Analysis Of Synchronous Movement Of Vibrating System Driven By Double Vibrators On The Same Axis

The vibrating mill that is driven by double vibrators along the same axis is taken as our typical research object.The synchronous movement is studied theoretically. This result could provide a theoretical foundation for the studies regarding synchronous movement under more complex vibration system as well as the studies that aim to decrease the mass of vibration system by applying synchrony.In the first instance,it is assumed that the vibrating body does not have cone-sharp vibration movement.The mechanics model for the vibration system is obtained by reasonably simplifying it.The dynamical equations governing the movement are established based on Lagrange theorem.By solving the dynamical equations,our result reveals that the moving trajectory of vibrating body is consistent with the difference between the two vibrators' angle.While the vibrating body moving,when the difference of the two vibrators' angle increases,the amplitude of vibrating body's centroid declines.When the difference of two vibrators reaches 180 degrees,the amplitude of the mass center of vibrating body is zero.In the next place,under the condition of cone-sharp vibration of the vibrating body,the dynamical equations governing the movement are established.By discussing the dynamical equations,the vibrating body will have cone-sharp vibration if there is variation between the two vibrators' angle.While the angle of variation between the two vibrators increases,the amplitude of vibrating body's centroid declines.When the angle of variation between two vibrators reaches 180 degrees,the amplitude of the mass center of vibrating body is zero and the amplitude of the two sides of axis achieves its largest.Under this extreme circumstance,a completely cone-shape movement emerges in the vibrating system disturbing its working.