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GÖMZE A. László
RHEOLOGY Compilation of Scientific Papers I.
Published by IGREX Ltd.
2015
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László A. Gömze
RHEOLOGY
Compilation of Scientific Papers I.
Copyright © 2015 by IGREX Engineering Service Ltd.
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All rights reserved. No part of this publication must be
reproduced without a written
permission from the copyright holder
RHEOLOGY
Compilation of Scientific Papers I.
Written by: Prof. Dr. Laszlo A. Gömze
Articles in this volume should be cited as follows:
L.A. Gömze (2015) RHEOLOGY, Compilation of Scientific Papers I.,
Published by IGREX, Hungary
or
(year of original publishing) , pp…
ISBN 978-963-12-3088-8
Published in Hungary – IGREX Engineering Service Ltd. Igrici,
Hungary
Printed in Hungary – Passzer 2000 Ltd. Miskolc, Hungary
[email protected]
mailto:[email protected]
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Content
Preface
..........................................................................................................................................
6
Mathematical analysis of plastic clay comminution
.....................................................................
8
Some Problems of Dimensioning the Smooth Rolls Used for Crushing
Clay Minerals ............... 18
Rheology and Flow Conditions of Clay during Smooth Roll
Comminution ................................. 26
Rheological principles of asbestos cement body extrusion
........................................................ 36
Rheological examination of extrudable asbestos cement bodies
.............................................. 46
Universal roto-viscous for examination of materials in silicate
industry .................................... 56
Mathematical analysis of the post-pressing state of stress in
asbestos cement products made
in screw press
..............................................................................................................................
64
Choice of Technical Parameters for Screw Presses
....................................................................
72
Investigation of mechanical stresses developing in ceramic
bodies during their rollering ........ 82
Pressure distribution in extruder heads and dies during forming
ceramic bodies ..................... 90
Investigation of rheological properties of asphalt mixtures
....................................................... 96
The effect of temperature and composition to the rheological
properties of asphalt pavements
...................................................................................................................................................
104
Alumina-based hetero-module ceramic composites with extreme
dynamic strength - phase
transformation of Si3N4 during high speed collisions with
metallic bodies .............................. 114
Investigation of Rheo-Mechanical Properties of Asphalt Mixtures
as Function of Temperatures
and Pressures
............................................................................................................................
124
Mechanical stress relaxation in hetero-modulus, hetero-viscous
complex ceramic materials 132
Effect of methyl-cellulose on injection molding properties of
alumina powders .................... 140
Investigation of porcelain slip casting
.......................................................................................
142
Modelling of flow properties of asphalt mastics
......................................................................
146
Ceramic based lightweight composites with extreme dynamic
strength ................................. 156
Linear viscous-elastic properties of asphalt mastics using
creep-recovery technique ............. 164
Qualification Methods of Al2O3 Injection Molding Raw Materials
........................................... 172
Methods and equipment for investigation rheological properties
of complex materials like
convectional bricks and ceramic reinforced composites
.......................................................... 180
Acknowledgment
......................................................................................................................
194
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Dedicated to the Participants of ic-rmm2
The 2nd International Conference on Rheology and Modeling of
Materials
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Preface
Despite the fact that the rheology is a relatively young
scientific discipline it is used in wide
range by mathematicians, phisicists, chemists, biologists,
medics, geologists and engineers. In
my early engineering practice between 1973-1985 knowledge of
rheology helped me in
development and design new construction of machines and
equipment for ceramic and
building industries, waste water treatment plants and plastic
industry.
From 1986 as managing director of the Hollohaza Porcelain
Manufactury Co. understanding
the rheology helped me in development of productivity our
company technology lines,
machines and equipment and improve the quality of production and
final products. Thanking
to this me and my company were awarded in USA with the World
Selection Trophy for Quality
and Export Merit in 1999.
Connecting the technological processes and modeling the
materials with rheology contributed
us at IGREX Ltd. to develop a new family of ceramic reinforced
or ceramic based light weight
hetero-modulus, hetero-viscous and hetero-plastic complex
composite materials with
excellent physical and mechanical properties including hardness,
thermal schock resistance
and extreme dynamic strength.
The experiences in rheology I have started in Moscow (Russia) as
a student under the
supervision of professors A.V. Turenko and S.G. Silenok in 1970.
As a student and later as a
young engineer and ‘scientist’ I have learned a lot especially
from prof. Sergei Silenok who was
one of the inventors of the famous ‘Katyusha’ multiplier rocket
launcher. Since then I am
author of three doctoral thesys (PhD., Dr.Eng.Sc. and
Dr.Habil.), author or co-author two
patents and more than 250 scientific papers.
My research and publication activity can be devided on the
following three periods.
- From 1970 to 1985 I have strong collaboration with my Russian
professors and young
scientific colleagues and I published my results together with
them or alone in
Hungarian or in Russian languages.
- From 1986 I could organize my Hungarian group and until 2005 I
published our results
mainly in Hungarian.
- Since 2008 I am trying to publish my results only in English
except the education guides
for the students at the University of Miskolc.
In this book are collected some of the papers in chronological
sequence to give an overview
about my 40-years activity in rheology. The Hungarian origin
papers were translated into
English by myself, so I would like to apologize for the
grammatical mistakes and for my poor
English.
Prof. Dr. GÖMZE, A. László
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Mathematical analysis of plastic clay comminution
1Gömze A.L., 2Turenko A.V., 2Nazarov V.
1Épületkerámia Co. Ltd, Budapest, 2University of Civil
Engineering, Moscow
(Translated from Hungarian: A képlékeny agyag aprításának
matematikai elemzése)
Published in journal Építőanyag (1974) vol. 26., 9, pp.
348-354.
Abstract
Recent results have proved that from the point of flow plastic
clay can be considered as an
incompressible liquid of high viscosity. On basis of these
findings the paper describes a calculation which
mathematically proved the mixing and homogenization of clay in
the roller gap, determines velocity
gradients, optimum degree of comminution and the shearing
stresses in the body. A certain type of
quarried clay, having 22% moisture content is used as a model;
the dynamic viscosities of this clay have
been determined by the Moscow Architectural University,
Department of Machinery. The physical
parameters on the roller gap can be properly adjusted for the
optimum comminution of the model clay
by changing gap width and the circumferential velocities of the
rollers.
Keywords: clay, comminution, elasticity, material, rheology,
shear rate, viscosity
1. Introduction
On the basis of prediction of the material structures, physical
and mechanical properties of
clay minerals it can be determined that we only can get good
quality products if the material
structures are changed properly under crashing of the raw
materials during the green
technology processes. This means that during the comminution
process it is necessary to
create the required grain and microstructures of the
convectional brick clays. One of the most
important equipment of raw material processing technology is the
high speed rollers with
smooth shells. By M. J. Sapozhnikov [1] the high speed rollers
can be divided to crude crushers
with roller gaps of t=3mm and for fine crushers with roller gaps
t≤1mm. On this equipment the
pressure and shear stresses can be variated in a large area
depending on roller gaps and
revolutions per minute of the rollers. At the same time the
quality of comminution and green
structure of crushed clays strongly depend on the shear stresses
developing in the materials
during passing through the role gap.
By L. L. Kosliak [2] during the design of constructions of
high-speed rollers the main attention
has been turned on the developed pressure stresses in the lumps
of clays however we can
influence very strongly on the plasticity of clay minerals
changing the conditions of crushing. A
considerable mixing and increase of plasticity and
homogenization can be occurred in the
convectional brick clays during passing through roller gaps of
the smooth high speed rollers.
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Based on the above to develop a method which is capable to
explain the mixing process,
describes the deformation and speed gradients, the shearing
stresses, the tension and surface
pressure on the roller shells as well as braking force and
energy absorption and dynamic
viscosity in the clay body passing the roller gaps have a great
importance. A very similar
method was developed by Silenok S. G. and Martynov V. D. at the
Mechanical Engineering
Faculty of the Civil Engineering University of Moscow. In this
work the method of
determination of the inside friction ratio is not described. The
values of viscosity and shear
ratios were taken from the data determined by the research group
of Turenko A. V.
experimentally for certain Russian convectional brick clay with
relative moisture of 22%.
At present our knowledge for determination of required data to
design adequate construction
of high speed rollers is not enough. Thanking to this the
quality of fired bricks is not good
enough however the processing technology was strongly controlled
including forming, drying
and firing.
The aims of the present work are to describe mathematically in
general and to show
graphically the physical and mechanical processes which occur in
the convectional brick clays
inside of the roller gap of KEMA-A/WF10 high speed roller. It is
known from the work of Hajnal
L. [3] that the clay minerals are losing their mechanical
strength at moisture of 15-20%. At the
same time the clay minerals using at the ceramic bricks industry
usually have relative moisture
more than 15-20%.
The research works made in capillary and rotary viscometer in
the last few years in accordance
to the examination of the flow properties of the plasticized
clays have confirmed that these
clay minerals behave like the incompressible liquids with high
value of viscosity and can be
described with equation of:
τ = τ0 + ηdu
dx (1)
Where:
τ – shear stress [Pa],
τ0 – static yield strength or static yield point [Pa],
η – dynamic viscosity of the clay body [Pas],
du/dx – deformation speed or shear rate [1/s] (in present case
the gradient of speed
developed in the clay body in process of passing through the
roll gaps).
The fact that the flow of plasticized clay is occurred analog to
the deformation of materials
with high viscosity allow us to use the continuous hydrodynamic
theory for the analysis
physical and mechanical processes taking place in convectional
brick clays during their crushing
by smooth high speed rollers. Thanking to this the equilibrium
of mechanical stresses in the
infinitively small volume of clays in the gap of roller shells
can be described by equation:
dp
dy=
dτ
dx (2)
Where:
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dp/dy - gradiens of pressure stress in the direction of motion
[Pa],
dτ/dx – gradiens of shear stress [Pa].
This equation (2) is used for the basic equation to determine
the speed distribution and
mathematically describes the values of deformation, speed
gradients and shear stresses of
individual clay particles inside the roller gap.
In the Fig. 1. can be seen the sematic drawing of the smooth
high speed roller crusher. In the
drawing R1, ω1, v1 are the radius, the angular and the
peripheral speed of the slower roller and
R2, ω2, v2 are the radius, the angular and the peripheral speed
of the faster roller, t0 is the
nominal gap between the roller shells and L is the length of the
rollers. All geometrical
parameters are in meter.
Fig. 1. Sematic drawing of the smooth high
speed roller crusher roller
Fig. 2. Speed distributions inside the smooth
high speed roller crusher gap of
KEMA-A/WF-10, when t0=1 mm and i=1,5
2. Speed distribution of crushed materials like convectional
brick
clays in the roller gap
Using equation (1) the equation (2) can be rewrite as:
dp
dy=
d
dx τ0 + η
du
dx (3)
After double integration from (3) we will get:
U =1
η −τ0x + c1x +
dp
dy
x2
2+ c2 (4)
Where: c1 and c2 are the constants of integration.
These constants can be determined from the following boundary
conditions:
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U = v1 , if x = +t
2
U = iv1 , if x = −t
2
Where:
U - the speed of the clays in the roller gap [m/s],
i - the relationship between the peripheral speeds of the
rollers (i=v2/v1).
After the substitutions and planning the equations the constants
of integration can be
described as:
c1 =v1 1−i
t+τ0
c2 =v1 1+i
2−
dp
dy
t2
8 (5)
Substitution of c1 and c2 into equation (4) the speed
distribution of clay body inside the roller
gap can be described by equation (6):
U =1
8η
dp
dy 4x2 − t2 +
v1 1−i
tx +
v1 1+i
2 (6)
The value of dp/dy can be found from the volumetric performance
of the roller crusher. The
volumetric performance can be described as:
V1 = ULdxx2
x1 (7)
Where: V1 is the volumetric performance for unit time.
Substituting U from eq. (6) to eq. (7) and taking into
consideration the boundary conditions
x1=-t/2 and x2=t/2. V1 can be described as:
x1 = −t
2 and x2 =
t
2
V1 = L 1
8η
dp
dy 4x2 − t2 +
v1 1−i
tx +
v1 1+i
2 dx
+t/2
−t/2 (8)
Solving eq. (8) the volumetric performance of roller crusher
is:
V1 =Lv1 1+i
2t−
L
12η
dp
dyt3 (9)
At the same time the volumetric performance of the high speed
roller crushers through the
nominal gap t0 can be described as:
V2 = Lv1+iv1
2t0 =
Lv1 1+i
2t0 (10)
As the volumetric performance of roller crushers is constant in
any optional section of the
roller shell gap we can say that V1=V2, which means:
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Lv1 1+i
2t−
1
12η
dp
dyt3 =
Lv1 1+i
2t0 (11)
From where:
dp
dy=
6ηv1 1+i
t3 t− t0 (12)
Substituting (12) into eq. (6), the speed distribution of
plasticized clay materials inside the
roller gap during crushing can be determined by equation
(13).
U =3v1 1+i t−t0
4t3 4x2 − t2 +
v1 1−i
tx +
v1 1+i
2 [m/s] (13)
Where: the dimensions are the following v1 [m/s], t, t0 and x
[m].
It is obvious from eq. (13) that the speed distribution inside
the roller shell gap doesn’t
depends on physical and mechanical properties of materials
during the crushing of plasticized
clay bodies having rheology properties described by eq. (1). The
values and distribution of
speed of clay particles inside the roller shell gap are
influenced by only their geometrical
position in the gap, size parameters of the rollers and the
peripheral speeds of shells.
It is necessary to mention that in case of the two rollers of
the crusher have the same
peripheral speeds the part of eq. (13) will turn to zero by the
following:
v1 1− i
tx = 0
The speed distribution of plasticized convectional brick clay
particles inside the smooth roller
crusher gap at different sections of KEMA-A/WF 10 high speed
roller are shown in the Fig.2-
Fig.6. This equipment had the following technical parameters:
D=1000 mm, L=650 mm. The
revolution of the slower roller is n1=150 rpm, v1=7.8 m/s. The
revolution of the faster roller is
n2=220 rpm, v2=11.5 m/s.
The ratio of the peripheral speeds is:
i =v2
v1=
11.5
7.8≅ 1.5 .
To analyze the eq. (13) the following nominal gaps and the
peripheral speed ratios were taken:
t01=0.5 mm, t02=1 mm, t03=2 mm; i1=1, i2=1.5, i3=2.
The session in the roller shell gaps were taken as the
followings:
t1= t0+1.5 mm, t2= t0+9.5 mm, t3= t0+49.5 mm.
The speed distribution at coordinate axis y was used
non-proportional scaling for the easier
representation and understanding.
At peripheral speed ratio v2=1.5v1 the Fig.2-Fig.4 show how
strong the speed distribution of
plasticized clay particles depend on the value of the nominal
gap. For example at the t1
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segment a counter-flow already exists at t0=0.5 mm while in the
other two cases there is
obviously only one direction motion. In the figures it can be
well seen that decreasing the
nominal gap the speed vectors of the counter-flow or whirl-flow
are increased, thus the mixing
of the material particles is increasing.
Fig.3. Speed distributions inside the smooth
high speed roller crusher gap of
KEMA-A/WF-10, when t0=0,5 mm and i=1,5
Fig.4. Speed distributions inside the smooth
high speed roller crusher gap of
KEMA-A/WF-10, when t0=3 mm and i=1,5
Fig.5. Speed distributions inside the smooth
high speed roller crusher gap of
KEMA-A/WF-10, when t0=1 mm and i=1
Fig.6. Speed distributions inside the smooth
high speed roller crusher gap of
KEMA-A/WF-10, when t0=1 mm and i=2
Comparing the Fig.2, Fig.5 and Fig.6 it is well seems that
increasing the peripheral speeds of
rollers the speeds of individual particles and the shear rates
inside the materials are also
increasing. Especially impressive how strong is the influence of
the geometrical locality of the
crushed materials inside of the roller gaps on shear rate. The
influence of peripheral speed
ratio i=v2/v1 on shear rate is also quite impressive.
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3. The speed gradients or shear rates developing in the
materials in
the roller gaps
The gradient of speeds or shear rates developing in the crushed
materials passing through
roller gap can be determined from eq. (13) taking its derivative
by x as the following:
du
dx=
6xv1 1+i t−t0
t3+
v1 1−i
t [s-1] (14)
These gradients of speed or shear rates show us the different
between the layers of material
during its crushing and passing through the gap of the smooth
high speed roller crusher. It is
necessary to determine and know the values of the developed
shear rates because the
effective viscosity values of convectional brick clays generally
are given as function of shear
rate in coordinate system as η = f(du/dx).
3.1. Determination of the most efficient crushing ratio
When the smooth high speed rollers are used for crushing hard
minerals like rocks and stones
the optimum crushing ratio is d/d1=3-5 by Sapozhnikov, M.J. [4],
where d – the original, d1 –
the crushed sizes of granules. Meanwhile if the high speed
rollers are used for crushing
minerals like mined convectional brick clays with water
containment about or more than 15
m% the optimum crushing ratio is d/d1=8-10.
The optimum crushing ratio can be determined from eq. (13) using
boundary conditions when
at a certain roller gap section t the speed of materials U=0 at
the axis x=0, namely:
U =3v1 1+i t−t0
4t3 −t2 +
v1 1+i
2= 0 (15)
Solving the equation (15) on the value of cross section in where
there is no counter-flow the
following ratio to the nominal roller gap can be got:
t = 3t0
Because of that at the gap cross section of t=3t0 all volume of
crushed material is moving only
one direction – to the direction of nominal roller gap – the
most efficient crushing ratio can be
get in case when the average original diameter of granules is:
d=t=3t0.
Of course when the diameters of rollers are 1 m or more and the
nominal roller gap is 1 mm or
less a very good and efficient crushing of materials can be also
observed in case when the
average value of original diameter of granules will be
d=5t0.
When the smooth high speed roller crushers are used for crushing
convectional brick clays
with water containment more than 15 m% very good efficiency can
be obtained at average
original granule sizes of d=(8-10)t0 thanking to the good
adhesion and relatively high external
friction ratio of clay minerals at roller surfaces.
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3.2. The shear stress developing in the materials in the roller
gap
It is obvious from the eq. (1) that the convectional brick clays
can be modeled as non-
Newtonian fluids. So putting the eq. (14) to eq. (1) the shear
stress developing in the materials
during their crushing in the gaps of the smooth high speed
rollers can be determined as:
τ = τ0 + η 6xv1 1+i t−t0
t3+
v1 1−i
t (16)
Substitute into (16) the following two boundary conditions:
x1=+t/2 and x2=-t/2, for the shear
stress developing in the crushed materials at the surface of the
slow roller can be determined
as:
τ+t/2 = τ0 + η 3v1 1+i t−t0
t2+
v1 1−i
t (17)
and at the surface of the quick roller is:
τ−t/2 = τ0 − η 3v1 1+i t−t0
t2+
v1 1−i
t (18)
Let’s see is there any cross section of the roller gap where the
developed in material shear
stress equal with the yield stress, namely τ=τ0. In this case
both (17) and (18) can be rewritten
as:
3v1 1+i t−t0
t2+
v1 1−i
t= 0 (19)
From eq. (19) the critical cross section in where the shear
stress in the crushed materials
developed by rollers is equal with their static yield points
(τ=τ0) can be determined as:
t =3
2t0
i+1
i+2 (20)
The Fig.7-Fig.10 show the shear stress distribution in MPa
developed in the materials at the
surfaces of the rollers during their crushing on smooth high
speed roller KEMA-A/WF-10 as
function of nominal gaps and speed ratios when the peripheral
speed of slower roll v1=const.
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Fig.7. Shear stress distributions inside the
smooth high speed roller crusher gap of
KEMA-A/WF-10, when t0=1 mm and i=1,5
at the surfaces of ‘slow’ (a) and ‘quick’ (b)
rollers
Fig.8. Shear stress distributions inside the
smooth high speed roller crusher gap of
KEMA-A/WF-10, when t0=1 mm and i=1 (1)
and i=2 (2) at the surfaces of ‘slow’ (a) and
‘quick’ (b) rollers
Fig.9. Shear stress distributions inside the
smooth high speed roller crusher gap of
KEMA-A/WF-10, when i=1 and t0=2 mm (1)
and t0=0.5 (2) at the surfaces of ‘slow’ (a) and
‘quick’ (b) rollers
Fig.10. Shear stress distributions inside the
smooth high speed roller crusher gap of
KEMA-A/WF-10, when the effective viscosity,
ηe=const. in whole gap, t0=1 mm and i=1,5 at
the surfaces of ‘slow’ (a) and ‘quick’ (b)
rollers
4. Conclusions
Using the Bingham rheological model (eq. (1)) and mechanical
stress distribution in materials
during their crushing in gap of high speed rollers (eq. (2)) and
boundary conditions taken from
technical parameters of the crusher, were successfully given and
mathematically determined
the flow speed distribution (eq. (13)), shear rate distribution
(eq. (14)) and shear stress
distribution (eq. (16)) developing in materials like
convectional brick clays. Furthermore the
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optimum crushing ratio was given (t=3t0) where all material
particles are moving only to
direction of nominal gap. The critical cross section was also
determined (eq. (20)) in where the
shear stress in the crushed materials developed by rollers is
equal with their static yield points.
References
[1] Sapozhnikov, M.J.: Mehanicheskoe obrudovanie dlya
proizvodstva stroitelnyh materialov I
izgelij. Mashinostroenie, 1962.
[2] Kosljak, L.L.: Effektivnye rezhimy raboty valcov tonkogo
pomola. Steklo i keramika, 1960. 11.
[3] Hajnal, L.: Betonadalék agyagrög szennyeződésének
hidromechanikus aprítása. Építőanyag,
1972. 2.
[4] Sapozhnikov, M.J.: Szilikátipari gépek és berendezések I.
Építésügyi Kiadó, 1953.
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Some Problems of Dimensioning the Smooth Rolls Used
for Crushing Clay Minerals
Gömze, A.L.
University of Miskolc
(Translated from Hungarian: Agyagásványok aprítására használt
simahengerek
méretezésének néhány specifikus problémája)
Published in journal Építőanyag (1980) vol. 32., 11., pp.
428-432.
Abstract
In this work the author tries to describe the advantages and
disadvantages of traditional methods used
for determination fundamental technical parameters of high speed
roller crushers used for
comminution of raw materials in ceramic industry. Comparing the
different traditional methods the
author has fined that mechanical and matemathical description
given by Russian scientist Sapozhnikov is
one of the best approaches of this problem.
Keywords: clay, crushing, friction, mechanical stress, moisture,
power consumption, pressure, rheology,
viscosity
1. Introduction
In spite of the smooth high speed roller crushers are relatively
poor equipment, the required
power consumption and mechanical stresses and strains developing
during crushing the
plasticized clay minerals are not exactly described until today.
Thanking to this circumstance in
1973 Gy. Peter [1] was not able to describe the required power
consumption of these
machines as it was given by Levenson [2] in 1940. Meanwhile
other authors like Silenok [3] and
Martynov [4] have described the mechanical loads and required
power consumptions based
on empirical evidences. The crushing productivity and throughput
performance (m3/h) of these
machines were also described by them based on their empirical
evidences. Unfortunately the
method described by Hungarian author *1+ is quite old and
doesn’t take into consideration the
phisico-mechanical properties of crushed raw materials like
convectional brick clays with
mined range of moisture.
Sapozhnikov [5] have described the mechanical and dynamical
phenomenon (tensions and
biasing forces, technologically required, power consumptions)
taking place during crushing of
minerals on smooth high speed rollers based on law of classic
theoretical mechanics. Further
developing of own theory he has tried to give mathematical
answer [6] on the biasing forces
and power consumption. These mathematical equations are quite
accurate approach the real
values.
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2. Calculation method of high speed roller crushers by
Sapozhnikov
The required power consumption of smooth high speed roller
crushers can be determined as
P = Pt + PS [W] (1)
where:
Pt – the technological required power consumption (W),
PS – friction of bearings and shafts (W)
The technological required power consumption can be determined
as:
Pt = P1 + P2 [W] (2) where:
P1 – the required power consumption for crushing the materials
like plasticized clay minerals,
P2 – the required power consumption to defeat the friction
developing between the crushing
materials and the surface of roller shells
Using the laws of classic theoretical mechanics the required
power consumption during
crushing minerals on high speed rollers can be determined by
Sapozhnikov as
P1 = 1,15 ∙ αr ∙ ςtωLR ∙ 2 T∙t0μ
tgα2
−1 T∙t0
t0
μ
tgα2 − 1 cosα (3)
where:
αr – the retraction angle in radians
ςt – the static yield point of plasticized clay minerals the
values of which by [6] are (3-5)105 Pa
ω – the angular speed of rollers, s-1
L – the working length of rollers, m
R – the radius of rollers, m
t0 – the nominal gap between the rollers, m
T – the thickness of dispatched clay mineral strip, m
µ - the friction ratio developing between the crushing materials
and the surface of roller shells
By Sapozhnikov the required power consumption to defeat the
friction developing between
the crushing materials and the surface of roller shells can be
determined as
P2 = µP1 (4)
so the value of technological required power consumption can be
determined by the following
equation:
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P1 = 2,3 μ+ 1 ατ ∙ ατωLR ∙ 2 T∙t0μ
tgα2
−1 T∙t0
t0
μ
tgα2 − 1 cosα (5)
It is necessary to remark that the equation (4) is true only if
the clay minerals are sliding with
the same speeds as the peripheral speeds of crusher rollers.
Thanking to this circumstance it
would be necessary to examine and give the real values of
sliding speeds both in equation (4)
and (5), otherwise the power consumption of high speed roller
crushers determined by these
equations will remarkable higher than it technologically
required.
Determining the required power consumptions of friction of
bearings and shafts Sapozhnikov
has used a permanent mechanical pressure distribution on the
surface of roller shells and get
mathematical equation as
PS = 2πωdf Gg 2 +
1,15ατςt L T∙t0∙cosα
2
μ
tgα2
−1 1−cos α
∙ T∙t0
t0
μ
tgα2 − 1 (6)
where:
d – diameter of shafts, m
f – the rolling resistance of bearings, f=0,001
G – the mass of the roller, kg
g – the gravity acceleration, cm/s2
The fundamentally mistake of the equation (6) is that
Sapozhnikov is using a permanent value
of pressure distribution on retraction arc length meanwhile this
pressure distribution very
strong depends on geometrical place of materials on the
retraction arc. The very strong
influence of the geometrical position on the developed value of
pressures on the retraction arc
of rollers was shown by authors [7, 8] or [9, 10]. This means
that it is impossible to use a
permanent pressure value on whole π/2 angle of “retraction
arc”.
The clay minerals in the roller gap develop tension and biasing
force on the rollers and their
bearings and the value of this tension can be determined by [6]
as
F =ατ
2ςB DKL N (7)
where:
ςB – the compressive strength of clays, Pa
In case of toothed crusher this compressive strength of
plasticized clay minerals equal
about 3*105 Pa and smooth high speed roller crushers 3-4*105 Pa
by Sapozhnikov.
D – the diameter of rollers, m
K – the level of saturation of roller gaps during crushing,
K=0,4-0,6
L – the working length of rollers, m
-
21
The main problem with equations (3)…(7) of Sapozhnikov is that
he has recommend to use ςt
and ςB for characterization of plasticized clay minerals during
the crushing where he
recommend that
ςt ˃ ςB (8)
which is contradict to the real mechanical properties of
plasticized clay minerals. That is also
problem that equations of (3)…(6) ignore the situations when
ω = ω1 ≠ ω2
R = R1 ≠ R2 (9)
Inspite of these deficiency the method developed by Sapozhnikov
is quite remarkable as it is
the first method which takes into consideration almost all
construction types of roller crushers.
At the same time equation (6) tries to give the mathematical
model to determine on the basis
of friction and mechanical properties of clay minerals and
technical parameters of equipment
the developing mechanical forces and required power consumption
of roller crushers.
3. Specific problems of calculation method of smooth high
speed
rollers
The technical parameters of crushers – including the smooth high
speed rollers also – have to
be calculated on the basis of physical and mechanical properties
of materials being crushed. In
accordance to the materials should be differ as solids and as
liquid like viscous body.
3.1. The clay minerals as solids
The required power consumption of clay minerals as solid
material (when the relative moisture
is smaller than 15%) must be determined on the so-called volume
theory. In this case the
requirement value of crushing energy can be determined by
Hooke’s law:
W =ς2V
2E Nm (10)
where:
W – the required energy for elastic deformation until the crush
of the body, Nm
ς – breaking strength of the materials, Pa
E – Young module, Pa
V – the value of the crushed body of material, m3
From equation (10) in his diploma thesis T. Keller [11] has
tried to give a mathematical
calculation of required technological power consumption of high
speed rollers.
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22
3.2. The clay minerals as Bingham-like material
The experiments realized at the Brick Plant of ÉTCSV in Mályi
have shown that the convection
of brick clays with relative moisture larger than 12-15% are
very similar to so-called Bingham-
materials and their rheo-mechanical properties can be
characterized as
τ = τ0 + ἑη (11)
The fact that the convectional brick clays with relative
moistures more than 12-15% are acting
as Bingham-like materials was experimentally justified by
Hallman [12] and Turenko [13]. In
the Hungarian scientific literature [9, 10] and the [14-17]
papers show some specific problems
of calculation methods of forming and crushing of structural
liquid-like materials as glasses at
800oC or higher and clay minerals and convectional brick clays
at normal temperature.
During crushing on smooth high speed roller of clay materials
used in ceramic industry this
kind of specific problems are the followings:
a. the values of friction ratio developing between the clay
minerals and the surface of
smooth high speed roller shells and
b. the values of dynamic viscosity of the clay minerals and
their changing during crushing
3.2.1. The friction ratio developing between the clays and
roller shells
The principal shame of laboratory equipment use for examination
of friction ratio developing
between the plasticized clay minerals and steal surface is shown
in Fig. 1.
For the experimental determination of friction ratio the
moisture of clay minerals, the speed of
movements and the pressure forces were change in the measurement
serials. In each of them
the experiments were repeat three-times and one of these serials
is shown in Table 1.
In Fig. 2 we can see how the values of friction ratio are
depends on the values of contact
surfaces (2.a), speeds of slide (2.b.), mechanical stresses on
surface (2.c.) and the moisture of
convectional brick clays (2.d)
Fig.1. The schematic drawing of the
measurement
Fig.2. The friction ratio of convectional brick
clays as function of surface (a), speed (b),
pressure (c) and relative moisture (d)
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23
Table 1. Friction ratio between convectional brick clay “Malyi”
and steal surface
m Aa
cm2 G*g
N W %
v m/s
Fn N
ςn [N/cm2] FS
N µ
I. II. III.
1
31,769 4,5 15 0,12
24,5 87 84 89 18,315 0,7476
2 44,5 155 158 152 33,750 0,7584
3 64,5 230 227 230 49,783 0,7718
4 84,5 300 280 290 63,043 0,7461
5 104,5 355 349 352 76,522 0,7323
6 124,5 420 415 415 90,580 0,7275
7 144,5 490 480 485 105,435 0,7279
8 164,5 545 540 550 118,478 0,7202
9 185,5 610 590 590 129,710 0,6992
10 205,5 635 630 628 137,174 0,6675
11 225,5 685 688 680 148,768 0,6579
12 250,5 780 775 760 168,576 0,6650
13 270,5 825 819 820 178,551 0,6601
14 290,5 870 879 881 190,580 0,6560
In Table 1. the following symbols were used:
m: number of experiments, Aa: surface of sliding plasticized
clay, G*g=m*g: gravitation force of
the metallic matrix of instruments, W: relative moisture, v:
speed of sliding, Fn: normal force
acting on the surface during experiments, ςn: normal pressure
acting on the surface of clay
during the experiments, FS: measured friction force, µ: friction
ratio
3.2.2. The dynamic viscosity of plasticized clay minerals
There are many arguments which are influence on dynamic
viscosity (η) of clay minerals and
convectional brick clays. The most important of them are the
temperature, moisture
percentage and the working shear rate.
During the working of smooth high speed roller crusher the
temperature and the relative
moisture of convectional brick clays have constant values so the
dynamic viscosity (η) can be
examined only as function of shear rate (Fig.3.). The values of
dynamic viscosity were
determined experimentally by HAAKE Rotovisco instrument.
On the basis of the viscosity values get on HAAKE laboratory
equipment we can turn to the
dynamic viscosity of clay minerals inside the gap of high speed
roller can be calculated by
equation:
ηg = an ∙ ηm Ns/m2 (12)
where:
a – coefficient, the values of which for the Malyi brick clays
are a=0,5-0,6
n – exponent
ηm – the dynamic viscosity measured on the laboratory equipment,
Pas
-
24
The exponent n can be determined as
n =lgε g
ε m
lg2 (13)
where:
ἑg – the shear rate developing in the material (clay mineral)
during passing through gap of
rollers, s-1
ἑm – the shear rate in the laboratory equipment, s-1
The change of dynamic viscosity of plasticized clay minerals and
convectional brick clays
depending on their position inside of the roller gap is shown in
Fig.4. The ‘1’ is the average
dynamic viscosity of plasticized clay minerals which are found
between the coordinate axis ‘y’
and slower roller, the ‘2’ is the average dynamic viscosity of
plasticized clay minerals between
the coordinate axis ‘y’ and faster roller. At the same time the
‘3’ and ‘4’ are the values of the
dynamic viscosity of plasticized clay minerals direct at the
surface of the slower and the faster
rollers.
Fig. 3. The dynamic viscosity of the
convectional brick clays as function of
shear rate
Fig.4. Influence of position on the dynamic viscosity
of clay minerals and conventional brick clays during
passing through the roller gap
4. Conclusions
Summarizing the above described research work the following
conclusions can be determined:
a. At present already mathematical methods are available using
of which the dynamic
loads and developing on smooth high speed roller stresses and
strains can be
determined during the crushing both solids and plasticized clay
minerals.
b. These new methods taking into consideration both the physical
and mechanical
properties materials (ςB, ςt, η, µ) and construction parameters
(L, R, t0, v1) of the roller
equipment.
c. If our task is to develop new construction of smooth high
speed roller equipment for
plasticized clay minerals or convectional brick clays with
moisture more than 15% it is
-
25
necessary to taking the consideration the dynamic viscosity (η)
and friction ratio (µ) of
these materials.
d. The friction ratio of clay minerals very strong depends not
only on theirs relative
moistures but from the slide speeds and the developing pressure
stresses also.
e. At constant working temperature and relative moistures the
values of dynamic
viscosity of the clay minerals and convectional brick clays
first of all depends on the
shear rate developing in the materials inside of the roller
gap.
References
[1] Peter, Gy.: Kerámiaipari Gépek, Budapest, 1974. p.
46-47.
[2] Levenson, L.B.: Droblenie i grohochenie poleznyh iskopaemyh,
Moscow, O.N.T.I. 1940
[3] Silenok, S.G., Grizak, Ju.S., Lysenko, V.D, Nefedov, D.E:
Mehanicheskoe oborudovanie dlya
proizvodstva vyazuschih stroitel’nyh materialov, Moscow,
1969.
[4] Martinov, V.D, Sergeev, V.P: Stroitel’nye masiny, Moscow,
1970. p. 53-56.
[5] Szapozsnyikov, M.J., Bulavin, J.A: Szilikátipari gépek és
berendezések I. Budapest, Építésügyi
Kiadó, 1953.
[6] Sapozhnikov, M.J.: Mehanicheskoe oborudovanie predpriyatii
stroitel’nyh materialov, izdelii i
konstruktsii. Moscow, 1971. p. 55-67.
[7] Zolotartskii, A.Z: Obrabotka glinyanoi massy v val’cah,
Stroitel’nye materialy, 1969. No.3. p. 26-
28.
[8] Turenko, A.V., Silenok, S.G: Opredelnie optimal’nyh rezhimov
glinoobrabatyvayuschego
oborudovaniya na osnove svoistv plastichnyh glin. Iz. d. MISZT,
Stroitel’nye mashiny i
obroduvanie, 1978. p. 156-172.
[9] Gömze, A.L.: Kerámiaipari simahengerművek
hatékonyságnövelésének matematikai alapjai. I.
Építőanyag, 1980. 4. sz. p. 134-140.
[10] Gömze, A.L.: Az üveghengerlésnek néhány elméleti kérdése a
feldolgozandó üvegolvadék fiziko-
mechanikai tulajdonságainak figyelembevételével. Kézirat,
Miskolc, NME, 1980. március, p. 29-
43.
[11] Keller, T.: Kerámiaipari finomhengerművek kapacitásának
növelése, Diplomaterv, NME Szi.
1979/6.
[12] Hallmann, E.: Berechnung der Schnecke von Strangpessen für
plastische Stoffe, Die
Ziegelindustrie, 1962. p. 425-431.
[13] Turenko, A.V.: O pererabatyvaemosti plastichnyh gliyanyh
past, Stroitel’nye materialy, 1974/10.
p. 32-33.
[14] Gömze, A.L.: A képlékeny agyag aprításának matematikai
elemzése, Építőanyag, 1974/9. p. 348-
354.
[15] Gömze, A.L.: Kerámiaipari törőhengerművek törés elleni
védelme, GTE kiadvány, Miskolc, 1978.
p. 165-170.
[16] Gömze, A.L.: Az anyagfeladás egyenetlenségének hatása
kerámiaipari simahengerművek
dinamikai igénybevételére, GTE Kiadvány, Miskolc, 1979. p.
454-458.
[17] Gömze, A.L.: Kerámiaipari simahengerművek vizsgálatának
néhány újabb eredménye, GTE
Kiadvány, Miskolc, 1980.
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26
Rheology and Flow Conditions of Clay during Smooth Roll
Comminution
1Gömze, A. L. – 2Chirskoi, A.S. – 2Silenok, S.G. – 2Turenko,
A.V.:
1University of Miskolc
2Civil Engineering University of Moscow
(Translated from Hungarian: Agyagok reológiája és áramlási
viszonyai simahengerekkel
végzett aprításkor)
Published in journal Építőanyag (1981) vol. 33., 12, pp.
441-446.
Abstract
Behavior and flow conditions of clay bodies pulled into the gap
of smooth rolls was studied by
structural, physic-mechanical and stress analysis. Material flow
properties are dealt with by taking static
yield point (τ0), plastic viscosity (η) and elasticity modulus
(Ε) of the examined clay into consideration.
Mathematical connexions are derived showing that the flow of the
clay, kneaded through the gap, and
thus the mixing efficiency of smooth rolls are primarily
influenced by material properties, particularly
and E. The properties of the comminuted particles are affected
by the mechanical-structural history of
the clay body, in this context and average hold time within the
roll gap can be calculated.
Keywords: clays, crushing, elasticity module, rheology, shear
rate, viscosity
1. Introduction
The energy efficient technology of ceramic industry requires raw
materials and clay minerals
with smaller and smaller relative moisture. Because of this it
is necessary to make suitable the
smooth high speed roller to crush clay minerals and convectional
brick clays with smaller
moisture ratio. To achieve this requirement it is necessary to
study and examine deeper the
physical and mechanical properties of clays as well as develop
the methods and equipment of
measurement also.
2. Some specific properties of crushed clay particles
Examining the physical and mechanical properties of clay
minerals and convectional brick clays
there are several factors which are influencing on geometrical
shapes, sizes and distribution of
clay particles crushed on smooth high speed rollers. From them
probably the most important
are the mineral and chemical composition of clay, including
their geological ages, moisture
ratio, the technological processes before crushing like mining,
transporting, storage, etc. and
construction parameters of roller crushers like roller gap,
shell peripheral speeds, diameters of
rollers. For a certain mineralogical composition and roller
crusher and roller gap the
-
27
geometrical shapes and sizes of the crushed clay particles
depend first of all on relative
moisture of clay body and time of its passing through roller
gap.
The realized experiments have shown that increasing the relative
moisture of raw materials
like convectional brick clays increasing the volume of flat
crushed clay particles as it is shown in
Fig. 1. This means that larger thickness (‘a’) of particles are
close to the nominal gap (t0)
meanwhile their lengths (‘b’) and highs (‘c’) can be several
times larger than their thickness
(equation (1)).
b = m1t0
c = m2t0 (1)
where coefficients m1 and m2 usually much larger than 1.
Where the maximum thickness of crushed particles can be larger,
equal or smaller than the
nominal gap of smooth high speed roller crushers, as
amax ≥
≤t0 (2)
The distribution of the crushed particle thickness also was
examined as function of relative
moisture of convectional brick clay. It is well seen and clearly
visible in Fig.2. that increasing
the moisture the average particle thicknesses are decreasing. At
the same time it is necessary
to mention that increasing the relative moisture of the clay
minerals and convectional brick
clays will increase their propensity of adherence to roller
shells and to themselves. Finally after
crushing during the transportation and mixing there will be
found particles with much higher
thicknesses than the roller gap was.
Fig. 1. The geometrical shapes of crushed clay
particles as function of moisture
Fig. 2. Distribution of grain thicknesses
comparing with nominal roller gap
This propensity is especially strong visible in the clay
containers and clay warehouses of the
ceramic and brick plants. Especially strong coagulation and
propensity can be observed in clay
warehouses in where these crushed particles spend longer
time.
From Fig.2. also well seeing that during crushing on high speed
rollers clay minerals with
smaller moisture we can get much more volume (percentage) of
crushed clay particles with
smaller sizes than the nominal gap (t0) of the crushing machine.
In spite of this a relatively high
-
28
portion and quantity of crushed particles will have thickness
larger than the nominal gap of
roller crusher.
a ˃ t0 (3)
This phenomenon can be explained partly by the structure of
these clay minerals and partly by
the ‘memory’ properties of these materials.
The schematic structure of clay minerals and convectional brick
clays is shown in Fig.3. It is well
seeing in this figure that increasing the relative moisture the
solid particles of clay minerals are
covered with thin water films and thanking to this phenomenon
the volumes of individual
pores and gaps are decreasing. The growth of particle sizes
after comminution also strong
depends on the numbers and geometrical sizes of pores and gaps
with air. The reason is that
the pressure of closed airs in these pores and gaps are
considerably increasing during passing
through the roller gap, and after crushing these pressured airs
burst and increase the sizes of
crushed clay particles. In a certain case this pressed air in
the pore is capable to explode the
particles itself. From other hand when the raw material has
increased moisture the air closed
inside the pores can easier move to the surface of particles and
because of this the sizes of
crushed clay particles will not increase so intensively after
the crushing.
It is necessary to remark that the growth of particle sizes
after crushing on high speed rollers
can be also observed at clay minerals and convectional brick
clays with quite high moisture
ratio. The character of growth of the crushed particle sizes as
function of time after crushing is
shown in Fig.4. It is well visible on this figure that the
particle size growth is very intensive in
the first few seconds and after 110 seconds this growth process
is finishing and after 3 minutes
the growth process is fully finished.
Fig.3. Schematic microstructure of
convectional brick clays and clay minerals
1-capillary, 2-opened pores, 3-closed pores,
4-water films, 5-solid particles
Fig.4. Volume changes of clay particles after
crushing as function of time
During the experiments the considerable increases of crushed
particles were observed and
these increases very strong depended on the passing time in the
roller gap. The theoretical
passing time was described in paper [1]. Really this passing
time through roller gap very strong
depends on the saturation/fullness of the roller gap with clays
during the crushing process.
This fullness (saturation) can be determined by equation
(4).
-
29
t1 = k1 R+
T0+t02
T0−t0 4R− T0−t0 −2αt R
t0v1 l+i (4)
where:
αt – the retraction angle at the widths of fed “clay tapes” on
the high speed roller crushers.
In optimal cases these widths are equal with rollers gap.
i – ratio between the peripheral speed of faster and slower
rolls
k1 – saturation/fullness ratio of the rollers gap or mill gap,
k1=0.4-0.6
R – radius of crushing roller, m
T0 – the widths of fed “clay tapes”, in optimal case it is equal
with the roller gap at the
retraction angle, T0=T, m
v1 – peripheral speed of slower roller shell, m/s
Generally the passing time of clay minerals and brick clays
particles in the roller gaps much less
than the average passing time (t1) because of the average width
of fed “clay tapes” (T0) much
less than the roller gap (T) at the retraction angle.
The growth of productivity of ceramic plants and high speed
roller crushers together with
“memory” properties of clay minerals and convectional brick
clays are required more detailed
information about the rheological properties of this time of
materials.
During the realized experiments the Volterra equation seemed to
be suitable to describe the
“memory” properties of clay minerals and convectional brick
clays as function of time and
stresses:
ε tt =1
E ς tt + L(tt
tt0
, τ) τ ς
τ dτ (5)
where:
E – Young-module of clays
tt – time spent by clay particles after leaving the roller
gap
L(tt, τ) – that part of equation which takes into consideration
how the ς(tt) unit stress effecting
through time interval will influence on the deformation of
crushed clay particles after
tt time
To determine the “memory” properties of clay minerals and
convectional brick clays with
mined moisture Erzhanov [2] has recommended an exponent equation
like:
L t1, τ = θe−χ t1−τ (6)
where θ and χ parameters of creep and relaxation.
Analyzing the above it is easy to understand that using the
exponent parts the equation (5) will
be equivalent with the equation (7):
a0ε + a1d iε
dtini=1 = b0ε+ b1
mj=1
d jε
dtj (7)
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30
This equation has rheological character and of which the
Maxwell-, Kelvin- and Burgess
rheological equations are only partial cases. At a constant
working temperature of the
convectional brick clays the coefficients a0, a1, b0, b1 are
constants in the equation (7).
In the future the examination of relationship would be necessary
between the particle sizes
and distribution, moisture, module elasticity, viscosity,
porosity and “memory” properties of
clay minerals to improve the technological processes in ceramic
industry.
3. Deformation of clays
The unity of deformation volume, deformation speed and stress
condition is true for all kind of
materials. So the degree of deformation of clay minerals and
convectional brick clays in the
gap of smooth high speed roller strong depends on the mechanical
stresses developed in
particles by the roller shells. These mechanical stresses can be
determined studying the stress
condition of an elementary or infinitive volume of clays in
roller gap. So the equilibrium of
mechanical stresses in an infinitive volume of clay can be
described as:
δςx
dx+δτxy
δy+δτxz
dz+ X = 0
δτyx
δx+δςy
δy+δτyz
δz+ Y = 0 (8)
δτzx
δx+δτxy
δy+δςz
δz+ Z = 0
if the following boundary conditions are realized:
Pkx = ςxcos(kx) + τxycos(ky) + τxzcos(kz)
Pky = τxycos(kx) + ςycos(ky) + τyzcos(kz) (9)
Pkz = τzxcos(kx) + τxycos(ky) + ςzcos(kz)
In the equations (8) and (9) the following symbols are used:
ςx, ςy, ςz, τxy, τxz, τyz – the pressure and shear stresses
X, Y, Z – the projection on x, y, z coordinate axis of inside
mechanical stresses
developing in materials to keep equilibrium of stresses
Pkx, Pky, Pkz – the resultants on x, y, z coordinate axis of
mechanical stresses developed
by external mechanical forces
The continuum, uninterrupted deformation of clay minerals have
crushed in the gap of smooth
high speed roller crushers can be described by equation Cauchy,
as:
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31
ε x =δu
δx; γ xy =
δv
δx+δu
δy;
ε y =δv
δy; γ xz =
δw
δx+δu
δz; (10)
ε z =δw
δz; γ yz =
δw
δy+δv
δz;
where:
έx, έy, έz – the shear rates into direction of coordinate
axis
u, v, w – the projection of deformation volume into direction of
coordinate axis
Ẏxy, Ẏxz, Ẏyz – the volume of deformation angles
Relationship between deformation and mechanical stresses of
convectional brick clays with
mined moistures was described in detail in paper [3]. This work
was also described that in high
speed roller crushers the technologically required energy
consumption is distributed for
elastic, plastic and viscous deformations of crushed materials.
Thanking to this the
convectional brick clays with mined moisture (W˃15%) and can be
modeled as Bingham
system (Fig.5.) and characterized with rheological equation
(11):
τ – τ0 = ηέ (11)
where:
τ – shear stress, Pa
τ0 – the static yield stress or yield point, Pa
η – plastic viscosity of clay minerals, Pas
έ - shear rate, s-1
Fig.5. Simplified rheological model of
convectional brick clay with mined moisture
-
32
4. Flow conditions in the gap of smooth high speed roller
crushers
There are used smooth high speed roller crushers with higher and
higher peripheral speed of
roller shells (v1≥10 m/s) in the ceramic industry. The high
peripheral speeds and the relatively
small (t0≤1 mm) roller gaps give an opportunity to take into the
consideration the movement
of crushed materials only to vertical direction, to direction of
nominal gap of roller machine. In
this case the stress equilibrium of the infinitive small
particles by author [4] can be determined
as:
δςy
δy= −
δτyx
δx (12)
There are several works (*5+…*8+) tried to describe the
technological parameters and power
consumptions of smooth high speed rollers used for crushing of
plasticized clay minerals with
rheological properties like Bingham materials. In this case the
flow distribution of crushed
convectional brick clays in the rollers gap can be determined
[9] with equation (13):
U =3v1 1+i t−t0
4t3 4x2 − t2 + v1
1−i
tx + v1
1+i
t (13)
where:
t – the size of roller gap in section t, m
x – the distance from the center (y axis) where the crushing
particle is being in the gap, m
The speed distributions of crushed materials in the roller gap
by equation (13) are shown in
Fig.6. as function of diameter (D=2R) and peripheral speeds (v1,
v2).
At the same time it is necessary to remark that the clay
minerals and convectional brick clays
with mined moisture have elastic properties very often.
Especially it is necessary to take into
consideration the elastic property of these materials during
their crushing in gap of high speed
roller, when the peripheral speed is: v1 ˃ 10 m/s. So the speed
distribution of particles of
convectional brick clays in the roller gap can be described also
when both their viscous and
elastic properties are taking into consideration.
In this case the flow speed of clay particles near the slower
roller can be described by equation
(14):
vy1 =1
2η
6ηω1
T−
2Ey
RT
t
2− x
t+2x
4− x0 + Kω1 R
2 − y2 (14)
and the flow speed of elastic-viscous clay particles near the
faster roller can be determined as:
vy2 =1
2η
6ηω2
T−
2Ey
RT
t
2− x
t+2x
4− x0 + Kω2 R
2 − y2 (15)
Where:
E - elastic module of the convectional brick clay, Pa
ω1 and ω2 – the angular speed of the slower and faster rollers,
s-1
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33
K - coefficient of slip of the clays on the roller shells
x0 - thickness of central zone of clay flow in the gap during
crushing, m
y - distance of the examined gap section from x axis, m
Fig.6. The speed distribution of clay particles
in the roller gap determined by equation (13)
Fig.7. In the gap of smooth high speed roller
crushers the speed distribution of clay
minerals and convectional brick clays
determined by equations (14)…(17)
The thickness of central zone of clay flow can be determined
as:
x0 =τ0T(1+R)
3ηω1−Ey+
ηkRT (2R2−y2) ω1−ω2
t0R+y2 3ηR ω1+ω2 −2Ey−2τ0RT
(16)
and its speed in the gap as:
v0y =1
2η
3η ω1+ω2
T−
2Ey
RT
t
2−x0
2+ Kω1 R
2 − y2 (17)
The determined by equation (16) and (17) speed distribution of
convectional brick clays with
viscous and elastic properties at mined moisture is shown in
Fig.7.
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34
5. Conclusions
In spite of the equations (14)…(17) seem more complicated than
developed by *9+ equation
(13), they have remarkable advantages especially when the
peripheral speeds of roller shells
are much more than 10 m/s. The advantages of these equations
also that they taking to
consideration not only the technological parameters of equipment
like diameters of rollers,
peripheral speeds, nominal roller gap, but also the viscosity,
static yield point and elastic
module of convectional brick clays.
In spite of the equations (13)…(17) look quite complicated most
of the ceramic companies and
convectional brick plants have computing facility for simulation
by them the flow processes
inside of the gaps of the smooth high speed roller crushers
nowadays.
References
[1] Gömze, A.L.: Kerámiaipari simahengerek
hatékonyság-növelésének matematikai alapjai II,
Építőanyag, 1980. 9. sz. pp. 339-345.
[2] Erzhanov, Z.S., Parchevskii, L.Ya.: Polzhuchesty gornyh
porod Donbassa pri izgibe, Izvestiya
vyschih uchebnyh zavidenii, Gornyi Zhurnal, Moscow, 1958. No.
9.
[3] Gömze, A.L.: Az aprítandó agyagásványok fiziko-mechanikai
tulajdonságai, mint a
simahengerművek dinamikus igénybevételét döntően befolyásoló
tényezők, BME Kiadvány,
“Fiatal oktatók-kutatók II. tudományos fóruma”, Budapest, 1980.
okt. 18.
[4] Gömze, A.L.: Kerámiaipari simahengerművek
hatékonyság-növelésének matematikai alapjai I.,
Építőanyag, 198. 4. sz. pp. 134-140.
[5] Turenko, A.V.: O pererabatyvaemosty plastichnyh glinyanyh
past, Stroitel’nye materialy,
Moscow, 1974. 10. sz. pp. 32-33.
[6] Zolotarskii, A.Z.: Obrabotka glinyanoi massy v val’cah,
Stroitel’nye materialy, Moscow, 1974. 10.
sz. pp. 32-33.
[7] Gömze, A.L.: Az anyagfeladás egyenetlenségének hatása
kerámiaipari simahengerművek
dinamikai igénybevételére, GTE Kiadvány, Miskolc, 1979. pp.
454-458.
[8] Gömze, A.L.: Kerámiaipari simahengerművek vizsgálatának
néhány újabb eredménye, GTE
Kiadvány, Miskolc, 1980. pp. 47-52.
[9] Gömze, A.L.: Turenko, A.V., Nazarov, A: A képlékeny agyag
aprításának matematikai elemzése,
Építőanyag, 1974. 9. sz. pp. 345-348.
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35
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36
Rheological principles of asbestos cement body extrusion
1Gömze, A.L. – 2Eller, E.A. – 2Silenok, S.G.
1University of Miskolc
2University of Civil Engineering, Moscow
(Translated from Hungarian: Azbesztcement masszák
extrudálhatóságának reológiai alapjai)
Published in journal Építőanyag (1982) vol. 34., 1, pp.
17-22.
Abstract
Asbestos cement wall panels were manufactured by extrusion and
the encountered rheological
principles discussed. Laboratory examination showed that
overdose of methyl cellulose plasticizing
agent has an inverse effect: it impairs rheological properties,
especially the effective viscosity of the
body. The effect of deformation velocity upon effective
viscosity is shown by diagrams. During extrusion
the Barus-effect and relaxation most not be neglected either.
The rheology of asbestos cement bodies
of ω˂35% water content can be well described in terms of the
Shwedoff-bodies and with the rheological
equation:
τ =E
2ηp1 1+μ ε ηp1 + τ0 − τ
Keywords: cement, effective viscosity, extrusion, flow rheology,
shear rate, viscosity, yield
1. Introduction
In our days the energy efficiency is one of the most important
criteria on basis of which the
companies or industrial sectors are profitable or have losses.
It is well known that the total
energy demand of building industry is composed from the
following three parts: the required
energy to produce building materials, energy to build and
maintain the buildings, heating and
cooling the buildings in winter and in summer times.
The energy demand for heating and cooling the buildings very
strong depends not only on the
geometrical structures and sizes of the buildings but
thermo-physical properties and
parameters of the used building materials. Recognizing the
importance of thermo-physical
properties of building materials in the last 10-15 years the
thermally isolation properties
became to one of the most important factors during development
the new building materials.
Thanking to this recognition the asbestos cement materials
became into prosperity building
materials in the socialist countries since the beginning of
1970s. These materials have a
relatively small density, heat transparency and have increased
mechanical strength, voice and
liquid (water) isolation properties.
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37
Usage asbestos cement as building material has especially large
importance in the Soviet
Union where the asbestos as raw material available almost
without limitation [1] and has a
large range of different climate regions. Comparing with the
other building materials the
advantages of asbestos cement products are that they have
relatively low density, increased
mechanical strength, fire- and corrosion proof, resist to rot
and blight, more over in dry
condition they have excellent dielectric properties. At the same
time their production requires
only a few energy and labor.
2. New directions in the production of asbestos cement
building
materials
In the building industry the self-supported structural elements
are coming more and more
important among the asbestos cement building materials. This
tendency was very well
represented in the world expo STROIDORMAS’81 and its symposiums
in Moscow in June, 1981.
On this world expo the largest interest for engineers and
specialists aroused the ISPRA –
PADERNO DUGNANO Italian Company’s SIDERCAM product family MILANO
and MAGNUM
products [2]. There was also increased interest to the large
size wall panels with hollows from
the Soviet Union. This Italian firm produce self-supported plus
mechanically loadable asbestos
cement panels (Fig.1.) for roofing with combined technology.
This type of roofing is very
attractive because it doesn’t need holder beams and has
excellent heat and water isolating
properties.
The principle of the combined technology is that the asbestos
cement elements (sheets) are
produced by the traditional methods. Further the sheets are
putting into raised wavy profile
matrices and put on them the steel tapes (Fig.1.a) and lay the
upper asbestos cement sheets
(Fig.1.b.). Finally they are pressed vertically into the raised
wavy profile matrices (Fig.1.c).
After that the pressed panels are cured in autoclave during of
which the upper and lower
sheets came into monolithic structure (Fig.1.d).
Fig.1. Schematic draw of Milano and Magnum
panels
1-steel, 2-asbestos cement, 3-insulator
Fig.2. Schematic draw of the wall panels from
the Soviet Union
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38
The schematic draw of the extruded in the Soviet Union asbestos
cement wall panel is shown
in the Fig.2. The advantages of the extrusion method is that
changing the profile and sizes of
the extruder die the geometrical profile can be changed easily
as desired, meanwhile the
length also can be produce by the consumer requirements.
3. Production of asbestos cement wall panels by extrusion
The extrusion technology in production of asbestos cement wall
panels has already 10-15
years experiences based on the knowledge taken from the
extrusion of ceramic bricks and roof
tiles made from convectional brick clays. Understanding the
importance of rheological
properties of raw materials the extrusion lines and equipment
for production of asbestos
cement wall panels have started with high technological level
comparing with traditional brick
plants.
In spite of that the traditional technological lines are using
asbestos cement suspensions with
water contents W˃60 m%, the water content of the asbestos cement
masses is less than 30%
in the extrusion technology. The extrusion technology has
several advantages comparing with
the traditional technologies like the relatively small (near 0%)
waste water emission, decreased
energy consumption and increased mechanical strength of
products.
During the extrusion technology the asbestos cement pastes
(W˃20%) there are very intensive
homogenization and compaction processes when the materials are
moving to the direction of
the extruder head and a forming process moving through the
extruder die. The schematic
draw of extruder and its main elements is shown in Fig.3 where
the names of the machine
parts are taken from [3].
The advantages of extrusion technology comparing with the
traditional technological
processes are the followings:
- continuous production
- there is no requirements to develop, use and maintain special
metallic forms
- less inquiry of water and no waste water emission
- less costs of environment safety and protection
- increased productivity
- the geometrical profiles can be changed quickly as required by
market
- increased mechanical strength of final products
At the same time during the extrusion of asbestos cement wall
panels we can meet several
problems like material congestion in the funnel, formation of
“wolf tooth” on the surface
especially on the narrow sides, knots and material structuring
and “s” shaped cracks. The
heating of the extruder cylinder and the asbestos cement masses
in it is not harmful because
of the heating the viscosity will decrease considerably thanking
of which the extrudability is
increasing and the required energy consumption of forming is
decreasing.
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39
Fig.3. Schematic draw of extruder
1-funnel, 2-cylinder, 3-screw axis, 4-screw, 5-head
screw, 6-head, 7-die, 8-cavity forming plug
A-feed zone, B-transport and compacting zone, C-
remover zone, D-compacting zone, E-profile forming
zone
Fit.4. Schematic draw of capillary
viscometer
At the same time the mechanical compression and shear stresses
very strong depends on the
geometrical position of mass in the screw channel. Because of
this the application of extrusion
technology has a certain limitation. The over-compacted material
structure can increased the
mechanical strength of final products but unlikely will
considerably decrease their heat
insulator properties.
4. Rheological examination of asbestos cement pastes
From scientific works [1, 4, 5] and [6] we already know that the
asbestos cement pastes with
water-cement ratio w/c˂35% are so called Bingham-Shwedoff
materials and can be
characterized with rheological equation of:
τ − τ0 = ηp1ε (1)
where:
τ – shear stress (Pa),
τ0 – dynamic (static) yield point of the Bingham-Shwedoff paste
(Pa),
ηp1 – plastic viscosity (Pas),
ἐ - shear rate (s-1)
During the investigation of rheological properties of asbestos
cement paste we can take into
consideration only the so-called “effective viscosity” which at
the Bingham material systems
[7] and [8] can be determined through outside and inside
friction ratios and No. consistency
and by the effective viscosity as:
ηe =τ
ε = ηp1 +
τ0
ε (2)
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40
It is obvious from the (2) that increasing the shear rate the
effective viscosity will decrease
proportionally. This phenomenon is very important during
optimization the technological
parameters like geometrical sizes and rpm of extruder screw and
the extrusion process. The
effective viscosity of asbestos cement pastes with water-cement
ratio w/c˂35 m% was
measured on capillary viscometer (Fig.4) the principle of which
is well-known from the
literature [9, 10].
The outside and inside friction ratio of these asbestos cement
pastes were measured on
equipment developed by docent Martynov, V.D. in the Department
of Engineering Equipment
of the University of Civil Engineering in Moscow. At the
constant value of D diameter the shear
rate very strong depended on the values of pressure forces (F),
meanwhile the flow speeds
have depended on temperature (T) and water-cement ratio or water
containment (W). So the
shear rate could be determined as:
ε = Φ(F) (3)
and the effective viscosity as:
ηe = f(ε ; W; T) (4)
It is obvious that at constant value of temperature and water
containment the effective
viscosity only depends on pressure forces (F) and the value of
shear rates:
ηe = f Φ(F) = f ε (5)
Using capillaries with circle cross section the shear rate can
be determined as:
ε = dv
dr=
4Q
πR2=
8v
D (6)
where:
Q – volume of asbestos cement pastes pressed through the
capillaries within a unit time, m3
R and D – the radius and diameter of capillaries, m
v – the speed of the material “bulk” through the capillaries,
m/s
Using capillaries with parallelogram cross section [7] the shear
ratio can be determined as:
ε = dv
dh=
6Q
BH2=
6v
H (7)
and the value of shear stresses developing at the capillary
walls can be determined as:
τ =∆pH
2L (8)
where:
H – thickness of the capillary hole, m
B – width of the capillary hole, m
L – length of the capillary hole, m
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41
For the examination of rheological properties of asbestos cement
pastes were used cements
from factories of Surovsk, Brjansk, Akmjansk and Voskresensk. To
the asbestos cement pastes
were added methyl-cellulose as plasticizer in volume of 0.50,
0.75 and 1.00 m% of cement, and
the measurements were realized at permanent temperature. The
results of experiments are
shown in Fig.5. and Fig.6. as function of shear rates, and in
Fig.7. as function of water
containment.
Fig.5. The effective viscosity as
function of shear rate at methyl-
cellulose plasticizer values of
a-0.50%, b-0.75%, c-1.00%
Fig.6. The effective viscosity as
function of shear rate at constant
value (0.75%) of plasticizers and at
different water containments
Fig.7.The effective viscosity as function
of water containment at different
volumes of methyl-cellulose
plasticizers
It is obvious from Fig. 5 that overdose of methyl-cellulose
plasticizer will increase the value of
effective viscosity with increasing the shear rate. This means
that overdose of methyl-cellulose
will increase not only the production costs but decrease the
efficiency of the extrusion
processes. At water containment W=27.7 m% the lowest values of
effective viscosity were
achieved at volume of 0.50 m% methyl-cellulose on cement. At
this volume ratio of plasticizer
we get the best surface quality of extruded asbestos cement
panels also in the industrial
experiments.
The dependence of effective viscosity of asbestos cement pastes
used for extrusions of wall
panel from water containment is shown in Fig.7. From this figure
it is obvious that increasing
the water containment the values of effective viscosity are
decreasing. At the same time there
is no direct correlation between the volumes of methyl-cellulose
plasticizers and the effective
viscosity, this means that extrusion technology is very
sensitive to the used plasticizers and
their volumes.
It is necessary to mention that the asbestos cement pastes with
water-cement ratio less than
35 m% behave themselves under Barus-effect [11, 12, 13]. This
means that these asbestos
cement pastes after pressing through capillary with diameters D0
will get larger diameter of D1
after a certain time (Fig.8). This Barus-effect after the
extrusion was observed also in the plant
experiments during extrusion of asbestos cement wall panels.
Together with Barus-effect very
often were observed surface defaults and cracks just after the
extrusion process.
The observed Barus-effects during extrusions of asbestos cement
pastes and the accumulated
knowledge in fields of extrusion on convectional brick clays
[14-17] encouraged the Authors to
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42
expand the experiments to find for asbestos cement pastes with
water-cement ratio ≤ 35 m%
the deformation as function of time.
Examining the deformations as function of times of asbestos
cement pastes was found three in
widely different stages of elastic, viscous and plastic
deformation. Very similar deformation
behavior was observed at the convectional brick clays, but the
elastic deformation of the
asbestos cement pastes is considerably larger.
The realized rheological experiments and extrusion processes had
shown that in the plasticized
asbestos cement pastes the relaxation of residual forming
mechanical stresses strong depend
on time. This together with the observed Barus-effect confirm
that asbestos cement pastes
with water-cement containment ≤ 35 m% can be modeling as
Hooke-element connected with
parallel Maxwell and Saint-Venant elements (Fig.9).
Fig.8. The essence of Barus-effect Fig.9. Rheological model of
extrudability
asbestos cement paste
This is the biggest different comparing with the convectional
brick clays where a Hooke-
element is connected with a parallel Newton and Saint-Venant
element. On the basis of
rheological model show in Fig.9 the rheological equation can be
described as materials of
Shwedoff:
τ−τ0
ηp 1+
τ
G= ε (9)
where the shear module is:
G =E
2(1+μ) (10)
In (10): E-the module of elasticity, μ-Poisson ratio of the
material.
After the certain transformation from (9) and (10) the time
dependent shear stress can be
described as:
τ = E
2ηp 1 1+μ (ε ηp1 + τ0 − τ) (11)
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43
The (11) is a complicated rheological equation, based on which
to design the construction and
develop control system for extrusion of asbestos cement panels
looks quite difficult.
5. Conclusions
The realized experiments both investigation of rheological
properties and extrusion process of
wall panels in the industry have shown that the plasticized
asbestos cement pastes with water-
cement ratio ≤ 35 m% have understandable rheological properties
and have good
extrudability. In the same time the quality of extruded wall
panels has depend on several
factors.
One of the most important factors which influence on the quality
of final products is the
rheological properties of the plasticized mass is effective
viscosity. The effective viscosity
includes the plastic viscosity, static yield point and their
relationship to the shear rate.
The realized experiments in accordance to the rheological
properties of plasticized asbestos
cement paste have shown that overdose of plasticizers like
methyl-cellulose and others can
considerably increase the viscosity (Fig.5. and Fig.7.), in
results of which the required energy
consumption of extrusion is increasing unlikely as well as the
qualities like surface, smoothness
and mechanical strength of extruded products are decreasing. In
accordance to the
optimization of geometrical and technological parameters of
extruder machine and extrusion
process it is very important to understand that increasing the
shear rate of plasticized asbestos
cement mass in the extruder channel the effective viscosity
decreasing considerably.
During the rheological tests on capillary viscometer the
Barus-effect was observed. This means
that asbestos cement pastes with water-cement ratio ≤ 35 m% can
be modeling as Shwedoff
material system.
To develop exact mathematical methods and design extruder
machines for production of
asbestos cement panels and other building and constructional
materials further – more
detailed – examinations of rheological and mechanical properties
of plasticized asbestos
cement pastes are necessary.
References
[1] Timasev, V.F., Grizak, Yu.S: Technologia asbestocementnyh
izdelii, Moscow, Stroiizdat, 1970.
p.12.
[2] ISPRA-PADERNO DUGNANO catalogue: SIDERCAM il tetto
pedonabile ISPRA, Milan, 1981. p. 1-
20.
[3] Péter Gy.: Kerámiaipari gépek, Műszaki Könyvkiadó, Budapest,
1974.
[4] Berkovich, T.M., Komarov, V.A.: Formovanie krupnorazmernyh
asbestocementnyh listov iz
koncentrirovannyh suspenzii, Moscow, 1969.
[5] Bernei, I.I.: Osnovy formovanii asbestocementnyh izdelii,
Moscow, 1969.
[6] Valyukov, E.A., Volchek, I.Z.: Proizvodstvo asbestocementnyh
izdelii metodom ekstruzii,
Moscow, 1975.
-
44
[7] Bernhardt, E.: Pererabotka termoplastichnyh materialov,
Goshimisdat, Moscow, 1962.
[8] Wilkonson, W.A.: Nen’yutonovskie zhidkosti. Gidromehanicka,
permesivanie i teploobmen,
“MIR” Moscow, 1964.
[9] Mózes Gy., Vámos E.: Reológia és reometria, Műszaki
Könyvkiadó, Budapest, 1968.
[10] Gorazdovzkii, T.Ya., Sarbatova, L.F.: Eksperimental’nye
metody i principalnye shemy sredstv
reologicheskih issledovanii, Moscow, 1976.
[11] Barus, C.: Proc. Amer. Acad. Arts Sci., Series 2. 19. (No.
27.), 13., 1893.
[12] Barus, c.: Amer. J. Sci., Seris 3, 45. (No. 148.), 87.,
1893.
[13] Merrington, A.C.: Nature, 152, 663., 1943.
[14] Gömze, A.L., Turenko, A.V., Nazarov, A.: A képlékeny agyag
aprításának matematikai elemzése,
Építőanyag, 1974., 9. sz. pp. 348-354.
[15] Gömze, A.L.: Kerámiaipari simahengerművek vizsgálatának
néhány újabb eredménye. GTE
kiadvány, Miskolc, 1979. pp. 454-458.
[16] Gömze, A.L.: Kerámiaipari simahengerművek vizsgálatának
néhány újabb eredménye. GTE
Kiadvány, Miskolc, 1980. pp. 47-52.
[17] Gömze, A.L.: Kerámiaipari simahengerművek méretezésének
specifikus problémái. Építőanyag,
1980. 10. sz., pp. 378-384.
[18] Gömze, A.L.: Az aprítandó agyagásványok fiziko-mechanikai
tulajdonságai, mint a
simahengerművek dinamikus igénybevételét döntően befolyásoló
tényezők. BME Kiadvány,
Budapest, 1980. okt. 18.
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45
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46
Rheological examination of extrudable asbestos cement
bodies
1Gömze, A. L. – 2Eler, E.A.
1University of Miskolc
2University of Civil Engineering, Moscow
(Translated from Hungarian: Extrudálható azbesztcement masszák
reológiai vizsgálata)
Published in journal Építőanyag (1983) vol. 35., 1. pp.
28-34.
Abstract
A newly elaborated and an apparatus developed upon that enabled
the complex rheological texting of
extrudable, plasticized asbestos cement bodies. From the point
of extruding, particularly the design of
extruder parameters, simple Shwedoff- or Bingham-body
characteristics can be attributed to the
asbestos cement body. Most important experimental data concern
density increase under pressure,
effective viscosity and external friction of the body, these
enable to find optimum technological
performance of extruders used for the manufacture of large size
asbestos cement walling materials.
Keywords: asbestos, cement paste, external friction extrusion,
modeling, rheology, shear stress
1. Introduction
To examine and understand the rheological properties of
plasticized asbestos cement bodies
with water containment W=20-30% is necessary for investigation
of extrusion technology and
processes of asbestos cement building materials and wall panels.
The plant experiments of
TOSHIBA wall panel extruder at Voskresensk in the Soviet Union
have made understandable
that supply the market with extruded asbestos cement building
materials of required
geometrical sizes, shapes, surface smoothness and mechanical
properties is possible only on
the basis of knowledge the rheological properties of raw
materials like the plasticized asbestos
cement pastes.
2. The aims of investigations
The rheological properties of cement pastes reinforced with
asbestos fibers are not enough
known until today especially when their water containment is
about W=20-30 m%. This kind of
composite material structure is a very important raw material
for pr
