Self-Synchronization Of Two Coupled Exciters In A Vibrating System Of Spatial Motion

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 and lack analyses on inertia coupling.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 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 (no-ideal energy source) in the system. Therefore, it is necessary to develop the theory of mechanic-electric coupling in synchronization system.A new vibrating mesh structure was proposed according to the theories of self-synchronization for vibration system with two Coupled Exciters. The vibrating mesh of three directional motions has elliptical motion in xy-plane and linear vibration in z-direction. When the sieve materials have accumulated, the exciting force of vertical direction can toss them, avoid the blocked phenomenon, remove the manual clearance, and improve screening efficiency.lt is much better than the flat vibrating mesh; furthermore the stability of self-synchronization for vibration system is increased.The theories of self-synchronization for vibration system with two Coupled Exciters are studied in this paper. The works in this paper are described as follows:(1) Equations of motion of Vibrating Machine of Spatial Motion with two Coupled Exciters including Parallel-axes and cross-axes are established, according to Lagrange's equations. (2) The theories of self-synchronization of two Coupled Exciters in a Vibrating Machine of Spatial Motion are 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 is 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 sin(2α) or sin(2α+θc) 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) Analysis of the coupled dynamic characteristics of the two exciters are obtained, including load coupling, general dynamic symmetry, general dynamic symmetry and the impact factor of Stability of synchronization.(5) The method of bisection about the angular velocity and the phase difference of the synchronous operation are given.(6) The computer simulations are carried out to verify the results of the theoretical analysis afore-mentioned.