THEORETICAL STUDY OF THE PROCESS OF INTERACTION OF PARTICLES OF WEED IMPURITIES IN THE FLOW OF RAW COTTON WITH THE WORKING BODIES OF THE CLEANING MACHINE

ТЕХНИЧЕСКИЕ НАУКИ

THEORETICAL STUDY OF THE PROCESS OF INTERACTION

OF PARTICLES OF WEED IMPURITIES IN THE FLOW

OF RAW COTTON WITH THE WORKING BODIES

OF THE CLEANING MACHINE

Abstract: the article proposes to use the Euler equations to describe the motion of a stationary flow in the cleaning zones, which allows to determine the laws of pressure, density and velocity distribution along the arc of contact of a moving layer of raw cotton with a mesh surface in the process of impact impact with spikes on the pulp. It has been established that the pressure, densities and flow rates along the cleaning arc as a result of hammer spikes vary in steps, with a decrease in pressure and density and an increase in the flow velocity along this arc.

In world practice, large-scale research is being carried out to improve the technique and technology for processing cotton with high contamination, especially machine harvesting. In this area, the development of theoretical foundations of the technology for cleaning from weeds, the development of mathematical models that contribute to the establishment of optimal cleaning modes without negative impact on the initial quality indicators of cotton, the development of efficient and resource-saving devices, an effective technology for preparing raw cotton for the cleaning process, optimization of modes and parameters machines are becoming increasingly important.

In this article, the study of the possibility and preference of cleaning cotton before rioting, the development of an effective technology for preparing raw cotton for storage, based on this method, as well as the effect of this method on the release of trash from the cotton composition and on the initial quality indicators of cotton fiber are relevant.

The scientific significance of the research results is explained by the fact that in the process of research, the regularities of the movement of cotton in the working chamber of the purifier were revealed, the process parameters were optimized by means of mathematical models of the interaction of cotton with the surface of the working organs, and regularities were revealed that express the influence of the process parameters on the cleaning efficiency. The theoretical significance of the research results is due to the fact that, as a result of the research carried out on the recommended technology for cleaning cotton, a new arrangement of peg drums, working surfaces helps to preserve the natural indicators of the quality of raw cotton, to increase the efficiency of cleaning cotton from weeds and improve product quality.

To describe the process of purification of a stationary flow of raw cotton from weeds, it is proposed to use the model of A.G. Sevostyanov. The regularity of the distribution of the amount of released impurities both in the areas between the pegs and between the sections of the cleaning zone was established and it was shown that the largest amount of released impurities is released in the areas between the first and third pegs, then its slight drop occurs

in the areas between the next pegs. This circumstance should be taken into account when

choosing the length of the contact zones of the raw material with the mesh surface.

The equation of motion of the raw cotton flow in each section is described by the Euler equation

dVJ dP nr r ■ \\ -f 2

PjVj — = -— + PjgR(cos a- f sm a) - fPjVj

da da (1)

, p. = p. (a) Vj = v : (a) p = Pj (a) A A f

where J J , J J , and J J density, speed and pressure of

a,, <a<a. raw cotton in sector J J

Equation (1) contains 3 unknowns: p , p and v. To close it, we use the equation of

state of a compressible medium, which establishes a relationship between pressure p and

density p :

p = pc [1 + A(p - pc )] (2)

and the condition of conservation of mass for stationary motion of the flow

PvSo = Q0

S = k Lh

Here 0 0 is the cross-sectional area of the flow layer, h is the thickness of the

layer, L is the length of the drum, 0 is the coefficient characterizing the decrease in the area of contact of the raw material with the surfaces of the pegs. Q0 is the productivity of

the purifier, ^c is the density and pressure when the raw material enters the cleaning zone, A is the constant characterizing the compressibility of the raw material.

From dependencies (2) and (3) with A <<1 we determine the speed

v = v[1 - A(p - Pc)] (4)

Under impact action with a splitter on the surface of the contact of a particle, the flow

v = Bv, v B < 1

acquires the velocity c k , where k is the linear speed of the splitting, where H

is the coefficient of speed reduction, determined empirically, in [1] the average flow rate in v = 0.5 vk

the cleaning zone is taken cp k .

Assuming c in formula (4), we find the density of the raw material when the raw

material enters the cleaning zone c s v

To determine the pressure rc, we consider the known pressure r 0 the density of the

raw material P° in the feed zone. Then putting P P° and P P<0 to formula (3), we find

Pc = P0 - (P0/ Pc -1)/A (5). From the requirement of the absence of separation of raw materials from the splitting

surface it follows Pc > 0, which means ~ < 1 + P0 A . On the other hand, the condition

Pc < P

^ > 1

of rarefaction of raw materials in the cleaning zone rc which gives pc , must

be fulfilled.

Thus, to implement the process of loosening the raw material without breaking contact

with the splitter, it is necessary that the density ratio p satisfies inequality

The limitation on the pressure value r0 (or the splitting speed) follows from the condition that there is no damage to the seeds during the impact interaction of the splitter

with the raw material. If we denote by k the limiting impact force at which the seeds are

p < P / S

damaged, then assuming in formula (6) Pc k 0, we obtain

po < Pk / S 0 + (Po/Pc - 1)/A .

We introduce a new variable according to the formula a = s/R (a is the central

angle, R is the radius of the drum). Taking into account (2) and (4), we write down the

equation for pressure p .

dp — a— = RPg(sina - f cosa)[1 + A(p - pc)] - Qof [1 - A(p - pc)] (6)

Equation (6) is reduced to the form:

(1 - Apc )F (a)Rpog - Q°v°f (1 + pA)

— = F1(a) p + F2(a) (7)

where F2(a) = A[RPogF1(a) + Qofvo] , F4(a) = a

Fl(a) = sin a- f cos a, a = 1 - Q0 vcA S 0

p(0) = p

The solution to equation (7) satisfying condition r v 7 ^c is represented in quadratures

p = F3 (a)[~p^— + f F4(a)da] P ^ A F3(0) J F3(a) J (8)

where F3 (a) = exp [JF2 (a)da].

We use formula (8) to determine the pressure p in each section.

Let us consider the case when the contact of the flow of raw cotton in the first section

„ , . 0 < a < a0 a0 < a < 2a0

with the mesh surface occurs in four sections 00 0,

p = A = F3 (a)[ "Fpor + ] F^Tda] 0 <a<a° (9)

F3(0) ° F3(a) at (9)

p = p = f3 + j-FT(-)da] „Jq < a < a

F3(aoo) a F3(a) at 0

p i F (a)

p=p3 = F3 (a)[ fT^ + J "Fhid^ at a < i < i

^3(2«q) 2jq F3(a) JaT 0 0 (H)

p = p4 = F3 i)[-p^- + J F^i at3iQ < i < 4«о (i2)

F3(3i0) 3JQ F3(a) at (12)

Similarly, for the second section, we have

p = * = F&(J)[FT4Q) + at 0 <J<JQ (13)

pSo m+ J F4(j),

p = " = F3(J)[Fi + JШа] a, Jq <«<2J

p = p = f3(j)[F727T + j fT^ a. 2jq <«<3j

p7o J F4(a)

, + J t^rda] t 3aQ <a < 4a0

f3 (3<jq ) 3jq f,(a) at 0 0 (16)

p = p = fs(«)^ ч + | ^ da] ^ 3jq <a< 4j where

pc = A(«q) -" 1]/A p2c = p2(2a0) --1]/A v v

p3c = p3(3ao)--1]/A p4c = p<(4a0)--1]/A

p5c = psJq) --1]/A p6c = p26(2a0) --1]/A

plc = p7(3ao) - [ ^^ -1]/A

For the calculation, the reduced coefficient of friction between the mesh and raw cotton was used according to the formula f = f (1 - n), where n = S / SQ, S is the area of the

mesh occupied by open areas, 0 is the total area of the mesh.

Let us consider the process of separating weed impurities from the composition of raw cotton when it moves along a mesh surface. Following [3], the relationship between the

mass m of the raw cotton entering the cleaning zone and its density p is represented in

dm dp the form m p

where Я = 1/(1 + a) , a > q is the proportionality coefficient.

I integrate the last equation that satisfies the conditions m = m9 (mQ is the mass of raw cotton entering the zone between the first and the second splitter of the cleaning zone of

raw cotton per unit time), p = pc with a = 0 for the cleaning zone between the first and second splitting, we get

— = [1 + A(p - p ]z Taking into account dependence (3), we have m0 1 c for

The mass of the separated impurity referred to the mass m0, between the first and

second, second and third, third and fourth pegs and after the impact of the fourth peg is determined by the formula

&1 = ... - =1 - [1 + A(Pi-P0cf at 0 <a<a0

S2 = si(a0) — = si (a0)[1 + A(P2 - Pic )]\\t a0 < a < 2a0

s3 = s2(2a0)[1 + A(P3 - P2c ]Z at 2a0 <a< 3a0, S4 = S3 (3a0)[1 + A(P4 - P3c ]Z at 3a0 < a < 4a0

Similarly, for the second cleaning zone, we have

s8 = s7(3a0)[1 + A( p8 - P7c ]Z at 3a0 <a< 4a0

Where pressure Pi (i = 1,2,3 -8) is determined using formulas (9) - (16). The total mass of the separated trash impurities (referred to the total mass of raw cotton on the surface of the mesh) from the two cleaning zones is presented as a sum

M = ^ jsida + ^ js4+tda i=1 (i-1)«0 i=1 (i-1)«0 Analysis of the results. (Figure 1-3) shows the graphs of the distribution of the density, velocity and mass of the separated impurities (referred to the mass of raw cotton) along the arc of contact of the raw cotton with the mesh surface of the first cleaning zone at two values of the productivity of the cleaning machine.

In calculations it is accepted: R = 0 2M, ® = 50c 1 Vc = 38Mc ; h = 0 018M. L = 1.7M, a0 = 450, k0 = 0.8, S0 = ¿0 hL = 0.02448M2, f = 0.1,

p 40Kr/M , P° 2500na, A = 7-10 1/na. From the analysis of the graphs, it follows that as a result of the impact of the pegs, the density and velocity in the sections of the flow layer at the impact sites change abruptly, while the density changes insignificantly

during transitions to the sections between the pegs, an intensive increase in speed is observed, this is noticeable at high machine productivity (Fig. 2).

The graphs of the distribution of the masses of trash impurities released from the flow (referred to the mass of the unrefined mass of raw cotton), shown in Fig. 4, show that a high cleaning effect is observed in the area between the first and second splits, then there is a decrease in the mass of separated trash impurities, a significant impurities in the sections

between the second and third headers are observed at high values of productivity Q . It can

be seen that an increase in the value of parameter z leads to an increase in the mass of emitted trash. Based on the calculations, the total mass of trash impurities isolated from the cleaning zone was calculated.

Fig. 1. Density distribution p(Kr/M of raw cotton in the area of the first cleaning section for two

performance values Q0

Fig. 2. The distribution of the flow rate of raw cotton v( Wc) in the area of the first cleaning section

for two performance values Q0

Fig. 3. The mass distribution of the selected weed imPurities (referred to the mass of raw cotton of raw) s (in Percent) in the first section of the cleaning at two values ofProductivity Q0 different

values of parameter

X:1 -X = 0.06 2-X = 0.08 3-X = 0.1 4-X = 0.12

Tables 1 and 2 show the amounts of separated trash impurities in the areas between the pegs and their total weight (referred to the weight of raw cotton) at different values of

parameter 1 and two values of productivity . From the analysis of the tabular data, it follows that the total mass of the released impurities can increase significantly at large

values of the parameter 1. In this case, intensive release of trash impurities occurs in the areas between the first and second grates.

Table 1. Values of the mass of seParated trash imPurities between the Pegs and their total mass (attributed to the mass of raw cotton, in%) in the first section of the cleaning zone at

Q0 = 20 / 9Kr/c and different values of the Parameter 1

X 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.2 0.24

a0 < a < 2a0 1.438 1.901 2.356 2.803 3.242 3.674 4.098 4.515 4.925 5.328

Table 2. Values of the mass of separated trash impurities between the pegs and their total mass (referred to the mass of raw cotton, in%) in the first section of the cleaning zone at (1) and different

values of the parameter (2)

z 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.2 0.24

a0 < a < 2a0 1.438 1.901 2.356 2.803 3.242 3.674 4.098 4.515 4.925 5.328

Conclusions: It is proposed to use the Euler equations to describe the motion of a stationary flow in the cleaning zones, which makes it possible to determine the laws of distribution of pressure, density and velocity along the arc of contact of a moving lay er of raw cotton with a mesh surface in the process of impact by pegs on the fibrous mass. It has been established that the pressure, density and flow velocity along the cleaning arc as a result of blows with coke changes abruptly, with a decrease in pressure and density and an increase in the flow velocity along this arc. This indicates a process of significant loosening of the flow during the transition from the cleaning section to the second and there is a slight change in their values in other cleaning sections. It is proposed to use the model of A.G. Sevostyanov to describe the process of cleaning raw cotton from weeds. Equations have been drawn up to determine the amount of separated impurities both in the areas between the pegs and between the sections of the cleaning zone. It has been established that the largest amount of emitted impurities is released in the areas between the first and third pegs, then it falls slightly in the areas between the next pegs. This circumstance should be taken into account when choosing the length of the contact zones of the raw material with the mesh surface.

References