Synchronization of Two Homodromy Rotors Installed on a Double Vibro-Body in a Coupling Vibration System

Abstract

A new mechanism is proposed to implement synchronization of the two unbalanced rotors in a vibration system, which consists of a double vibro-body, two induction motors and spring foundations. The coupling relationship between the vibro-bodies is ascertained with the Laplace transformation method for the dynamics equation of the system obtained with the Lagrange’s equation. An analytical approach, the average method of modified small parameters, is employed to study the synchronization characteristics between the two unbalanced rotors, which is converted into that of existence and the stability of zero solutions for the non-dimensional differential equations of the angular velocity disturbance parameters. By assuming the disturbance parameters that infinitely approach to zero, the synchronization condition for the two rotors is obtained. It indicated that the absolute value of the residual torque between the two motors should be equal to or less than the maximum of their coupling torques. Meanwhile, the stability criterion of synchronization is derived with the Routh-Hurwitz method, and the region of the stable phase difference is confirmed. At last, computer simulations are preformed to verify the correctness of the approximate solution of the theoretical computation for the stable phase difference between the two unbalanced rotors, and the results of theoretical computation is in accordance with that of computer simulations. To sum up, only the parameters of the vibration system satisfy the synchronization condition and the stability criterion of the synchronization, the two unbalanced rotors can implement the synchronization operation.

Synchronous Control of Multi-Motor Coupled With Pendulum in a Vibration System

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Conditions for self-synchronization of inertial vibrators of vibratory conveyors in general motion

“…Extensive studies concerning synchronization of dynamic systems we can find in papers by Blechman (1971,2000), specific applications in papers, e.g. Michalczyk (2012), Michalczyk and Cieplok (2014) and more (Hou et al, 2017;Michalczyk and Pakuła, 2016;Zhao et al, 2011;Fang et al, 2015;Karmazyn et al, 2018;Francke et al, 2010). The principles of building vibrating machines with a vibratory drive are known (Goncharewich and Frolov, 1990;Michalczyk, 1995;Cieplok, 2009Cieplok, , 2018, in particular conditions of synchronous motion with distinction between working in the desirable and undesirable state.…”

Multi-frequency Vibration Synchronization and Stability of the Nonlinear Screening System

“…Usually, when the phase differences between the exciters are close to 0 degrees, the system obtains in-phase vibration synchronization. Instead, the system realizes anti-phase vibration synchronization when the phase difference is close to 180 degrees [5]- [12]. For the equipment working in in-phase synchronization, the system can obtain the linear, circle or elliptical motion trajectories; correspondingly, the equipment of linear vibrating screen, circle vibrating screen, the elliptical vibrating screen appear.…”