Nonlinear and chaotic dynamics of a vibratory conveying system

Abstract

In this work, a simulation model of a vibratory conveying system is presented. The simulation model is based on a continuous contact formulation in vertical direction which is extended by a friction force in horizontal direction to simulate a conveying process. In contrast with complex 3D simulation tools, it enables the understanding of previously unexplained phenomena such as multiple feeding velocities at the same excitation amplitude, which are observed in practical measurements. The parameters that have an influence on this effect are investigated, and a method for predicting and adjusting the occurrence of multiple solutions is developed. It is shown that the calibration of the system is very difficult in practice, as it depends significantly on the initial conditions which are difficult to reproduce and predict. It is also shown that the system can exhibit chaotic behavior in some configurations. These chaotic states are shown with the simulation model by means of parameter studies, and the point at which the system becomes chaotic is predicted with the method of Lyapunov exponents and fractal dimensions. Knowledge of the chaotic states can be used to calibrate the conveyor, as they depend only on the excitation and not on the initial conditions. The interdependencies of the initial conditions are also discussed in more detail. Therefore, this work provides a deeper understanding of complex conveying processes using a simple simulation model.