Abstract
A dynamical model is proposed in this paper to study the synchronization and stability of the secondary isolation system with a dual-motor excitation. After deducing the dynamic equations of the system by Lagrange’s equation, the Laplace transform is used to deduce the displacement responses of the system when the system operate in steady state. The synchronous balance equation and stability condition of the system is derived with average method, and the relationship between the coefficient of synchronous ability and the geometric parameters of the system is discussed. It can be found that synchronization ability of the system is gradually increased with the increase between two motors mounting distance; meanwhile the larger difference of the mass between the two unbalanced rotors, the more difficult to implement synchronous operation of the system. Moreover, the stable phase difference of the vibrating system being as the key determinant to reach synchronization is discussed numerically. The research result shows that the synchronous behavior of the system is influenced by rotation direction of the rotors, mounting position of two motors, and mass ratios between unbalanced rotors and vibrating body. The correctness of theoretical analyses is verified by simulation results with Runge-Kutta method.
Highlights
Synchronization phenomena exists in many aspects of life, such as synchronization in uncoupled neuron system [1], gears [2] and coupled self-sustained electromechanical devices [3]
The stable phase difference of the system is weak affected by the mass ratios (η, η ) of the rotors
2) Synchronization ability of the system is gradually increased with the increase between two motors mounting distance; the larger difference of the mass between the two unbalanced rotors, the more difficult to implement synchronous operation of the system
Summary
Synchronization phenomena exists in many aspects of life, such as synchronization in uncoupled neuron system [1], gears [2] and coupled self-sustained electromechanical devices [3]. Some serious accidents are caused such as bolt looseness, fatigue failure of the supported platform and even hazardous for mankind's physical and mental health In this context, Li proposed a vibrating machine with a two-stage vibration isolation frame and discussed its self-synchronization theory, which found that self-synchronous motion is achieved when the parameters of vibration system simultaneously satisfy the condition of self-synchronous motion and the stability condition [16]. In present work, taking dynamical model of the secondary isolation system with a dual-motor excitation for example, the synchronous stability will be discussed by the Poincare method, which provide theoretical guidance for designing new types of vibrating isolation machines.
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