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.
Highlights
Belt drive mechanics is an extensively studied research area with applications in power transmissions, conveyors, elevators, and processing of metals and polymers
Results of the present paper contribute to the broader research topic, which aims at efficient mathematical modeling of the steady state motion of a belt in contact with two rotating pulleys, including contact conditions and dynamic effects—in the spirit of the analysis presented in [22], but with no geometric simplifications
We considered the steady state motion of a straight shear deformable beam in partial contact with a moving rough surface under the assumptions of the small strain theory
Summary
Belt drive mechanics is an extensively studied research area with applications in power transmissions, conveyors, elevators, and processing of metals and polymers. The perfect adhesion (no-slip) condition between the moving belt and the surface of a rotating pulley results in concentrated tangential contact forces in the case of a string model of the belt [14,30,33]. It is, known that the singularity in the normal contact force vanishes with the introduction of shear flexibility of the rod, see contributions [3,7], in which the tensioning of the belt on the pulleys is treated. The argumentation rests heavily on the condition of conservation of the total material length of the beam within the control domain, which follows
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