Effects of deformation in the dynamics of belt drive

Abstract

The dynamics of a belt drive is considered in the framework of a nonlinear model of an extensible elastic string. Under the assumption of contour motion, in which the trajectories of particles of the string are pre-determined, we transform the general equations of string dynamics to the spatial description. Further simplification regarding the absence of slip of the belt on the surface of the pulleys leads to a new model with a discontinuous velocity field and concentrated contact forces. It is shown how the computed parameters of steady operation of the drive are influenced by the chosen strain measure for the string, and differences in the behavior of synchronous and friction belt drives are pointed out. For a sample set-up, we study the dependence of the maximal transmitted moment on the angular velocities of the pulleys and on the pre-tension of the belt.

On static contact of belt and different pulleys

“…We combine the equations at both segments into a single system and distinguish the values by the indices (...) (1) , (...) (2) , (...) (3) . We note that this transformation extends the formulation for the problem of laying process of underwater pipeline [11] where contact of an initially straight beam with a flat rigid surface is considered.…”

“…Until recently, one-dimensional models of elastic strings were widely used, cf. [2,3,4]. The exact solution for nonlinear steady state equations of extensible string is obtained in [3] by assuming zones of perfect and sliding friction contact between the belt and the pulley.…”

“…The exact solution for nonlinear steady state equations of extensible string is obtained in [3] by assuming zones of perfect and sliding friction contact between the belt and the pulley. A spatial description of the belt contour motion is suggested in [2]. An idealized point friction model allows extending this result to the transient dynamics, see [4].…”

Oscillations of a visco‐elastic belt drive

“…Also the length L of the belt's free portion is an unknown quantity, which is obtained as part of the solution of the boundary value problem. Contrary to [2] we assume, that no slipping occurs between the belt and the drums.…”

Nonlinear statics of extensible elastic belt on two pulleys

“…Different types of deformations of the elastic belt can be taken into account to model the drive. In the previous works [2][3][4] the model of an extensible string is applied to study the contour motion with the constant trajectory. However one needs a more sophisticated rod model with account for at least bending stiffness [5] since the friction forces are not applied on the belt axis [6].…”