UDC 622.742.002.5
PROBABILISTIC SIMULATION OF VIBRATORY SCREENING
UNDER HIGH LOADING CONDITIONS
V. P. Nadutyi
1
and E. C. Lapshin
1
Translated from Novye Ogneupory, No. 9, pp. 58 – 61, September, 2004.
Original article submitted June 3, 2004.
An integral criterion, based on the concept of a probability flow, is proposed to characterize the effect of segre
-
gation and sieving in a simulated process of screening.
A way towards enhancing the productivity of vibratory
screening is to carry out the process at high loading rates. As
is generally believed, the particle size gradation involves
processes of segregation and sieving.
Recently, there has been an increased interest in mathe-
matical simulation of the screening process considering that
the engineering and economic characteristics of the produc-
tion process are to a significant extent controlled by the effi-
ciency of separation of precursor materials. Quite a number
of models to this effect have been developed; some of them
were reviewed, for example, in [1, 2]. However, these mod-
els disregard the effect of segregation and sieving on the
screening process, which introduces uncertainty in a rational
engineering design of the screen. It is important to emphasize
the stochastic nature of the screening process, especially for
highly productive screens, with a processing rate reaching
1000 tons of raw material per hour. Effective simulation is
possible only if a sufficiently complete set of physical pa
-
rameters is taken into account.
Our goal in this study was to develop a concept model of
the effect of segregation and sieving on the screening process.
At the Institute for Engineering Geology Mechanics
(IEGM), a mathematical model of the kinetics of the screen
-
ing process has been developed [2, 3]. Its basic principles are
as follows. In a loose (fine-grained) medium, a reference vo
-
lume is singled out; the volume is partitioned into n – 2 unit
layers. Each unit layer is identified by an index i; the sieve
and the space beneath it are identified as i = n – 1 and i = n.
Fine particles subjected to vibratory excitation are trans
-
ferred with the probability p
ij
from the unit layer i to the unit
layer j. This transition will be called the step k
m
. During the
sieving process, the reference volume decreases in height,
which is simulated by a stepwise decrease over the thickness
of a unit layer. Each quantity, controlled by the volume
height, is identified by the index m which is the same as the
number of the upper unit layer (m = 1, 2, ..., n – 3).
The distribution of particles over unit layers is characte-
rized by a vector which is a row of state probabilities.
P
m
=
PP P P
n
m
123
, , , ...,
, (1)
where P
i
is the probability for a particle to be found within
the unit layer i (i = 1, 2, ..., n ).
The kinetics of screening is described by the relationship
P
m
(k
m
)=
P
m - 1
(k
m –1
)
p
ij
m
k
m
. (2)
The elements of a stochastic matrix must satisfy the nor
-
malization condition
P
i
i
n
=
å
=
1
1
,
p
ij
i
x
=
å
=
1
1
||
furthermore, with allowance made for the screening kinetics,
it is necessary [2, 4] that p
in
= 0 and p
nn
=1.
Events and the corresponding transition probabilities are
given below:
Transition probability Event
p
ij
for j = i +1,i and j < n –2 ...........Delivery
of particles to sieve
p
ij
for j = i –1,i and j < n –2.....Removal of particles
from sieve
p
ij
for j = i, i and j < n –2 ....Particles remain in layer i
p
n –1,n
........................Sieving
p
n –1,n –1
....................Sieve blinded
p
n –1,n –2
.................Sieve self-cleaned
Refractories and Industrial Ceramics Vol. 45, No. 6, 2004
453
1083-4877/04/4506-0453 © 2004 Springer Science+Business Media, Inc.
1
Institute for Engineering Geology Mechanics, National Academy
of Sciences of Ukraine, Dnepropetrovsk, Ukraine.
@Phil_Robichaud
@deepthiw
@JoseServera