar 

  4. Koval’skii, B.S., Stressed State and Strength Criteria under Contact Pressure, Nauchn. Zapiski Khar’k. Aviats. Inst., Kharkov, 1941, vol. 5.

  5. Foppl, A., Lectures on Technical Mechanics, Teubner, B.G., Ed., Leipzig, 1907, vol. 5.

  6. Hoeprich, M.R. and Zantopulos, H., Contact Deformations along the Straight Line: Cylinder between Two Flat Plates, in Trudy Amerikanskogo obshchestva inzhenerov-mekhanikov. Problemy treniya i smazki (Works of American Society of Mechanical Engineers. Problems of Friction and Lubrication), Moscow: Mir, 1974, no. 3, pp. 193–198.

    Google Scholar 

  7. Johnson, K.L., Contact Mechanics, Cambridge: Univ. Press, 1985; Moscow: Mir, 1989.

    MATH  Google Scholar 

  8. Nakhatakyan, F.G. and Kosarev, O.I., Elastic Bodies Approach in Hertz Contact Problem, Probl. Mashinostr. Avtomatiz., 2010, no. 1, pp. 102–106.

  9. Nakhatakyan, F.G., Mechanics of Contact Approach of Elastic Bodies in Hertz Problem, J. Mach. Manuf. Reliab., 2010, vol. 39, no. 5, p. 444

    Article  Google Scholar 

  10. Airapetov, E.L., The Way to Determine the Contact Deformation of Spur Gears Teeth, Vestn. Mashinostr., 1967, no. 1, pp. 32–35.

  11. Timoshenko, S.P. and Goodier, J.N., Theory of Elasticity, McGraw-Hill, 1934; Moscow: Nauka, 1975.

    Google Scholar 

  12. Prochnost’, ustoichivost’, kolebaniya. Spravochnik (Strength, Stability, Oscillations. Handbook), Birger, I.A. and Panovko, Ya.G., Eds., Moscow: Mashinostroenie, 1968, vol. 2.

    Google Scholar 

  13. Ponomarev, S.D., Biderman, V.L., Likharev, K.K., et al., Raschety na prochnost’ v mashinostroenii (Strength Calculations in Machinery Manufacturing), Moscow: Mashgiz, 1958, vol. 2.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Moscow, Russia

    F. G. Nakhatakyan

Authors
  1. F. G. Nakhatakyan
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Original Russian Text © F.G. Nakhatakyan, 2011, published in Problemy Mashinostroeniya i Nadezhnosti Mashin, 2011, No. 5, pp. 63–67.

About this article

Cite this article

Nakhatakyan, F.G. Solution of a plane contact problem of the theory of elasticity on the basis of an elastic half-space model. J. Mach. Manuf. Reliab. 40, 458–462 (2011). https://doi.org/10.3103/S1052618811050141

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S1052618811050141

Keywords

Search

Navigation