A Solution Method for the Contact Problem of Free Rolling on a Rigid Foundation of a Cylindrical Body with a Deformable Rim

The contact problem of free rolling on a rigid foundation of a cylindrical body consisting of a non-deformable central part and an elastic rim is considered. A technique for an analytical solution is developed on the basis of a second-order asymptotic approximation. The contact interaction of the composite body with a non-deformable foundation under the action of a vertical force is investigated as a calculation example assuming a small rolling resistance moment. The calculated distributions of normal and tangential contact stresses, the distribution of the stress tensor intensity in the rim near the contact area, and the “force—displacement” dependence are obtained. These data are compared with the estimates obtained by the authors on the basis of finite element modeling and the results of using an alternative version of the asymptotic approximation. A conclusion is made about the advantages of the developed technique in comparison with the known asymptotic approach in terms of the accuracy of calculating the contact parameters and the simplicity of the applied mathematical apparatus. It is shown that the maximum of the stress tensor intensity is localized on the line of action of the vertical force (axis of symmetry) for a deformable rim material with Poisson's ratio n less than 0.4 and on the inner surface of the rim near the boundary of the adhesion and slip zones for n > 0.4. The data derived are used to analyze the loading of roller interfaces of mining equipment.

1. Baryshnikova A.M., Baryshnikov M.P., and No-sov L.V. Development of Production Technology for Polymer Coated Wire Based on the Study of the Stress State Scheme in the Progress of Drawing // The theory and progress engineering of metallur-gical production. — 2020, no. 3(34), 21—25

2. 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 Me-chanical Engineering Science. — 2009 (223), no. 11, 2487—2499

3. Novatskii V. Teoriya uprugosti [Theory of Elastici-ty]. — Moscow: Mir. — 1975 (in Russian)

4. Aleksandrov V.M., Mkhitaryan S.M. Kontaktnye zadachi dlya tel s tonkimi pokrytiami i prosloyka-mi [Contact Problems for Solids with Thin Coatings and Layers]. — Moscow: Nauka. — 1983 (in Rus-sian)

5. Argatov I.I. Depth-Sensing Indentation of a Transversely Isotropic Elastic Layer: Second-Order Asymptotic Models for Canonical Indenters // Int. J. of Solids and Structures. — 2011 (15), 3444—3452

6. Mozharovskii V.V., Kuzmenkov D.S. Metodika opredeleniya parametrov komtakta indentora s ortotropnym pokrytoem na uprugom izotropnom osnovanii [Method for Determining Parameters of Contact between Indenter with Orthotropic Coating on Elastic Isotropic Space] // Problemy fiziki, ma-tematiki I tekhniki [Problems of Physics, Mathe-matics and Technics]. — 2016, no. 4 (29), 74—82 (in Russian)

7. Wu J. and Ru C.Q. An Analytical Solution to the Adhesive Cylindrical Indentation of a Compressi-ble Elastic Thin Layer // The Journal of Adhesion. — 2021 (97), no. 14, 1291—1309

8. Jaffar M.J. Asymptotic Behaviour of Thin Elastic Layer Bonded and Unbonded to a Rigid Founda-tion // Int. J. Mech. Sci. — 1989 (31), 229—235

9. Chernous D.A., Kodnyanko E.V. Asimptoticheskij podhod k resheniyu kontaktnoj zadachi dlya tela kacheniya s tonkim deformiruemym obodom // Mekhanika mashin, mekhanizmov i materialov. — 2023, № 1(62), 79—87 (in Russian)

10. Shil'ko S.V., Chernous D.A., Panin S.V. Modeliro-vanie bionicheski adekvatnyh antifrikcionnogo i soedinitel'nogo sloev endoproteza sustava // Fizi-cheskaya mezomekhanika. — 2022 (25), № 5, 106—113 (in Russian)

11. Kodnyanko E.V., Chernous D.A. Ispol'zovanie modeli Vinklera dlya analiza kacheniya kolesa s deformiruemym obodom // Mekhanika. Issledo-vaniya i innovacii. — Gomel': BelGUT. — 2022, № 15, 92—99 (in Russian)

12. Bahrami M.R. ANSYS Tutorial: An Introduction to Elasticity and Contact Problems in Mechanical APDL 15.0. — St. Petersburg: Peter the Great St. Petersburg Polytechnic university. — 2018

13. Skip shahtnyj: pat. 11460 Resp. Belarus', MPK V66V 17/32 / V.Ya. Prushak, V.Ya. Shcherba, D.A. Morev; zayavitel' Soligorskij Institut problem resur-sosberezheniya s Opytnym proizvodstvom – № u 20170053; zayavl. 22.02.2017 (in Russian)

14. Yakovlev S.N. Raschet poliuretanovyh detalej, rabotayushchih na szhatie pri staticheskoj nagruzke // Nauchno-tekhnicheskie vedomosti Sankt-Peterburgskogo gosudarstvennogo politekhnicheskogo universiteta. Mashinostroenie. — 2014, № 1 (190), 137—142 (in Russian)