Theoretical and Experimental Study on Synchronization of the Two Homodromy Exciters in a Non-Resonant Vibrating System

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.

Selected synchronous state of the vibration system driven by three homodromy eccentric rotors

“…In other cases, the movement of the vibration system is elliptic motion, of which amplitude is less than that of two ERs. 15 Figure 5 explains that the vibration system has the selected synchronous state, which reflects the coupling dynamic characteristic of the vibration system.…”

On the Synchronization of Two Eccentric Rotors with Common Rotational Axis: Theory and Experiment

“…Use (3), (6), and (7) and apply Lagrange equation (8) to obtain the equations of motion of the vibration system as follows [9][10][11][12][13][14]:…”

“…This method considers the effect of damping and dynamic characteristics of induced motor. By applying the average method of small parameters, Zhang deduced the condition that vibration synchronization transmission for two ERs with reverse rotational direction and gave the result of the select motion characteristic for the vibration system driven by two ERs with same rotational direction [12,13]. He also gave the result that using three ERs instead of two on a single base cannot improve the effective power in the far-resonant vibration system [14].…”

Differential Movement Synchronous Tracking Control Strategy of Double‐Shaking Table System Loading with Specimen

“…The common synchronous control strategies are the parallel control, the master/slave control, the virtual-shaft control, the cross-coupling control, the relative coupling control, adjacent cross-coupling control, ring coupling control, and so on [10][11][12][13][14][15][16][17][18]. Koren initially proposed the crosscoupling control [12], which, yet, is difficult to be applied to more than two systems.…”

“…To improve synchronous control precision, the control algorithms are also further studied by researchers, such as traditional PID control, adaptive feed forward control, ∞ control, iterative learning control, sliding mode control, fuzzy control, and neural network control [10,11,[17][18][19][20][21][22][23][24][25]. Sun and Chiu developed a nonlinear control algorithm to address the motion synchronization of a dual-cylinder electrohydraulic lifting system [23].…”