Abstract:
A theory of rolling of round bodies in the normal mode with adhesion conditions satisfied on the entire contact area is proposed. This theory refines the classical Coulomb's theory of rolling in which the rolling moment is directly proportional to the pressing force (e.g., the weight of the rolling body). The rolling moment of cylinders is found to be directly proportional to the pressing force raised to a power of 3/2, and the rolling moment of balls and tori is proportional to the pressing force raised to a power of 4/3. It is shown that the normal mode of uniform rolling can only be provided for a certain ratio of the elastic constants of the materials of the round body and the base forming an ideal pair. The Coulomb problem is solved for the cases of rolling of an elastic cylinder over an elastic half-space, of an elastic ball over an elastic half-space, of an elastic torus over an elastic half-space, and of a cylinder and ball over a tightly stretched membrane. The rolling law is derived for such cases. The rolling friction coefficients, the rolling moment, and the rolling friction force are calculated.
Keywords:
theory of rolling, Coulomb problem, rolling law, rolling moment, rolling friction coefficient, normal mode of rolling.
Citation:
G. P. Cherepanov, “Theory of rolling: solution of the Coulomb problem”, Prikl. Mekh. Tekh. Fiz., 55:1 (2014), 218–226; J. Appl. Mech. Tech. Phys., 55:1 (2014), 182–189
\Bibitem{Che14}
\by G.~P.~Cherepanov
\paper Theory of rolling: solution of the Coulomb problem
\jour Prikl. Mekh. Tekh. Fiz.
\yr 2014
\vol 55
\issue 1
\pages 218--226
\mathnet{http://mi.mathnet.ru/pmtf1115}
\elib{https://elibrary.ru/item.asp?id=21903156}
\transl
\jour J. Appl. Mech. Tech. Phys.
\yr 2014
\vol 55
\issue 1
\pages 182--189
\crossref{https://doi.org/10.1134/S0021894414010210}
Linking options:
https://www.mathnet.ru/eng/pmtf1115
https://www.mathnet.ru/eng/pmtf/v55/i1/p218
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Filipe Marques, Paulo Flores, J. C. Pimenta Claro, Hamid M. Lankarani, “Modeling and analysis of friction including rolling effects in multibody dynamics: a review”, Multibody Syst Dyn, 45:2 (2019), 223
F C Ciornei, S Alaci, I C Romanu, I Mihai, V C Lazar, “Aspects concerning the friction for the motion on an inclined plane of an axisymmetric body”, IOP Conf. Ser.: Mater. Sci. Eng., 477 (2019), 012036
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S Alaci, R-D Pentiuc, F C Ciornei, I C Romanu, L Irimescu, F Buium, “Employment of hyper-cycloidal oscillatory motion for finding the coefficient of rolling friction. Part 1: Theoretical model”, IOP Conf. Ser.: Mater. Sci. Eng., 514:1 (2019), 012002
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F C Ciornei, S Alaci, C Dulucheanu, C Ciornei, M C Ciornei, “The effect of mass eccentricity upon tribological test results”, IOP Conf. Ser.: Mater. Sci. Eng., 444 (2018), 022016
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S Alaci, F C Ciornei, I C Romanu, M C Ciornei, “Upon the relationship between rolling friction and sliding friction”, IOP Conf. Ser.: Mater. Sci. Eng., 400 (2018), 042002
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