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Acta Mech 232, 1971–1982 (2021)
https://doi.org/10.1007/s00707-020-02800-w
ORIGINAL PAPER
Alexandra A. Zobova ·Irina G. Goryacheva
Effect of contacting bodies’ mechanical properties
on the dynamics of a rolling cylinder
Received: 19 June 2020 / Revised: 17 July 2020 / Accepted: 9 August 2020 / Published online: 5 September 2020
© Springer-Verlag GmbH Austria, part of Springer Nature 2020
Abstract This paper investigates the influence of the material properties on the deceleration dynamics of a
deformable cylinder rolling with slipping on a half-space of the same material. The interaction of the cylinder
and the half-space is described by the 2D quasistatic contact problem of viscoelasticity (Goryacheva: J Appl
Math Mech 37(5):877–885, 1973; Contact mechanics in tribology. Kluwer, Dordrecht 1998) which includes
as limiting cases the absolutely rigid and elastic materials. Full dynamical analysis of the problem including
the phase portrait, the dependence of the deceleration distance on the mechanical properties of the contacting
bodies and on the friction coefficient is provided. The qualitative features of deceleration are justified by
asymptotic analysis.
1 Introduction
A huge variety of friction models and numerous papers on their comparative studies in the dynamics of
rigid bodies systems show that the phenomenon of frictional contact is an important and complicated object
of study [3]. However, the papers in the field of system dynamics often use non-smooth models [4–7]or
phenomenological models based on some simplifications of the mechanical behavior of deformable bodies
[8–12]. Besides, dynamical effects appearing due to the coupling between friction force and spinning torque in
3D dynamics of convex bodies have attracted attention recently (see, for example, [13–16] and the references
therein). However, these models are also based on the phenomenological approach developed in [17,18]. At
the same time, the continuum mechanics papers devoted to contact interaction are mostly focused on study
of the contact and internal stress distribution and the energy losses for various loading conditions and type of
motion [19–23], thermo-effects [24] and wear [25]. This lack between the fields indicates that it is necessary
to use the contact mechanics models for analysis of the system dynamics.
The paper is devoted to the study of the deceleration process of a cylinder rolling over a base from the same
material taking into account the stress distribution within the contact area which follows from the solution of
the contact problem [2]. The mechanical properties of the contacting bodies are described by the viscoelastic
model. The solution of the contact problem includes two limiting cases—a rigid cylinder on a non-deformable
The part of the work related to the dynamic analysis was performed under the support of the Russian Foundation for Basic
Research (Project 19-01-00140), and the part related to the contact problem analysis within the framework of a State assignment,
State registration No. AAAA-A20-120011690132-4.
Alexandra A. Zobova (B
)
Lomonosov Moscow State University, Moscow, Russia
E-mail: alexandra.zobova@math.msu.ru
Irina G. Goryacheva
Institute for Problems in Mechanics of the Russian Academy of Sciences, Moscow, Russia
E-mail: goryache@ipmnet.ru
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