Computer model for sieves' vibrations analysis, using an algorithm based on the false-position method

American Journal of Applied Sciences, Jan, 2009 by Dinu I Stoicovici, Miorita Ungureanu, Nicu Unguranu, Mihai Banica

INTRODUCTION

Establishing the most favorable vibration operation conditions for swinging screens is the essential problem when devising such equipment. The amplitude and the frequency of vibrations are the decisive factors that influence the vibrating conditions. The sieves operate best in over-critical angular resonant regime, at high frequencies coupled with small amplitudes for materials with a mainly fine grading, and at small frequencies coupled with high amplitudes for sorting materials with mainly coarse grading.

In the literature(1), (2), there are guiding principles that recommend how to adopt the frequencies, the amplitudes, and how to adopt the dynamical conditions.

The most used vibrating system in screening construction bulk material is the inertia one. In Fig. 1 the main components of such equipment are presented.

[FIGURE 1 OMITTED]

For the case of sorting construction bulk material on vibrating screens with inertia driving system, the over-critical regime is generally adopted, because it has lower sensitivity to perturbations. For example, when an over-dose of bulk material occurs accidentally on the screen, the equipment presents a tendency to go to lower values of frequencies, and also, the amplitude to go to higher values Fig. 2. There is the advantage of obtaining an intense regime, and that will free faster the surface of the screen from the over-dose.

[FIGURE 2 OMITTED]

During a normal vibratory functioning regime, there are two periods of time from the point of view of the movements of the sieve: the first one (Interval index I in Fig. 3-4) in which the movement of the screen makes possible the acceleration, the deceleration and/or the stop of the particle movements on the screen surface, but the particle will stay all the time on this surface.

[FIGURE 3 OMITTED]

[FIGURE 4 OMITTED]

And a second one (Interval index II) in which the movement of the screen makes possible the jump of the particle from the surface of the screen.

Generally is accepted(1-3) that the sieve moves describe an ellipse. In this case, the equestion are Fig. 6,

[FIGURE 6 OMITTED]

[xi] = a*sin ([omega]t - [epsilon]) [eta] = b*sin ([omega]t) (1)

In formula (1),[xi]-represents the elongation of the sieve motion on [OMICRON][xi], axis, [eta]-represents the elongation of the sieve motion on [OMICRON][xi] axis, a-represents the half of the amplitude of the movement on [eta]-line, b-represents the half of the amplitude of the movement on [eta]-line; co-represents the angular frequency of the movement; [epsilon]-the difference of phase.

The acceleration in this case on [eta]-line is:

[eta] = -b*[[omega].sup.2]*sin ([omega]t) (2)

The maximum value of expression (2) is:

[eta] = -b*[[omega].sup.2] (3)

The expression of gravitation acceleration component on [eta]-line is:

[g.sub.n] = g*cos [alpha] (4)

In order to be able to define the movement conditions for each of those intervals, the throwing coefficient (symbol c) can be used. The throwing coefficient is defined as the minimum value of the ratio between the force capable to throw up the particle, and the gravity of this particle:

c = [[[b*[[omega].sup.2]*sin [omega]t]/[g*cos [alpha]]]] = [[b*[[omega].sup.2]]/[g*cos [alpha]]] = [1/[K.sub.0]] (5)

In this inertia system, the particle jumping state often used is one single jump corresponding to one, two or several complete oscillations of the screen. This state of the jump is established(1), (3) by the values of the throwing coefficient: for instance, the particle will begin to move only when the throwing coefficient c is greater that 1. That is because in sorting bulk material only a dynamical regime where the particle jumps over the surface is possible to adopt. That will give the first condition:

c>1 (6)

Also, this jump occurs (3) and takes place in the same time when the screen makes a complete oscillation. That will give the second condition:

c = [square root of (1 [[pi].sup.2])] = 3.29 (7)

There are also other conditions that must be realized, that imposed for the throwing coefficient other values, in order to obtain the best dynamical behavior for the screen. Other conditions to impose are:

* The particle in its jump must move higher than the thickness of the wire from which the sieve is made

* The length of the particle jump must be big enough the particle to pass at least in the next eye of the sieve,

* The dynamical regime must be sufficient to avoid a weak jump of the particle

So, from all these considerations the throwing coefficient must have, for the construction bulk materials, values in-between:

2.5[less than or equal to]c[less than or equal to]3.25 (8)

We have two possible situations from the point of view of the particle's movements on the sieve:

* The particle jump is less than a complete sieve oscillation, so the particle will move together with the sieve before another jump will occurs (Fig. 3)

* The particle jump is as long as the one complete sieve oscillation is. This is the ideal case, and means that the particle stays on the sieve only in the moment of its fall on the sieve, and immediately after the particle is thrown again by the sieve oscillation (Fig. 4)