Experimental research of interrelation of mining mass layer porosity and defor-mation forces on flat surfaces of disintegrators
Deformation of granite layer with granite fraction less than 0.5 mm was experimentally studied in order to determine normal-pressure distribution on the flat working surfaces of disintegrators. Series of tests with material compression between two plates without lateral restrictions was conducted, a...
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irk-123456789-1586372019-09-09T01:25:56Z Experimental research of interrelation of mining mass layer porosity and defor-mation forces on flat surfaces of disintegrators Titov, A.A. Deformation of granite layer with granite fraction less than 0.5 mm was experimentally studied in order to determine normal-pressure distribution on the flat working surfaces of disintegrators. Series of tests with material compression between two plates without lateral restrictions was conducted, and distribution of porosity factor along the radius of deformation zone was determined. Experiment with compression of different quantities of material in the mortar with the punch down to pressures of 40 MPa was carried out in order to calibrate pressure depending on the material porosity. Compression curves were built for different masses of the sample. For the case of material compression without lateral restrictions, regression curve of dependence between material porosity and pressure was built on the base of compression force balance equation. This curve coincides with compression curve for minimal mass of material sample compressed in the mortar. Distribution of normal pressures on the top plate was determined, at that, experimental curve was more flat than the theoretical one. The pressure high concentration in the center of deformation zone and underloading of its periphery were confirmed. Виконані експериментальні дослідження деформації шару граніту фракції менше 0,5 мм з метою отримання розподілу нормального тиску на плоских робочих поверхнях дезінтеграторів. Проведено серію дослідів із стискання матеріалу між двома плитами без бокових обмежень та встановлено розподіл коефіцієнта пористості матеріалу вздовж радіуса зони деформування. Для тарування тиску в залежності від пористості, проведено експеримент із стискання різних кількостей матеріалу в ступці із пуансоном до тиску 40 МПа. Отримано набір компресійних кривих для різних мас навішування. Для випадку стискання матеріалу без бокових обмежень, з рівняння балансу зусилля стискання отримано регресійну криву залежності коефіцієнта пористості від тиску, яка добре співпадає із компресійною кривою при стисканні в ступці навішування матеріалу мінімальної маси. Отримано розподіл нормального тиску на поверхні верхньої плити, при цьому експериментальна крива є більш пологою, ніж теоретична. Підтверджено високу концентрацію тиску в центрі зони деформування та недовантаженість її периферії. Выполнены экспериментальные исследования деформации слоя гранита фракции менее 0,5 мм с целью получения распределения нормальных давлений на плоских рабочих поверхностях дезинтеграторов. Проведена серия опытов по сжатию материала между двумя плитами без боковых ограничений и установлено распределение коэффициента пористости материала вдоль радиуса зоны деформирования. Для тарировки давления в зависимости от пористости, проведен эксперимент по сжатию разных количеств материала в ступке с пуансоном до давлений 40 МПа. Получен набор компрессионных кривых для разных масс навески. Для случая сжатия материала без боковых ограничений, из уравнений баланса усилия сжатия получена регрессионная кривая зависимости коэффициента пористости от давления, которая хорошо совпадает с компрессионной кривой при сжатии в ступке навески материала минимальной массы. Получено распределение нормальных давлений на поверхности верхней плиты, при этом экспериментальная кривая более пологая, чем теоретическая. Подтверждена высокая концентрация давлений в центре зоны деформирования и недогруженность ее периферии. 2017 Article Experimental research of interrelation of mining mass layer porosity and defor-mation forces on flat surfaces of disintegrators / A.A. Titov // Геотехнічна механіка: Міжвід. зб. наук. праць. — Дніпро: ИГТМ НАНУ, 2017. — Вип. 137. — С. 56-64. — Бібліогр.: 4 назв. — англ. 1607-4556 http://dspace.nbuv.gov.ua/handle/123456789/158637 621.926: 622.73 en Геотехнічна механіка Інститут геотехнічної механіки імені М.С. Полякова НАН України |
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Deformation of granite layer with granite fraction less than 0.5 mm was experimentally studied in order to determine normal-pressure distribution on the flat working surfaces of disintegrators. Series of tests with material compression between two plates without lateral restrictions was conducted, and distribution of porosity factor along the radius of deformation zone was determined. Experiment with compression of different quantities of material in the mortar with the punch down to pressures of 40 MPa was carried out in order to calibrate pressure depending on the material porosity. Compression curves were built for different masses of the sample. For the case of material compression without lateral restrictions, regression curve of dependence between material porosity and pressure was built on the base of compression force balance equation. This curve coincides with compression curve for minimal mass of material sample compressed in the mortar. Distribution of normal pressures on the top plate was determined, at that, experimental curve was more flat than the theoretical one. The pressure high concentration in the center of deformation zone and underloading of its periphery were confirmed. |
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Titov, A.A. |
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Titov, A.A. Experimental research of interrelation of mining mass layer porosity and defor-mation forces on flat surfaces of disintegrators Геотехнічна механіка |
| author_facet |
Titov, A.A. |
| author_sort |
Titov, A.A. |
| title |
Experimental research of interrelation of mining mass layer porosity and defor-mation forces on flat surfaces of disintegrators |
| title_short |
Experimental research of interrelation of mining mass layer porosity and defor-mation forces on flat surfaces of disintegrators |
| title_full |
Experimental research of interrelation of mining mass layer porosity and defor-mation forces on flat surfaces of disintegrators |
| title_fullStr |
Experimental research of interrelation of mining mass layer porosity and defor-mation forces on flat surfaces of disintegrators |
| title_full_unstemmed |
Experimental research of interrelation of mining mass layer porosity and defor-mation forces on flat surfaces of disintegrators |
| title_sort |
experimental research of interrelation of mining mass layer porosity and defor-mation forces on flat surfaces of disintegrators |
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Інститут геотехнічної механіки імені М.С. Полякова НАН України |
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2017 |
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| citation_txt |
Experimental research of interrelation of mining mass layer porosity and defor-mation forces on flat surfaces of disintegrators / A.A. Titov // Геотехнічна механіка: Міжвід. зб. наук. праць. — Дніпро: ИГТМ НАНУ, 2017. — Вип. 137. — С. 56-64. — Бібліогр.: 4 назв. — англ. |
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Геотехнічна механіка |
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AT titovaa experimentalresearchofinterrelationofminingmasslayerporosityanddeformationforcesonflatsurfacesofdisintegrators |
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2025-07-14T11:11:49Z |
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2025-07-14T11:11:49Z |
| _version_ |
1837620538001850368 |
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ISSN 1607-4556 (Print), ISSN 2309-6004 (Online) Геотехнічна механіка. 2017. № 137
56
УДК 621.926: 622.73
Titov A.A., Ph.D. (Tech.), Associate Professor
(SHEI “NMU”)
EXPERIMENTAL RESEARCH OF INTERRELATION BETWEEN ROCK
LAYER POROSITY AND DEFORMATION FORCES ON THE FLAT
SURFACES OF DISINTEGRATORS
Титов О.О., канд. техн. наук, доцент
(ДВНЗ «НГУ»)
ЕКСПЕРИМЕНТАЛЬНІ ДОСЛІДЖЕННЯ ВЗАЄМОЗВ’ЯЗКУ
ПОРИСТОСТІ ШАРУ ГІРНИЧОЇ МАСИ ТА ЗУСИЛЬ ДЕФОРМУВАННЯ
НА ПЛОСКИХ ПОВЕРХНЯХ ДЕЗІНТЕГРАТОРІВ
Титов А.А., канд. техн. наук, доцент
(ГВУЗ «НГУ»)
ЭКСПЕРИМЕНТАЛЬНЫЕ ИССЛЕДОВАНИЯ ВЗАИМОСВЯЗИ
ПОРИСТОСТИ СЛОЯ ГОРНОЙ МАССЫ И УСИЛИЙ
ДЕФОРМИРОВАНИЯ НА ПЛОСКИХ ПОВЕРХНОСТЯХ
ДЕЗИНТЕГРАТОРОВ
Annotation. Deformation of granite layer with granite fraction less than 0.5 mm was
experimentally studied in order to determine normal-pressure distribution on the flat working
surfaces of disintegrators. Series of tests with material compression between two plates without
lateral restrictions was conducted, and distribution of porosity factor along the radius of
deformation zone was determined. Experiment with compression of different quantities of
material in the mortar with the punch down to pressures of 40 MPa was carried out in order to
calibrate pressure depending on the material porosity. Compression curves were built for
different masses of the sample. For the case of material compression without lateral restrictions,
regression curve of dependence between material porosity and pressure was built on the base of
compression force balance equation. This curve coincides with compression curve for minimal
mass of material sample compressed in the mortar. Distribution of normal pressures on the top
plate was determined, at that, experimental curve was more flat than the theoretical one. The
pressure high concentration in the center of deformation zone and underloading of its periphery
were confirmed.
Keywords: disintegrator, deformation zone, loose material, compression curve, pressure
distribution.
Introduction. Processing of fine-sized lumpy materials in disintegrators is
combined with compressive influence on material layer as a consequence of two
(usually) working surfaces rapprochement. Firstly, the layer is compacted with
repacking of particles, and, than, their disintegration on smaller pieces is carried out
[1]. The effect of “crushing in layer”, when the material is put between working
surfaces in 3-5 and more layers, is used in disintegrators to enhance the process
selectivity and to reduce the flat particles share [2]. That’s why, it is important to take
into consideration the dependence of the material layer fractional porosity on the
compression pressure during designing of disintegrators operating parts.
© А.А. Титов, 2017
ISSN 1607-4556 (Print), ISSN 2309-6004 (Online) Геотехнічна механіка. 2017. № 137
57
The dependence is sufficiently non-linear.
The dependence of the of granite fraction minus 0.5 mm layer (height more than
10 mm) fractional porosity on the pressure has been obtained in a mortar with a punch
for the range up to 4 MPa [3]. The experimental data are approximated best by
equation
)exp()( min0min
mpaeeee , (1)
where 0e - initial fractional porosity; mine - consolidation limit; a & m - coefficients;
p - pressure.
The conditions of material deformation in disintegrators differ usually from the
case of a mortar and a punch by absence of side restrictions for material. So, the forces
of side thrust lead to the particles pushing out to the periphery of deformed zone [4].
The distribution of pressure on the working surfaces for the case of flat deformed zone
is obtained based on the regularities of loose material mechanics. It is shown, that there
is high pressure concentration in the zone center, while the periphery has sufficiently
lower loadings and, therefore, it doesn’t take part in the disintegration process. This
conclusion requires for additional experimental justification while having appropriate
pressure level on working surfaces, that is actual for designing of rational schemes of
operating parts.
The goal of this work is to determine experimental dependences of the material
compression pressure distribution on flat surfaces of the deformed zone without side
restrictions, taking into consideration the layer porosity change by the pressure.
The idea of this work is to use the compression dependence of material
compression in a mortar for obtaining the distribution of normal pressures on flat
surfaces of the deformed zone while compressing without side restrictions.
Basic part.
1. Deformation of material between plates without side restrictions.
The source material is crushed granite of fraction -0.5 mm. The modelling of
disintegration has been fulfilled by the press unit with maximum force of 30 kN.
The material portion has been filled in the form of a cone on a static horizontal
steel plate. After that, an upper steel plate and a dynamometer have been put on it.
The material cone has been settled a little, becoming the truncated one (fig 1) with
the height of 0H and the diameters of the upper and the lower bases being equal
correspondingly to 0,1D and 0,2D . The fractional porosity 0e has been calculated.
Futher, the series of tests on the material compression with varied force levels,
equal approximately to Р 5, 10, 20 и 30 kN, has been carried out. Here, the initial
material layer height 0H has been the same for all the tests.
After the material compression with the set force level, the truncated cone had
less height H and also increased base diameters 1D & 2D (see fig. 1). It is obvious,
that the material porosity after compression is increasing from the center to the
periphery. The set of ring splitters of diameters id , made of thin metal, has been used
ISSN 1607-4556 (Print), ISSN 2309-6004 (Online) Геотехнічна механіка. 2017. № 137
58
in order to determine the dependence of the layer porosity change along the deformed
zone radius. Firstly, after the press unit unloading and removing the upper plate with
the dynamometer, the splitter of the largest diameter has been put symmetrically
relative to axes of the truncated cone and carefully pressed into the material layer to
the contact with the lower plate. The material left outside the splitter has been
weighed. The splitter has been carefully put off, and the another splitter of less
diameter has been set. The operation has been repeated for all the material rings.
Figure 1 – Scheme of the material compression without side restrictions:
1 – upper plate; 2 – lower plate; 3 – ring splitter
Further, the following parameters have been calculated:
- volume of the material:
2
1
4
iii dd
H
V , m
3
; (2)
- bulk weight of the material:
i
i
i
V
m
, kg/m
3
; (3)
ISSN 1607-4556 (Print), ISSN 2309-6004 (Online) Геотехнічна механіка. 2017. № 137
59
and also fractional porosity iе .
The volume of the last peripheral sector:
2
4
2
221
2
15
412
d
H
DDDD
H
V , m
3
. (4)
The material rings average radiuses have been the calculated coordinates along х
axis. Here, the mean radius value is not usable, because the material rings of the
same width have different masses. So, the average radiuses have been calculated by
formula:
i
i
i
F
I
r
,
, m, (5)
where iI , - polar inertia moment of i-ring relative to the central axis, which is
determined in accordance with the expression
4
1
4
,
32
iii ddI , m
4
; (6)
iF - area of i-ring, which is find by formula
2
1
2
4
iii ddF , m
2
, (7)
from where one will have
22
1
2
1
2
ii
i
dd
r , m. (8)
The last peripheral ring has a complicated form – a truncated cone with a circular
cut, so the radius of inertia is corresponded to the expression:
H
H
dhhF
dhhFhr
r
0
0
5
)(
)()(
, m, (9)
where )(hr - the current radius of inertia for the 5-th ring section at a height h from
the lower plate:
2
)(
2
1
)(
2
4
2 dhd
hr , m; (10)
)(hd - the current outside diameter of the 5-th ring section at a height h :
ISSN 1607-4556 (Print), ISSN 2309-6004 (Online) Геотехнічна механіка. 2017. № 137
60
122)( DD
H
h
Dhd , m. (11)
Following the results of calculations, the values determined from expression (9)
are almost match the radius of the upper cone base 15,0 D .
2. Material deformation in a mortar with a punch.
For this purpose, the series of tests on compression of investigated granite
fraction -0.5 mm has been fulfilled in the mortar of diameter 31.5 mm with a punch.
This has allowed, for the force up to 30 kN, to reach the pressure up to 40 MPa, that
leads to the granite particles destruction, concerning high concentration of stresses.
The definite material mass from range of 20-143 grams has been filled in the
mortar. The tests with slow compression have been conducted for each mass with the
force being in range of 2-30 kN. The average fractional porosity has been calculated
then. The results of experimental data processing are offered at the figure 2.
The results for each material loading mass have been approximated by
dependence (1) using the least squares method. As one can see from the plots, the
average fractional porosity rises while increasing the loading mass, having constant
final pressure. This effect may be explained as an influence of friction forces on the
mortar sides.
3. Pressure values calibration using fractional porosity values and analysis
of results.
One may obtain the pressure values from the condition, that the sum of all forces
from ring sectors, transmitted to the plate, must be equal to the specified force of
working surfaces mutual pressing:
dynplsp
i
ii GGPPFp
5
1
, N, (12)
where P - average pressing force by dynamometer indications, N;
plG – weight of the upper plate;
dynG – weight of the dynamometer.
Here, the pressure is expressed by the fractional porosity, according to (1) and
having zero consolidation limit, in such a way:
m
i
i
e
e
a
p
1
0ln
1
, Pa. (13)
Here, for the 5-th (peripheral) ring sector, the value of the fractional porosity has
been averaged concerning different contact areas on the upper and the lower plates.
So, the calculated maximum diameter of this sector has been determined in
accordance with (8):
2
4
2
55 8 drd , m. (14)
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61
Figure 2 – Dependence of the fractional porosity on the compression pressure in the mortar:
1 – m = 20 g; 2 – m = 40 g; 3 – m = 70 g; 4 – m = 100 g; 5 – m = 143 g
As a result, there is a system of four equations of type
1
4
ln
11 5
1
2
1
2
1
0
i
iii
m
isp
dd
e
e
aP
, (15)
each equation per every value of compression force.
It makes sense to obtain the regressive dependence of the fractional porosity on
the value of pressure at the working surface as the same to the expression (1).
Finally, the real values of force are in good correspondence with specified forces,
calculated by the regression equation and determined from equation (12) as sums of
ring sectors forces (table 1).
Table 1 – Real and calculated deformation forces
Test number 1 2 3 4
Real
force, kN
5,02 9,63 19,5 29,4
Calculated
force, kN
5,47 7,93 22,0 26,3
Deviation, % +9,0 -17,7 +12,6 -10,5
ISSN 1607-4556 (Print), ISSN 2309-6004 (Online) Геотехнічна механіка. 2017. № 137
62
The analysis shows, that obtained regressive curve (fig. 3) has good coincidence
qualitatively and quantitatively with the data for pressing in the mortar of granite
mass 20 g, having minimal influence of effect of the material friction with the mortar
sides.
Figure 3 – Comparison of data on the material compression in the mortar (1) and between plates (2)
Additionally, the curves of pressure distribution in the radial direction of the
deformed zone at the upper plate are determined based on the regression equation
(fig. 4).
Figure 4 – Distribution of normal pressure at the upper cone base:
1 – experiment; 2 – theory [4]
ISSN 1607-4556 (Print), ISSN 2309-6004 (Online) Геотехнічна механіка. 2017. № 137
63
Comparison with the data [4] for the case of the material layer slow deformation
shows, that the gradient of pressure increase from the disk periphery to its center is
lower, than the theoretical one. So, it requires the necessity to supplement the
process basic mathematical model, but, nevertheless, high irregularity of the pressure
distribution has been confirmed, see the data in table 2.
Table 2 – Intensity of the normal pressure distribution
Share of the deformed zone,
central circle area, %
1 10 25-28 50-55
Share of the total force, % 10-15 70-72 87-90 97-98
cppp / 10,5 7,0 3,3 1,9
Conclusions
1. The possibility to model the mining mass deformation processes between the flat
surfaces of disintegrators, based on the data of material compression in a mortar with a
punch, is shown.
2. The series of experimental dependences of the fractional porosity of granite fraction less than
0.5 mm on the compression pressure in a mortar is determined in a range up to 40 MPa.
3. The regression dependence of the granite layer fractional porosity change on the
pressure, for the case of its compression between two plates without side restrictions, is
obtained.
4. Good coincidence of the experimental results on the compression in a
mortar and free compression between plates is shown.
5. The obtained experimental curve of the pressure distribution along the
radius of the deformed zone upper base is more flat, that is claimed by theory, but
the distribution is also very irregular.
_________________________________
REFERENCES
1. Revnivtsev, V.I., Barzukov, O.P., Ivanov, N.A. [and others] (1984), “Basic dependences of loose
material layer condition changes during compression”, Mineral dressing, no. 4, pp. 3-6.
2. Revnivtsev, V.I., Denisov, G.A., Zarogatskiy, L.P. and Turkin, V.Y. (1992), Vibrational
disintegration of hard materials, Nedra, Moscow, Russia.
3. Nadutyy, V.P. and Titov, A.A. (2017), “Analysis of influence of loose mining rocks compactibility
on the process of their deformation between flat surfaces of disintegrators”, Vibration in engineering and
technology, no. 1(84), pp. 35-40.
4. Nadutyy, V.P. and Titov, A.A. (2016), “Analysis of Stressed condition of the flat deformed zone of
vibrational disintegrators taking into consideration material throwing-out”, Vibration in engineering and
technology, no. 3(83), pp. 54-58.
СПИСОК ЛИТЕРАТУРЫ
1. Основные закономерности изменения состояния слоя сыпучего материала при сжатии [Текст] /
В.И. Ревнивцев, О.П. Барзуков, Н.А. Иванов [и др.] // Обогащение руд. - 1984. - №4. - С. 3-6.
2. Вибрационная дезинтеграция твердых материалов [Текст] / В.И. Ревнивцев, Г.А. Денисов,
Л.П. Зарогатский, В.Я. Туркин. – М.: Недра, 1992. – 430 с.
3. Надутый , В.П. Анализ влияния уплотняемости сыпучей горной массы на процесс ее
деформирования между плоскими поверхностями дезинтеграторов / В.П. Надутый, А.А. Титов //
Вібрації в техніці та технологіях. - 2017. - №1(84). - С.35-40.
4. Надутый, В.П. Анализ напряженного состояния плоской зоны деформирования вибрационных
дезинтеграторов с учетом выброса материала / В.П. Надутый, А.А. Титов // Вібрації в техніці та
ISSN 1607-4556 (Print), ISSN 2309-6004 (Online) Геотехнічна механіка. 2017. № 137
64
технологіях. - 2016. - №3(83). - С.54-58.
_______________________________
About the author
Titov Aleksandr Aleksandrovich, Candidate of Technical Sciences (Rh.D), Associate Professor in the
Department of Mining Machines and Engineering, State HEI “the National Mining University”, Dnipro,
Ukraine, alextitovalex77@gmail.com
Об авторе
Титов Александр Александрович, кандидат технических наук, доцент кафедри горных машин и
инжиниринга, Государственный ВУЗ «Национальный горный университет», г. Днепр, Украина,
alextitovalex77@gmail.com.
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Анотація. Виконані експериментальні дослідження деформації шару граніту фрак-
ції менше 0,5 мм з метою отримання розподілу нормального тиску на плоских робочих
поверхнях дезінтеграторів. Проведено серію дослідів із стискання матеріалу між двома
плитами без бокових обмежень та встановлено розподіл коефіцієнта пористості матері-
алу вздовж радіуса зони деформування. Для тарування тиску в залежності від пористо -
сті, проведено експеримент із стискання різних кількостей матеріалу в ступці із пуан -
соном до тиску 40 МПа. Отримано набір компресійних кривих для різних мас навішу-
вання. Для випадку стискання матеріалу без бокових обмежень, з рівняння балансу зу-
силля стискання отримано регресійну криву залежності коефіцієнта пористості від ти-
ску, яка добре співпадає із компресійною кривою при стисканні в ступці навішування
матеріалу мінімальної маси. Отримано розподіл нормального тиску на поверхні верх-
ньої плити, при цьому експериментальна крива є більш пологою, ніж теоретична. Під-
тверджено високу концентрацію тиску в центрі зони деформування та недовантаже-
ність її периферії.
Ключові слова: дезінтегратор, зона деформування, сипкий матеріал, компресійна крива,
розподіл тиску.
Аннотация. Выполнены экспериментальные исследования деформации слоя гранита
фракции менее 0,5 мм с целью получения распределения нормальных давлений на плоских
рабочих поверхностях дезинтеграторов. Проведена серия опытов по сжатию материала между
двумя плитами без боковых ограничений и установлено распределение коэффициента
пористости материала вдоль радиуса зоны деформирования. Для тарировки давления в
зависимости от пористости, проведен эксперимент по сжатию разных количеств материала в
ступке с пуансоном до давлений 40 МПа. Получен набор компрессионных кривых для разных
масс навески. Для случая сжатия материала без боковых ограничений, из уравнений баланса
усилия сжатия получена регрессионная кривая зависимости коэффициента пористости от
давления, которая хорошо совпадает с компрессионной кривой при сжатии в ступке навески
материала минимальной массы. Получено распределение нормальных давлений на поверхности
верхней плиты, при этом экспериментальная кривая более пологая, чем теоретическая.
Подтверждена высокая концентрация давлений в центре зоны деформирования и
недогруженность ее периферии.
Ключевые слова: дезинтегратор, зона деформирования, сыпучий материал,
компрессионная кривая, распределение давлений.
Статья поступила в редакцию 22.11.2017
Рекомендовано к печати д-ром техн. наук В.П. Надутым
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