Affiliations: School of Mechanical Engineering and Automation,
Northeastern University, Shenyang, Liaoning, China
Note: [] Corresponding author: Xue-Liang Zhang, School of Mechanical
Engineering and Automation, Northeastern University, Shenyang 110004, Liaoning,
China. E-mail: luckyzxl7788@163.com
Abstract: In this paper we give some theoretical analyses and experimental
results on synchronization of the two non-identical exciters. Using the average
method of modified small parameters, the dimensionless coupling equation of the
two exciters is deduced. The synchronization criterion for the two exciters is
derived as the torque of frequency capture being equal to or greater than the
absolute value of difference between the residual electromagnetic torques of
the two motors. The stability criterion of synchronous state is verified to
satisfy the Routh-Hurwitz criterion. The regions of implementing
synchronization and that of stability of phase difference for the two exciters
are manifested by numeric method. Synchronization of the two exciters stems
from the coupling dynamic characteristic of the vibrating system having
selecting motion, especially, under the condition that the parameters of system
are complete symmetry, the torque of frequency capture stemming from the
circular motion of the rigid frame drives the phase difference to approach PI
and carry out the swing of the rigid frame; that from the swing of the rigid
frame forces the phase difference to near zero and achieve the circular motion
of the rigid frame. In the steady state, the motion of rigid frame will be one
of three types: pure swing, pure circular motion, swing and circular motion
coexistence. The numeric and experiment results derived thereof show that the
two exciters can operate synchronously as long as the structural parameters of
system satisfy the criterion of stability in the regions of frequency capture.
In engineering, the distance between the centroid of the rigid frame and the
rotational centre of exciter should be as far as possible. Only in this way,
can the elliptical motion of system required in engineering be realized.
