Abstract
The self-synchronization of rotors mounted on different vibrating bodies can be easily controlled by adjusting the coupling parameters. To reveal the synchronization characteristics of a weakly damped system with two rotors mounted on different vibrating bodies, we propose a simplified physical model. The topics described in this paper are related to coupling dynamic problems between two vibrating systems. Both synchronization and vibratory synchronization transmission of the system are studied. The coupling mechanism between the two rotors is analyzed to derive the synchronization condition and the stability criterion of the system. The vibration of the system is described by an averaging method that can separate fast motion (high frequency) from slow motion (low frequency). Theoretical research shows that vibration torque is the key factor in balancing the energy distribution between the rotors. Taking the maximum vibration torque (MVT) as a critical parameter, we investigate the synchronization characteristics of the vibrating system in different cases. The curve of the maximum vibration torque (MVT) versus coupling frequency is divided into several parts by the coupling characteristic frequency and the input torque difference between the rotors. Simulations of the system with coupling frequencies from different parts are carried out. For the system with rotational frequencies larger than the natural frequencies, the coupling characteristic frequency or characteristic frequency curve should be considered. When the coupling frequency is close to the characteristic frequency or the vibration state is close to the characteristic frequency curve, self-synchronization of the two rotors can be obtained easily. Under certain conditions when the coupling effect between the rotors is strong enough, the rotors can maintain synchronous rotation even when one of the two motors is shut off after synchronization is achieved, which is called vibratory synchronization transmission. Vibratory synchronization transmission of the system occurs in a new synchronous condition, and the phase difference between the rotors takes on a new value, that is, the system approaches a new synchronization state.
Highlights
In addition to chaos, synchronization is an important concept in the research of nonlinear vibration
The simulation results show that in the after-resonance system, the coupling effects of the system will be strong when the coupling frequency is close to the characteristic frequency, and self-synchronization of the two rotors occurs
When there is a large difference between the coupling frequency and the characteristic frequency, it will be difficult to achieve selfsynchronization
Summary
Synchronization is an important concept in the research of nonlinear vibration. The self-synchronization theory of rotors was developed by Blekhman [1,2, 21] with the averaging method, and the synchronization conditions and stability of the vibrating system were summarized in the middle of the 20th century. Wen and Zhao et al [22,23,24] modified the averaging method by introducing two variable perturbation parameters and proposed two small parameters to average the angular velocity of the two exciters and their phase difference This method is useful for investigating the synchronization of a vibrating system with two nonidentical coupled exciters, and the dynamic characteristics of the induction motor are more involved. It was found that the coupling performance of two rotors mounted on the same vibrating body was not the strongest and that the setup is not suitable for some heavy-load and high-impact conditions. As vibratory synchronization transmission is obtained after the motor of rotor i is shut down, the corresponding synchronization index DTi can be expressed as
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