Synchronous Coupling Characteristics of a Dual Vibrator-Driven Vibration System with Two Internal Degrees of Freedom

This paper designs a double-cylinder vibrating ball mill system driven by double motors, which consists of two internal rigid bodies and an external rigid body with two vibrators. The theoretical conditions for achieving synchronous behavior in the system are explored using the averaging method, and characteristic analysis is performed based on this. Then, the numerical results are calculated by using the Runge–Kutta method. The mutual comparison between characteristics and numerical results examines the correctness of the theoretical investigation in the present paper. It also indicates that the system exhibits synchronous behavior in all three regions, and for engineering applications, Region I is a better choice. The advantage of Region I is that the internal rigid body has an elliptical motion with a large amplitude, and the external rigid body has almost no vibration. This can utilize the amplitude of the synchronous behavior and reduce the dynamic load transmitted by the system to the foundation. Additionally, the results show that key structural parameters significantly affect the feasible range of stable synchronization behavior. The research results can provide design guidelines to optimize the ideal working range of the new vibration grinding equipment in engineering.