The disturbance influence on vibration of a belt device driven by a crank mechanism

Abstract

As well as technological forces, real-life belt and conveyor systems are loaded by disturbing effects that have a mostly random character. To analyze importance of their influence on belt and conveyor system behavior, a computational model was set up in which the disturbances were represented by the discretization and round-off errors occurring during the solving of the governing equations, which is a new and original idea. The simulations that were carried out show that the disturbances can spawn hidden and co-existing attractors and transitions between vibrations of different periods or between regular and chaotic motions and reverse bifurcations. The main contribution of the paper is a new and original way to modeling of the systems’ inaccuracies and disturbances having frequently a random character by means of numerical inaccuracies caused by round-off errors and set tolerances of the solution methods for solving the equations of motion. The computational simulations give evidence that these factors have the same effect as inaccuracies and uncertainties of real machines on their behavior. The simulation showed that these factors can lead to qualitatively different system behavior, like the transitions between the regular and chaotic regimes. The physical validity of all operating regimes was proved by the theorem of the time change of the kinetic energy. The main goal of the presented article is to point out that small deviations from the rated state can cause qualitatively different behavior of the machine systems.