Synchronization for a vibrating system with octa-motors drives on an isolation frame

Abstract

The aim of this paper is to investigate combination of vibration isolation for four vibrating machines with eight unbalanced rotors to eliminate the dynamic forces that the system acts on the foundation. By using the average method of modified small parameters and modal analysis, we deduce the dimensionless coupling equations of the eight unbalanced rotors, which convert the problem of synchronization for the eight unbalanced rotors into that of existence and stability of zero solutions for the dimensionless coupling equations. By combining the existence of zero solutions for the dimensionless coupling equations with the general dynamic symmetry for two coupled unbalanced rotors in one vibrating machine, the synchronization criterion and the stability criterion are obtained by using the generalized Lyapunov equation, Lyapunov criterion and Routh-Hurwitz criterion. Computer simulations are carried out to verify the above theoretical results. The results of computer simulation demonstrate that a pair of unbalanced rotors in one vibrating machine can synchronize at a phase difference of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>π</mml:mi></mml:math>, the phase differences among the four vibrating machines are between the two opposite. The four vibrating machines can vibrate only in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>z</mml:mi></mml:math>-direction, while the isolation frame is at rest during the working process. When the power supply of one motor in any vibrating machine is switched off, the coupling characteristics of the system can transfer energy from the unbalanced rotors with power supply to that without power supply to extend synchronization of the eight unbalanced rotors.