Investigation of friction induced vibrations on a nonlinear two degree of freedom mathematical model and experimental validation

This article investigates the dynamic behavior of a low order nonlinear mathematical model, which is developed based on an existing mass-sliding belt experiment. First, the proposed model is developed with kinematic and friction nonlinearities, and the corresponding governing equations are obtained. Governing equations are then solved numerically for certain operating parameters, and the characteristics of different dynamic responses are investigated. It is observed from the numerical solutions that the dynamic response of the system can be deterministic or chaotic based on the set of operating parameters. Furthermore, the period doubling mechanism is found to be the path from deterministic to chaotic behavior. Second, experiments are performed at a wide range of operating parameters in order to calculate the dynamic friction coefficient, which are used in artificial neural network models for the generation of friction models as functions of operating parameters. It is observed that these operating parameters have significant influence on the variation of the dynamic friction coefficient. Third, the friction models developed with artificial neural network approach are implemented in the nonlinear mathematical model, and numerical solutions are obtained at the same operating parameters. Finally, the numerical results of the low order nonlinear mathematical model are compared to the experimental data, and it is concluded that there is a good correlation between the model predictions and measurements from the perspectives of fundamental frequencies and the characteristics of the dynamic responses. Hence, a better insight about the dynamic response behavior of the mass-sliding belt experiment is achieved through the bifurcation analyses.