The self-synchronous theory of a dual-motor driven vibration mechanism without shimmy

The paper focuses on the self-synchronous motion and stabilizing conditions of a vibration mechanism driven by dual-motor, which can eliminate the shimmy. The differential equations of motion of the vibration mechanism are derived by applying Lagrange's equation and the dimensionless coupled equations of the exciters with a modified average small parameter method are obtained. The condition of existence for zero solution of the dimensionless coupled equation is used to derive the condition for the self-synchronous motion of the vibration mechanism. The stability condition of self-synchronous motion is obtained according to the Routh-Hurwitz criterion. Afterward, the numerical simulations are carried out to verify the results of the theoretical analysis. The results are concluded that increasing the mass ratio of the two exciters and decreasing the frequency ratio along the vertical direction, the angle of the resonant excitation and the mass ratio of the inner rigid body against the vibration system are all able to enhance the ability of self-synchronization of the vibration mechanism. The simulation results are finally validated by experiments.