CC BY
14
Section 14. Agriculture
Alijanov Djabpar, senior lecturer, doctor, of philosophy technics Tashkent institute of irrigationand agricultural mechanization engineers, Republic of Uzbekistan (TIIAME), Abdurokhmonov Shavkatjon Khasanovich,
senior lecturer, Tashkent institute of irrigationand agricultural mechanization engineers, Republic of Uzbekistan (TIIAME), E-mail: abduroxmonov.shavkatjon@bk.ru Makhatov Shamsiddin Razzoqovich, assistant professor, Tashkent institute of irrigationand agricultural mechanization engineers, Republic of Uzbekistan (TIIAME),
SIMULATION OF GRAIN MOVEMENT IN THE WORKING CHAMBER
Abstract: the article deals with the investigation of the process of free movement of particles in the rotor grooves under various operating and geometric parameters of the working chamber and obtaining the equation of the theoretical productivity of the working chamber of the crusher.
Keywords: grain material, working chamber, rotor, stator, groove, motion, destruction.
This work is c°ntinuati°n of works [1; 2] it is also directed working chamber. From this scheme, we will receive drM = ^ to receiving model of the movement of grain in the working 2
chamber. where i = 0,1,2.... - number of the crushed particles mi = 2',
The movement of grain in a groove of a rotor represents number of degenerations Nt = mt -1 itself discrete process i.e. alternation ofstops and movements. d30 = 5Mu{^th0 = 10 MM,a0° = 6,71°,a0 = 13,240 [l,iakl] At the time of jamming of grain between working surfaces of
a rotor and the stator there is a stop of its movement in the
The algorithm for a research of the movement of grain in
, ,CJ c c , the working chamber presented in a general view in (fig. 2):
radial direction. At the same time, if deformation of a particle ° r ° °
• ^a^u^u • j . .. t.j-u • .. , 1. In the operator of size f ,a>,r„,r ,r ,r , B,S,A get out,
is > A that there is a destruction. When jamming a particle r -»>><)> k> 3> 3K>r> > o
and deformation insufficient for destruction there can also be mpacY entered after their calculations [2. equation (10);
a stop, but only on condition that centrifugal force will be less 1 equation (2)].
or is equal to the sum of all resistance forces. 2. Counter of number of steps of i. For the equal initial
As a first approximation process of destruction of sepa- sizes of grains both cereal, and bean it is enough to have
rate grain it is possible to present in the form schemes in fig. i =0.1... 5 at a gap 8= 0, and deformation destruction
1, considering that each destruction halves a particle exactly. A = 445mm .
In fig. 1 the example of consecutive destruction of a wee- 3. Definition of value of radius of a particle at the time of
vil with an initial diameter of 5 mm to particles of 0.625 mm destruction takinginto account a possible accidental devia-
in size which it is less critical 2r3k = 0.89mm at is given tion from size I — I 2r3k = 0.89mm at S = 0 and therefore freely go out of the V 2 )
+i =ly l + P
where p - the operator of a randomizition chosen in the range of possible deviations of r^. On the basis of the experi-
mental data of distributions of fineness of particles at the exit from the working chamber
p=(0 * °,2). tjL
Figure 1. The scheme of destruction of grain at S = 0 and the rated diameter of grain
4. Calculations r [2, equation-3]
5. The solution of the differential equation of the movement of grain in a matrix form
0 1 "
(l + C • sin X- cosX + N • cos2 X) - A • cos A
"X (1) "
.X (2)_
w
X (1) X (2)
0
cos2 X
■ B
For use of PVM and the decision in a cover of Mat lab will conveniently present in a vector form: function y prime= = udpol(t, r);
y prime = |0 1; ®2(l + C- sin A-cosA + N-cos2A)-A-cosA^-
[1) m] -b
6. To calculate time of the movement between destructions of a particle
7. To calculate time of stops of a particle
XTPi =z—
ri
8. Operator of comparison r3i+j < r3k. If the condition is
not met, to pass to operator 2 if the condition is met, a free exit of particles of r from the working chamber is provided - to pass to operator 9.
9. To find calculate T = ^^ + ^Tpj the time spent of a particle in the working chamber.
10. To print values T, r, r3i and to receive function graphs x(t).
For production of calculations on PVM with use of a cover of Mat lab, we developed the following files [3]:
1. Main abd8.m file
2. Auxiliary abd8.a file
3. Auxiliary.abd8.v file
Calculations show that number of destructions of grain, coordinates of points of destruction depend on the initial sizes of grain, the established 5 rotor stator gap. In fig. 3 it is shown co = 140 p / c, and in the table 1 results of calculation for different initial r30 within the operating range of a gap 5 . The received results show increase in the size of particles at the exit at increase 5 and r .
The number of destructions and number of the destroyed particles decrease with increase 5 and reduction of r30. At the same time, the size of particles at the exit significantly differs from 5 the size of the established gap. However, by consideration of set of the particles coming to the working chamber, which sizes submit to normal distribution it is possible to determine the average sizes of particles at the exit. Ways of the accounting of number of the destroyed particles and their sizes have given in (table 2).
r
Figure 2. The block - the scheme of an algorithm for a research of the movement of a particle of grain in the working chamber
rE, UO
MM 100 90 SO 70 60 50 40 30 20 10
h ---- /
f
/
/
<5 /
't
0
0,005
0.01
0.015
0.02 t. c
Figure 3. Movement and coordinates of points of destruction of grain in the working chamber at a> = 140c_1,A = 0,5mm (forthe working chamber with geometrical parameters
r0 = 15mm,rK = 100mm,h0 = b = 10mm, A = B = 50mm
Figure 4. An arrangement of coordinates of points of destructions for particles with an initial radius of grain r30 = 2.0^3.5mm (digit 1.2.3,- respectively number of destruction, a text against these digits - coordinates of destruction, digits in brackets indicate the initial size of grain)
Results on number of destructions and the sizes of the leaving particles depending on the initial sizes r30 and a rotor stator gap are given 5 .
Feature of working process is the discrete movement of the destroyed particle with a short-term stop at the time of destruction. From fig. 4 it is visible that the working area of destruction of particles r30 = 2 ... 3.5mm fluctuates between the first point "1" and the last "3" - at S = 0 and makes distance (95.2-44.14) mm. The randomized nature of destructions leads to insignificant change of length of the working area and average size of particles at the exit that confirmed by a series of again of the implementable modes of calculations. In this zone, there is a sharp reduction of speed of a flow of material determining the flow capacity (productivity) of the Apparently
working chamber. Therefore, it is necessary, first to determine the average speed of particles (fig. 4)
r - r
v =
cp
z*
Where: rk - radius working cameras, m; r i - the coordinate of the first destruction, m; 2t< - calculate time of the movement of particles on an interval (rk-r).
For receiving, 2t it is necessary to consider the scheme (fig. 5) of distribution of simultaneous destructions on sites of a way, which defined by time 1/z a rotor turn. So, for a = 140c— has 22.3 r p s and time of turn for one groove t ' = 0,0075c.
0,0075c
JL
0,0075c
0,0075c
1
0,0056c 1
1 'I 1_) 1 2 22^233331
H =44, 14mm 55,1mm 68,9mm 86,0mm 0,097mm
—I
r0=100MM
Figure 5. The scheme of distribution of simultaneous destructions from the moment of the beginning of destructions to an exit
From fig. 4 and 5 that in the range ofrx = 44.14 ... 55.1 mm are crushed at the same time 2 particles of the first destruction, on r2 = 55.1 interval ... 68.9 mm only one particle of the first destruction. On r3 = 68.9 interval, 86 respectively - both particles of the first and three particles of the second crushing are in r4=86.0 interval ... 97.0 mm.
Since the number of intervals of destructions (or turns of a rotor on one groove) makes around four with alternation a rotor groove - the bottom of the stator and a groove of a rotor - a stator groove, time of movement should be increased twice, i.e.
Yjt = 2(3t'+ 0.0056) = 0.0562c,
In addition, average size of flow rate
0.097 - 0.04414 0.05286
v = -
cp
0.0562
0.0562
= 0.94 m / c
Here 0.097 - the outside radius of a rotor necessary for a free exit of particles [2, tab. 1].
In the course of movement in a groove of the working chamber flux density changes as a result of crushing, and also as a result of stretching and compression of a flow. From (fig. 5), it is visible that compression of a flow begins with r = 44.14mm value and density reaches the maximum value in the range of 68.9 ... 97mm. If to consider that lump linearly depends on fineness ofparticles, then for wheat (rz o = 6mm y0= = 0.75 kg/m3, r k = 0.1mm y = 400kg/m3) let us receive the lump equation y = 59.3, r3 = 394 kg/m3 convenient for use when calculating weight productivity of the working chamber. For the accounting of reduction of flux density at the expense of its arrangement, we will enter coefficient of reduction of density
2rcp 0,66 K == ^ = 0,103 n I, 6,39
Where 2rcp =0.66 mm - the average size of diameter of a particle at the exit from the working chamber (will be determined by these tab. 2 and tab. 3);
l1 = 95.24-88.85 = 6.39 - the site length, a zone of the last destruction of particles (fig. 5).
Productivity of the working chamber can be determined on a formula:
Q = 3600z• B • d3p • vcp•y K„ k g/h;
Where z - number of grooves of a rotor, piece;
Groove V - width at the exit, mm:
The d3 cp-average size of diameter of particles at the exit from working cameras, mm;
The vc p - average size of flow rate in a zone of destructions, m/s;
Y - The volume mass of the crushed product at the exit, kg/m3;
Kn - coefficient reduction of flux density.
For the considered case for the working, chamber with the o = 140 1 / c, B = 50 mm z = 6, S = 0, mm parameters the initial radius of r30 = 2.0 grain ... 3.5mm, Q = 3600 • 6 • 50 • 0,66• 10-6 • 0,94 • 413,5 • 0,103 = 28,54 kg/h.
Respective for the same conditions on at S = 2 Q = 3600 • 6 • 50 -1,72 • 10-6 • 1,55 • 445 • 0,05 = 64,5 kg/h.
Results of calculations of productivity depending on a rotor stator gap gave in tab. 1. From tab. 1 it is visible that the theoretical productivity of the working chamber with a diameter of 200 mm and
Table 1. - Theoretical productivity of the working chamber with a diameter of 200 mm and between grooves 50 mm wide
w, p/c Q, kg/h for the sizes of particles r30 = 2-3.5mm (wheat, barley)
S = 0 S = 0.5 S = 1 S = 1.5 S = 2
60 16.8 18.0 22.1 24.8 30.3
80 15.7 21.5 26.0 30.3 36.6
100 23.1 24.6 27.8 35.9 44.4
120 25.3 28.3 30.7 41.8 53.6
140 28.5 31.5 37.5 48.7 64.5
* Average values on 5 numerical implementations on PVM are
Width between grooves of 50 mm at the exit both increase in rotating speed and clearance increase leads to growth of productivity. Dependences on sections w or dw or 3 have linear character. In general, theoretical productivity reflects the flow capacity of the working chamber of the considered type, but owing to the probabilistic nature of process of destruction of particles can fluctuate within ± 10 percentage of average value.
shown
In addition, a series of calculations based on the abd8a file made for determination of the maximum flow capacity of the working chamber at free (without destruction) the radial movement of grain. Results presented in tab.1, and examples of implementation of processes of the movement of grain in a graphic view of fig. 6. The research of influence of a corner which defines linearity of the differential equation the movement of particles in rotor grooves shows its insignificant influence processes A < 5 + 60.
a) at (o= 80c - b) at c = 140c1
Figure 6. Free movement of grain in the working chamber
Table 2. - The sizes of the destroyed particles and their coordinate for the working chamber with r0 = 15 mm; rk = 100 mm at r30 = 2.0mm
Destruction on two equal particles 2.0 1.0 0.5 0.25
The size of particles at the accidental nature of destruction 2.0 0.9 0.6 0.22
5 = 0 r3k = °.445 69.69 86.72 95.24 *
88.42 93.54 *
Coordinate of the destroyed particle of r, mm 5 = 0.5 r3k = 0.609 73.96 91.00 * *
92.70 * *
5 = 1 rk = 0.804 78.23 95.27 * *
96.97 * *
5 = 1.5 r„. = 1.119 82.51 * * *
* * *
5 = 2.0 r, = L374 86.78 * s* *
* * *
*-free exit ofparticles (for examplefor r30=2,0mm and S= 0 on 3 steps ofcrushing at r3i = 0,5 + 0,6 mm r3i = 95,24 + 93,5 there will also be the last destruction and particles the size r3i = 0,25 + 0,22 will have a free exit from the working chamber). Similar calculations made for the grain 5.0 sizes; 4.0; 3.5; 3.0; 2.5 mm
Conclusions
1. Researches of process of free movement of particles in rotor grooves at different regime and geometrical parameters of the working chamber conducted. Special files are for this purpose developed and used on PVM in the Mat LAB system. Reduction of motion speed of particles on inclined grooves, i.e. reduction of flow capacity of the working chamber received.
2. It established that at the time of jamming and destruction the particle in a groove stops, i.e. the movement has discrete character. The special algorithm allowing defining the number of destructions, the speed and the time spent of a particle in the working chamber developed for a research of this movement. For approach of process of destruction to real,
the operator of randomization providing the different sizes of particles after destruction of an initial particle entered into a computing algorithm.
3. Comparison of the movement of grain in working to the camera at free movement and the movement rather increases at a grinding with a minimum clearance S = 0 and at wp < 80 with-1. At wp > 140-1 with and a coarse grinding (for wheat S = 2 ^ 2.5 mm) grain motion speeds with crushing and without crushing are almost indiscernible.
4. The equation of theoretical productivity of the working chamber of a crusher and the corresponding implementations for wheat and barley for the working chamber with r = 100 mm, S = 0 ^ 2mm, w = 60 ^ 140-1 is received with.
k ' P
Table 3. - Number of destructions and the size of particles at the exit from the working chamber
Destruction on two equal particles r30 = 5mm r30= 4mm r30 = 3.5mm r30 = 3.0mm r30= 2.5mm r30= 2.°mm
The size of particles at accidental nature of destruction N m r , зк ' мм N m r , зк ' мм N m r , зк ' мм N m r , зк ' мм N m r , зк y мм N m r , зк y мм
Coordinate of the destroyed particle of r, mm 8 = 0 r3k < 0.445 15 16 0.335 15 16 0.31 7 8 0.41 7 8 0.40 7 8 0.30 7 8 0.22
S = 0.5 r3k < 0.609 15 16 0.335 7 8 0.54 7 8 0.41 7 8 0.40 3 4 0.55 3 4 0.6
S = 1.0 r3k < 0.864 7 8 0.77 7 7 0.54 3 4 0.72 3 4 0.73 3 4 0.55 3 4 0.6
S = 1.5 r3k < 1.119 7 8 0.77 3 4 1.04 3 4 0.72 3 4 0.73 3 4 0.55 1 2 0.9
S = 2.0 r3k < 1.374 3 4 1.37 3 4 1.04 3 4 0.72 3 4 0.73 1 2 1.3 1 2 0.9
N-number of destructions; m, r3k-quantity and the size of particles at the exit; r k- the most admissible size of particles at the exit; data are obtained based on randomized calculation
Tabale 4. - The main indicators of a flow of material at free movement
Rotating speed co,c 1 The time spent in the slave. to the camera t, с Speed at the exit from the slave. cameras u, м/с Average speed ucp м/с Productivity of the exit Q0 кг/час
w = 60 0.054 4.8 1.57 3.39
w = 80 0.039 5.8 2.18 4.71
w = 100 0.031 7.4 2.74 5.91
w=120 0.025 9.1 3.14 7.33
w=140 0.023 11.2 3.69 7.97
Note: up= ; Q0 = z • b • h-vcp-10-6 • 3600 ; r0 = 0,015 K = 0,1, Kp that ro = 3,5
References:
1. Alijanov D., Abdurokhmonov Sh. To the choice of geometric parameters of a rotor crusher / Journal. "Agro Ilm - Agriculture of Uzbekistan" - Tashkent,- No.4 (8).- 2008 y.- P. 67-68.
2. Alijanov D., Abdurokhmonov Sh. About the destruction of grain in the working chamber of the crusher / Materials of the International Scientific and Practical Conference "Problems of innovative and competitively capable development of agro engineering science at the present stage". Collection of scientific papers. Part 1,- Almaty,- 2008 y.- P. 175-178.
3. Dyakonov V. P. A guide to PC MatLAB,- Moscow. "The science",- 1993 y.s
