Several Special Self-synchronous Theory Of Vibrating System Driven By Two Or More Motors

The synchronous phenomena and problems can be easily found in nature and technological departments. With the development of science & technology and modern industry, self-synchronous machinery is widely used in many fields such as metallurgy, energy sources, national defense and chemical industry, etc. Consequently, the study of synchronization characteristic of the kind of machine receives more and more recognition. In vibration machine field, the mechanical system driven by two or more motors need generally cooperate to complete uniform task, so that the synchronization characteristic of the machine is realized, and the technics purpose is reached. So it is important to apply at vibration engineering for vibration synchronization theory. Therefore, the further study should be done to investigate the dynamics characteristics of the synchronous vibrating system and to provide theoretical basis for the design of this sort of system by using the theory of electromechanical coupling. There are significant theory and engineering values for solving engineering application problem.The dissertation takes the project, based on Professor Wen bangchun has presented vibration synchronization theory for vibration synchronization system in machine vibration using engineering science field, several special self-synchronous theory of vibrating system driven by two or more motors are carried out. The works are financed by the Key Project of National Natural Science Foundation of China (No.50535010), and supported by the Shenyang Key Laboratory of Mechanical Vibration and Dynamic Design of Product. And the main contents are as follows:Considering the effect of the small change of the exciter’s angular velocity to the electromagnetic torque, by using the synchronous frame of stator voltage, the relationship of the electromagnetic torque of an induction motor in the quasi-steady-state operation and the exciter’s angular velocity is deduced. It provides theoretical basis for the dynamics analysis of the vibrating system when the electromechanical coupling is considered.The problem of frequency capture of the two coupled exciters in the vibrating system driven by two exciters whose mass moments are not equal is analyzed. With introduction of two disturbance quantities to average angular velocity of two exciters and their phase difference, the problem of synchronization is converted into that of existence and stability of solution for the equation of frequency capture. By dimensionless processing to the parameters of the system, the self-synchronization condition of the vibrating system which is driven by two exciters whose mass moments are not equal is deduced. The stability condition of synchronous operation is receieved based on Routh-Hurwitz rule.The toque of frequency capture of the vibrating system is quantitative analyzed theoretically. The study show that one half of product of the torque of frequency capture and the sine of phase difference between two exciters acts on the motor with the leading phase as load torque to decrease its angular velocity, and the other half acts on another motor with the lagging phase as driving torque to increase its angular velocity. The bigger the phase difference between two exciters is, the bigger this torque is. The toque of frequency capture has an effect on limiting the increases of the phase difference between two exciters but does not do work to the system when the system is in a stable operation state. When the phase difference reaches a certain value, the angular accelerations of two motors are zero at the same time and the two motors operate at the synchronous state.The dynamic coupling feature of the two exciters whose mass moments are not equal is quantitative analyzed. The study shows that the load torque of each exciter consists of three items, including the torque of sine effect of phase angles, that of coupling sine effect and that of coupling cosine effect. The torque of frequency capture results from the torque of coupling cosine effect, which is equal to the product of the kinetic energy and the coefficient of coupling cosine effect. The condition of implementing the frequency capture depends on the parameters of two motors and the coefficient of coupling cosine effect of the two exciters.The dynamic model of the vibrating ball mill is established, and the synchronization problem of the vibrating system driven by two eccentric exciters in the same axes but not connected by joint shaft. The motion equations and the steady-state response of the vibrating ball mill are derived by using Lagrange Equation. The self-synchronization and stability conditions of synchronous operation of the vibrating system are deduced by using Hamilton theory, and it provides theoretical basis for the design of vibrating ball mill.The vibrating system with two motors is dynamics analyzed; the equations of motion and the steady-state responses of the vibrating system are deduced. Then the self-synchronization criterion of the vibrating system and stability criterion of synchronous operation after the vibrating system implementing vibratory synchronization transmission are analyzed after the synchronous rotation of two motors at the steady-state, the power supply of one motor is cut off, which means that the power source is only supplied to one motor. The motion law of the vibratory synchronization transmission is analyzed by computer simulation on the basis of the analysis of the self-synchronization criterion of the vibrating system and stability criterion of synchronous operation after the vibrating system implementing vibratory synchronization transmission. The motion laws of the vibratory synchronization transmission of the two exciters are analyzed when the phase differences of the two exciters are 0 degree and 180 degree. And the motion laws of the vibratory synchronization transmission of the two exciters are also analyzed when the mass moments of the two exciters are equal and not equal.The self-synchronous theory of the vibrating system driven by three motors is investigated. The mathematics model of electromechanical coupling of the vibrating system driven by three motors is established, and the self-synchronization and stability conditions of synchronous operation of the vibrating system are deduced by using Hamilton theory. The motion law of the vibrating system driven by three motors is analyzed through simulation, and it provides theoretical basis for the design of the vibrating system driven by several motors.By the way of omnipotence experimental table as investigating object, several kinds of self-synchronous vibrating machine are experimental investigated and analyzed when the experimental table is driven by two motors or three motors and the mass moments of the exciters are equal and not equal. The features of vibration synchronization and vibratory synchronization transmission of the vibrating system are investigated. Through the experiment and investigation to the omnipotence experimental table, the conclusions are validated that the vibrating system can implementing stable operation of vibration synchronization and that of vibratory synchronization transmission.