167 / 2021-03-31 17:10:44

The Effect of Damping on Self-Synchronization in Two Unbalanced Rotors

Self-Synchronization,Nonlinear Vibration,Self-Excited Vibration,Shooting Method

When self-synchronization occurs in a system in which multiple nonlinear self-excited oscillators with different natural frequencies are coupled, the frequencies of all of the oscillators are entrained due to the interaction. While to date many researchers have examined characteristics of this phenomenon, its mechanism has not been completely clarified. In order to provide new insights into the mechanism, this paper considers a system consisting of two unbalanced rotors which are driven by DC motors installed in a rigid body with their axes horizontal and parallel. The rigid body is supported by elastic and damping elements and constrained to translational motion in the vertical plane perpendicular to the motor axes. Considering that not only the frequency and amplitude of the rigid block but also the stability in a synchronized state is important when using the synchronous rotation of the unbalanced rotors for the vibration source in a vibratory machine, the effect of the damping on self-synchronization is examined. Numerical calculations including the stability analysis for the synchronous solution (periodic solution) are performed by the shooting method for various values of the voltage supplied to the DC motor and the damping to demonstrate the relationship between these parameters and the characteristics of self-synchronization.