| Self-synchronization of rotors is one of the most remarkable phenomena, and has open up fresh opportunities in the vibration technology. Since the discovery of self-synchronization phenomenon, the theory of mechanic-electric coupling in self-synchronization vibrating system has been developed for nearly half century, many valuable theoretical results have been obtained. At present, a variety of vibrating machinery has been widely used in industry.There are also some deficiencies in such theories so far. Firstly, the current theories are based on the phase dynamic approach and ignore the feature of frequency capture. They are only suitable to analyze the synchronization of the system with two asynchronous motor of the close dynamic parameters and lack of the study on the self-synchronization. Well, there are many outstanding strongpoint of non-resonating system in practicality and the parameters of the four induction motors can not be escaped. Secondly, the dynamic characteristics of asynchronous motor are less considered.Actually, self-synchronization of vibration systems is the effect of mechanic electric coupling and the state of motion of considered systems is closely relative to the dynamic parameters of asynchronous motor in the system. Therefore, it is necessary to develop the theory of mechanic-electric coupling in synchronization for non-resonating system to supervise the system designing and the manufacture. It has the value not only in study but also in reality.The theories of self-synchronization and phase control for resonating system with four-motor drives are studied in this paper. The works in this paper are described as follows:(1) The force analysis for the eccentric lumps in the vibrating system of circular motion has been carried out and the mathematical equations have been developed by means of calculating the kinetic energy, the potential energy and the viscous dissipation of the vibrating system.(2) Theories of self-synchronization with four-motor drivers rotating in the same direction and the reverse directions are been studied by using mechanical-electric coupling theory. At first, in the synchronous frame of stator voltage, the electromagnetic torque of an induction motor in the quasi-steady-state operation is derived. Secondly, averaging the equations of motion of the four eccentric rotors over the period of possible synchronous operation, the equations of frequency capture are derived. The concept of torque of frequency capture is proposed, the conditions of the frequency capture are obtained, and the nonlinear equations of calculating the capture rotating velocity and the phase difference between the four eccentric lamps are derived. At last, the condition of stability is obtained using the Lyapunov criterion and Routh-Hurwitz criterion, and the condition of realizing vibratory synchronous transmission is obtained.(3) Based on the theoretical analysis, the characteristc of torque of frequency capture in the self-synchronization vibration system is obtained, part of the products of the torque of frequency capture and the sine of the phase difference between the four eccentric lamps acts on the motor of the phase leading as the load torque to limit the increasement of its rotating velocity, and another acts on the other motor as the driving torque to limit the reduction of its rotating velocity. During the steady-state operation of the vibrating system, the torque of frequency capture does not do work.(4)This paper propose the theory which is about energy choices and resolve the four-motor-driven shaker between two of four eccentric rotors's phase is%, and deal with the self-synchronization problems of four-motor drive system's stability successfully.(5) The computer simulations are carried out to verify the results of the theoretical analysis afore-mentioned. |
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