1_2023_sen_11

Title of the article ASYMPTOTIC APPROACH TO SOLVING THE CONTACT PROBLEM FOR A ROLLING BODY WITH A THIN DEFORMABLE RIM
Authors

CHERNOUS Dmitry A., Ph. D. in Eng., Assoc. Prof., Associate Professor of the Department “Technical Physics and Theoretical Mechanics”, Belarusian State University of Transport, Gomel, Republic of Belarus, This email address is being protected from spambots. You need JavaScript enabled to view it.">This email address is being protected from spambots. You need JavaScript enabled to view it.

KADNIANKA Alena V., Engineer for Scientific and Technical Information of the Department of Scientific and Technical Information, JSC “Soligorsk Institute of Resources Saving Problems with Pilot Production”, Soligorsk, Republic of Belarus, This email address is being protected from spambots. You need JavaScript enabled to view it.">This email address is being protected from spambots. You need JavaScript enabled to view it.
In the section MECHANICS OF DEFORMED SOLIDS
Year 2023
Issue 1(62)
Pages 79–87
Type of article RAR
Index UDK 620.178
DOI https://doi.org/10.46864/1995-0470-2023-1-62-79-87
Abstract On the basis of an asymptotic approach to solving the elasticity theory boundary value problem for a thin strip rigidly linked to a non-deformable base, the differential equations are derived for determining the normal and shear loads distributed on the strip face free from fastening. These equations are used to solve the contact problem for a rigid cylinder with a thin elastic rim with a non-deformable horizontal rough support surface. The cylinder loading by a vertical force is considered for a given cylinder center settling. The calculated diagrams of contact pressure and shear contact stresses are obtained. In contrast to the previously used methods, the developed technique makes it possible to take into account the presence of adhesion and slip zones in the contact area, as well as to use a mathematically strict solution of the constitutive equations for contact pressure and shear contact stress. The value of the vertical force acting on the rigid cylinder for a given cylinder center displacement is determined. The stress tensor intensity distribution in the rim is established. The results of the developed technique application are compared with the calculated estimates obtained on the basis of the exact solution of the boundary value problem for a strip of arbitrary thickness and within the method, involving the use of the Winkler base simplified model. The dependences of the results error for the developed method on the thickness and Poisson's ratio of the rim material are obtained. The paper describes the effect of the rim-support surface friction coefficient on the contact pressure, shear contact pressure, and the maximum intensity of the stress tensor in the rim. It is concluded that it is reasonable to use the developed technique at solving contact problems for rolling elements with a relatively thin elastic rim.
Keywords contact problem, thin layer, asymptotic approximation, contact pressure, shear contact pressure, stress tensor intensity
  You can access full text version of the article.
Bibliography
  1. Nowacki W. Teoria sprężystości. Warszawa, Państwowe wydawnictwo naukowe, 1970.
  2. Aleksandrov V.M., Mkhitaryan S.M. Kontaktnye zadachi dlya tel s tonkimi pokrytiyami i prosloykami [Contact problems for solids with thin coatings and layers]. Moscow, Nauka Publ., 1983. 487 p. (in Russ.).
  3. Fabrikant V.I. Solution of contact problems for a transversely isotropic elastic layer bounded to an elastic half-space. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of mechanical engineering science, 2009, vol. 223, iss. 11, pp. 2487–2499. DOI: https://doi.org/10.1243/09544062JMES1643.
  4. Argatov I.I. Depth-sensing indentation of a transversely isotropic elastic layer: Second-order asymptotic models for canonical indenters. International journal of solids and structures, 2011, vol. 48, iss. 25–26, pp. 3444–3452. DOI: https://doi.org/10.1016/j.ijsolstr.2011.08.011.
  5. Mozharovsky V.V., Kuzmenkov D.S. Metodika opredeleniya parametrov kontakta indentora s ortotropnym pokrytiem na uprugom izotropnom osnovanii [The technique for determining the parameters of a contact for indenter with the orthotropic coating on the elastic isotropic substrate]. Problems of physics, mathematics and technics, 2016, no. 4(29), pp. 74–82 (in Russ.).
  6. Aleksandrov V.M. Asymptotic solution of the contact problem for a thin elastic layer. Journal of applied mathematics and mechanics, 1969, vol. 33, iss. 1, pp. 49–63. DOI: https://doi.org/10.1016/0021-8928(69)90113-0.
  7. Jaffar M.J. Asymptotic behaviour of thin elastic layers bonded and unbonded to a rigid foundation. International journal of mechanical sciences, 1989, vol. 31, iss. 3, pp. 229–235. DOI: https://doi.org/10.1016/0020-7403(89)90113-6.
  8. Mozharovskiy V.V., Starzhinskiy V.E. Prikladnaya mekhanika sloistykh tel iz kompozitov. Ploskie kontaktnye zadachi [Applied mechanics of layered composite solids: plane contact problems]. Minsk, Nauka i tekhnika Publ., 1988. 271 p. (in Russ.).
  9. Johnson K.L. Contact mechanics. Cambridge, Cambridge University Press, 1985. 510 p. DOI: https://doi.org/10.1017/CBO9781139171731.
  10. Starovoytov E.I. Osnovy teorii uprugosti, plastichnosti i vyazkouprugosti [Foundations of theory of elasticity, plasticity and viscoelasticity]. Gomel, Belorusskiy gosudarstvennyy universitet transporta Publ., 2001. 344 p. (in Russ.).