Synchronization of Two Self-Synchronous Vibrating Machines on an Isolation Frame

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.

Electromechanical coupling characteristics and synchronization control of two-hammer synchronous vibration system

“…The simulation model is established according to Eqs. (5)- (10), and the electromechanical coupling process is obtained by numerical simulation using previously mentioned ideal conditions. The software used for developing the simulation programming is MATLAB/Simulink.…”

“…Inoue and Araki et al [9] discovered three-octave synchronization for double motor driving vibrators. Wen et al [10][11][12][13][14] established the synchronization condition of two vibratory hammers, and applied it to engineering successfully. But about this method, there are strict requirements on structure and dynamic characteristics of the mechanical system, and easy to out of step, thus it is not suitable for all mechanical systems.…”

Conditions for self-synchronization of inertial vibrators of vibratory conveyors in general motion

“…Extensive studies concerning synchronization of dynamic systems we can find in papers by Blechman (1971,2000), specific applications in papers, e.g. Michalczyk (2012), Michalczyk and Cieplok (2014) and more (Hou et al, 2017;Michalczyk and Pakuła, 2016;Zhao et al, 2011;Fang et al, 2015;Karmazyn et al, 2018;Francke et al, 2010). The principles of building vibrating machines with a vibratory drive are known (Goncharewich and Frolov, 1990;Michalczyk, 1995;Cieplok, 2009Cieplok, , 2018, in particular conditions of synchronous motion with distinction between working in the desirable and undesirable state.…”

Double synchronization states of two exciters with horizontal asymmetric structure in a vibrating system

“…This method emphases on the research of mathematical models but ignores the actual conditions in engineering. On the basis of the averaging method, Zhao uses two groups of perturbation small parameters combing Routh-Hurwitz criterion to gain the self-synchronization condition and the stability condition of a series of vibrating systems [5][6][7][8]. The averaging method and the modified averaging method of small parameters further improve the theory of self-synchronization and set up a solid foundation for engineering application.…”