On static contact of belt and different pulleys

Belyaev, Аlexander K.; Елисеев, В. В.; Irschik, Hans; Oborin, Evgenii

doi:10.1088/1757-899x/208/1/012004

Cited by 3 publications

(2 citation statements)

References 28 publications

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“…Finally, we show the results of numerical work and compare them with the previous results for the extensible model without shear [4] and the model without extension and shear [5]. A special case of different pulleys is studied in [6]. The rod is considered as a Cosserat line [2,13,15,36].…”

Section: Figmentioning

confidence: 91%

Contact of two equal rigid pulleys with a belt modelled as Cosserat nonlinear elastic rod

et al. 2017

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The setting of a looped drive belt on two equal pulleys is considered. The belt is modelled as a Cosserat rod, and a geometrically nonlinear model with account for tension and transverse shear is applied. The pulleys are considered as rigid bodies, and the belt-pulley contact is assumed to be frictionless. The problem has two axes of symmetry; therefore, the boundary value problem for the system of ordinary differential equations is formulated and solved for a quarter of the belt. The considered part consists of two segments, which are the free segment without the loading and the contact segment with the full frictionless contact. The introduction of a dimensionless material coordinate at both segments leads to a ninth-order system of ordinary differential equations. The boundary value problem for this system is solved numerically by the shooting method and finite difference method. As a result, the belt shape including the rotation angle, forces, moments, and the contact pressure are determined. The contact pressure increases near the end point of the contact area; however, no concentrated contact force occurs. Mathematics Subject Classification

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Section: Figmentioning

confidence: 91%

Contact of two equal rigid pulleys with a belt modelled as Cosserat nonlinear elastic rod

et al. 2017

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“…2. As the positions of the touching points S 1 and S 2 are not known in advance we opt for a coordinate transformation, compare [4,5]…”

Section: Introduction and Semi-analytic Approachmentioning

confidence: 99%

Mixed Eulerian–Lagrangian description in the statics of a flexible belt with tension and bending hanging on two pulleys

Scheidl

Vetyukov

Oborin

et al. 2018

Proc Appl Math and Mech

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Studying the mechanics of thin, axially moving strings, beams or plates (e.g.: belt drives, cable cars, . . . ) at mixed Eulerian-Lagrangian description, which features the transformation of material coordinates to spatial ones, is more appropriate than the classical material (Lagrangian) one, see [1,2]. Aiming at testing a newly proposed non-material finite element formulation we study the statics of a looped belt as a rod hanging in contact with two pulleys. Numerical experiments demonstrate rapid mesh convergence as well as correspondence to semi-analytical results and conventional Lagrangian finite element solutions.This is an open access article under the terms of the Creative Commons Attribution-Non-Commercial-NoDerivs Licence 4.0, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.

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Flexible belt hanging on two pulleys: Contact problem at non-material kinematic description

Vetyukov

Oborin

Scheidl

et al. 2019

International Journal of Solids and Structures

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We propose a non-material finite element scheme for modelling large deformations of a closed flexible rod supported by two rigid pulleys in the field of gravity. The mixed Eulerian-Lagrangian kinematic description of circumferential and transverse displacements is beneficial for simulations of moving belt drives. The necessary C 1 inter-element continuity in a compound coordinate system with Cartesian and polar domains requires a nonlinear finite element approximation. The theoretically predicted singular reaction force distribution prevents us from using the technique of Lagrange multipliers for normal contact. A novel semi-analytical solution of the static problem based on the integration of the equations of the nonlinear theory of rods in the free spans as well as in the segments of contact with pulleys is presented for the sake of validation. We demonstrate the mutual convergence of simulation results for a benchmark problem and additionally justify them by comparison against conventional Lagrangian finite element solutions.

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On static contact of belt and different pulleys

Cited by 3 publications

References 28 publications

Contact of two equal rigid pulleys with a belt modelled as Cosserat nonlinear elastic rod

Contact of two equal rigid pulleys with a belt modelled as Cosserat nonlinear elastic rod

Mixed Eulerian–Lagrangian description in the statics of a flexible belt with tension and bending hanging on two pulleys

Flexible belt hanging on two pulleys: Contact problem at non-material kinematic description

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