Research On Self-Synchronization Theory Of A Single Mass Nonlinear Vibrating System With Two Motors Drives

The synchronous vibration machinery is widely used in mining, light industry and other fields. Extensive research has been devoted to the theory of mechanic-electric coupling in self-synchronization vibrating system and many theoretical results have been obtained since1960s’. However, most of the literature studied from the perspective of linear or quasi-linearization to simplify nonlinear vibration system, which involved less the synchronization theory of vibration system with nonlinear factors. And most mechanical systems are nolinear vibration system in engineearing. Thus, it is necessary to consider comprehensively nonlinear elements of vibrating system in order to in-depth analysis the self-synchronization phenomenon of the vibration system.In the paper, the nonlinear elastic elements of the vibration system are considerd. The self-synchronizaiton conditions and stability conditions of nonlinear vibration system with double motors running in the same and reverse rotation are researched. The works in this paper are described as follows:(1) The mathematical model of electromagnetic torque of a squirrel-cage three phase asynchronous vibration motor and the expression of elastic force of nonlinear spring are established. By applying Lagrange method, the electromechanical coupling dynamic models of single-mass nonlinear vibration system with two motors in same and reverse rotation are established.(2) The vibration response analytic solutions in horizontal direction, vertical direction and twist direction are solved by using KBM approach. Based on Hamiton’s principle, the synchronization conditions of single-mass nonlinear vibration system with two motors in same and reverse rotation are deduced. By applying an first approximation method of the stability of nonlinear system, the gradual stability conditions at the equilibrium point are deduced when single-mass nonlinear vibration system with two motors in same and reverse rotation realize synchronous run. (3) The Simulink simulation model of three-phase ac asynchronous motor and the electromechanical coupling dynamic models of vibration system are established by Matlab/Simulink software. Through numerical simulation, the effects of the electromagnetic torque difference ΔTe of two motor, the quality Ma of vibration system, the overlap angle θi of eccentric block (eccentricity ri), the distance li beween rotation center of two eccentricity masses and the center of mass of the vibration body and the friction resistance moment coefficients fdi on motor shaft on self synchronization are describe quantitatively.(4) In the paper, the numerical simulation of single-mass nonlinear vibration system with two motors running in same and reverse rotation under the conditions of several typical disturbances are researched. The self-synchronizaiton implementation capability when the initial conditions of two motors are different and a motor is disturbed at synchronizanous runtime are analysed.(5) A experimental table which is driven by dual exciting motors is established. The synchronization tests are done at the same and reverse rotation state when two motors are at ideal working state, the the overlap angles of eccentric block of two motors are different and the supply frequency of one motor is disturbed at sysnchronizanous runtime. Through the contrast of the experimental results with numerical simulation results, the accuracy and effectiveness of the theory and simulation are justified to some extent.