The Application of Dynamic Synchronization in the Aggregation of Vibration Exciters of an Adaptive Vibrating Mill

Abstract

Vibrating mills are one of the most advanced types of grinders, which have high productivity and combine a sufficiently high intensity of technological action with a relatively simple construction. The main parameter of vibrating mills is the amount of maximum power transmitted to the load through the chamber by the vibrating exciter at a given value of the forcing power developed by it. It was found that the maximum power is transmitted to the load when the chamber moves along a circular trajectory. Thus, it was determined that an equivalent forcing power should be applied near the center of inertia of the oscillating part of the vibrating mill. The aggregation of vibration exciters can significantly reduce the time and cost of engineering and manufacturing of vibrating mills, while simplifying their maintenance and repair. In other cases, the use of several low-power vibration exciters instead of one of equal power is due to the need to disperse the forcing power over the vibrating working body of a large-sized vibrating mill. The article considers the dynamic scheme of a vibrating mill with aggregated vibration exciters, which will ensure their self-synchronization. A mathematical model of a three-axis vibrating installation with four uniformly rotating vibration exciters is proposed in the form of a system of ordinary linear differential equations, which allows studying the movement of its actuators. The solutions of the system of differential equations corresponding to the stable synchronous and out-of-phase motions of the unbalance shafts of a three-mass four-vibrator two-chamber vibrating mill with active additionally installed rotating unbalanced masses are also presented. Based on the received results, the graphs of functions describing the steady oscillatory motion (A = const) of the executive bodies of the vibrating mill were constructed.