Study On The Theories Of Self-synchronization And Phase Control For Vibrating System With Two-motor Drives

Although extensive research has been devoted to the theory of mechanic-electric coupling in self-synchronization vibrating system and many theoretical results have been obtained since 1960s', there are also some deficiencies in such theories. On one hand, 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. When there are bigger differences in the parameters of the two induction motors, the synchronization of the system can not even be realized. On the other hand, the dynamic characteristics of asynchronous motor are less considered. Actually, self-synchronization of vibration s ystems 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 (no-ideal energy source) in the system. Therefore, it is necessary to develop the theory of mechanic-electric coupling in synchronization system.The theories of self-synchronization and phase control for vibration system with two-motor drives are studied in this paper. The works in this paper are described as follows:(1) By virtue of d'Alembertian principle, the force analysis for the eccentric lumps in the vibrating system of circular motion is carried out and the effects of asway motion and circle motion of the machine body on the synchronization of the two eccentric rotors are obtained. Based on the characteristics of motion of the vibratory system, the observer of the difference between the phases of the two eccentric lumps is designed by using the two acceleration signals measured from the two symmetrical positions in the machine body to overcome the difficulty of the phase difference measurement. A PI controller is designed to control the phase difference between the two eccentric lumps and the computer simulations are carried out to verify the effectiveness of the proposed scheme.(2) Theories of self-synchronization with twin-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 two 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 two eccentric lamps are derived. At last, the condition of stability is obtained using the 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, i.e., one half of the products of the torque of frequency capture and the sine of the phase difference between the two 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) The theory of coupling dynamics is employed to study the synchronous characteristc of two dissimilar coupled exciters in an un-resonant vibrating system. The two exciters are driven by the two induction motors rotating in the same direction and reverse directions, respectively. The condition of realizing the frequency capture and the condition of synchronous stability in the vibrating systems is obtained.(5) The computer simulations are carried out to verify the results of the theoretical analysis afore-mentioned.