Energy Transfer and Saving in a Nonlinear Coupled Vibrating System Based on the Method of Composite Synchronization Transmission

ABSTRACT The vibrating screening equipment in industry usually requires power supply to each driving motor to keep up with its normal operation. The self‐synchronization transmission motion of two motors can achieve the screening requirement and save electrical energy by driving one single inductor motor. Nevertheless, this technology is currently only applicable to the condition of two motors. The self‐synchronization transmission of multiple motors (more than 2) can't be applied in industry. To solve this problem, the theory of the composite synchronization transmission is proposed and the energy transfer mechanism is investigated on a nonlinear coupled vibrating system with three eccentric rotors (ERs) driven by inductor motors. The mathematical model of the coupled system is first established. Then the synchronization conditions and stability criteria are given through the Routh‐Hurwitz stability criterion. The method of radial basis function‐neural network adaptive sliding model (RBF‐NNASMC) is introduced in the self‐synchronization transmission to realize the composite synchronization transmission. In addition, the controller is designed combined with the dynamical model. The stability of the controlling system is proved by the Lyapunov stability theory. Finaly, numerical results are given to illustrate the consistency with the theory and the effectiveness of the control method. The results indicate that the theory of composite synchronization transmission can realize the energy transfer by the vibrating system so as to save the electric energy. It provides a novel reference for the energy‐saving design in the vibrating screening with multiple motors.