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IssuesArchive of Issues2003-4pp.52-58

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V. Ph. Zhuravlev, "Friction laws in the case of combination of slip and spin," Mech. Solids. 38 (4), 52-58 (2003)
Year 2003 Volume 38 Number 4 Pages 52-58
Title Friction laws in the case of combination of slip and spin
Author(s) V. Ph. Zhuravlev (Moscow)
Abstract Rolling of rigid bodies along rough surfaces in the case of point contact is commonly considered with the assumption that there is no relative slip at the contact point, which leads to a nonholonomic model. Contensou [1] showed that such an approach is unsatisfactory. He has established that the friction force at the starting instant of motion vanishes if the motion of the body has a spin component, however small it were, and hence, no-slip conditions cannot be implemented. Contensou's investigations have been completed in [2]. In this paper, apart from the friction force at the point of contact, the moment of this force was calculated. Moreover, the integral expressions for these quantities were reduced to elementary functions and then Padé approximations were utilized to form the ultimate relations for the model of the contact force. The study of the relationship between sliding friction and spinning friction was extended in [3] to the case where the contact region is not a point. In that paper, Padé approximations were utilized to obtain expressions for the friction force and torque for the contact of a homogeneous disk with a plane and the dynamics of such a disk was investigated. In the present paper, the relationship between the slip and the spin is studied for the case of an arbitrary axially symmetric distribution of normal stresses in the contact region. Particular examples are given.
1.  P. Contensou, "Cuoplage entre frottement de glissement et frottement de pivotement dans la theorie de la toupie," in Kreiselprobleme Gyrodynamics: IUTAM Symp. Celerina, 1962, pp. 201-216, Springer, Berlin, 1963.
2.  V. Ph. Zhuravlev, "On the model of dry friction in the problem of rolling of rigid bodies," PMM [Applied Mathematics and Mechanics], Vol. 62, No. 5, pp. 762-767. 1998.
3.  A. A. Kireenkov, "On the motion of a homogeneous otating disk along a plane in the case of combined friction," Izv. AN. MTT [Mechanics of Solids], No. 1, pp. 60-67, 2002.
4.  L. A. Galin, Contact Problems in Elasticity and Viscoelasticity [in Russian], Nauka, Moscow, 1980.
5.  A. Yu. Ishlinskii, B. N. Sokolov, and F. L. Chernousko, "On the motion of planar bodies in the presence of dry friction," Izv. AN SSSR. MTT [Mechanics of Solids], No. 4, pp. 17-28, 1981.
Received 17 March 2002
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