 | | 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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| V. I. Ostrik and A. F. Ulitko, "Frictional contact of two rotating elastic disks," Mech. Solids. 42 (5), 760-770 (2007) |
| Year |
2007 |
Volume |
42 |
Number |
5 |
Pages |
760-770 |
| Title |
Frictional contact of two rotating elastic disks |
| Author(s) |
V. I. Ostrik (Institute of Applied Physics, National Academy of Sciences of Ukraine, Petropavlovskaya 58, Sumy, 40030, Ukraine, ostrik_v@rambler.ru)
A. F. Ulitko (National Taras Shevchenko Kyiv University, Vladimirskaya 60, Kiev, 01033, Ukraine, igor_ulitko@infomania.com.ua) |
| Abstract |
We study the problem of constrained uniform rotation of two precompressed elastic disks made of different materials with friction forces in the contact region taken into account. The exact solution of the problem is obtained by the Wiener-Hopf method.
An important stage in the study of rolling of elastic bodies is the Hertz theory [1] of contact interaction of elastic bodies with smoothly varying curvature in the contact region under normal compression. Friction in the contact region is assumed to be negligible. If there are tangential forces and the friction in the contact region is taken into account, then the picture of contact interaction of elastic bodies changes significantly. Although the normal contact stress distribution strictly follows the Hertz theory for bodies with identical elastic properties and apparently slightly differs from the Hertz diagram for bodies made of different materials, the presence of tangential stresses results in the splitting of the contact region into the adhesion region and the slip region. This phenomenon was first established by Reynolds [2], who experimentally discovered slip regions near points of material entry in and exit from the contact region under constrained rolling of an aluminum cylinder on a rubber base. The theoretical justification of the partial slip phenomenon in the contact region, discovered by Reynolds [2], can be found in Carter [3] and Fromm [4]. Moreover, Fromm presents a complete solution of the problem of constrained uniform rotation of two identical disks. Apparently, Fromm was the first to consider the so-called "clamped" strain and postulated that slip is absent at the point at which the disk materials enter the contact region.
Ishlinskii [5, 6] gave an engineering solution of the problem on slip in the contact region under rolling friction. Considering the problem on a rigid disk rolling on an elastic half-plane, we model this problem by an infinite set of elastic vertical rods using Winkler-Zimmermann type hypotheses. Numerous papers of other authors are surveyed in Johnson’s monograph [7].
The exact solution of the problem on the constrained uniform rotation of precompressed rigid and elastic disks under the assumptions of Fromm’s theory is contained in the papers [8, 9]. In the present paper, we generalize the solution obtained in [8, 9] to the case of two elastic disks made of different materials. |
| References |
| 1. | H. Hertz, Über die Berührung fester elastischer Körper,"
J. Reine Angew. Math. 92, 156-171 (1881). |
| 2. | O. Reynolds,
"On Rolling Fricion,"
Philos. Trans. Roy. Soc.
166, 155-163 (1875). |
| 3. | F. W. Carter,
"On the Action of a Locomotive Driving Wheel,"
Proc. Roy. Soc.
112, 151-157 (1926). |
| 4. | H. Fromm, "Berechnung des Schlupfes beim Rollen Deformierbarer
Scheiben," Z. Angew. Math. Mech. 7 (1), 27-58 (1927). |
| 5. | A. Yu. Ishlinskii,
"On the Rolling Friction,"
Prikl. Mat. Mekh.
2, 245-260 (1939)
[J. Appl. Math. Mech. (Engl. Transl.)]. |
| 6. | A. Yu. Ishlinskii,
Applied Mechanics Problems, Vol. 2
(Nauka, Moscow, 1986)
[in Russian]. |
| 7. | K. L. Johnson,
Contact Mechanics
(Cambridge University Press, Cambridge, 1987; Mir, Moscow, 1989). |
| 8. | A. F. Ulitko,
"Exakte Lösing des Kontaktproblems für Zwei Zylinder
unter Berücksichtigung der Reibung,"
Z. Angew. Math. Mech.
80 (7), 435-455 (2000). |
| 9. | V. I. Ostrik and A. F. Ulitko,
"Uniform Rotation of Precompressed Rigid and Elastic Disks
with Friction Forces in the Contact Region Taken into Account,"
in Problems of Mechanics. Collection of Papers Dedicated to
A. Yu. Ishlinskii on the Occasion of his 90th Birthday,
Ed. by D. M. Klimov (Fizmatlit, Moscow, 2003),
pp. 619-634
[in Russian]. |
| 10. | Ya. S. Uflyand,
Integral Transforms in Elasticity Problems
(Nauka, Leningrad, 1967)
[in Russian]. |
| 11. | B. Noble,
Methods Based on the Wiener-Hopf Technique
(Pergamon, New York, 1958; Izd-vo Inostr. Lit., Moscow, 1962). |
|
| Received |
12 September 2005 |
| Link to Fulltext |
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