Study On Synchronization Mechanism Of The Rotor-pendulum System

Synchronization theory is widely used in practical engineering applications,most people study synchronization theory of the rotor system or the pendulum system,The synchronous theory of the rotor-pendulum system is less.Rotor-pendulum system is widely used in mining,screening,aerospace and other fields,so it is necessary to study on synchronization theory the rotor-pendulum system.In this paper,the rotor-pendulum system is based on mechanical screening background,The dynamic model of dual motor driven rotor-pendulum system is established,The self-synchronization condition and stability condition of the single mass?double mass rotor-pendulum system with the same rotation and reverse rotation are studied.Then the numerical simulation and experimental verification are carried out,and the main contents are as follows:(1)The dynamic model of the single mass?double mass rotor-pendulum system with the same rotation and reverse rotation is established,and the differential equations of motion are obtained by the Lagrange equation.(2)The steady state response of the rotor coupled pendulum system to horizontal x,vertical y,vibrating mass swing angle ? and pendulum rod swing angle ?1 is solved by Laplasse transform method.By using Hamilton principle,the self-synchronization conditions of the dual drive rotor-pendulum system of the same rotation and reverse rotation(simple body and double mass)are solved.The stability condition of the system self-synchronization operation is obtained by using the extremum condition of Hamilton principle.(3)The rotor-pendulum system is numerically simulated by MATLAB/Simulink,and the system is simulated under normal working conditions.The steady phase difference,the steady speed difference and the elliptical trajectory of the center of mass of the rotor-pendulum system are obtained.(4)Considering the change of system parameters on the rotor-pendulum system self synchronization,the effects of the two motor power supply frequency difference,vibration body quality,pendulum length and initial pendulum angle on the rotor-pendulum system self synchronization are analyzed quantitatively.The effects of initial phase difference,initial angular velocity difference and system disturbance on the system synchronization stability are also considered.(5)A dual motor driven coupled rotor pendulum test bed is built,and its natural frequency is measured by modal test.In the same direction rotation and reverse rotation two cases,experiments are carried out on the system under normal conditions and two motor power supply frequency difference is not zero,and through comparing the test results and simulation results,the reliability and correctness of the numerical simulation are proved to some extent.