 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
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| In English (Mech. Solids): | | 3212 |
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| A. A. Kireenkov, "Combined model of sliding and rolling friction in dynamics of bodies on a rough plane," Mech. Solids. 43 (3), 412-425 (2008) |
| Year |
2008 |
Volume |
43 |
Number |
3 |
Pages |
412-425 |
| DOI |
10.3103/S0025654408030138 |
| Title |
Combined model of sliding and rolling friction in dynamics of bodies on a rough plane |
| Author(s) |
A. A. Kireenkov (Institute for Problems in Mechanics, Russian Academy of Sciences, pr-t Vernadskogo 101, str. 1, Moscow, 119526, Russia, kireenk@ipmnet.ru) |
| Abstract |
We propose combined models of friction for circular surfaces of contact between interacting bodies under conditions of combined dynamics, where the body takes part in the rolling motion in addition to sliding and spinning. In constructing the models, we used numerous experimental results published in the literature concerning the distortion of the symmetric diagram of distribution of contact stresses in the direction of the rolling velocity. To describe this distortion, we propose a linear law with a single coefficient depending on the rolling direction and velocity. Under the assumption that the Coulomb law in differential form holds for a surface element in the interior of the contact spot, we constructed integral representations of the resultant moment and the resultant vector of friction forces.
We show that the relation between the rolling friction and the sliding friction results in the appearance of a nonzero friction force component directed along the normal to the trajectory of motion.
To avoid the use of multiple integrals in the equations of motion, we replace the exact integral representations of the resultant moment and the resultant vector of friction forces by the corresponding Padé approximations. The models thus obtained can be considered as combined rheological models of sliding and rolling friction. To obtain a correct description of the interrelation between the rolling friction and sliding friction in the complete statement of the problem based on these models, it is necessary to known at most six coefficients, which can be determined experimentally for solving the real practical problems.
The equations of the model were exactly integrated in elementary functions for the case in which the distribution of normal contact stresses obeys the Hertz law. |
| Received |
05 March 2008 |
| Link to Fulltext |
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