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We study synchronization of two eccentric rotors (ERs) with common rotational axis in the vibration system of the far-resonant spatial motion. We deduce the dimensionless coupling equation of two ERs with applying the average method of small parameters. We convert the synchronization problem into the existence and stability of solving the zero solutions for the dimensionless coupling equations. By introducing the synchronization torque and the difference between the residual torques of two motors, we obtain the synchronization condition that two ERs achieve the synchronized motion. We derive the stability condition of the synchronized motion, which satisfies Routh-Hurwitz criterion. We discuss numerically the choosing motion feature of the vibration system, which indicates that the vibration system has two steady motion modes. The synchronization torque forces the phase difference to approach π when the structural parameters of the vibration system satisfy the condition of the spatial cone motion, and the synchronization torque drives the phase difference to approach zero when those satisfy the condition of the spatial circle motion. Finally, through the comparison and analysis of experimental data, the structural parameters of the vibration system satisfying the above two conditions can guarantee the synchronization stability for two ERs.

On the Synchronization of Two Eccentric Rotors with Common Rotational Axis: Theory and Experiment