Steady state motion of a shear deformable beam in contact with a traveling surface

Abstract

A shear deformable beam moving along a straight path is considered as an idealization of the problem of stationary operation of a belt drive. The partial contact with a traveling surface results in the shear deformation of the beam. The tangential contact force grows near the end of the contact zone. Assuming perfect adhesion of the lower fiber of the beam to the traveling surface (no slip), we analytically demonstrate the necessity of accounting for concentrated contact forces and jump conditions, which is important for modeling the belt–pulley interaction. Along with dynamic effects, we further consider a frictional model with zones of stick and slip contact and demonstrate its convergence to the results with perfect adhesion at growing maximal friction force.

Belt–pulley interaction: role of the action line of friction forces

“…The rigid pulley is a cylinder rotating with a constant velocity . The present work is an extension of the previously published paper [ 6 ], where the similar problem was discussed for a flat pulley. The introduction of the (small) transverse displacements and of the corresponding force factors is the novel point in this research.…”

“…Now, we can substitute Eqs. (6) and (11) in the balance of moments and derive the second-order differential equation for the angle…”

“…The last condition is the conservation of material length (see, e.g., [6]). According to this condition, the total integral of ε over the considered segment (0, L) must vanish:…”

“…The introduction of the (small) transverse displacements and of the corresponding force factors is the novel point in this research. The belt is assumed prestressed, which also differsentiates the present model from [6]. In this work, we consider quasistatic motion, because the inertial terms do not qualitatively change the behavior in the belt-pulley contact area.…”

“…However, the authors of [8] use some simplifying assumptions in the contact segment. The friction interaction is assumed to occur at the belt's middle axis, whereas in the papers [2,6] it is at the bottom fibers. Shifting the contact forces to the belt's middle axis leads to certain simplifications in the problem formulation, for instance, to constant stretch in the sticking region.…”