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IssuesArchive of Issues2001-6pp.52-57

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P. A. Kruchinin, M. Kh. Magomedov, and I. V. Novozhilov, "Mathematical model of an automobile wheel for antilock modes of motion," Mech. Solids. 36 (6), 52-57 (2001)
Year 2001 Volume 36 Number 6 Pages 52-57
Title Mathematical model of an automobile wheel for antilock modes of motion
Author(s) P. A. Kruchinin (Moscow)
M. Kh. Magomedov (Moscow)
I. V. Novozhilov (Moscow)
Abstract An automobile is a complex controlled mechanical system with an extremely broad spectrum of motion components-from the motion along a highway during many hours to high-frequency vibrations of its structure. For this reason, when investigating the dynamics of an automobile, engineers utilize various mathematical models, depending on the purpose of the investigation and the range of the spectrum of motions to be considered [1-3]. In the present paper, we suggest a mathematical model describing the motion of an automobile on a time scale of about dozen milliseconds. This time scale is characteristic of the operation of an antilock braking system. This model explains unwanted high-frequency vibrations during braking [3-5] that fail to be described by the traditional quasistatic models by Carter, Rockard, and Fromm.
References
1.  A. A. Khachaturov (Editor), Dynamics of the System "Road-Tire-Automobile-Driver" [in Russian], Mashinostroenie, Moscow, 1976.
2.  I. V. Novozhilov, Fractional Analysis. Methods of Motion Decomposition, Birkhäuser, Boston, 1997.
3.  C. L. Clover and J. E. Bernard, "Longitudinal tire dynamics," Vehicle Syst. Dynam., Vol. 29, No. 4, pp. 231-259, 1998.
4.  O. I. Karuzin, P. I. Malyugin, and A. I. Fedotov, "Specific features of operation of an antilock braking system subject to perturbations," in Reliability and Active Safety of an Automobile [in Russian], pp. 31-38, MAMI, Moscow, 1985.
5.  F. Gustafsson, "Monitoring tire-road friction using wheel slip," IEEE Control Systems, Vol. 18, No. 4, pp. 42-49, 1998.
6.  M. V. Keldych, "Shimmy of the front wheel of a three-wheeled landing gear," Trudy TsAGI, No. 564, 1945.
7.  M. A. Levin and N. A. Fufaev, Theory of Rolling of a Deformable Wheel [in Russian], Nauka, Moscow, 1989.
8.  H. B. Pacejka, "In-plane and out-of-plane dynamics of pneumatic tyres," Vehicle Syst. Dynam., Vol. 8, No. 4-5, pp. 221-251, 1981.
9.  I. V. Novozhilov, "Rolling of a wheel," Izv. AN. MTT [Mechanics of Solids], No. 4, pp. 50-55, 1998.
Received 25 October 1999
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