 | | 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
| Total articles in the database: | | 12882 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8071
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| In English (Mech. Solids): | | 4811 |
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| P.K. Plotnikov, "Friction Force Model and Rolling Dynamics for a Ball on a Rough Surface with Presliding Displacement Taken into Account," Mech. Solids. 48 (1), 47-56 (2013) |
| Year |
2013 |
Volume |
48 |
Number |
1 |
Pages |
47-56 |
| DOI |
10.3103/S0025654413010056 |
| Title |
Friction Force Model and Rolling Dynamics for a Ball on a Rough Surface with Presliding Displacement Taken into Account |
| Author(s) |
P.K. Plotnikov (Saratov State Technical University, Politekhnicheskaya 77, Saratov, 410054 Russia, pribor@sstu.ru) |
| Abstract |
A model of sliding and spinning friction forces for a ball in the form of finite relations obtained by integrating the tangential stresses over the contact area whose parameters are determined by Hertz's theory for the "ball-rough horizontal surface" tribological conjunction pair is supplemented with a model of rolling friction torques. The combined model is peculiar in that the presliding displacement effect in rolling and spinning friction torques is taken into account. It is shown that the ball motions in the presliding displacement zone are of quasilinear character and, under shock perturbations, have the form of damping vibrations in the three orientation angles. The numerical parameters of the rolling and spinning friction model are experimentally determined for the presliding displacement zones, while the sliding friction parameters and partly the spinning friction parameters are calculated. Mathematical modeling permits one to discover new properties of the ball, namely, its deceleration in rolling, the onset of damping vibrations at the beginning and end of motion, and the transient process parameters. |
| Keywords |
rolling friction, presliding displacement, spinning, slip, ball, characteristic, tribological conjunction pair, modeling |
| References |
| 1. | V. D. Kuznetsov,
Solid-State Physics, Vol. 4
(Poligrafizdat, Tomsk, 1947)
[in Russian]. |
| 2. | A. V. Verkhovskii,
"Presliding displacement Effect at the Beginning of the Motion of Unlubricated Surfaces,"
Zh. Prikl. Fiz.
13 (3-4), 311-315 (1926). |
| 3. | I. V. Kragel'skii, M. N. Dobychin, and V. S. Kombalov,
Friction and Wear: Calculation Methods
(Mashinostroenie, Moscow, 1977; Pergamon, Oxford, 1982). |
| 4. | A. V. Verkhovskii and V. M. Avraamov,
"Presliding displacement Effect at the Beginning of Motion of a Roll,"
Izv. Tomsk. Politekh. Inst.
61 (1), 53-54 (1947). |
| 5. | S. V. Pinegin,
Rolling Friction in Machines and Instruments
(Mashinostroenie, Moscow, 1976)
[in Russian]. |
| 6. | V. I. Maksak,
Presliding Displacement and Rigidity of Mechanical Contact
(Nauka, Moscow, 1975)
[in Russian]. |
| 7. | V. Ph. Zhuravlev,
"The Model of Dry Friction in the Problem of the Rolling of Rigid Bodies,"
Prikl. Mat. Mekh.
62 (5), 762-767 (1998)
[J. Appl. Math. Mech. (Engl. Transl.)
62 (5), 705-710 (1998)]. |
| 8. | P. Contensou,
"Couplage Entre Frottenment de Glissement et
Frottenment de Pivotement Dans la Theórie de la Toupie,"
in Kreiselprobleme Gyrodynamics, IUTAM Symp. Celerina
(Springer, Berlin etc., 1962; Mir, Moscow, 1967),
pp. 201-216 (60-77). |
| 9. | V. Ph. Zhuravlev,
Foundations of Theoretical Mechanics
(Fizmatlit, Moscow, 2008)
[in Russian]. |
| 10. | P. K. Plotnikov,
"Models of Friction Forces for One-Dimensional Kinematic Pairs
and Properties of Motion of Rigid Bodies,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 4, 66-80 (2003)
[Mech. Solids (Engl. Transl.)
38 (4), 39-51 (2003)]. |
| 11. | V. Ph. Zhuravlev and D. M. Klimov,
"On the Dynamics of the Thompson Top (Tippe Top)
on the Plane with Real Dry Friction,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 6, 157-168 (2005)
[Mech. Solids (Engl. Transl.)
40 (6), 117-127 (2005)]. |
|
| Received |
11 February 2010 |
| Link to Fulltext |
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