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Khankelov Tavbai Karshievich, Tashkent Institute for Design and Construction of Highways, Candidate of Technical Sciences, Associate Professor, E-mail: karshiev_97@mail.ru Mukhamedova Nafisa Baxodirovna, Tashkent Institute for Design and Construction of Highways,
Assistant,
E-mail: nafis_8828@mail.ru
DETERMINATION OF THE MAIN PARAMETERS OF THE DEVICE FOR SORTING SOLID HOUSEHOLD WASTE
Abstract: The issues of implementation of the main statements of the theory of impact to the definition of rational parameters of a sorting device are considered in the paper.
In addition, the design of a sorting device is proposed which will improve the efficiency of the process of household waste sorting.
Keywords: solid household waste, sorting, impact, metal strip, flight range, sorting device, impulse. Existing technologies for collection, transportation from iron scrap, air pollution is reduced by 86%, wa-
and processing of solid household waste (SHW) in Uzbekistan do not provide for their sorting before stacking at landfills.
At the same time, sorting of solid waste (metal, plastic, glass, paper, etc.) before stacking makes it possible to save raw materials and territories for landfills, and also helps to improve the environment.
So in comparison with the smelting of steel from primary raw materials at the output of 1 ton of steel
ter by 76%, and the amount of solid waste by 97%. In comparison with the production of paper from primary raw materials, when it is extracted from recycled paper, air pollution is reduced by 73%, water by 25%, and the amount of solid waste by 39% [1, 17].
In this regard, research aimed at developing and justifying the rational parameters of a device for sorting solid waste is relevant and of great economic importance.
Figure 1. Scheme of the proposed sorting device. 1 -rotor; 2 - organic parts; 3 - solid parts; 4 - bunker; 5 - metal strip
Based on the analysis of the SHW sorting process, the design of a sorting device has been developed (Fig. 1). The principle of the device is as follows. The
waste is fed into the bunker via a feeder. Slipping along the surface of a metal strip, the waste falls into the zone of rotating rotor, and then the blades strike on the waste,
and toss it along a horizontal or slightly upward trajectory. Solid, dense and elastic particles get high speed and fly along a longer trajectory, while soft and inelastic particles fly off only a short distance.
To evenly feed the waste, the device is equipped with a metal strip 5.
The feed layer can be adjusted depending on the fractional composition.
In addition, the impulse S, applied to the rotor blade on the side of the constituents of the waste under the impact, causes impact forces of pressure on the bearings in which the axis of rotation of the rotor is fixed. Accordingly, there appear reactions of bearings equal to these forces, but oppositely directed, which in turn negatively affect the durability of the structure.
In order the reactive impact impulses vanish under the strike on the body rotating around a fixed axis, the point of application of the impact pulse S must be spaced from the axis of rotation z at a distance d, that is, the center of impact must be at a distance d from the axis of rotation
Jz
d = ■
m„ ■ x
(1)
where Jz is a moment of inertia of the body relative to the axis passing through the axis of rotation, mB is a mass of the body, xc is a coordinate of the center of gravity of the body [2, 549].
In order to prevent negative effect of reactive pulses and to increase the impact efficiency from the rotor blade, the blade is designed in the form of a pendulum, the bulk of which is concentrated in the impact zone. The design of the rotor blade and shute along which the waste moves allow us to consider the process of collision of the rotor blade with the components of the waste as a flat impact.
Consider the collision of two bodies A and B (where A is a rotor blade, B is the waste components).
The rotor blade is represented as a plate. The rotor blades rotate uniformly around the fixed axis, and the components of the waste perform arbitrary plane motion before and after impact (Fig. 2). Introduce a fixed coordinate system xy by directing the y axis parallel to the impact line, and two translationally moving coordinate systems whose origin is in the centers of gravity of the bodies, and the axes are parallel to the x and y axes of the fixed coordinate system. The projections of absolute ve-
locities of the centers of gravity are denoted by uA uB (on the x-axis) and by uA , UB, (on the j-axis); angular velocities of the bodies by &A and &B.
Additional indices - and + mark the pre-impact and post-impact state.
Figure 2. Design scheme of the process of rotor blade collision with the constituents of the waste
The moments of inertia of the bodies relative to the axes passing through the centers of gravity, as well as the masses of the bodies denote as JA and JB and mA, mB,
respectively. The points of the impact contact are de* * * * * *
noted by the letters A and B , and xA yA, xB yB - are the coordinates of these points in corresponding moving coordinate axes. The velocities of the points A and B in the projections on x andy axes are equal.
UA = UA -®Ay! UA = UA + ®A ■ XA 1 (2)
uB = ub-®ByB UB =uB +®B ■ XB Let Sx and Sy be the values of the components of the impact pulse parallel to x and y axes; then the equations of the quantities of motion and the moments of the quantities of motion for each of the bodies are written in the form
mA (UA + UA-mB (UB +-UB -
J A (&A +-®A - ) =Sx • y* + S.. ' X A
) = • y A + Sy
mA (UA +- UA- ) = Sx mB (UB +- UB- ) = -Sx JB (®b +-®B- ) = -Sx
■yB - Sy
• X„
(3)
Six equations (3) contain eight unknowns - the six projections of post-impact velocities and two quantities Sx and Sy.
To close the system of equations, Newton's hypothesis is used.
+ -VB + =-R(uA --UB -) (4)
where R is a restoring coefficient and one of the hypotheses of tangential interaction, for example, the Routh hypothesis
|S*| < f Sy (5)
f - is a dynamic coefficient of friction.
Equality sign is used when slip occurs in the tangential direction between the bodies.
From eight relations (3) - (5) one can find the normal impact impulse Sy (6) S = (1 + R)(ub_ +g>B_ ■ xB-Ua--aA • Xa) y 11 x X '
— ■+ —+ 71 (Xa - f ■ yA) + ^ (Xb - f ■ yB)
mA mB J a Jb
through which all other unknowns are expressed [3, 123-124].
Sx = f • Sy
f • Sy
UA + = UA -+■
UB + = UB -
mA
f • 5y
mK
®A +=®A-+JLaA-f-yA)
J A
UA + =UA -+■
m
ub + =ub -+■
m
®b + -+ J-(f ■ + XB )
J B
(7)
If the results of equality (7) are used for the process of collision of the rotor blade with the components of the waste, then the equations of the waste component containing impact values are of greatest practical interest, since in this motion the rotational part can be ignored. In addition, this body (constituents of solid household waste) can be considered as a material point.
UA + = UA - +
f • 5y
m
UA + = UA -+■
m
(8)
are eas-
(9)
The values of pre-impact velocities uA _, ily determined from the design and technological parameters of the sorting device.
It is known that the projections of the pre-impact velocities of the constituents of the waste are equal to
uA_ ~-\Jv0 + 2gh ■ cosa _ >
uA_ = ^/u02 + 2gh ■ sina
where u0 is the rate of falling of the constituents of the waste from the end of the conveyor;
h is the height of the falling of the waste; a is the angle of inclination of the bunker shute relative to the horizon.
Introduce the notations
Sy Ua + — \jvo + 2gh ■ cosa + c ■ f
= C, I-
mA uA +=-yu02 + 2gh ■ sina + c
The absolute value of the post-impact velocity is
u =VuA++1 = >/(u2+2gh) cos2 a+2cf ■
■■¡Jul + 2ghcosa+c2f2 + (u02 + 2gh) sin2a + (11) + 2c^/ u02 + gh sina + c2 — yj (v02 + 2gh) + c2(1 + f2) +
(10)
+ 2cy]u02 + 2gh •(f cosa + sina) taking into consideration that 1 + f2 ~ 1
^(u02 + 2gh) + c2 + 2c •
(12)
•■sjvl + 2gh • (f cosa + sina)
After the end of the impact process (12), elastic components of the waste will move as free undeform-able bodies and the equation of their motion will present a parabola.
y = xtga
h
2 •U • cos'a
• x
(13)
The maximum height of the trajectory of the constituents of the waste and the range of the flight can be determined by the following formulas:
H = +Uc-
2g
• sin a,
L = ^
where H - is the maximum height of the trajectory of the constituents of waste; L - is a range of flight of the constituents of the waste.
Thus, from equations (12), (13) and (14), depend-sin a (14) ing on the value of the restoring factor, mass, shape, moment of inertia, and the angle of rebound of the constituents of the waste, it is possible to determine the design and technological parameters of a sorting device.
The received constructive and mode parameters will allow to develop the physical model of a sorting device.
References:
1. Sanitary purification and cleaning of populated areas. Reference book / ed. A. N. Mirny, N. F. Abramov. - Moscow. Stroyizdat, - 1990.
2. Bat M. I., Dzhanelidze G.Yu., Kelzon A. S. Theoretical mechanics in examples and problems, volume-II, Dynamics. - Moscow. "Science", - 1985.
3. Panovko Ya. G. Introduction to the theory of mechanical impact. - Moscow. - 1977.
