Theoretical, numerical, and experimental study on the synchronization in a vibrator–pendulum coupling system

For a vibrating system where the pendulum and vibrators are coupled together, the relevant dynamic model and the corresponding synchronization problem are rarely studied, due to its complex dynamic coupling relationships. In this paper, a vibrator–pendulum coupling system is proposed to study its synchronization principle; here, the pendulum is driven by the synchronous motion of the two vibrators directly. By exploiting the system motion differential equations and their vibration responses, the synchronization criterion of the two vibrators is deduced via the average method. After that, the stability criterion for the synchronous states is presented according to the convergence and divergence characteristics of the perturbed differential equation in the balanced state. Based on the theoretical results, the synchronous stable states and motion characteristics of the system under different parameter conditions are discussed by numerical qualitative analyses, and the reasonable parameters matching principles in designing the real vibrating machine are provided. A series of numerical simulations and experiments are further given to examine the validity of the theoretical methods and the obtained results. The dynamic model and research results presented in this paper can be applied to design a new kind of vibrating jaw crusher; in this case, the pendulum is served as the moving jaw and can work with its swing motion trajectory under the premise of the stable zero-phase difference between the two vibrators.