Abstract
To solve the limitation of vibration synchronization, this paper investigates the dynamics of a vibration system driven by three homodromy eccentric rotors (ERs) using control synchronization. According to the synchronous condition and the stability condition, the changes of the phase differences of the three-ERs system and the two-third ERs system are obtained. Based on the electromechanical mathematic model of the vibration system and the master-slave control strategy, the synchronous target that three ERs achieve the same phase motion is converted into velocity and phase tracking of ERs. Considering the coupling characteristic of the self-adjusting of the system in the state of vibration synchronization, the velocity and phase controllers are designed by employing discrete-time sliding mode control. An experimental system for control synchronization is designed, including hardware composition and software programming. For the feedback signal used to match control targets, a method of calculating velocity and the phase difference is proposed from engineering. Recording the rotational velocities, phase differences, and system response, three group experiments with different control schemes are achieved. According to the experimental data, the coupling characteristic of the vibration system adopting control synchronization is analyzed, which can provide the basis for designing vibration machines using control synchronization.
Highlights
Self-synchronization of the vibration system is a special non-linear phenomenon first discovered by Huygens
Because the vibration synchronization restricts the application of the three eccentric rotors (ERs) structure, we propose control synchronization to solve this limitation of the vibration system
This work investigates the coupling characteristic of the vibration system excited by three ERs using the control vibration through theory and experiment, presents a control strategy including control schemes and controllers, and designs a complete control system including hardware and software
Summary
Self-synchronization of the vibration system (vibration synchronization) is a special non-linear phenomenon first discovered by Huygens. Synchronization of ERs is of great significance in engineering and technology fields, which is used to design vibration machines [9,10,11,12]. When it comes to the research of synchronization in a vibration system, Blekhman [2,9] was the first to explain the synchronization mechanism of two ERs theoretically by applying the method of the direct separation of motions.
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