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

Abstract

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

On static contact of belt and different pulleys

“…Furthermore we apply the Newton method using built-in function FindRoot (Mathematica). We use our solution of the problem with equal pulleys [28] as an initial guess in order to begin the computations performed with the numerical continuation method.…”

“…The presented study is an extension of the work [28]. Here we introduce significant complexity by rejecting the assumption of equal pulleys accepted there.…”

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

“…We begin the narration with a novel semi-analytical solution, that extends the previously published analysis of a contact problem with no gravity (Belyaev et al, 2017a), and further…”

A rod model for large bending and torsion of an elastic strip with a geometrical imperfection

“…Many essentially nonlinear solutions to problems of in-plane deformations of rod structures are available in the literature. Thus, a contact of a closed elastic rod with cylindrical pulleys is analyzed in [14][15][16]. Denoël and Detournay [17] used Eulerian kinematic formulation in the problem of deformation of an elastica within a channel contacting both its walls.…”