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Effect of contacting bodies’ mechanical properties on the dynamics of a rolling cylinder

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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.
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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 [47]or
phenomenological models based on some simplifications of the mechanical behavior of deformable bodies
[812]. 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, [1316] 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 [1923], 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
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
... The applications of the quasistatic solutions of the corresponding contact problems for elastic [47] and viscoelastic [2] contacting bodies to the dynamics of an infinite cylinder (with horizontal axis) that rolls or slides along a half-space which border is horizontal or inclined are investigated in [48][49][50][51][52][53]. The external field is gravity, the acceleration in z-direction is neglected based on investigations [54], so it is assumed that z ≡ 0 in Eq. (7). ...
... Dynamics of the elastic or viscoelastic cylinder of radius R rolling over the half-plane of the same material is studied in [49][50][51][52][53]. According to the quasistatic solutions [2,47], the contact region is divided in two subregions: stick and slip zones, which width and position depend on the velocity of the cylinder center ẋ and creep ratio δ = ωR−ẋ x . ...
... The case of a viscoelastic materials of the cylinder and foundation is considered in [52,53]. It is shown that deceleration consists of two phases: on the first stage the relative sliding velocity ωR −ẋ decreases almost linearly in time and this stage is governed primarily by friction coefficient. ...
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This review presents a collection of the solved dynamic problems taking into account the normal and shear stress distributions in the contact region due to the deformation of contacting bodies. The considered dynamic problems differ in the number of degrees of freedom and the type of relative displacements of contacting bodies (2-D models with rolling and sliding, 3-D models with sliding and spinning, 3-D models with sliding, rolling and spinning). The contact mechanics solutions are used in formulation of the dynamic problems, which are studied based on the analytical or semi-analytical approach. The effects of the mechanical properties of the contacting bodies and the contact conditions on the dynamics are analyzed and discussed.
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