Double synchronization states of two exciters with horizontal asymmetric structure in a vibrating system

Abstract

Synchronization of two exciters with asymmetric structure is more widely used in engineering, such as vibrating conveyer, dewatering screen, vibrating screen, however, the synchronization state of two exciters with asymmetric structure in the sub-resonant and super-resonant states is less considered, and it is a valuable research topic. Firstly, we establish a kind of weakly nonlinear vibrating system driven by two exciters with opposite rotation directions and asymmetrical structure. Using Lagrange equations, the differential equations of the vibrating system are obtained. Secondly, we apply Fourier series expansion to obtain the nonlinear elastic force of the nonlinear stiffness. Thirdly, we introduce the modified averaging method of small parameters and Hamilton’s principle to get the criterions of synchronization synchronization stability of two exciters. The theoretical analysis shows that the phase differences are stabilized in the vicinity of Pi phase difference in a super-resonant state when l0 approaches to le, otherwise, in the neighborhood of zero phase difference in a sub-resonant state. Then, the above theory is verified by experiments. The stable phase difference, amplitudes responses and energy consumption are also discussed. This research provides the foundation and guidance for the synchronization of two exciters with horizontal asymmetrical structure and engineering design.