 | | 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
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| V.Ph. Zhuravlev and D.M. Klimov, "Theory of the Shimmy Phenomenon," Mech. Solids. 45 (3), 324-330 (2010) |
| Year |
2010 |
Volume |
45 |
Number |
3 |
Pages |
324-330 |
| DOI |
10.3103/S0025654410030039 |
| Title |
Theory of the Shimmy Phenomenon |
| 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)
D.M. Klimov (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr-t Vernadskogo 101, str. 1, Moscow, 119526 Russia, klimov@ipmnet.ru) |
| Abstract |
The shimmy phenomenon is the appearance of angular self-excited vibrations of the carriage wheels. Such self-excited vibrations provide a serious safety hazard for motion, which explains the great interest of scientists in this phenomenon [1-6]. This problem is most serious for the aircraft fore wheels.
It is commonly agreed that the main cause of the shimmy phenomenon is the tyre deformation [2]. We do not doubt this thesis, but still we note that this cause is not unique. The shimmy phenomenon can be observed in everyday life in the case of various hand trucks with rigid wheels, where the reference to the elastic tyre is out of place.
In what follows, we show that the theory of polycomponent dry friction can completely explain the shimmy phenomenon for absolutely rigid wheels, and hence can be at least one of the causes of this phenomenon in the general case.
Dry friction has been ignored by the scientists in their explanations of the shimmy phenomenon, because this friction has not been fully investigated until now, and it has been impossible to explain the shimmy phenomenon in the framework of the former representations. |
| Keywords |
shimmy, polycomponent dry friction, Padé approximation |
| References |
| 1. | 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)]. |
| 2. | M. V. Keldysh,
"Fore Wheel Shimmy of a Three-Wheel Landing Gear,"
in Selected Works. Mechanics
(Nauka, Moscow, 1985),
pp. 491-530. |
| 3. | K. S. Kolesnikov,
Self-Excited Vibrations of Car Steering Wheels
(Gostekhteorizdat, Moscow, 1955). |
| 4. | J. Medzorian,
"An Investigation of Landing Gear Shimmy: Tire Models, Tire Test Methodologies, Analysis and Parameter Studies,"
in 1999 World Aviation Conf. San Francisco, CA
(1999),
Docum. No. 1999-01-SS27. |
| 5. | H. B. Pacejka,
Tyre and Vehicle Dynamics
(Butterworth-Heinemann, Oxford, 2002). |
| 6. | Y. Rocard,
Dynamique Général des Vibrations
(Masson, Paris, 1949). |
| 7. | J. Svendenius,
"Tire Models for Use in Braking Applications,"
in Department of Automatic Control, Lund Institute of Technology
(Lund, 2003). |
| 8. | I. G. Goryacheva,
Mechanics of Friction Interaction
(Nauka, Moscow, 2001). |
| 9. | V. Ph. Zhuravlev,
"On the Model of Dry Friction in Problems of Rigid Body Dynamics,"
Uspekhi Mekh., No. 3 (2005). |
| 10. | 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)]. |
| 11. | V. Ph. Zhuravlev and D. M. Klimov,
"The Causes of the Shimmy Phenomenon,"
Dokl. Ross. Akad. Nauk
428 (6), 761-765 (2009)
[Dokl. Phys. (Engl. Transl.)
54 (10), 475-478 (2009)]. |
|
| Received |
08 December 2009 |
| Link to Fulltext |
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