DETERMINATION OF THE PHASE ANGLES FOR THE BEGINNING OF BUCKWHEAT GRAINS SLIDING AND SEPARATION ON THE SIEVE STEPPED SURFACE OF THE OSCILLATING CONVEYOR CONCAVE Текст научной статьи по специальности «Электротехника, электронная техника, информационные технологии»

МАШИНОСТРОЕНИЕ

УДК 664.74.001 DOI 10.24412/2311-6447-2022-2-210-218

Определение фазовых углов начала скольжения и отрыва гречишных зёрен на ситовой ступенчатой поверхности деки вибротранспортёра

Determination of the phase angles for the beginning of buckwheat grains sliding and separation on the sieve stepped surface of the oscillating conveyor concave

Профессор СЛ. Соколов (ORCID 0000-0002-4971-3015), доцент A.A. Яшонков (ORCID 0000-0002-1431-679X), профессор A.A. Фалько (ORCID 0000-0001-5525-79IX)

(Керченский государственный морской технологический университет) кафедра машин и аппаратов пищевых производств, тел. 8-978-081-12-34 E-mail: mapp7(5jmail.ru

Professor S.A. Sokolov, Associate Professor A.A. Yashonkov, Professor A.L. Fal'ko (Kerch State Marine Technological University) chair of Food Production Machines and Apparatuses, tel. 8-978-081-12-34 E-mail: mapp7(amail.ru

Реферат. Транспортирование сыпучих сред всегда являлось актуальным процессом на пищевом и перерабатывающем производстве. Такое транспортирование, как правило, осуществляется на вибрационных конвейерах или машинах, близких по конструкции. Более того, чистое транспортирование сыпучих продуктов на пищевых предприятиях является достаточно редким явлением. Все такие перемещения обычно представляют сложные процессы, где с транспортированием совмещают ещё один или несколько процессов переработки продукта. Вибрационные транспортирующие машины являются простыми в устройстве и обслуживании. Эти машины надежны, имеют низкую удельную энергоемкость и невысокую себестоимость. В них возможно объединение различных технологических процессов при вибрационном перемещении сыпучих пищевых сред. Ступенчатые и другие рельефные поверхности для рабочих органов машин и аппаратов пищевых производств применяются очень мало. Но широким научным исследованиям этот вопрос не подвергался. Рассмотрены вопросы определения фазовых углов начала скольжения и отрывы гречишных зерен при их вибротранспортировании.

Summary. The transportation of bulk media has always been one of the most relevant processes in food and processing industries. Such transportation is usually carried out on vibrating conveyors or machines of similar design, moreover, the clean transportation of bulk products at food enterprises is a rather rare phenomenon, all such movements usually represent complex processes, where one or more product processing processes are combined with transportation. Vibrating transporting machines are simple in the device and service. These machines are reliable, have low specific power consumption and the low cost price. Combining different processes at vibrating movement of bulk food masses can be done in them. Stepped and other raised surface for the working bodies of machines and equipment for food production are used very little. But this question was not exposed to wide scientific researches. In this article, the issues of determining the phase angles of the beginning of sliding and the feedback of buckwheat grains during their vibration transport are considered.

Ключевые слова: вибротранспортирование, вибротранспортёры, виброперемещение, фазовый угол, ситовая поверхность, ступенчатая поверхность, дека.

Keywords: vibrotransportation, vibroconveyors, vibration displacement, phase angle, sieve surface, stepped surface, concave.

© C.A. Соколов, A.A. Яшонков, A.A. Фалько, 2022

It is known that the specific performance of all vibratory conveyors depends on the average velocity of the particle layer vibrodisplacement along the concave, so the design of a new vibratory conveyor with reciprocating vibrations of the concave in the horizontal plane obeys the same law.

Analytical identification of the phase angles of sliding and separation during vibratory transportation of buckwheat grains. Determination of their dependence on the geometric and kinematic characteristics of a new vibration conveyor actuating element.

To determine the phase angles for the beginning of buckwheat grains sliding and separation on the stepped surface of the vibroconveyor concave, we use the graphical method and computer algebra systems of the class of Maple and Mathcad computer-aided design systems

When analyzing the works [1-8], it was revealed that the primary task is to establish the theoretical dependence of the movement speed for a layer of bulk material on the vibration parameters that generates system of vibration displacement modes. And it is necessary to start solving this problem by determining the phase angles of sliding and separation beginning when bulk masses move along the stepped concave of a vibratory conveyor that performs reciprocating movements in a horizontal plane.

According to [9], at certain geometrical a, LCT, hCT and kinematic A and w parameters of a stepped concave fluctuations, loose product particles begin the process of sliding up the sieve surface of the step. The sliding process starts at some undetermined time to.

Using the scheme of forces and the system of differential equations compiled according to it, the authors of work [9] derive an equation for the relative motion of a particle (at undetermined time t=to):

A ■ a

■ cos a ■ sin a t - /л ■ (g

cos a + A

sm a

■sin ca t ) -

sin a =0

(1)

:

со

Based on the particle motion equation (1), the initial phase slip angle cpo = w to is determined as follows:

g> = со ■ f = arcsin

g ■ ( fi • cos a + sin a ) \ A ■ a> (cos a - li ■ sin a )

• (2)

Detecting of the initial slip angle cpo was carried out using the Maple [10-11] software package depending on the amplitude A of concave vibrations at different values of the angle of the inclined surface of the concave step a. The range of oscillation frequency and amplitude values was chosen based on practical research data. The oscillation frequency of the actuating element is (v=25Hz) w=157 c1, the coefficient of friction was taken for buckwheat (moisture content 2.8%) on a stamped steel sieve (cell 16x2.2 mm) p=0.65. Based on the data obtained, graphical dependencies are plotted which are shown in Figures 1 and 2.

-а

1.4 1.2 а н

и 1/1

-Е 0.80.6 0.4 0.2

0.00

Amplitude

0 009

Inclination angle й, rad

Fig. 1. The initial phase angle of particle sliding depending on the amplitude of the concave oscillations

1.000

0.500

0.000

0,003 0.004 0,005 0,006 0,007 0,008 0.009 A. m

Fig. 2. The initial phase angle of particle sliding depending on the amplitude of the concave oscillations: 1 - cpo = 0,0031 ■ A2 - 0,0415 x A + 0,1966; R2 = 0,9924, a = 10°; 2 - cpo = 0,0037 ■ A2 -0,0497 x A + 0,2343; R2 = 0,9918, a = 15°; 3 - cpo = 0,0044 ■ A2 - 0,0592 x A + 0,2804; R2 = 0,9924, a = 20°; 4 - <p0 = 0,0054 ■ A2 - 0,0724 x A + 0,3399; R2 = 0,9909, a = 25°; 5 - cpo = 0,0067 ■ A2 - 0,0899 x A + 0,4206; R2 = 0,9916, a = 30°; 6 - cpo = 0,0087 ■ A2 - 0,1160 x A + 0,5370; R2 = 0,9911, a = 35°; 7 - cp0 = 0,0123 - A2-0,1621 x A + 0,7329; R2 = 0,9895, a = 40°; 8 - <p0 = 0,0219 • A2 - 0,2773 x A + 1,166; R2 = 0,9833, a = 45°; 9 - cp0 = 0,0285 ■ A2 - 0,4046 x A + 1,9399; R2 = 0,9974, a = 50°; 10-q>0 = 0,0249 * A2 - 0,4164 x A + 2,3961; R2 = 0,9997, a = 55°

According to the obtained values of the initial slip angle cpo depending on the concave oscillation frequency v at different values of the inclined surface angle of the concave step a, the graphical dependences shown in Figures 3 and 4 are plotted.

The oscillation amplitude of the concave was taken as A = 0.005 m, the coefficient of friction for buckwheat (moisture content 2,8 %) on a stamped steel sieve (cell 16x2.2 mm) //=0.65. The amplitude of oscillations and the range of frequency values were taken based on the data of practical studies.

Oscillation frequency V. c"1 Inclination angle a. rad

Fig. 3. The initial phase angle of particle slip depending on the concave oscillation frequency

An analysis of the presented dependences shows that the increase in the values of cpo occurs with a decrease of the amplitude and an increase of the inclination angle step. The nature of the increase in the values cpo changes at different values of the angle a, the values of cpo increase evenly up to a= 35 degrees, a sharp increase in the value occurs at <2=35,55 degrees. The order of parallel parabolic curves arrangement relative to each other in Fig. 2. and Fig. 4., shows that cpo depends on the amplitude and frequency approximately equally, i.e. zones of rational geometric parameters on the diagrams will coincide.

To determine the phase angle of separation cpi, let us compose an equation of forces along the OY axis (Fig. 2) acting at the moment when the concave moves from the middle to the extreme left position at N = 0 (the moment of separation).

m ■ A ■ со ■ sin a ■ sin a tx - m ■ g ■ cos a = 0

whence we can write down an expression to determine cpi :

(3)

cp = CO

=

arcsm

£Г

-etg a

A ■ со

+ 71

(4)

The separation phase angle cpi was detected using the Maple software package. The oscillation frequency of the actuating element is (v=25Hz) w=157 C"1, the coefficient of friction was taken for buckwheat (moisture content 2.8 %) on a stamped steel sieve (cell 16x2.2 mm) ¡1=0,65. Oscillation frequency w and range of amplitude values A are chosen based on the data of experimental studies.

Based on the obtained values, graphical dependences are plotted, which are shown in Figures 5 and 6. Theoretical curves (figure 6) were obtained by parabolic alignment of the calculated data.

2

Fig. 4. The initial phase angle of particle slip depending on the concave oscillation frequency: 1 - (po = 0,0042 ■ v2 - 0,0558 ■ v + 0,2307; R2 = 0,9926, a = 10°; 2 - cpo = 0,0050 ■ v2 - 0,0669 - v + 0,2753; R2 = 0,9930, a = 15°; 3 - cp0 = 0,0060 • v2 - 0,0805 ■ v + 0,3304; R2 = 0,9928, a = 20°; 4 - cpo = 0,0074 ■ v2 - 0,0981 ■ v + 0,4010; R2 = 0,9922, a = 25°; 5 - cpo = 0,0092 ■ v2 - 0,1216 ■ v + 0,4956; R2 = 0,9922, a = 30°; 6 - cpo = 0,0121 ■ v2 - 0,1588 ■ v + 0,6380; R2 = 0,9915, a = 35°; 7 - cpo = 0,01 73 ■ v2- 0,2240 ■ v + 0,8784; R2 = 0,9892, a = 40°; 8 - cp0 = 0,0345 ■ v2 - 0,4204 ■ v + 1,4964; R2 = 0,9754, a = 45°; 9 - cp0 = 0,0483 ■ v2 - 0,5983 ■ v + 2,3667; R2 = 0,9775, a = 50°; 10 - cp0 = 0,0408 xv2- 0,6221 x v + 3,0537; R2 = 0,9998, a = 55°

Fig. 5. Phase angle of separation depending on the concave amplitude

Fig. 6. Phase angle of separation depending on the concave vibration amplitude: 1 - q>i = 0,0018 ■ A2 - 0,0240 x A + 0,1139; R2 = 0,9912, a = 55°; 2 - q>i = 0,0021 ■ A2 - 0,0285 x A + 0,1357; R2 = 0,9919, a = 50°; 3 - cpi = 0,0026 ■ A-2 - 0,0345 x A + 0,1627; R2 = 0,9922, a = 45°; 4 - cpi = 0,0030 ■ A2 - 0,0408 x A + 0,1941; R2 = 0,9926, a = 40°; 5 - cpi = 0,0037 ■ A2 - 0,0494 * A + 0,2330; R2 = 0,9917, a = 35°; 6-cpi = 0,0044 ■ A2 - 0,0598 x A + 0,2827; R2 = 0,9919, a = 30°; 7 - cpi = 0,0055 • A2 - 0,0747 x A + 0,3520; R2 = 0,9918, a = 25°; 8 - tpi = 0,0073 ■ A2 - 0,0978 x A + 0,4564; R2 = 0,9919, a = 20°; 9-cpi = 0,0104 ■ A2 - 0,1384 x A + 0,6351; R2 = 0,9907, a = 15°; 10- cpi = 0,0192 ■ A2 - 0,2461 x A + 1,0564; R2 = 0,9855, a= 10°

The dependence q>i= cpi(v) was determined using the Maple software package at different angles a. The oscillation amplitude of the actuating element was A=0,005 m, the coefficient of friction was taken for buckwheat (moisture content 2,8 %) on a stamped steel sieve (cell 16x2.2 mm) /2=0.65. The oscillation amplitude A and the frequency range v were chosen based on practical research data.

Based on the obtained values, there were plotted graphical dependencies, shown in Fig. 7 and 8.

Inclination angle, rad Oscillation frequency, c'1

Fig. 7. Phase angle of particle separation depending on concave oscillation frequency

(pl.nd 1.200 -

1,000

0,800

0,600

0,400

0,200

0,000 -

Hz

Fig. 8. Phase angle of particle separation depending on the concave oscillation frequency: 1 -cpi = 0,0031 x V2 - 0,0415 x v + 0,1719; R2 = 0,9927, a = 55°; 2 - (pi = 0,0037 x v2 - 0,0501 x v + 0,2071; R2 = 0,9929, a = 50°; 3 - cpi = 0,0045 x v2 - 0,060 x v + 0,2473; R2 = 0,9929, a = 45°; 4 -(pi = 0,0054 x v2 - 0,071 7 x v + 0,2953; R2 = 0,9933, a = 40°; 5 - cpi = 0,0065 * v2 - 0,0868 x v + 0,3557; R2 = 0,9927, a = 35°; 6 - cpi = 0,0080 x v2 - 0,1062 x v + 0,4341; R2 = 0,9928, a = 30°; 7-cpi = 0,0102 xv2- 0,1345 x v + 0,5451; R2 = 0,9920, a = 25°; 8 - cpi = 0,0137 * v2 - 0,1792 x v + 0,7153; R2 = 0,9908, a = 20°; 9 - cpi = 0,0211 x v2 - 0,2695 x v + 1,0361; R2 = 0,9870, a = 15°; 10 -cpi = 0,0237 xv2- 0,3359 x v + 1,4477; R2 = 0,9961, a= 10°

The analysis of the presented dependences shows that the increase in the values of cpi occurs with a decrease of the amplitude A, with a decrease of the oscillation frequency v and with a decrease in the step inclination angle a. The nature of the increase in the values of cpi changes intensively with a decrease in the angle a. Thus, at a =35a55 degrees the values of cpi increase evenly, and at a =10 35 degrees, a sharp increase in the value occurs. The order of parallel parabolic curves arrangement relative to each other in fig. 6. and fig. 8., shows that cpi, as well as cp0, depends on the amplitude and frequency approximately equally.

This means that the zones of rational geometric parameters on the dependences cp0= cpo( A) and cpo= cpo(v), as well as cpi= cpi (A) and cpi = cpi(v) will coincide. Considering that a sharp increase in the values of cpo and cpi in practice can lead to an uncontrolled process of flight or sliding of a particle over a sieve surface, it should be assumed that the rational angle of the step in this case will be an angle close in value to a= 35°.

As a result of analytical studies, the phase angles of slip and separation were determined during the vibration transportation of buckwheat. Their dependences on the geometric and kinematic parameters of the stepped concave of a new vibration conveyor were established.

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