Purpose The anti-phase self-synchronization of the co-rotating multi-exciters makes the total excitation force not increase but decreases. Although electronic controlled synchronization can achieve good synchronization performance, due to its complexity and cost in synchronization control of vibration system, it has been rarely applied in vibration mechanical systems until now. The existing synchronization conditions of multiple exciters in a vibrating system are only necessary, not sufficient. Thus, an elliptical vibrating system excited by four exciters with elastic coupling coaxial three-exciter was proposed, and the synchronization and stability conditions were studied. Methods The sufficient and necessary synchronization condition of the new elliptical vibrating system was established according to the Zero-point theorem for continuous functions on closed intervals. The synchronization stability criterion of this new vibrating system was established by Lyapunov’s indirect method. The numerical calculations of the synchronicity index, the phase difference angle and the stability index of are carried out, and the stable motion is verified by experiments. Results With the change of the stiffness (kϑ) of the coupling elements, the system may be self- synchronization, near-self-synchronization, transitional synchronization, un-synchronization, and coupling synchronization. In self-synchronization, there are two steady states of the system, but their trajectories are identical. In near-self-synchronization, the steady motion state of the system shows local bifurcation, which disappears with the increase of the stiffness of the coupling elements. In self-synchronization, there are two steady states of the system, but their trajectories are identical. In near-self-synchronization, the steady motion state of the system shows local bifurcation, which disappears with the increase of the stiffness of the coupling elements. In coupling synchronization, with the increase of the stiffness of the coupling element, the phase difference angle of the two stable synchronization states gradually shrinks, finally there is only one stable state. Conclusion The system has multiple synchronization states in any kϑ, and has multiple stable states when kϑ< kϑc. The number of synchronization states gradually decreases with the increase of kϑ, finally maintains two synchronization states and one of which is stable.

Synchronization and Stability Analysis of a Four-Exciter Elliptical Vibration System with Coaxial Elastic Coupling Three Vibrators

期刊论文
发表日期：

2025年12月16日

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Duyu Hou,
Zheng Liang,
Pan Fang,
Yongjun Hou,
Mingjun Du

摘要

Purpose

The anti-phase self-synchronization of the co-rotating multi-exciters makes the total excitation force not increase but decreases. Although electronic controlled synchronization can achieve good synchronization performance, due to its complexity and cost in synchronization control of vibration system, it has been rarely applied in vibration mechanical systems until now. The existing synchronization conditions of multiple exciters in a vibrating system are only necessary, not sufficient. Thus, an elliptical vibrating system excited by four exciters with elastic coupling coaxial three-exciter was proposed, and the synchronization and stability conditions were studied.

Methods

The sufficient and necessary synchronization condition of the new elliptical vibrating system was established according to the Zero-point theorem for continuous functions on closed intervals. The synchronization stability criterion of this new vibrating system was established by Lyapunov’s indirect method. The numerical calculations of the synchronicity index, the phase difference angle and the stability index of are carried out, and the stable motion is verified by experiments.

Results

With the change of the stiffness (k_ϑ) of the coupling elements, the system may be self- synchronization, near-self-synchronization, transitional synchronization, un-synchronization, and coupling synchronization. In self-synchronization, there are two steady states of the system, but their trajectories are identical. In near-self-synchronization, the steady motion state of the system shows local bifurcation, which disappears with the increase of the stiffness of the coupling elements. In self-synchronization, there are two steady states of the system, but their trajectories are identical. In near-self-synchronization, the steady motion state of the system shows local bifurcation, which disappears with the increase of the stiffness of the coupling elements. In coupling synchronization, with the increase of the stiffness of the coupling element, the phase difference angle of the two stable synchronization states gradually shrinks, finally there is only one stable state.

Conclusion

The system has multiple synchronization states in any k_ϑ, and has multiple stable states when k_ϑ< k_ϑc. The number of synchronization states gradually decreases with the increase of k_ϑ, finally maintains two synchronization states and one of which is stable.