Abstract
We investigate synchronization of two asymmetric exciters in a vibrating system. Using the modified average method of small parameters, we deduce the non-dimensional coupling differential equations of the two exciters (NDDETE). By using the condition of existence for the zero solutions of the NDDETE, the condition of implementing synchronization is deduced: the torque of frequency capture is equal to or greater than the difference in the output electromagnetic torque between the two motors. Using the Routh-Hurwitz criterion, we deduce the condition of stability of synchronization that the inertia coupling matrix of the two exciters is positive definite. A numeric result shows that the structural parameters can meet the need of synchronization stability.
Highlights
Synchronization was addressed as two or more systems possessing the same speed, phase, trajectory, or other physical states [1,2]
In a vibrating system with the two identical unbalanced rotors, analytical investigation is greatly simplified by combining the differential equations of the two exciters into the differential equation of the phase difference between the two exciters and various types of vibrating machines have been developed in industrial engineering, such as self-synchronous vibrating feeders, self-synchronous vibrating conveyors, self-synchronous probability screens, self-synchronous vibrating coolers, etc. [9,10,11,12,13,14]
From the results of the theoretical and numeral investigation given in the above sections, the following remarks can be stressed: (1) In the vibration system driven by two motors installed asymmetrically and rotating in the inverse directions, the condition of realizing frequency capture to reach the synchronous operation of the motors is that the torque of frequency capture of the system is greater than the difference between the electromagnetic torques and that of damping torques of the two motors, namely, the synchronization index Da is greater than 1
Summary
Synchronization was addressed as two or more systems possessing the same speed, phase, trajectory, or other physical states [1,2]. Synchronization of two self-excited oscillatory system is a classical problem in the theory of synchronization [5]. Taking the disturbance parameters of the phase difference and average velocity of the two unbalanced rotors as the small parameters, the authors convert the problem of synchronizations of two unbalanced rotors into that of existence and stability of the zero solutions of the differential equations of the small parameters [18,19,20]. We investigate synchronization of two asymmetric exciters in a vibrating system.
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