 | | 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: | | 12804 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4760 |
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| A.A. Kireenkov, "Coulomb Law in Generalized Differential Form in Problems of Dynamics of Rigid Bodies with Combined Kinematics," Mech. Solids. 45 (2), 166-175 (2010) |
| Year |
2010 |
Volume |
45 |
Number |
2 |
Pages |
166-175 |
| DOI |
10.3103/S0025654410020020 |
| Title |
Coulomb Law in Generalized Differential Form in Problems of Dynamics of Rigid Bodies with Combined Kinematics |
| Author(s) |
A.A. Kireenkov (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr-t Vernadskogo 101, str. 1, Moscow, 119526 Russia, kireenk@ipmnet.ru) |
| Abstract |
We suggest an exact integral model of sliding and spinning friction constructed under the assumption that the Coulomb law in generalized differential form holds for the surface element in the interior of the contact spot.
We show that, just as in the case of the classical Coulomb law in differential form, the friction force is directed oppositely to the relative sliding velocity but, compared with the results obtained in [3], the expressions for the friction force and torque contain additional polynomial terms.
To avoid using integral representations in equations of motion, we construct models of friction based on the first- and second-order Padé expansions of the corresponding exact integral model. These models can be viewed as generalized rheological two-dimensional first- and second-order models of friction, because, when solving actual problems, their coefficients can be determined experimentally. Moreover, compared with the results of [3], the second-order model is determined by the same number of coefficients as the first-order model. This fact simplifies the use of the second-order model when solving dynamic problems.
As an example of use of the suggested models, we study the dynamics of torsional vibrations of an elastically fixed cylindrical rod one of whose ends rests on an infinite band moving at a constant velocity. |
| Keywords |
coupled sliding and spinning friction models, Padé expansion, torsional vibration |
| References |
| 1. | P. Contensou,
"Couplage Entre Frottenment de Glissement et
Frottenment de Pivotement Dans la Théorie de la Toupie,"
in Kreiselprobleme Gyrodynamics
(IUTAM Symp. Celerina, Berlin etc., Springer; Mir, Moscow, 1967),
pp. 201-216 (60-77). |
| 2. | 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)]. |
| 3. | V. Ph. Zhuravlev and A. A. Kireenkov,
"Padé Expansions in the Two-Dimensional Model of Coulomb Friction,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 2, 3-13 (2005)
[Mech. Solids (Engl. Transl.)
40 (2), 1-10 (2005)]. |
| 4. | Ya. G. Panovko,
Mechanics of Deformable Solids
(Nauka, Moscow, 1985)
[in Russian]. |
| 5. | A. A. Kireenkov,
"On the Motion of a Homogeneous Rotating Disk along a Plane in the Case of Combined Friction,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 1, 60-67 (2002)
[Mech. Solids (Engl. Transl.)
37 (1), 47-53 (2002)]. |
| 6. | L. A. Galin,
Contact Problems of Elasticity and Viscoelasticity
(Nauka, Moscow, 1980)
[in Russian]. |
| 7. | V. Ph. Zhuravlev,
"Friction Laws in the Case of Combination of Slip and Spin,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 4, 81-88 (2003)
[Mech. Solids (Engl. Transl.)
38 (4), 52-58 (2003)]. |
| 8. | A. A. Kireenkov,
"Torsional Vibrations in Systems with Combined Dry Friction,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 3, 36-40 (2009)
[Mech. Solids (Engl. Transl.)
44 (3), 361-365 (2009)]. |
| 9. | V. Ph. Zhuravlev and D. M. Klimov,
Applied Methods in Vibration Theory
(Nauka, Moscow, 1988)
[in Russian]. |
|
| Received |
22 October 2009 |
| Link to Fulltext |
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