Development of a mathematical model of a vibrating polyfrequency screen as a dynamic system with distributed parameters

Heorhii Shevchenko,Serhii Holobokyi,V.b Shevchenko

doi:10.1051/e3sconf/202016800062

Abstract

A mathematical model of a vibrating polyfrequency screen as a dynamic system with distributed parameters has been developed. The dynamic system of solids of finite sizes was chosen as the design scheme for the screen: framework, sieves with bulk material and impactors, the contact interaction of which occurs through two-side bonds and collisions on surface areas that have elastic-damping coverings. It is shown that a change in the amplitude of the exciting force has a significant effect on the dynamics of vibration impactors of a polyfrequency vibrating. There is an amplitude value at which the impactor passes from the mode without interacting with elastic bonds to the vibro-impact mode. The impactor movements begin to change disproportionately altered by the exciting force amplitude. It is shown that the start of the impactors in the screen substantially depends on the exciting force. Changes in the amplitude of the exciting force make it possible to achieve chaotic oscillations of impactors, which in turn leads to oscillations of screen surfaces with a continuous frequency spectrum, i.e. to the operation mode of the screen, which is most appropriate for dehydration and separation of fine mineral fractions.

Highlights

Efficient extraction, dehydration and enrichment of fine fractions of mineral raw materials is possible on vibrating screens, the screening surface of which make polyfrequency oscillations with a continuous infinite frequency spectrum and with accelerations up to thousands of m/s2 [1]
In developing the mathematical model of the screen, the following assumptions were made: - taking into account that the structural elements of the screen have substantially different stiffness, one part of the structural elements is modeled by absolutely solid bodies, and the other part is by Voigt's elastic-damping bodies;
In accordance with the assumption made above about the existence of ideal two-side bonds, excluding horizontal movements of solids and their rotation about the vertical axis, we assume that the centers of mass On of all bodies Sn, n = 1, N, of the dynamic system can make small movements only along the axis Oz of the main system Oxyz, there are no displacements along the axes Ox and Oy, and the bodies Sn themselves can make small rotations with relative to the axes Onξn and Onηn, at the same time, rotation of the bodies relative to the axes Onζn is excluded

Summary

Introduction

Dehydration and enrichment of fine fractions of mineral raw materials is possible on vibrating screens, the screening surface of which make polyfrequency oscillations with a continuous infinite frequency spectrum and with accelerations up to thousands of m/s2 [1]. The result of this simplification is the design schemes of the rod, membrane, plate, and shell that are widely used in applied mechanics [18]. Such an approach is used, for example, in researches of the dynamics of vibrating machines with elastic elements [19]

Method

Research results and discussion

Conclusions