Synchronization of an Exciter and Three Cylindrical Rollers with Different Dry Friction via Dynamic Coupling

Abstract

In this paper, the dynamics of a mechanical exciter and three cylindrical rollers (CRs) with the non-identical friction coefficients interacting through a rigid platform is considered. Sufficient conditions for the existence and stability of synchronous solutions in the coupled system are derived by using the average method of modified small parameters and Routh-Hurwitz principle. The obtained theoretical results are illustrated and analysed based on numerical calculations. In the analysis, the numerical results are presented for simple one-parameter variation, as well as for a group of varied parameters, when the influence of the coupling structure’s parameters on synchronization and stability is studied. An appropriate selection of the key parameters will eventually lead to desired synchronization performance. Finally, the theoretical and numerical results are supported by computer simulations. The stable synchronized states can be observed in the simulations even when there are unavoidably small differences in the three friction coefficients. If we mismatch the friction coefficients of the CRs, they are seen to synchronize with a constant phase difference. The key feature of the proposed coupled system is the dynamic coupling torque, which serves as the vehicle for transferring energy from an induction motor to three CRs without the direct driving sources and the synchronization controller for maintaining the originally synchronous and stable states against the disturbance in the simulations.