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IssuesArchive of Issues2012-2pp.155-159

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V.Ph. Zhuravlev, "On Plane Self-Excited Vibrations of a Cantilever Suspended Wheel," Mech. Solids. 47 (2), 155-159 (2012)
Year 2012 Volume 47 Number 2 Pages 155-159
DOI 10.3103/S002565441202001X
Title On Plane Self-Excited Vibrations of a Cantilever Suspended Wheel
Author(s) V.Ph. Zhuravlev (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr-t Vernadskogo 101, str. 1, Moscow, 119526 Russia, zhurav@ipmnet.ru)
Abstract Torsional vibrations of a wheel about its leg axis arising in the carriage rectilinear motion were dubbed the shimmy phenomenon. Because of insufficient understanding of dry friction laws in the case of point contact, the causes of the shimmy phenomenon were explained by specific features of tyre deformation [1-3].

But this phenomenon is also observed in the case of rigid (for example, metallic) wheels. The recently developed theory of polycomponent dry friction [5-11] was used to explain the shimmy phenomenon in [4]. It was discovered there that the shimmy phenomenon arises if sliding friction prevails over rolling friction.

In the present paper, it is shown that self-excited vibrations are also possible if, conversely, rolling friction prevails over sliding friction, but these vibrations then occur in the rolling plane. Such self-excited vibrations are close in their physical meaning to the vibrations studied in textbooks on the theory of oscillations in the problem called an oscillator with dry friction on an infinite belt [12]. In contrast to this problem, the order of the system considered below is greater, and, in addition to sliding friction, rolling friction is present as well.
Keywords pseudo-shimmy, dry friction, self-excited vibrations of the wheel cantilever suspension, averaging method
References
1.  M. V. Keldysh, "Fore Wheel Shimmy of a Three-Wheel Landing Gear," in Selected Works. Mechanics (Nauka, Moscow, 1985) [in Russian], pp. 491-530.
2.  V. S. Gozdek, "Reaction of the Ground on a Vibrating Rolling Wheel with an Elastic Tire," Dokl. Akad. Nauk SSSR 186 (5), 1031-1033 (1969) [Soviet Phys. Dokl. (Engl. Transl.) 14, 536 (1969)].
3.  H. B. Pacejka, Tyre and Vehicle Dynamics (Butterworth-Heinemann, Oxford, 2002).
4.  V. Ph. Zhuravlev and D. M. Klimov, "Theory of the Shimmy Phenomenon," Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 3, 22-29 (2010) [Mech. Solids (Engl. Transl.) 45 (3), 324-330 (2010)].
5.  V. V. Andronov and V. Ph. Zhuravlev, Dry Friction in Problems of Mechanics (NITz "Regular and Chaotic Dynamics," Moscow-Izhevsk, 2010) [in Russian].
6.  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)].
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.  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, 3-14 (2005) [Mech. Solids (Engl. Transl.) 40 (2), 1-10 (2005)].
9.  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)].
10.  P. Contensou, "Couplage Entre Frottenment de Glissement et Frottement 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).
11.  R. I. Leine and Ch. Glocker, "A Set-Valued Force Law for Spatial Coulomb-Contensou Friction," Europ. J. Mech. A. Solids 22, 193-216 (2003).
12.  V. Ph. Zhuravlev and D. M. Klimov, Applied Methods in Vibration Theory (Nauka, Moscow, 1988) [in Russian].
13.  D. M. Klimov, "On One Type of Self-Excited Vibrations in a System with Dry Friction," Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 3, 6-12 (2003) [Mech. Solids (Engl. Transl.) 38 (3), 1-7 (2003)].
Received 25 January 2011
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