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Modélisation des systèmes de dimension infinie - Application à la dynamique des pneumatiques

Abstract : This thesis is dedicated to the modelling of a class of wheels with tyre, considered as a mechanical system with an infinite number of degrees of freedom. We analyze such a system by methods of analytical dynamics. Stationary modes of rolling of a wheel on a plane are studied in both cases when the wheel slips or does not slip. The mechanical system includes deformable and non-deformable parts. The non deformable part is the rim, which is represented by a rigid body with six degrees of freedom. The deformable part is the tyre, which is made of three parts the tread, through which the wheel and the plane are in contact, and two sidewalls, connecting the tread to the rim. In the reference configuration, the tread is a circular cylinder, and the sidewalls are two parts of toroidal surfaces. The structure of modem tyres is such that one can find three families of inextensible wires at each point of the tread and one family at each point of the sidewalls. The tyre is filled by a perfect gas under pressure, whose evolution is isothermal. The rim of the wheel is subjected to some external force F and external moment M. When the wheel rolls, it is in contact with the plane on some unknown part of the tread. The rolling can occur without or with slip in the zone of contact. In this work, we model this mechanical system and its movements are studied by methods of analytical mechanics.
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Submitted on : Friday, September 3, 2010 - 9:28:16 AM
Last modification on : Monday, April 9, 2018 - 10:48:44 AM
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  • HAL Id : pastel-00001850, version 1



Ivan Kogevnikov. Modélisation des systèmes de dimension infinie - Application à la dynamique des pneumatiques. Mathématiques [math]. Ecole des Ponts ParisTech; Université d'Etat de Moscou Lomonossov, 2006. Français. ⟨NNT : 2006ENPC0003⟩. ⟨pastel-00001850⟩



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