Affiliations: School of Mechanical Engineering and Automation,
Northeastern University, Shenyang 110004, China | Hebei State-owned Minerals Development &
Investment Co., Ltd., Shijiazhuang, 050021, China
Abstract: This paper investigates synchronization of two self-synchronous
vibrating machines on an isolation rigid frame. Using the modified average
method of small parameters, we deduce the non-dimensional coupling differential
equations of the disturbance parameters for the angular velocities of the four
unbalanced rotors. Then the stability problem of synchronization for the four
unbalanced rotors is converted into the stability problems of two generalized
systems. One is the generalized system of the angular velocity disturbance
parameters for the four unbalanced rotors, and the other is the generalized
system of three phase disturbance parameters. The condition of implementing
synchronization is that the torque of frequency capture between each pair of
the unbalanced rotors on a vibrating machine is greater than the absolute
values of the output electromagnetic torque difference between each pair of
motors, and that the torque of frequency capture between the two vibrating
machines is greater than the absolute value of the output electromagnetic
torque difference between the two pairs of motors on the two vibrating
machines. The stability condition of synchronization of the two vibrating
machines is that the inertia coupling matrix is definite positive, and that all
the eigenvalues for the generalized system of three phase disturbance
parameters have negative real parts. Computer simulations are carried out to
verify the results of the theoretical investigation.
