Theory Research On System Synchronization Behavior Of Rotors Coupling With Pendulum

As the development of the advanced science,synchronization vibration screens are widely applied in various fields,such as metallurgy,energy,food materials,national defense and chemical industry,etc.Because synchronizing characteristics is closely related to the work state of the vibration screens,the synchronization theory plays an important role in the vibration utilization engineering.Nowadays,linear vibrating screens are usually adopted in the drilling fluid screening engineering.However,the solid particles in the screen mesh is pushed by the throwing power in a single direction,which reduces the screening efficiency as the phenomenon of "plugging screen" and "pasting screen".Based on this background,a kind of rotor-pendulum vibration system is proposed in this paper to implement an elliptic motion with large amplitude,which improves the screening efficiency as the solid particles is thrown in the multi-direction.But for the study of synchronization of the rotor-pendulum vibration system,it is difficult to explain and analyze the synchronization phenomenon with the traditional theory considering the system with multi-DOF,multi-variable coupling as well as nonlinear factors,etc.Therefore,the synchronization investigation for the rotor-pendulum system is very significance in the theoretical application and practical engineering.Firstly,the dynamics model of the single-rotor-pendulum system is proposed.Based on the motor principles,the mathematic model of asynchronous machine in the system is established.Meanwhile,the mechanical dynamics model of the system is derived according to the Lagrange equation.And the steady-state response solutions of the system in multi-DOF are obtained by applying the Laplace method.Then considering the electrical characteristics of the system,the electromechanical coupling model of the system is given.Finally,it can be found that the elliptic motion and linear motion are implemented in the single-rotor-pendulum system.Next,the synchronization theory for a dual-rotor-pendulum system in a vibration body with the single DOF is studied.It can be found that synchronous behavior of the system is mainly affected by the spring stiffness,the installation angluar of motors and the rotation direction of rotors.Meanwhile,the"critical point" of synchronization leads to non-solution of the phase difference between the two rotors,which results in the dynamic characteristics of the system chaotic.Then,a vibration screen of dual-rotor-pendulum is proposed.The Poincare method is applied to derive the synchronous balance equation and the synchronous stability criteria for the system.It can be found that the synchronous behavior of system is influenced by the rotational direction of the rotors,frequency ratios,mass ratios and geometric parameters.And the non-equal mass of the rotors has little influence on the synchronous behavior of the system.Finally,the elliptical and linear motion can be obtained in mass center of the system when the parameters of the system satisfy some certain conditions.These results provide theoretical supports for the development of new vibration screens.Afterwards,a vibration screen of tri-rotor-pendulum is proposed.The synchronous condition the synchronous stability criterion of the system are drived with the modified average small parameter method,on which the synchronous behavior is determined with dichotomy method.The study results show that the stable phase difference of the tri-rotor-pendulum in the vibration system mainly are mainly determined by the rotational direction of the rotors,frequency ratios,mass ratios and geometric parameters.Finally,the experimental prototypes of the single-rotor-pendulum system,the dual-rotor-pendulum system and the tri-rotor-pendulum system are designed,and the correctness and effectiveness of the theoretical computations and numerical simulations are verified in the paper.