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7В перспективе предполагается экспериментальная проверка предложенного метода.
Литература
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2. Аз1зов Т.Н., Орлова О.М. Жорстшсть 1 мщ-нють при крученш зал1зобетонних двотаврових елеменпв з нормальними трщинами // Вчеш записки Тавршського нацюнального ушверситету 1мен1 В.1. Вернадського Сер1я: Техшчш науки Том 31 (70) № 3 2020. Частина 2. - С. 124-129.
3. Горнов В.Н. Исследование прочности и жёсткости сборных железобетонных перекрытий из лотковых настилов // Материалы и конструкции в современной архитектуре. - М.: Стройиздат, 1950.
4. Елагин Э.Г. Расчет перемещений железобетонных стержней прямоугольного сечения на стадиях работы с трещинами при совместном кратковременном действии моментов и продольной силы/
Э.Г. Елагин //Строительная механика и расчет сооружений. - 1991. - № 4. - С. 26-31.
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6. Коуэн, Г.Дж. Кручение в обычном и предварительно напряженном железобетоне: Пер. с англ. / Г.Дж. Коуэн; - М.: Изд-во литературы по строительству, 1972. - 104 с.
7. Рекомендации по проектированию стальных закладных деталей для железобетонных конструкций/ [разраб. НИИЖБ Госстроя СССР]. - М.: Стройиздат, 1984. - 87 с.
8. Улицкий Б.Е., Потапкин А.А, Руденко В.И., Сахарова И.Д., Егорушкин Ю.М. Пространственные расчёты мостов. - М.: Транспорт, 1967. - 404 с.
9. Azizov T., Kochkarev D. Calculation Model of Equivalent Cross-Section for Determining Displacement During Totsion of a Reinforced Concrete Element With Normal Cracks // Sciences of Europe. - 2020. -Vol 1, № 54(2020). - P. 15-18.
10. Azizov, T., Jurkowska, N., Kochkarev, D. Basis of calculation on torsion for reinforced concrete structures with normal cracks (2019) Proceedings of the fib Symposium 2019: Concrete - Innovations in Materials, Design and Structures, pp. 1718-1725.
В1БРОТРАНСПОРТЕР ДЛЯ ЗАВАНТАЖЕННЯ ТЕРКОВОГО ПРИСТРОЮ
CnipiH А.В.
к.т.н., доцент Teepdoxni61.В. к.т.н., доцент
Вовк В.Ю.
acnipaHmrn
Вiнницький нацюнальний аграрний yHieepcumem, Вiнниця VIBRO CONVEYOR FOR LOADING A GRATER DEVICE
Spirin A.
Ph.D., Associate Professor Tverdokhlib I.
Ph.D., Associate Professor Vovk V. graduate student Vinnytsia National Agrarian University, Vinnytsia
АНОТАЦ1Я
В статп розглянуп теоретичш передумови розробки транспортера для завантаження насшневого вороху люцерни в терковий пристрш. Надшна робота та висока яшсть технолопчного процесу у значнш мiрi залежать ввд способу подачi насшневого вороху у терковий пристрш. Встановлено, що найкраще для цього шдходять транспортери, у яких живильна с^чка здшснюе постшш коливання. Проведений аналiз сил, що дшть на елемент насшневого вороху (боб люцерни), який знаходиться на коливальнш поверхш. Графо-аналггична штерпретащя математично! моделi дозволила визначити рацюнальш конструктивно-техно-лопчш параметри транспортера.
ABSTRACT
The article discusses the theoretical prerequisites for the development of a conveyor for loading alfalfa seed heaps into a grater device. Reliable operation and high quality of the technological process largely depend on the way the seed heap is fed into the grater. It has been found that conveyors are best suited for this, in which the feed belt makes constant vibrations. The analysis of the forces acting on the element of the seed heap (alfalfa bean), which is located on the vibrational surface. The graphic-analytical interpretation of the mathematical model made it possible to determine the rational constructive and technological parameters of the conveyor.
Ключовi слова: терковий пристрш, живильник, вiбротранспортер, насшневий ворох, боб люцерни.
Keywords: grater, feeder, vibrating conveyor, seed heap, alfalfa bean.
Formulation of the problem. Almost all technologies for harvesting the seeds of perennial grasses, including alfalfa, require additional processing of the seed heap on special machines. One of the possible options for this operation is to use a special grater device [1]. Technological and quality performance of this device directly depends on the uniform supply of material to the device. The lack of reliable seed feeders of low-productivity grater devices, which are able to ensure a stable and even supply of material, justified the need to conduct their own research on this issue.
Analysis of recent research and publications. Vibrating machines, including those designed for the supply of bulk materials, are widely used in various industries and agriculture. In the works [2; 3] described a significant number of vibrating machines, including feeders. They state that the task of providing a metered supply of grain and similar bulk materials (including alfalfa seed heap) in small volumes to the working chamber of grinders and graters can be solved by using oscillating conveyors, in which the transportation process is carried out by high frequency oscillations with small amplitude. The advantage of oscillating conveyors is the simplicity of design and high reliability of the process, especially with low material feeds.
In a number of works [5; 6; 7] is considered the interaction of particles of loose medium (most often grains) with a vibrating surface. In work [6] is investigated the influence of the value of the initial specific load at the input of the vibrating screen on its discrete distribution on the working surface. In work [7] is resulted the mathematical model of grain movement by the vibrating stepped working body which allows to define influence of mode parameters of vibration action on technological and qualitative indicators of process of transportation.
Selection of previously unsolved parts of the overall problem. Practically all considered works are devoted to transportation of grain. We are interested in the process of transporting alfalfa seed heap and the behavior on the vibrating surface of its main component -alfalfa beans. This article is devoted to the consideration of some theoretical aspects of this process.
Presenting main material. Consider the movement of alfalfa beans by mass me on the surface AB vibrating tray mounted with a negative tilt angle a to the horizont (Fig. 1).
Fig. 1. The scheme offorces acting on the bean, placed on the surface of the vibrating tray
The magnitude of the angle of inclination of the surface of the vibrating tray to the horizont is insignificant and is within 1° < a < 3°, that will allow to provide stable dosed giving of a heap without its chaotic shift on a tray. If the plane AB provide oscillating motions directed at an angle p to the surface of the plane, then to the bean mass nth. located in this plane, gravity will
ac,G^Mcti„„f„rcefA = f„ra of
normal pressure N and alternating force of inertia I=a-a2 -ms-sinq.
The equilibrium condition of a bean on the surface AB in a fixed coordinate systemXOY can be written as: Ffr -mb -g-sin a ±I -cusp
N=rnbg-cosa±I'smJl' (1)
To move the grain on the surface of the tray from the point A to the point B it is necessary that the condition is fulfilled: ^ X (FXi ) > 0, a6o
/ ■ cos/? > mb-g-sina—F
Where
mb g sin a — N ■ f
a ■ o) - sin <p >
Hit,
■cos (3
(2)
Condition (2) can be fulfilled only in the presence of the phenomenon of micro-separation of the bean
from the surface AB, that is ^ Y) > 0. The separation of the bean occurs when its pressure on the surface of the tray is equal to 0:
N -mh g-c osa — a ■ oj 2 ■ mh ■ sin <p ■ sin /Î
where: a - amplitude of plane oscillations; a - angular velocity of the oscillation source; ç - phase angle of oscillation, cp = at.
= mb ' (S" cos a ~ a ' ' sin V ' sin/0 (3) Provided that g - cosa > a -a1 - sin q - sin /3, the bean is pressed against the surface of the tray AB
and moves with it, and otherwise when a ■a2 ■ sin p ■ sin ( > g ■ cosa - it will come off the surface of the tray. Phase oscillation angle p varies from 0 to 27, therefore the maximum value of the expression a ■a2 ■ sin p ■ sin ( acquired at sin p = 1
(p=n/2). Therefore, the maximum acceleration relative to the axis OY the tray (and the bean along with it) will
acquire in case IymsK = a - a2 ■ sin (.
In case, when g ■ cosa = a ■a2 ■ sin p ■ sin (, boundary conditions occur (the beginning of the sepa-
ration of the bean from the surface AB). Relation
r =
a -a2 • sin p
= 1 called the limit, and the coef-
g ■ cosa
ficient r - dynamic coefficient of the operating mode of the oscillating conveyor. At r<1 the load does not come off the surface of the tray (inertial conveyors), and at r>1 - moves in the mode of separation (vibrating conveyors) [8].
Given that the plane of the tray AB performs harmonic oscillations under the action of inertia I in the direction of its action (at an angle (to the plane AB), then the pattern of movement of the bean can be displayed as follows (Fig. 2).
Fig. 2. The scheme of the bean movement on the tray of the vibrating feeder
The diagram of the movement of the bean on the vibrating tray of the feeder of the grater device under the action of external forces is shown in Fig. 3.
Fig. 3. Diagram of the movement of the bean on the tray of the vibrating feeder
Starting from the middle position (p&=0) plane AB moves in the direction a-a by the amount of eccentricity a in the uppermost position (<pi = n/2). In this case, the
force of inertia ' = mh ' a ' ' sin <P will press the bean to the surface AB i provided that
Ff- > mh gain a + / ■ cos B ,, ,,
, they move together
without slipping. With further increase in the angle p (n!2 < p < 3^-/2), plane AB moves down the distance 2a, the force of inertia separates the bean from the surface of the tray AB and it performs a free flight, the trajectory of which is determined by the angle of throw (,
initial bean speed Vo i depends on the value of the dynamic mode factor r work of the vibrating feeder.
The moment of meeting the bean with the surface of the vibrating tray AB it is necessary to select so that it got on a tray at its movement forward and upwards (3^/2 < p < 7i/2) in a position where the time of their joint movement would be minimal, but sufficient to give the bean the necessary acceleration for the subsequent separation and movement along the surface of the tray in the direction from the point A to B (Fig. 3). Studies have shown that rational should be considered such modes of operation of the vibrating feeder, in which the
coefficient of dynamic mode Г is within 1 < Г < 3,3. At Г < 1 the feeder works as the inertial conveyor, without separation of material from a surface of a tray, and at Г >3,3 there are significant dynamic loads in the drive system [8].
From the point of view of ensuring a stable supply of the heap to the grater device, it is necessary to find the speed of its movement along the tray АВ in the direction from А to В (along the axis ОХ). Given the cy-clicity of the longitudinal movements of the tray, determine its maximum speed:
Vx = a-a2 • cosB = a-x-y-cosB, (4)
Jl max
ge a = x-y - the oscillation frequency of the
tray.
The average speed of the bean in the direction of
the axis OA'will be less than the maximum tray speed,
V? < Vf
-■■■■ -"'■'■ '■. Therefore, to determine the average speed of the bean along the tray, it is necessary to take jc
into account the speed factor Kh, which is determined from the expression [10]:
(5)
The value of the coefficient Ksh depends on the kinematic modes of operation of the vibrating feeder and is determined analytically, or graphically, by measuring the planimeter of the corresponding areas on the graph of the tray speeds [9].
In the most complete general case, changes of beans with the help of a vibrating tray can be created at the level of stages and, depending on their combinations, to reveal the number of modes of movement of materials [8]. Based on our conditions (high speed of movement of the vibrating tray) we will accept the I mode of movement of material which includes three stages: dispersal, free flight and braking of a bean (Fig. 4).
A
/p ^ AH — - \
^--^^ r \
s <p
Fig. 4. The schedule of movement of a bean on a surface of a vibrating tray of the feeder in a mode 1
Based on the physical-mechanical properties of the seed heap and in order to ensure its required supply to the grater device (50.. .150 kg/hour) there was a need for analytical justification of rational parameters and modes of operation of the vibrating tray of the feeder:
- dimensions and angle of inclination to the horizon of the bottom of the vibrating tray;
- frequency and direction of vibration of the vibrating tray;
- amplitude of oscillations (eccentricity of the crank);
- the speed of movement of the bean along the vibrating tray.
To ensure efficient movement of the bean on the surface of the vibrating tray in the direction from A to B, the angle of application of the excitatory force of the vibrator must be within 200 < B < 300 [9]. It is desirable that the line of action of the exciting force (angle B) passed through the center of inertia of the vibrating tray, which usually coincides with the center of mass with a symmetrical arrangement of the vibrating feeder units. If this requirement is not met, the system will re-
ceive additional loads in the form of torque, which prevents the movement of the heap on the tray and reduces its translational speed.
The feed pipes of the feeder must not be rigidly connected to the vibrating tray, so as not to affect the kinematic modes of its operation.
The use of the proposed scheme of the vibrating feeder allows to provide the required performance, but significantly complicates the design of the grater device. To eliminate this shortcoming, we hinge one end of the surface at a point O, a the second will oscillate around this hinge (Fig. 5).
Let's analyze the trajectories of particles on the oscillating surface and the surface itself, taking into account that the surface has an angle of inclination X to
the horizontal axis OX.
Consider the forces acting on a particle (bean, or elementary volume of material) that is on the surface
OXi at the point X when it performs angular oscillations with angular parameters 0, 0, 0
Fig. 5. Analysis of forces acting on a particle that is on an oscillating surface
From the point of view of ensuring the transporta- mine these components, consider their angular dis-
tion of material on an oscillating surface, it is important placements, velocities and accelerations of rotation of
to know the components of displacements, velocities the surface around the point O, which are expressed by
and accelerations of the points of this surface. To deter- the following dependencies (Fig. 5):
Yim r -sin [at)
0 = arctg
X
arctg
1M
L + r - cos [at)
r -co-(r + L -cos (cot))
0
0 =
L2 + r2 + 2 • L • r • cos (cot) L • r • (Z2 - r2)- co1 sin(iy/)
(L2 + r2 + 2 • L • r • cos(<®/))2
(6)
In the vertical plane on the material on the surface of OX1 (grain, for simplicity, take one bean) gravity
G = m • g and the force of inertia I, projection
of which on the axis OY define by expression:
, (7)
jc nit - bean weight, kg;
© - angular acceleration of the bean, c-2;
Xj - the distance of the bean to the center of oscil-
lation, m.
L - r [ LL - r2 )a2 - x - sin [at) [L2 + r2 + 2L - r - cos [at))2
Then, the condition of separation of a particle (volume element) from the surface of an oscillating plane:
m
■ cos(0 + a) — q) > 0
. (8)
At the moment of separation of the bean from the oscillating surface, the equation of equilibrium in the
projection on the axis OY will look like:
mb ■ 8 ■ x1 ■ cos(8 + a) — mb ■ g = 0 (9)
Substituting in the expression (9) value 0 and
0 with (6), after the corresponding transformations, we obtain:
cos
arctg
r- sin
in [at)
L + r -cos [at)
a
+ g = 0. (10)
Denoting the left side of the equation (10) through G, build graphs G = f(a,r,L,xi,a, me) depending on the angle of rotation of the crank q = at, analysis of which showed that at the time of separation of the grain from the plane is most significantly affected by the change in angular velocity a crank rotation AM. The separation
of the bean occurs when moving the plane from the uppermost position at the time of transition of the curve through the axis X (G = 0). On Fig.6 an example of determining the moment of separation of the bean from the plane at different values of the angular velocity of the crank and at fixed other parameters (r = 1,5 mm, L = 0,2 m, xi = 0,05 m, , a =20, mb = 0,04 g.).
G,m. c2 s2
Fig. 6. Determination of the moment of separation of the bean from the vibrating surface at different values a
Similarly, we can determine the influence of other factors on the conditions of separation of the particle and plot the dependences.
Conclusions and suggestions. The most expedient way of metered feeding of seed heap to the working chamber of the grater device of low productivity should be considered vibrating, characterized by high oscillation frequency and small amplitude.
Analysis of the movement of the bean on the oscillating plane allowed to determine the influence of the main factors on the rational parameters that provide a reliable metered supply of seed heap to the grater device of low productivity.
The conducted analytical researches are a basis for calculation of numerical values of giving of a seed heap to the grater device.
It should be noted that in determining the nature of the movement of the seed heap on the oscillating plane, it is necessary to take into account the effect of the flu-idized bed, which is the subject of additional studies.
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