CC BY
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© А.Н. Корчевский, A.B. Пластовец, 2015
УДК 622.764:621.928.6
А.Н. Корчевский, А.В. Пластовец
ОПИСАНИЕ ПАРАМЕТРОВ ДВИЖЕНИЯ МОБИЛЬНОЙ НАКЛОННОЙ ПОВЕРХНОСТИ В КАЧЕСТВЕ РАБОЧЕГО ОРГАНА АППАРАТА ПО РАЗДЕЛЕНИЮ МАТЕРИАЛОВ
Приведены аналитические выражения для определения скорости полюса деки вибрационного пневматического сепаратора и ее угловой скорости, которые могут бьть использованы при исследовании перемещения частиц по поверхности деки.
Ключевые слова: конструктивная схема, вибро- концентрационной стол, сепаратор, механическая система
A. Korchevskiy, A. Plastovets
DESCRIPTION OF THE MOVEMENT PARAMETERS OF THE MOBILE INCLINED SURFACE AS WORKING BODY FOR MATERIALS SEPARATION DEVICES
Analytical expressions for determination of board pole speed and it angle speed of oscillation pneumatic separator are presented, that can be used for research of particles moving on the surface of board.
Key words: Constructive scheme, vibro- concentrating table, separator, mechanical system
Problem and its connection with scientific and practical tasks
In recent years interest to gravitational devices in which the main working body is the inclined mobile surface renewed. By this principle the following equipment works: concentration tables (division occurs in the water environment), and also vibration pneumatic separators (division occurs in an air stream). Though the specified equipment also is applied to processing of the materials, differing by properties and grain size, but has similar designing parameters, statics, kinematics and dynamics parameters (as a mechatronic system).
Problem definition
At present the Department of Mineral processing of Donetsk National Technical University" (Donetsk) is involved in the creation of mobile concentrating complex for the purposes due to the technical specifications for products, when dealing not only with the primary mineral resources but also with the secondary which were regarded to the present timeis waste or unfit for recycling [7-9]. The purpose of this work is continuation of researches on creation of mathematical model of parameters of movement of working bodies of devices with an inclined plane.
The deck of vibro- concentrating tablehas a continuous surface and «fluidized bed» of shared material which created by the turbulent streams of the liquid flowing on an inclined surface. The deck is mounted to the second fixed frame by means of four drafts constructively implemented as an identical cylindrical drafts such as 3d, 4th, 5th and 6th. Compound of rods with deck and the frame carried out by means of cylindrical hinges, and, more precisely, the rods connected to the frame by hinges Oi, O2, O3, O4 (Fig. 1), but with the deck connected by hinges A, B, A1, B1 (Fig. 1).
In an equilibrium state deck leans on an axis of an electric motor which creates its vibration movements in an operating mode. O1 and O2 hinges move along the inclined plane (a frame 2) for the purpose of change of tilt angles of cores to a straight line which passes through O1 O2 points (an axis x1) (fig. 1).
For determination of speed of any point flow we will consider the point M(x,y) flow which radius vector F, and we will calculate its speed (fig. 2).
We will enter basis 01t1J1K1 of motionless system of coordinates 01x1y1 and basis A tJ of mobile system of coordinates of Axy (fig. 2) which are connected by the equation
1 = cos 9i - sin 9j , (1)
j1 = sin 9i + cos 9j . (2)
We will present F vector in two bases:
F = xi + yj ,
F = x11 + y1L
where x,y are set, and x1, y1 are calculated:
(3)
(4)
■Z2
Fig. 1. Constructive scheme of mechanical system of a separator
¿2
Fig. 2. The scheme for determination of deck pole speed and its angular speed
According to the theorem of speeds of points of the body under flat movement, speed of M is equal
V = Va +®F, (7)
where Va - strip speed VA = VAXi 1 + VA j1; ra - vector of deck
angular speed: ra = rak.
Projections of VA on axes x1, y1:
VAx1 = -^1ra1sin 9, (8)
VAy1 =-^1ra1cos 9. (9)
Then
or VA = ( VAx1 - )7 + ( VAy1 + rax1)h .
If we show speed vector VA as VA = V 1 + V1 its projections on axes x1, y1 may be evaluated:
V =- /1ra1 sin 9-ra( x sin 9 + y cos 9), (10)
V = /1ra1 sin 9 + ra(xcos 9-y sin 9), (11)
The module or size of speed of any point of deck can be calculated using formula V = (Vxf + Vyf)1/2. Deck angular acceleration
s = ra . Deck angular speed: ra = 91 — a2 sin 92 = 9p2, let's
- (a1 - a2 cos 92)2
differentiate it:
2a2 (cos 92 (1 - (a1 - a2 cos 92)2) + a2 sin2 92(a1 - a2 cos 92))ra2 s = s1--1 —--
(1 - (a1 - a2 cos 92 )2 - (a1 - a2 cos 92 )2 a2sin 92 s (12)
^1 - (ax - a2 cos 92 )2
Then we can calculate the acceleration of any point of the deck M (x, y) with the radius vector 7 = x1 { + y1 j1. According to the theorem on the determination of the acceleration of the body
points, committing plane rectilinear motion, acceleration of M equals
a = aA + aAM, (13)
Acceleration aAM:
AM , (14)
where a'AM = 6- r , anAM =rax(rax r). (15)
Vector of angular acceleration 6 = sk1. (16)
In the basis of the fixed coordinate system 01x1y1 acceleration is:
a = ax11 + \ l, (17)
where ax! = a'Axi + anAxi - - ®2, ayi = a'Ayi + aAyi +- ®2yx, x1 = x cos 9- y sin 9 y1 = x sin 9 + y cos 9.
Module of acceleration of any point on the deck:
a ^4 + 4 . (18)
Conclusions and directions for further research
Conducted analysis of the deck motion and its motion equation made it possible to find expressions for the pole velocity and angular velocity of the deck. Further research should be directed at establishing a relationship with the deck motion parameters and separation coefficients for various materials on an inclined moving surface.
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ABOUT AUTHORS _
Korchevskiy A.N., PhD of Donetsk National Technical University, Donetsk, korchev_al@ukr. net,
Plastovets A.V., Assistant of Donetsk National Technical University, Donetsk, plast199130@gmail.com.
КОРОТКО ОБ АВТОРАХ -
Корчевский А.Н., кандидат технических наук, доцент, заведующий кафедрой обогащение полезных ископаемых Донецкого национального технического университета, korchev_al@ukr.net,
Пластовец A.B., ассистент кафедры обогащение полезных ископаемых Донецкого национального технического университета, plast199130@gmail.com.
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