Transient modelling of flexible belt drive dynamics using the equations of a deformable string with discontinuities

Abstract

Dynamics of a belt drive is analyzed using a nonlinear model of an extensible string at contour motion, in which the trajectories of particles of the belt are predetermined. The equations of string dynamics at the tight and slack spans are considered in a fixed domain by transforming into a spatial frame. Assuming the absence of slip of the belt on the surface of the pulleys, we arrive at a new model with a discontinuous velocity field and concentrated contact forces. Finite difference discretization allows numerical analysis of the resulting system of partial differential equations with delays. Example solution for the acceleration of a belt drive and an investigation of its frequency response depending on the velocity are presented and discussed.

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

“…Moreover, material description implies regular re-meshing if a finer discretization is desired near the contact domains of a long belt drive, thus impacting the efficiency and accuracy of the analysis. For a simpler model with only contour motion of the belt, the advantages of the Eulerian kinematic description have been demonstrated in (Eliseev and Vetyukov, 2012;Vetyukov et al, 2017b) for transient dynamics with idealized friction, in (Rubin, 2000;Bechtel et al, 2000;Morimoto and Iizuka, 2012) for stationary (steady state) dynamics with exact resolution of the friction law and in (Oborin et al, 2018) for a transient quasi-static analysis with time variation of the zones of stick and slip. For multi-dimensional deformations of axially moving structures, axial and transverse deflections may be efficiently separated using mixed Eulerian-Lagrangian kinematic description.…”

Methods of instrument testing of smoke detectors performance

“…The analysis of statistics shows that in the event of a real fire, the systems of fire automatics do not work or work inadequately and do not fulfill their function. [26] This is due to the fact that, often, when designing, installing or during maintenance, errors and violations are made that cause system's malfunction. One of the main problems is that during visual inspection, focusing on the control panel and evaluating the correctness of the placement of fire detectors, it is impossible to assess the real operation of the fire alarm system.…”

On static contact of belt and different pulleys

“…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.…”

“…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].…”