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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. [ABSTRACT FROM AUTHOR]

In this paper we give some theoretical analyses and experimental results on synchronization of the two non-identical exciters. Using the average method of modified small parameters, the dimensionless coupling equation of the two exciters is deduced. The synchronization criterion for the two exciters is derived as the torque of frequency capture being equal to or greater than the absolute value of difference between the residual electromagnetic torques of the two motors. The stability criterion of synchronous state is verified to satisfy the Routh-Hurwitz criterion. The regions of implementing synchronization and that of stability of phase difference for the two exciters are manifested by numeric method. Synchronization of the two exciters stems from the coupling dynamic characteristic of the vibrating system having selecting motion, especially, under the condition that the parameters of system are complete symmetry, the torque of frequency capture stemming from the circular motion of the rigid frame drives the phase difference to approach PI and carry out the swing of the rigid frame; that from the swing of the rigid frame forces the phase difference to near zero and achieve the circular motion of the rigid frame. In the steady state, the motion of rigid frame will be one of three types: pure swing, pure circular motion, swing and circular motion coexistence. The numeric and experiment results derived thereof show that the two exciters can operate synchronously as long as the structural parameters of system satisfy the criterion of stability in the regions of frequency capture. In engineering, the distance between the centroid of the rigid frame and the rotational centre of exciter should be as far as possible. Only in this way, can the elliptical motion of system required in engineering be realized. [ABSTRACT FROM AUTHOR]