Content uploaded by Somtobe Olisah
Author content
All content in this area was uploaded by Somtobe Olisah on Feb 23, 2023
Content may be subject to copyright.
Somtobe Olisah MSc Thesis DOI: https://doie.org/10.0223/2023726626
Master Thesis
Investigation of multiple
stressing of cement clinker
in particle beds
by
Somtobe Emmanuel Olisah
Sustainable Mining and Remediation Management
Faculty of Geosciences, Geotechnics and Mining
Matriculation:
59621
February 2019
Supervisors:
1.
Prof. Dr. Carsten Drebenstedt
2.
Prof. Dr.Ing. Urs Peuker
3.
Dr.Ing. Thomas Mütze
4.
MSc. Lieven Schützenmeister
i
Declaration
I hereby affirm that this thesis is a presentation of my original research work.
Where contributions of others are involved, they were clearly indicated with due
reference to the literature and acknowledgments of collaborative research and
discussions.
February 24, 2019 Somtobe Emmanuel Olisah
ii
Acknowledgment
I would like to thank Prof. Dr.Ing Urs Peuker, Dr.Ing Thomas Mtze, and MSc. Lieven
Schützenmeister for the opportunity and guidance I received during this study. I am
grateful for this exposure to another whole new world of research. And to everyone at
MVAT who played a role towards the completion of this work, thank you.
My appreciation goes to Prof. Dr. Carsten Drebenstedt, thank you for your guidance and
for always putting your students’ best interests first. To Dr. Lippmann Günther, Dr. Nils
Hoth and the staff at MoRE, I appreciate your efforts to give the students all the support
they need.
I would like to specially express my immense gratitude to MSc. Lieven Schützenmeister.
His thoroughness and guidance were vital to the completion of this work. Thank you for
your patience in proofreading and correcting this work. I will remain forever grateful.
Lastly, thank you to my wonderful family and amazing friends, your constant support is
ever appreciated.
iii
Table of Contents
DECLARATION ........................................................................................................................................ I
ACKNOWLEDGMENT ............................................................................................................................. II
TABLE OF CONTENTS ............................................................................................................................ III
LIST OF TABLES ...................................................................................................................................... V
LIST OF FIGURES ................................................................................................................................... VI
SYMBOL DIRECTORY .......................................................................................................................... VIII
ABSTRACT ............................................................................................................................................. X
1 INTRODUCTION ............................................................................................................................ 1
1.1 BACKGROUND ............................................................................................................................... 1
1.2 SCOPE OF WORK ............................................................................................................................ 2
1.2.1 Influence of Grinding Pressure on Comminution using HPGR .............................................. 2
1.2.2 Simulation of HPGR Grinding Circuit Using PistonDie ......................................................... 3
1.2.3 Grindability Tests According to Zeisel ................................................................................... 3
2 LITERATURE REVIEW .................................................................................................................... 4
2.1 STRESS AND PARTICLE BREAKAGE ...................................................................................................... 6
2.1.1 Stress on Individual Particles ................................................................................................ 7
2.1.2 Stress on a Particle Bed ...................................................................................................... 12
2.2 COMPACTION .............................................................................................................................. 17
2.3 MULTIPLE STRESSING OF SOLID PARTICLES ........................................................................................ 19
3 MATERIAL AND METHODS ..........................................................................................................21
3.1 MATERIAL CHARACTERIZATION ....................................................................................................... 21
3.2 APPARATUS/EQUIPMENT AND PROCESSES ........................................................................................ 23
3.2.1 PistonDie Press .................................................................................................................. 23
3.2.2 Rollbock Machine ............................................................................................................... 24
3.2.3 Sieving and Particle Size Distribution Analyses .................................................................. 25
3.2.4 Laser Diffraction ................................................................................................................. 30
3.2.5 Zeisel Grindability Tests ...................................................................................................... 31
3.2.6 Grinding Circuit Simulation using PistonDie Tests ............................................................. 36
4 RESULTS AND DISCUSSION ..........................................................................................................37
4.1 PISTONDIE TESTS AT DIFFERENT GRINDING PRESSURES ...................................................................... 37
4.2 PISTONDIE GRINDING CIRCUIT TESTS .............................................................................................. 45
iv
4.2.1 Grinding Circuit Simulation ................................................................................................. 45
4.2.2 Particle Size Distribution Curve ........................................................................................... 47
4.2.3 HPGR ScaleUp Using PistonDie Grindability Data ............................................................ 48
4.3 BALLMILL GRINDABILITY TEST ACCORDING TO ZEISEL ........................................................................ 57
4.3.1 Ball Mill ScaleUp Using Zeisel Data ................................................................................... 59
4.4 DISCUSSION ................................................................................................................................ 67
5 SUMMARY AND CONCLUSION ....................................................................................................69
BIBLIOGRAPHY .....................................................................................................................................72
APPENDIX ............................................................................................................................................82
v
List of Tables
TABLE 1.1 PRESSURE INTERVALS USED IN PISTONDIE TESTS OF BOTH CLINKERS ......................................... 2
TABLE 3.1 CHEMICALMINERALOGICAL COMPOSITION OF CLINKER SAMPLE USED ANALYSED USING XRD 21
TABLE 3.2 DENSITY AND SHAPE OF STRESSED AND UNSTRESSED CLINKER USED IN THIS STUDY ................. 22
TABLE 3.3 PARAMETER VALUES FOR ZEISEL GRINDABILITY TESTS [7] ....................................................... 33
TABLE 4.1 GRINDING CIRCUIT DATA OF UNSTRESSED CLINKER, STOP CRITERION REACHED AFTER 4 CYCLES
.......................................................................................................................................................... 46
TABLE 4.2 GRINDING CIRCUIT DATA OF STRESSED CLINKER, STOP CRITERION REACHED AFTER 4 CYCLES.. 46
TABLE 4.3 MEASURED ENERGY ABSORPTION FOR EACH GRINDING CYCLE .................................................. 48
TABLE 4.4 SIZING PARAMETERS FOR HPGR SCALEUP [67] ....................................................................... 49
TABLE 4.5 SIZING PARAMETERS FOR BALL MILL SCALEUP ADOPTED FROM [73] ..................................... 59
TABLE 4.6 FACTOR C(Φ) [KW/(T.M)] AS RELATED TO MILL LOADING FACTOR AND TYPE OF GRINDING
MEDIA [73] ........................................................................................................................................ 60
TABLE 5.1 COMPARING THE MAJOR PARAMETERS CALCULATED FROM SCALEUP OF HPGR & ZEISEL TESTS
.......................................................................................................................................................... 70
TABLE 0.1 SIEVE ANALYSIS RESULTS FOR ALL GRINDING PRESSURES OF STRESSED CLINKER (PART 1) ....... 83
TABLE 0.2 SIEVE ANALYSIS RESULTS FOR ALL GRINDING PRESSURES OF STRESSED CLINKER (PART 2) ....... 84
TABLE 0.3 SIEVE ANALYSIS RESULTS FOR ALL GRINDING PRESSURES OF UNSTRESSED CLINKER (PART 1) .. 85
TABLE 0.4 SIEVE ANALYSIS RESULTS FOR ALL GRINDING PRESSURES OF UNSTRESSED CLINKER (PART 2) .. 86
TABLE 0.5 LASER DIFFRACTION RESULTS FOR MATERIALS < 315 µM OF STRESSED CLINKER....................... 87
TABLE 0.6 LASER DIFFRACTION RESULTS FOR MATERIALS < 315 µM OF UNSTRESSED CLINKER .................. 88
TABLE 0.7 COMBINED LASER DIFFRACTION AND SIEVE ANALYSES RESULTS FOR UNSTRESSED CLINKER .... 89
TABLE 0.8 COMBINED LASER DIFFRACTION AND SIEVE ANALYSES RESULTS FOR STRESSED CLINKER ......... 90
TABLE 0.9 PSD OF BOTH CLINKERS AFTER CONSTANT GRINDING POINT HAS BEEN REACHED IN THE 4TH
CYCLE ................................................................................................................................................ 91
TABLE 0.10 LASER DIFFRACTION RESULTS OF PARTICLES < 100 µM FOR BOTH CLINKERS ........................... 92
TABLE 0.11 ALL RESULTS FROM HPGR SCALEUP CALCULATIONS ............................................................ 93
TABLE 0.12 DATA FROM BLAINE MEASUREMENT OF BOTH CLINKERS USED TO DETERMINE THE SPECIFIC
ENERGY CONSUMPTION FOR GRINDING TO 3040 CM2/G ...................................................................... 98
vi
List of Figures
FIGURE 2.1 SCHEMATIC OF AN HPGR SHOWING GAP BETWEEN ROLLS’,ACCELERATION, GRINDING &
RELAXATION ZONES FROM [2]............................................................................................................. 4
FIGURE 2.2 PHASES LEADING TO PARTICLE BREAKAGE [19] ......................................................................... 6
FIGURE 2.3 STRESSSTRAIN CURVES FOR (A) LINEAR AND (B) NONLINEAR ELASTIC DEFORMATION
BEHAVIOUR, ADAPTED FROM [19, 23] .................................................................................................. 8
FIGURE 2.4 STRESSSTRAIN CURVES FOR: (A) INELASTIC AND (B) ELASTIC DEFORMATIONAL BEHAVIOUR
MODIFIED FROM [19] ........................................................................................................................... 9
FIGURE 2.5 : COMPRESSIVE LOADING OF SPHERES AND IRREGULARLY SHAPED PARTICLES: [1 PRIMARY
FRACTURES, 2 = SECONDARY FRACTURES (FINE MATERIAL RANGE)] [26] [27].................................... 9
FIGURE 2.6 CHARACTERISTIC FRACTURE PHENOMENA A) SMASHING B) CRUMBLING C) ABRASION [26] [23]
.......................................................................................................................................................... 11
FIGURE 2.7 COORDINATION NUMBER AND PORE NUMBER DEPENDENCE FOR SPHERES OF THE SAME SIZE
FROM [34] .......................................................................................................................................... 12
FIGURE 2.8 BULK DENSITY DISTRIBUTION (G/CM³) IN A MATERIAL BED AXIALLY STRESSED FROM ABOVE
[35] ................................................................................................................................................... 13
FIGURE 2.9 FORCEDISPLACEMENT CURVE FOR A PARTICLE BED LOADING ................................................. 14
FIGURE 2.10 PARTICLE SIZE DISTRIBUTION OF THE INITIAL FRACTION AND AFTER A SINGLE GRAIN AND
PARTICLE BED LOADING OF QUARTZ (A/M ENERGY ABSORPTION) [21, 38] ....................................... 16
FIGURE 2.11 SUBPROCESSES DURING COMPACTION OF A PARTICLE BED MODIFIED FROM [44] [45] .......... 17
FIGURE 2.12 PLASTIC DEFORMATION DURING LOADING MODIFIED FROM [44] [45] ..................................... 18
FIGURE 2.13 FORCEDISPLACEMENT CURVE WITH CORRECTED PRESS TRAVEL SCORR FROM A LINEARLY
ADJUSTED RELIEF CURVE ACCORDING TO [43] ................................................................................... 18
FIGURE 2.14 THE EFFECT OF WEAKENING DUE TO DAMAGE ACCUMULATION FROM REPEATED LOADING
EVENTS ( [53] .................................................................................................................................... 20
FIGURE 3.1 PARTICLE SIZE DISTRIBUTION OF INITIAL POLYDISPERSED CLINKER AND THE EXTRACTED
MONODISPERSED FRACTION USED FOR TEST WORK ............................................................................ 22
FIGURE 3.2 SCHEMATIC REPRESENTATION OF THE SHIMADZU HYDRAULIC PRESS [54]) .............................. 23
FIGURE 3.3 DIMENSIONS OF THE RUBBER STOPPER ..................................................................................... 24
FIGURE 3.4 THE ROLLBOCK MACHINE AT THE MVTAT LAB, TUBAF ........................................................ 24
FIGURE 3.5 (A) ILLUSTRATION OF SIEVE ANALYSIS[Q3(X)] [56] AND (B) SIEVE TOWER WITH R10 SIEVE SIZES
ON A SHAKER ..................................................................................................................................... 25
vii
FIGURE 3.6 (A) PARTICLES SORTED INTO SIZE CLASSES AND (B) PARTICLE SIZE INTERVALS [56] ................ 26
FIGURE 3.7 PSD CURVE SHOWING THE MEDIAN, X50 MODIFIED FROM [56] ................................................. 28
FIGURE 3.8 CUMULATIVE SUM FUNCTION COMPARISON OF DIFFERENT PSD CURVES MODIFIED FROM [56] 29
FIGURE 3.9 PLOT OF RRSB DISTRIBUTION CURVE ADAPTED FROM [56] ...................................................... 30
FIGURE 3.10 A SECTIONAL VIEW OF THE GRINDING BOWL (ABOVE) AND (BELOW) GRINDING BOWL PLACED
ON THE PIVOTMOUNTED TABLE MODIFIED FROM [7] ......................................................................... 32
FIGURE 3.11 THE BLAINE DEVICE SCHEMATIC [58] .................................................................................... 35
FIGURE 4.1 PRODUCT PSD CURVES FOR ALL GRINDING PRESSURES OF UNSTRESSED CLINKER ................... 37
FIGURE 4.2 PRODUCT PSD CURVES FOR ALL GRINDING PRESSURES OF STRESSED CLINKER ........................ 38
FIGURE 4.3 COMPARING THE PRODUCT PSD CURVES OF SELECTED GRINDING PRESSURE FOR BOTH
CLINKERS .......................................................................................................................................... 39
FIGURE 4.4 PLOT OF X50 OVER PRESSURE FOR BOTH CLINKERS .................................................................. 40
FIGURE 4.5 COMMINUTION RATIO PLOTTED OVER PRESSURE FOR BOTH CLINKERS ..................................... 41
FIGURE 4.6 ENERGY ABSORPTION FOR EACH GRINDING EVENT CORRESPONDING TO THE GRINDING
PRESSURES......................................................................................................................................... 42
FIGURE 4.7 COMPRESSION FOR EACH GRINDING EVENT AGAINST THE CORRESPONDING PRESSURES ........... 44
FIGURE 4.8 PSD CURVES FOR THE GRINDING CIRCUIT TEST PRODUCTS OF BOTH CLINKERS ........................ 47
FIGURE 4.9 ZEISEL GRINDABILITY PLOT OF SPECIFIC ENERGY CONSUMPTION OVER BLAINE FOR UNSTRESSED
CLINKER ............................................................................................................................................ 57
FIGURE 4.10 ZEISEL GRINDABILITY PLOT OF SPECIFIC ENERGY CONSUMPTION OVER BLAINE FOR STRESSED
CLINKER ............................................................................................................................................ 58
FIGURE 4.11 RRSB TEST: COMPARISON OF THE PSD OF GROUND CLINKER WITH THE RRSB DISTRIBUTION
.......................................................................................................................................................... 61
FIGURE 4.12 RRSB TEST: COMPARISON OF THE PSD OF CLINKER PRODUCT WITH NEW PARAMETERS OF THE
RRSB R² DISTRIBUTION .................................................................................................................... 62
viii
Symbol Directory
Modulus of elasticity
C (
)
Filling ratio
L/D
Length–Diameter ratio
Cr
Comminution Ratio
XRD
XRay Diffraction
Mi
Material index related to ore’s breakage property
Em,z
Energy required to grind clinkers to certain fineness during Zeisel test
Em,BM
Energy required to grind clinkers to a certain fineness during ball milling
ft
Conversion factor / transfer function
R90
Fineness value of mesh size 90 µm in percent
X63.2
Position parameter
VBM
Mill volume
mB
Mass of the grinding media
mdot
Width of the particle distribution / specific throughput
M
Throughput
S
Thickness of cakes / working gap
P
Power consumption of the ball mill
Pshaft
Power consumption (shaft)
Pz
Power consumption (counter)
K
Expansion constant
D
Diameter of the ball mill/rolls
L
Length of the ball mill/rolls
Q(x,Esp)
Particle size distribution function as a function of specific energy input
Q(x)
Particle size distribution
Fsp
Specific grinding force
ix
F
Grinding force
Relative speed
Critical speed
Density of cakes
Density of feed
ρmax
Maximum specific grinding pressure
Clinker subscript
Spec. free boundary energy
Lattice constant
σ
Tensile stress
ԑ
Strain
αk
Angle of compression
Quantity proportions
Ɵ
Standard compaction
U
Recycling load factor/Circulation factor
Ψ
circumferential speed of rolls
Β
Angle of force
x
Abstract
When material particles are stressed without breaking the tend to develop microcracks
which should make subsequent comminution easier and more efficient. This study
focuses on this by observing how prestressed cement clinker behaves under
comminution in comparison to the normal unstressed clinker. Both clinkers are stressed
under various pressure levels from 25 MPa to 200 MPa to obtain a wide range of results
for this investigation. This study also looks at the energy efficiency of the HPGR and the
ball mill. To this effect, Zeisel tests and grinding circuit tests are carried out using the ball
mill and pistondie press respectively. Further scaleup calculations are done for both the
HPGR and ball mill, to predict the dimensions and energy requirements for producing
200 t/h of the cement CEM I 32.5 R. Though some of the results were inconsistent owing
to errors perceived to have been equipmentrelated, the prestressed clinker grinds better
than the unstressed clinker at each pressure level suggesting higher efficiency. The ball
mill was generally found to require almost 5 times more energy to grind to finish than
HPGR. The use of a hybrid system involving HPGR and subsequent comminution by ball
mill is also observed to be more energy efficient than the ball mill only.
1
1 Introduction
1.1 Background
HighPressure Grinding Rolls (HPGR) technology was developed by the late Prof. K.
Schönert and his colleagues during their fundamental studies on interparticle breakage
[1]. Through the years it has kept advancing technically and has in recent times been
accepted as the standard technology for some ore industries [2, 3]. Over the last couple
of decades, HighPressure Grinding Rolls (HPGR) has been integrated into cement
grinding circuits worldwide, but still require attention in research. One major research
purpose is the development of a reliable model, which describes the function of HPGR as
accurately as possible.
The main focus of HPGR modelling is to predict the grinding result. Since grinding in
practice is usually carried out in circuit operations, most grains are subjected to multiple
stressing events in HPGR applications. The highpressure stressing leads to particle
fractures as well as a large number of microcracks in the material structure. These defects
reduce the energy required for further comminution. The present thesis is intended to
investigate this influence on clinker grinding using pistondie press tests. The influence
of previous stresses on the compaction process should also be taken into account.
HPGR owes its wide range of applications, both in the cement industry and the ore
industry at large primarily, to its great energysaving potential. According to Fuerstenau
& Kapur [4], the mobility or confinement of the materials being comminuted determines
the energy efficiency of the method used. The application of particlebed breakage during
comminution was found to increase the energy efficiency [5]. In this study,
supplementary Zeisel tests are carried out on a ball mill with the intension of comparing
and rating the energy requirements of this processes with that of HPGR. With a view to
further optimizing the sustainability of cement plants, the results obtained are used to
investigate the possibility of reducing the grinding pressure and in turn, the associated
energysaving potential.
2
1.2 Scope of Work
This study was aimed at carrying out three sets of experiments in order to achieve set
objectives. The first are tests on the pistondie press to determine the influence of grinding
pressure on particle comminution and also to examine the influence of preweakening of
particles by repeated stressing in particle comminution. The second test is the simulation
of HPGR grinding circuit using the pistondie and the third test is the grindability tests
according to Zeisel. Both second and third tests are used for scaleup of HPGR and ball
mill respectively to compare the energy efficiency of both processes. The tests involved
the prestressed and unstressed batches of monodisperse clinkers. For comparability, both
clinkers were of same type. The stressed clinker were gotten by grinding and sieving
larger particle sizes of the same clinker.
1.2.1 Influence of Grinding Pressure on Comminution using HPGR
Operating pressure of HPGR is the major parameter that determines the result of a
comminution process. As the pressing force is increased, there is a corresponding increase
in the intensity of comminution. However, if the pressure is too high, this could create
very hard flakes that are hard to disintegrate during the deagglomeration process hence
affecting the comminution results [6]. To examine this effect of pressure on comminution,
this experiment was carried out eight separate times for both samples used with pressures
from 25 MPa to 200 MPa (see table 1.1). Further comparison of the comminution results
was made to observe the influence of multiple stressing on the comminution products.
Table 1.1 Pressure intervals used in pistondie tests of both clinkers
Pressure (MPa)
Pressure (Pa)
Force (N)
25
25000000
63794
50
50000000
127588
75
75000000
191382
100
100000000
255176
125
125000000
318970
150
150000000
382764
175
175000000
446558
200
200000000
510352
3
1.2.2 Simulation of HPGR Grinding Circuit Using PistonDie
The simulation of grinding circuit was done using the pistondie to evaluate the energy
efficiency of the HPGR. In addition to comparing the energy requirement for both
clinkers to grind to finish product, the results are compared with similar results from the
ball mill tests for efficiency. For this purpose, scaleup calculations are done to determine
a number of HPGR operating parameters including:
• Length, L of roll
• Diameter, D of roll
• Specific throughput, mdot
• Angle of compression,
• Power consumption, P
• Specific grinding force, FSP
• Energy consumption, Em
1.2.3 Grindability Tests According to Zeisel
Grindability tests are means of determining system properties because these properties
influence the outcome of material comminution [7]. Grindability tests according to Zeisel
were carried out on both clinkers using the ball mill. Ball mills are however known to be
energy inefficient because of the energy lost as heat and wear when the tumbling mass of
balls create friction which transmits the input energy to the unconfined particles. Thus,
the results of this test are used in a comparative study (with the grinding circuit results in
section 1.2.2) to optimize the energy requirements for cement production. Scaleup
parameters of ball mill calculated include:
• Factor of transfer, ft
• Mass of grinding media, mB
• Energy consumption, Em,BM
• Length, L of the ball
• Diameter, D of the ball
• Speed, n of the ball
• Power consumption, P
4
2 Literature Review
High Pressure Grinding Rolls (HPGR) has become increasingly popular over the past
decade due to its great potential of improving capacity and improving energy
consumption in a grinding circuit ( [8, 9, 10]. In high pressure grinding rolls, comminution
occurs as a result of high interparticle stresses that are generated when a bed of material
is compressed as it moves through the gap between two pressurized rolls this high inter
particle stresses result in a much higher amount of fines when compared to conventional
crushing [10]. Figure 2.1 shows the basic schematic of the HPGR consisting of two rolls;
both rotating in a counter direction at the same speed. The floating roll is mounted in a
way that it is floating thereby pressing against the fixed roll. While working, the material
is fed into the system using the feed hopper and comminution occurs when the particles
pass through the multiple zones. The feed first goes into the acceleration zone while
always maintaining the minimum volume of material in the hopper. Then the material is
moved into the next zone where the particle bed breaks under high pressure and is
compacted in the process. The highest pressure acting on the material at this stage is
always compaction angles less than the force acting angle. As the material proceeds down
the HPGR the bulk density increases. The compression zone begins at the mark of the nip
angle and this is where interparticle breakage really occurs as the particle bed experiences
the highest grinding pressure here.
Figure 2.1 Schematic of an HPGR showing gap between rolls’,acceleration,
grinding & relaxation zones from [2]
5
The area with the least distance between the two rolls is known as the working gap and
the compression zone stops here. On the other side of the working gap is the critical gap
and it is defined by the nip angle. Certain factors influence the nip angle and they include
the roll speed, the roll surface pattern and the properties of the material [2]. Despite
pressure being the main stressing factor in HPGR, shearing also occurs as a result of
movement of the material through the system and the rotation of the rolls. According to
[100], larger mineral grains and coarse clinker grains requires more energy for it is
grindability as compared to smaller mineral grains and fine clinker grains.
HPGR has been found to be of great use in the cement industry as a pregrinding process
prior to conventional ball milling in a process referred to as Hybrid mode. This mode is
made effective by the combination of the energy efficient properties of highpressure
grinding and the ability of the ball mill to achieve high reduction ratios. According to
Schnert [8], the success of the hybrid method of grinding would be dependent on HPGR
already producing fraction of the circuit product and also weakening the particles which
remain unbroken.
The energy efficiency of the HPGRBall mill mode has been related to two major reasons.
First, HPGR consumes much less energy during low degrees of size reduction ratio as a
result of its compressive loading mechanism as opposed to its counterpart [11]. This has
also been the advantage of HPGR being used as pregrinder before ball milling. Despite
this advantage, HPGR is not widespread in the cement industry for finish grinding
because the cement product tends to have weaker binding characteristics [12]. The second
reason for the high efficiency is correlated to the external stresses applied by the grinding
rolls on the particle bed. The common conclusion by most researches is that during a
HPGR process, the effect of these external stresses damages the particles at various
degrees using high interparticular stresses that induce microcracks in particles [13, 14,
15, 16]. Subsequently, as a result of these microcracks, the damaged particles tend to
grind from certain feed size to a certain product size with a much lower energy
requirement [11, 17]
In order to form a basis for understanding and evaluating results obtained during this
study, some theoretical principles are discussed based on literature research. The
following subsections discuss stress, compaction and comminution with respect to the
6
behavioural properties of cement clinkers. Advanced knowledge in each case are treated
more specifically at necessary points during evaluation and discussion of results.
2.1 Stress and Particle Breakage
The basis for stressing on a particle bed is the simultaneous stressing of many individual
particles. A particle is deformed when an external force is applied to it, this leads to stress
being developed within the particle. When this developed stress exceeds to ultimate
stress, the said particle will break [18]. As shown in figure 2.2 below, combination of
actions of external loads and energy input results in deformation of particles leading to
breakage.
Figure 2.2 Phases leading to Particle breakage [19]
In his publication, [20] distinguished four main mechanisms through which a required
force and energy can be brought to a body to be stressed. These include:
a. Between two solid body surfaces
b. On a single surface: Impact Stress
c. Not acting on a solid surface: Mechanical energy introduction through the
surrounding medium.
d. Nonmechanical introduction of energy: Thermal and radiative stress/ blasting.
In both mechanisms (a) and (b) distinguished above, particles are stressed on solid body
surfaces. However, the difference between both mechanisms are of a fundamental nature
as the energy supplied during mechanism (b) depends on the movement made by the
7
stressed particles themselves and consequently the intensity and speed of the stress cannot
be set independently of each other. This is possible on the other hand with mechanism (a)
by means of either the applied movement of two pressure surfaces or through variation
of mass. Mechanisms (c) and (d) are differentiated by the nonmechanical methods of
energy introduction to the body. The mechanical means for energy introduction are
mostly based on the fact that pressure and shear forces are exerted on the particle surface
by the surrounding medium caused by current flow, sound stress or liquid impact [20].
Comminution
When crushing, the dispersity state of a system changes by overcoming binding forces. It
is naturally the principal aim of the material bed crushing process and is therefore in
opposition to the parallel compaction process. Comminution is determined by the actions
on and within the individual particles. Each individual particle is first deformed and
broken as soon as the deformation exceeds a certain stress limit [21]. The interactions of
the individual particles with their surrounding then have a significant influence on the
result of the process. These interactions could be that with adjacent solid surfaces and
fluid contained within the bed or the possibility for the particles to escape the stress. In
order to crush a solid, stresses must be exerted on the body to overcome the bonds at the
atomic level. There is never an ideal crystal lattice, but the solid has macroscopic,
microscopic or submicroscopic defects of all kinds, which lead to a lower breaking stress
than theoretically calculable. Local stress peaks with a high energy concentration are
located at these socalled inhomogeneity points, which is why the fracture forms and
spreads further at these weak points [22].
To understand this better, an overview of stress on individual particles is first looked at
followed by stress on a particle bed.
2.1.1 Stress on Individual Particles
A stress leads to an energy input by means of contact points, causing a threedimensional
state of stress to be formed within the particle, thereby deforming it. The behaviour of the
material during deformation can be illustrated with the aid of stressstrain curves (Figure
2.3 a and b) and is divided into the limit cases: Elastic, Plastic and Viscoelastic.
8
Figure 2.3 StressStrain curves for (a) Linear and (b) NonLinear elastic
deformation behaviour, adapted from [19, 23]
The area below the stressstrain curve is a measure of the energy, E introduced during
loading or recovered during unloading. This energy, E is given by the equation:
Equation 1
Where: = tensile stress
= strain
A linearelastic deformation is reversible, proportional to the external load, and
independent of time (figure 2.3a). Nevertheless, there are nonlinear elastic deformations
which are not proportional to the external load but are also reversible (figure 2.3b). An
inelastic deformation occurs if the loading and unloading curves do not coincide during
a reversible deformation (figure 2.4a). In this case, a part of the introduced energy is
dissipated, which can be seen in the stressstrain diagram from the area between the
loading and unloading curves [24].
9
Figure 2.4 StressStrain curves for: (a) Inelastic and (b) Elastic deformational
behaviour modified from [19]
Plastic deformation behaviour is characterized by time independence and irreversibility.
Thus, the deformation is preserved after the load is reduced due to the displaced bonds
between the atoms (figure 2.4b). Materials with time and temperaturedependent E
behave in a viscoelastic manner. Rapid loads and low temperatures tend to lead to
embrittlement, and this results in high stresses within the material even at low
deformations [24].
Contact Geometry is another major influence on Stress behaviour. As illustrated in figure
2.5 below, a sphere and an irregular particle are placed between two stress components
subjecting each particle to compressive stress. The sphere is loaded by the stress surfaces
at only two points while on the other hand, the irregular particle has at least four contact
points in order to maintain it at a stable position. As a result of the higher number of
contact points, the areas where force is transmitted increases, while the stress in the
contact areas is reduced [25].
Figure 2.5 : Compressive loading of spheres and irregularly shaped particles: [1
Primary fractures, 2 = Secondary fractures (fine material range)] [26] [27]
10
Additionally, adhesive forces between the fixed surfaces must not be neglected because
they effect tension at the contact points. It is then deformed into surface contact thereby
causing stress distribution in the area around the point of contact [26, 27]. The energy
density at the contact point is found to be higher and leads to secondary fractures [28, 29].
Single Particle Comminution
Single particle comminution describes the comminution of individual solid particles and
this was investigated with regard to the type, intensity and speed of the stress while being
described by comparing the fragments with the initial particles [30]. In comminution, the
stress energy, EB is distinguished from the comminution energy, EZ. The former
comprises the total energy input during the stressing while the latter only the energy
converted to fracture [22]. For comminution, the stress energy must therefore be as high
as the comminution energy. In order to ensure comminution on a technical scale, much
more than just the comminution energy is often provided. Excess supply causes an
increase in secondary and thus less effective breakage events or additional heat losses
[31].
The relative velocity between the particles and the stressing solid surface is called the
Stress velocity. The stress velocity can be adjusted independently to the intensity of the
compressive stress. When impact loading is considered, the two parameters remain
interdependent. The stress intensity is proportional to the square of the stress velocity
[20].
The surrounding medium can be in liquid or gaseous phase and its effects include:
a. the friction between the particles and the solid surface
b. the liability of the fragments
c. fracture formation, crack propagation and interfacial energy
d. elastic and plastic properties of the material.
The characteristic fracture phenomena and other characteristic values derived from them
are used to describe the success of comminution. These characteristics include the
breakage function B, selection fraction S, fracture probability P, massrelated specific
11
energy absorption Em, massrelated specific surface gain ΔSm and the energyrelated
surface gain EA, which is also referred to as energy utilization.
Figure 2.6 Characteristic fracture phenomena a) Smashing b) Crumbling c)
Abrasion [26] [23]
The characteristic fracture phenomena have three stages as shown in figure 2.6 above and
they include: Abrasion, Cleavage and Shattering. If only abrasion occurs, only partial
areas, for example roughness elevations, are rubbed off on the surface and the particle
almost completely retains its initial size. If the intensity is increased, corners and edges
will crumble. If the stress intensity is further increased, the particle is shattered, the
fracture surfaces expand over the entire particle and several particles smaller than the
initial size are produced [22].
12
2.1.2 Stress on a Particle Bed
When a particle bed is placed under stress, the external load acting on it affects a large
number of particles and the load is further transmitted over a corresponding number of
contact points. The particles found at the edge of the particle bed are loaded by both the
bed confining boundary and adjacent particles while within the particle bed load is
exclusively applied by adjacent particles. Since these particles found at edge of the
particle bed have comparatively fewer particles surrounding them resulting in fewer load
application points, the stress distribution in the contact areas of the particles at the edge
of the particle bed differs from that in the inner areas of the particle bed. As a result, the
position of the individual particle in the particle bed is decisive for its load, and the
geometrical limitation of the particle bed is one of the main influencing factors of the
particle bed load [32]. The number of points of contact a particle has with its neighbouring
particles is indicated by the Coordination Number, k [33]. This coordination number is
dependent on the ratio of void volume to solid volume, also referred to as the pore
number. As shown in figure 2.7 below an example of this using monodisperse balls. The
smaller the cavity volume, the larger the number of particle contacts and the greater the
resistance to further compaction [34]. Furthermore, increased number of contact points
leads to an increase in loss of friction and more of the absorbed stress is consequently
distributed through the contacts. For this reason, it is no longer possible to achieve
breaking strengths locally.
Figure 2.7 Coordination number and pore number dependence for spheres of the
same size from [34]
13
Figure 2.8 below shows the section through a cylindrical, closed particle bed which is
subjected to uniaxial pressure. The highest compression and hence the highest stresses
occur at the edge of the press plunger [35, 23]. This edge effect is due to the friction of
the material against the bounding walls. As a result, the lowest density and therefore the
lowest stresses occur at the lower edge of the material bed at the greatest distance from
the centre of the punch. [5] postulated that an ideal particle bed in a pistondie should
have these four characteristics:
a. Homogenous structure
b. Homogenous compaction
c. Known mass or volume of the compressed particles
d. Wall effects are negligible in comparison to the general sizereduction effect.
Figure 2.8 Bulk density distribution (g/cm³) in a material bed axially stressed
from above [35]
As the crosssectional drawing shows, the stress conditions in the interior of a particle
bed represent a complex problem that is difficult to measure. Until the 1990s, the loading
of particle beds was therefore mostly described using integral parameters and
supplemented with knowledge of the loading behaviour of individual particles. Similar to
the stressstrain curves of individual particles, forcedisplacement curves are recorded
during particle bed loading. These usually rise in a nearflat manner at the beginning and
14
increasingly steeper at higher loads (as seen in figure 2.9 below). The more finegrained
and thus more numerous the stressed particles are, the smoother the curves will be [36].
Figure 2.9 Forcedisplacement curve for a particle bed loading
The most important integral parameters for particle bed loading are the maximum
pressure and the massrelated energy absorption. The maximum pressing pressure, pmax
describes the ratio of the maximum external force, Fmax to the crosssectional area of the
particle bed, Apb.
pmax=Fmax
Apb
Equation 2
The energy absorption describes the ratio of the energy absorbed by the material to the
loaded or crushed solid mass. The absorbed energy is calculated analogously to Equation
1 from the area which is included in the forcedisplacement curves for loading and
relieving as well as the abscissa.
Equation 3
15
Where EV = volume specific energy absorption
M = mass
ρs = solid density
FB(s) = forcedisplacement curve during loading
FE(s) = forcedisplacement curve during relieving
For fracture mechanics, the volumerelated energy absorption represents the reference
value. For comminution, however, the massrelated term is more commonly used.
Irrespective of the terminology, energy absorption summarizes the energy consumption
of all microprocesses that occur during particle bed loading [37]. As clinker is a brittle
breaking material, plastic deformation takes on a rather subordinate role in its
comminution. With a decrease in its particle size, the proportion of plastic deformation
increases accordingly. The proportion of friction losses depends on the width of the
distribution, the number of contacts and the size of the particles [22].
Particle Bed Comminution
During comminution of materials in a particle bed, a large number of particles rather than
individual particles are stressed. The interactions between the particles and with the
confining structure have a considerable influence [38, 39, 40]. For the interactions, the
particles do not have to touch each other at the beginning of the loading [5]. Thus, the so
called single grain layer, which consists of particles of the same size, x, also belongs to
the particle beds. These particles have a very small distance (<2x) and only influence each
other at breakage. As in the case of single grain layers, individual coarse particles can
also come into contact with the upper and lower limits of the particle bed in flat
polydisperse particle beds. However, the direct contact of a particle with both surfaces is
often ruled out during the comminution of particle beds.
The progress of comminution in a particle bed is described in the same way as for single
particle comminution by changing the particle size. The breakage function, the selection
function, the specific surface growth and the energy utilization can be determined from
the change of the particle size distribution. The specific surface growth and thus
16
calculable energy utilization react sensitively to changes in the finegrain range, while the
coarser particle size ranges are not fully captured [21].
The percentage and function of the fracture do not depend on the changes in the fine grain
range. By stating how a broken particle is defined, these formulas also neglect the coarser
range. A particle can be broken but still so large that it fits into the initial fraction [21].
Figure 2.10 Particle size distribution of the initial fraction and after a single
grain and particle bed loading of quartz (A/M energy absorption) [21, 38]
In figure 2.10 above, the particle size distribution of a quartz fraction is compared after a
single grain and after a particle bed load. In the case of single particle size reduction, only
the really broken particles are listed. For particle bed loading, the curve consists of a
mixture of crushed and uncrushed material [21]. The distribution is more coarsegrained
since in a particle bed the energy distribution takes place through a larger number of
particle contacts and fewer fractures occur. In wide distributions, the small particles
protect the larger ones by dissipating the energy, which makes the comminution of the
large particles more difficult [41]. The main factors influencing the comminution of the
material bed are the stress intensity, the particle size and shape and the width of the initial
distribution, the material, stress speed and the dimensions of the material bed. Studies by
Göll [42] on influence of different materials during comminution show that the most
significant influence on comminution was exerted by the stress intensity.
17
2.2 Compaction
Compaction occurs when a particle bed is placed under pressure causing the particles to
rearrange and deform resulting in a tighter and denser packing and thereby increasing
solidification [43]. During the process, the highest degree of compaction occurs at the
edge of the pressure plunger. Hence, compaction reduces as the distance increases from
the edge of the plunger and from the centre of the particle bed. Figure 2.11 below shows
the subprocesses during the loading of a particle bed.
Figure 2.11 Subprocesses during compaction of a Particle bed modified from
[44] [45]
The first subprocess runs at low press pressures. The particles arrange themselves by
sliding off and turning around each other, filling the voids up in the magnitude of the
primary particles first. The frictional forces between the particles must be overcome and
elastic deformations of individual particles can occur. The fluid present is thereby
displaced from the pores and cavities. Increased stress can lead to cracks within the
particles and this can in turn lead to fracture. The fragments from the fracture then fill
further voids smaller than the initial particle size. In this subprocess the fluid is also
displaced or partially enclosed and also compacted.
Plastic deformation as illustrated in figure 2.12 below occurs at smaller particle sizes,
high temperatures and low compaction speeds. During deformation, contact points
become surface contacts and this causes higher friction forces and lower compaction [44,
1].
18
Figure 2.12 Plastic deformation during loading modified from [44] [45]
When the external load acting on a particle bed is relieved, the bed expands in the axial
direction. This happens due to the energy stored within the elastic stress field and is
referred to as back strain.
Oettel [43] observed that the relief curve with elastic back strain is largely linear (figure
2.13). Makowlew [46] made an approximate range of 0.1 – 0.9 Fmax for cement clinker
with a straight line. This gives a derivation of the corrected value, skorr by which the pure
elastic back strain can be inferred the difference between the corrected value and the
actual measured value at the end of the experiment indicates the irreversible
rearrangements. With an increase in the loading speed, there is a corresponding increase
in the elastic back strain [47].
Figure 2.13 Forcedisplacement curve with corrected press travel scorr from a
linearly adjusted relief curve according to [43]
Pressdistance, s in mm
kN
PressLoad, F in
19
2.3 Multiple Stressing of Solid Particles
The breakage behaviour of solid particles under cyclic stressing has been previously
studied in various disciplines with the influence of different forms of stress being
investigated. Pitchumany et al. [48] studied the stressing of single particle till fracture
using a nonlinear mechanism and thus explained the influence of stressing intensity,
particle size and microstructure on the material resistance against cyclic loading.
Beekman et al. [49] confirmed the result of this study by characterizing solid particles by
their fatigue duration, resistance to attrition and breakage mechanism when under impact
loads. In a more advanced test, King & Tavares [50] used continuum fracture mechanics
to explain solid particle breakage by repeated lowenergy stressing. The study explained
that the repeated impact tests help to gain information regarding the breakage pattern of
particles based on their history and thus observed a relation between fracture
accumulation and gradual weakening which ultimately leads to particle breakage.
In the study of deformation and breakage behaviour of particles by compression tests,
Antonyuk et al. [51] placed the materials under repeated loading/unloading conditions
while observing the breakage force and contact stiffness during the elastic and
elastic/plastic contact. Using Weibull statistics (equation 4), the breakage probability is
described as a function of the more mass related breakage energy.
Equation 4
Where; P(xt,ks,x63) = breakage probability as a function of xt, ks and x63
xt = quantity (timetofailure)
ks = shape parameter
x63 = 63% quantile
The study shows that more massrelated breakage energy is required to fracture smaller
particles than bigger ones. So far, a more general and complete description of the physical
phenomena that takes place during particle breakage is not yet available to aid the
prediction of the breakage parameters of particles by multiple stressing.
Vogel & Peukert [52] developed a model with respect to the Weibull statistics in order to
describe the breakage probability of particles by repeated impact. From this model, the
20
breakage probability by repeated stressing is found to be a function of the total amount of
energy stored in a particle by a sequence of repeated impacts. To further determine the
material parameters which are unknown as a means of validating the model, Vogel &
Peukert [52] passed out individual particle experiments using particles of different
materials ranging in sizes from 95 µm to 8 mm. The obtained result shows the breakage
probability to be a function of the specific impact energy. This means that the smaller
particles show lesser breakage probability due to its lesser contact area circumference, as
a result less flaws are affected by the critical tensile stress.
Figure 2.14 The effect of weakening due to damage accumulation from repeated
loading events ( [53]
In multiple impacts, the results from the first impacts of the particles as well as the second
and/or successive impacts are defined as the function of the total net energy, in order with
the Weibull statistics. This led to the conclusion that the energy that was provided by an
impact that however did not cause particle breakage was not wasted. It instead led to the
weakening of the material by increasing the number of internal flaws and extending
existing cracks within the particles. These are beneficial for the succeeding stress event.
For each number of successive loading events (n), the particle is weakened due to an
accumulation of damage (figure 2.14).
21
3 Material and Methods
3.1 Material Characterization
The investigation was carried out using cement clinker. A clinker is the burnt component
of cement which consists mainly of Tricalcium Silicate (Alite), Dicalcium Silicate
(Belite), Tricalcium Aluminate and Calcium Aluminate Ferrite. It is responsible for the
hydraulic properties of cement which enables it to solidify and harden through the
addition of water. The clinker used in this study is made available by thyssenkrupp
Industrial Solutions AG and has Alite and Belite as the main mineral components at
59.5% and 19.5% respectively. Other minerals present are detailed in table 3.1 below.
Table 3.1 Chemicalmineralogical composition of clinker sample used analysed
using XRD
Mineral
Composition %
Alite
59.5
Belite
19.5
C4AF
8.4
C3A
8.2
MgO
2.5
CaO
0.8
K2SO4
0.7
Ca(OH)2
0.3
(K,Na)3Na(SO4)2
0.2
All the tests were carried out using monodispersed size fraction x = 0,81 mm which was
prepared by sieving the initial polydispersed clinker with analytical sieving as detailed
later in section 3.2.3. Two sets of clinkers were used: unstressed, fresh clinker prepared
by sieving and the stressed, broken clinker prepared by stressing polydispersed clinker
in the range of 14 mm in a pistondie press at 150 MPa and sieving again afterwards to
extract 0.81 mm monodispersed fraction. The particle size distribution (PSD) curve for
the initial clinker sample and that of the stressed extracted monodispersed clinker is
22
shown in figure 3.1. The aim is to prepare an already stressed and broken material which
is not yet small enough to leave the grinding circuit and therefore is being stressed a
second time. To compare it with the fresh material, they are in the same size range.
Figure 3.1 Particle size distribution of initial polydispersed clinker and the
extracted monodispersed fraction used for test work
Table 3.2 Density and shape of stressed and unstressed clinker used in this study
Clinker
Unstressed
Clinker
Stressed
Clinker
Measuring Device
Size
0.8 – 1 mm
Sieving
Solid Density (kg/m3)
3204
Mercury Porosimetry
Bulk Density (kg/m3)
1171
1165
According to DINENISO 60
Shape  Circularity
0.87
0.84
CPA; Fa. Haver & Boecker
Both stressed and unstressed clinkers were measured for density and shape to ensure
similarity. The results showed near similar range of values (see table 3.2)
23
3.2 Apparatus/Equipment and Processes
A few laboratory equipment were used to obtain results for this investigation. The piston
die press was used for comminution of both clinkers at different grinding pressures and
was also used for grinding circuit tests while the ball mill was used in carrying out
grindability tests according to Zeisel. A detailed look at these equipment as well as the
processes involved are given in this subsection.
3.2.1 PistonDie Press
A Shimadzu UH500 kNA hydraulic piston press from the Institute for Thermal,
Environmental and Resource Processing Engineering (ITUN) is used for the stress tests
[54]. A schematic structure of the machine can be seen in figure 3.2 below. The load cells
and displacement sensors are located under the pressure plate. The force measurement
has an error tolerance of 3% Fmax, which corresponds to 15 kN for this press. The
displacement measurement has an error of 106 m. The pressure pot has a diameter, DDT
of 57 mm and a height, hDT of 50 mm and is mounted on the pressure plate. The piston is
mounted on the traverse. On this press, the pressure plate with the pressure pot moves in
the direction of the traverse. The measuring signal is recorded with a frequency of 50 Hz.
Meanwhile, the forcedisplacement curve is recorded on the LabMaster software
controlling the machine. The inherent expansion of the system is 0.587 µm/kN and is
taken into account in the evaluation of the forcedisplacement curves.
Figure 3.2 Schematic representation of the Shimadzu hydraulic press [54])
24
3.2.2 Rollbock Machine
After pressing, the material is usually stuck together in agglomerates. A process of
deagglomeration is required to disperse the particles without impacting further stress or
causing more breakage. The Rollbock machine is used in the dispersion of the samples
after every impact event. It includes a cylindrical porcelain vessel that has a 112 mm
height and an inside diameter of 106 mm. The sample is placed in this vessel after pressing
and to further aid the deagglomeration process, 10 large rubber stoppers (hst = 19 mm,
Dst1 = 14 mm, Dst2 = 17 mm) and 10 small rubber stoppers (hst = 17 mm, Dst1 = 10 mm,
Dst2 = 15 mm) are also placed inside the vessel which is shut tight.
Figure 3.3 Dimensions of the rubber stopper
The tight shut porcelain vessel is then placed on the rollbock machine and it is turned on.
For this study, the vessel is rotated on the machine for 20 minutes at the speed of 100
rpm. The sample is then extracted from the vessel carefully to avoid loss of material and
taken to sieve analyses.
Figure 3.4 the Rollbock machine at the MVTAT lab, TUBAF
Cylindrical porcelain vessel
25
3.2.3 Sieving and Particle Size Distribution Analyses
The methods employed in analysing the particle sizing of the samples during the course
of this study are analytical sieving and laser diffraction. After crushing and
deagglomeration, in order to obtain information on the grinding process, the samples were
sieved using analytical sieves from Fritsch “Analysette”. The sieving is done using the
R10 sieve in the range of 0.1 mm to 0.8 mm. According to [44], as a decrease in particle
size occurs, the sieving quality deteriorates as well due to the adhesive and frictional
forces that exceed the force of sieving. Hence, sieving quality is usually very poor below
60 µm particle size because the resulting air currents tend to swirl up the fine particles
[55]. For this reason, all particle size classifications below 100 µm were done using laser
diffraction.
For every sieve, the coarser fractions of the sample are retained while the finer portions
pass through the mesh. The pressure that enables the sieving process is applied to the
sieve tower by the electronic vibratory sieve shaker for a period of 10 minutes at an
amplitude of 2 mm.
Figure 3.5 (a) illustration of sieve analysis[Q3(x)] [56] and (b) Sieve tower with
R10 sieve sizes on a shaker
After the shaker is done, the material retained in each sieve is weighed and recorded while
the finer particles collected in the bottom tray are taken for laser diffraction. Both results
26
are used in plotting the particle size distribution curve for further observations and
analysis.
During sieving, the fine particles of the largest screen become the feed of the next sieve,
and this continues down through the sieves [56]. The feed is then split in several fractions,
Δmi. Each size class is given by the mesh size of the sieve used, the data set, xi – xi1 and
Δmi are generated hence thereafter.
Size Class Definition
The relative mass of the particles of definite sizes between two mesh sizes can be
determined from the analyses and the definition of the size classes (R10) has to be adhered
to accordingly. This defines the class and it is named by its upper limit, denoted with xi
and its mass fraction Δmi also belongs to the cut size [56]. The width of the size class with
upper size limit, xi is given to be Δxi. this general approach can be extended to other
quantities like surface, number, length, etc., but in this case the quantity, Δµi is considered
as it belongs to xi and Δxi.
Figure 3.6 (a) Particles sorted into size classes and (b) particle size intervals
[56]
27
Cumulative Sum Distribution
In Particle Size Distribution (PSD), the plot is usually a cumulative sum distribution. The
cumulative sum refers to the relative quantity (relative mass, relative number, etc.) that
has a property smaller than the size class, xi. If, for instance;
Q3 (xi) = 0.633, where xi = 50 µm
This means that 63.3% of the sample material comes from particles which are ≤ 50 µm.
Equation 5
Equation 6
Relative Quantity Q3 (xi)
The relative quantity is the sum of all mass fractions Δmi in order to determine mi, the
cumulative mass of all the particles below the size class xi. When the mass, mi is divided
by the entire mass, m of the original sample, the resulting quotient mi/m is the relative
mass which is smaller than the corresponding particle sizes.
Equation 7
Equation 8
28
Homogenous Function
The relative mass is usually plotted as the cumulative sum by making a sum of the relative
masses of all size classes that are smaller than the corresponding particle size, Q3 (xi).
This is a dimensionless parameter, but it is often expressed in percentage (%). It is
however possible to adjust the plotted diagram of the cumulative sum and generate a
homogenous curve from it [21]. In this case, the data points for Qr(xi) are plotted as a
function of xi. the curve connecting the points is then the homogenous function, Qr(x).
Equation 9
Equation 10
But,
Median Passing, X50
The use of just one particular parameter as the distribution representative has often been
deemed necessary in technical processes. The most common parameter used for PSD
analysis is the median value, x50,r.
Figure 3.7 PSD Curve showing the median, x50 modified from [56]
29
Particles smaller than the median value often represent 50 % of the characteristic sample
quantity. The PSD is thus partitioned into two by the median value line. According to
[21], the median value indicates that 50 % of the entire mass comes from particles below
this size.
For all size distributions representing the different quantities, r, the lower (xmin) and upper
(xmax) particle size limits are set. Differences between them are only expressed in the
shape of the curve.
Figure 3.8 Cumulative sum function comparison of different PSD curves modified
from [56]
Rosin, Rammler, Sperling and Bennett (RRSB) Function [DIN 66145]
After a PSD analysis, the obtained data is further used in quantitative calculations, for
example to predict the change in particle size distribution due to breakage events. This
could be done by using the entire set of information including all size classes (xi) and
quantities (µi) resulting in a population balance approach. Another possibility involves
the use of analytical functions to represent the size distribution with the ability to
transform this function using another process function that represents the change caused
by breakage or agglomeration. For this study the analytical function used is the RRSB
function, because it is the most commonly used in the cement industry [57]. The RRSB
function is one that basically makes use of two parameters to fit the particle size
distribution. The parameter, n represents the width of the PSD while x63.2 represents the
particle size.
30
According to Peuker [56], the mathematical form of the RRSB function gives neither the
minimal nor maximum value for x. Using a special probability grid as shown in Equation
14, the RRSB distribution represents the PSD as a straight line with respect to the RRSB
function. The abscissa is logarithmical, and the ordinate is scaled nonlinearly as a result
of the double logarithmic partition and can be used to deduce the parameter, x63.2.
Figure 3.9 Plot of RRSB distribution curve adapted from [56]
The RRSB distribution is mathematically a Weibull distribution which is often used in
the description of breakage events [56].
3.2.4 Laser Diffraction
After sieving, all materials less than 100 µm are analysed with a HELOS laser diffraction
machine which is made by Sympatec. Laser diffraction is a method captures the
Transformation fit into RRSBgrid;
Equation 13
Equation 14
31
interaction of particles using laser light by correlating the scattered pattern to the particle
size. Samples of 100 µm grain sizes and below were subject to laser diffraction. The
procedure could be carried out using the wet testing method (by suspending the sample
in ethanol) because agglomerates that are still present within the fine range are also
detected by this method [58]. However, for the purpose of comparability with the data
obtained from sieving, the dry method of measurement is used for this study.
The process of laser diffraction involves the determination of particle sizes by the action
of scattered light on the particles producing diffracted images. For irregularly shaped
particles, the diffraction image highly depends on the orientation and angles of the
particles. For a mathematic back calculation, the determined PSD is then smoothed [44].
As a result of the difference in the particle size of sieve analysis and laser diffraction data,
a “kink” occurs when both curves are joined together [59]. Despite this “kink”, the curves
do not overlap because of the sphere equivalence which causes finer results of particles
under laser diffraction as compared to those from sieving. All values are then further
calculated to obtain a sum distribution.
3.2.5 Zeisel Grindability Tests
To examine grindability, Zeisel developed a setup that is suitable for materials harder
than coal as an upgrade on the Hardgrove testing device though the underlying principle
of the ballring mill remained unchanged. Because the Hardgrove device had issues and
limitations in achieving certain degrees of fineness as well as lacking in means of
obtaining direct data on the grinding tests, Zeisel sought to solve these problems by
modifying the geometry of the grinding bowl and installing a torque measurement to the
setup. This ensured that PSD for all materials (even hard materials) are comparable to
industrial processes [7].
The testing device consists of the grinding bowl which has a narrower grinding path than
the Hardgrove device and eight steel balls that roll around the path (figure 3.10). Using
the rotating die, load is applied to the balls and as they are rolled around the path,
comminution of the material occurs due to friction and pressure. The bowl is pivot
mounted to enable the measurement of the grinding resistance. To begin the experiment,
30.25 g of the material is fed into the bowl (the additional 0.25 g is to account for material
32
loss) along with the eight balls and the machine is set to 400 revolutions for each cycle
which lasts for approximately 2 minutes. After each cycle, the fineness of the clinker is
measured.
Figure 3.10 A sectional view of the grinding bowl (above) and (below) grinding
bowl placed on the pivotmounted table modified from [7]
Through this, a function is derived to calculate the specific energy consumption (kWht1)
which depends on the specific surface or the fineness. As Zeisel observed, the only test
parameter which really affects the result is the breakage behaviour of the original sample
and while the other parameters (like the revolution speed and dieload) actually influence
the final fineness, they should not change the grindability whatsoever [60, 7].
33
Test Parameters for Zeisel Grindability Tests
Table 3.3 Parameter values for Zeisel grindability tests [7]
Parameter
Zeisel Values
Revolution
200 min1
Die Load
26kg
Sample weight
30.25 g
Measurements grinding results
Blaine [cm2 g1]
Targeted fineness
30004000 cm2 g1
Test material size fraction
0.81mm
Temperature
20°C
Humidity
60%
The specific surface according to Blaine is used in the characterization of grinding results
during Zeisel tests. Performing the tests as well as determining the Blaine is best
optimized under a controlled environment with 20 C temperature and 60 % humidity.
The grinding cycles which lasted for 2 minutes each were repeated a few times for each
sample until a specific surface of at least 3000 cm2g1 is attained.
Though the result of the Zeisel test could be affected by quite a number of parameters,
the influence of majority of these parameters is generally observed to be rather negligible.
When put together however, the collective influence could cause an anomaly in the results
thereby creating an uncertainty of the test procedure. The process parameters, parameters
concerning the device and its geometry, and that of the evaluation software must be
considered during the test itself.
34
HighPrecision Power Measurement
As earlier stated, Zeisel integrated a power measurement device in his test design, and
this proved to be the most important upgrade of the design. During comminution, the
torque that acts on the pivotmounted grinding bowl can be determined and from this the
grinding work is then deduced using the equation:
Equation 15
Where W = grinding work (in Nm), Md = torque (Nm),
= angular velocity (in s1).
The grinding work according to Bernutat [61], is derived from:
Equation 16
Where n = revolving speed (in rpm), Ff = elastic force (in N), l = lever arm (in m).
When the sample mass ms (in g) is considered, then the specific energy (in kWht1) can
be calculated as:
Equation 17
Blaine Determination
The CarmanKozeny equation is the basis used in the determination of specific surface
according to Blaine. If air streams through a bulk material with defined porosity, there is
a drop in pressure (Δp). To make this practical, the pore system is replaced by parallel
cylindrical capillaries which has both diameter and length that corresponds to the pouring
height. The measuring range of the Blaine device falls between 1000 and 6000 cm2g1 and
35
this method is most frequently used in the cement industry. Figure 3.11 below shows a
schematic diagram and a picture of the Blaine device as used in the study.
Figure 3.11 The Blaine device schematic [58]
After comminution, the sample is deagglomerated and a weighed portion is transferred
into the measuring cell and compressed using the compression piston. The manometer
liquid is sucked up to the upper mark. The time taken for the liquid to drop down to the
lower mark is measured on a stopwatch. With this the specific surface, Sm is calculated
using the following equations:
Equation 18
Where = density of solid in g/cm3, C= devicedependent constant (944.6 kg1/2m3/2s1),
ε = Porosity (0.45) , t = measured time between upper and lower mark on the manometer
in seconds , ηF = air viscosity in Pa·s.
36
3.2.6 Grinding Circuit Simulation using PistonDie Tests
The adaptation of HPGR using the pistondie press is applied here in order to carry out a
simulation of grinding circuits. The main aim for this simulation is to determine the
energy requirement for the entire grinding process of cement clinker to an industrial
standard. In every grinding circuit, an air classifier is needed. On an industrial scale, air
classifiers are used while on a pilot scale, sieving is used but this necessitates a prior
deagglomeration process. The press tests are carried out as explained in section 3.2.1 to
3.2.3 with a standard grinding pressure of 150 MPa according to Schnert [8]. Same
monodisperse clinker with 0.8 mm – 1 mm grain size range is used. 140g of the sample
is measured into the grinding pot via the hopper and the surface is gently flattened out
using a metal disc to ensure a uniform contact surface. Before the stressing process
begins, the height between the upper brink of the pot and surface of the sample is
measured using a calibrated ruler. This step is necessary for the positioning of the piston
before crushing in order to measure the compaction. The material is then stressed and
weighed, after which deagglomeration is done and the sample sieved using the R10 sieve
series. The fine materials (< 100 µm) are extracted as finished products while all the other
particles greater than 100 µm are mixed together again and supplemented with fresh
material to maintain the initial 140 g weight. This comminution cycle is repeated once
again and continues until the “stop criterion” has been achieved. When the amount of fine
materials (< 100 µm) does not differ so much from the last result, it can be said that a
constant operating point has been reached. The constant operating point is indicated when
the mass of the fine materials shows only a less than 3 % change between two consecutive
cycles. When this is observed, the stop criterion has been achieved and the final material
is sieved for a PSD analysis. The fine material from the final sieving is also analysed by
laser diffraction and the specific surface area is determined.
For each of the cycle required to achieve the constant operating point, a force
displacement diagram is plotted using data recorded by the software (LabMaster) during
grinding. This plot is required for the calculation of energy consumption.
37
4 Results and Discussion
Results obtained from the experiments outlined in the previous chapter are shown in this
chapter and further discussed with the aim of arriving at a conclusion with regards to the
subject matter. Pistondie tests of both clinkers at different pressures are compared in the
first subchapter (4.1). Then the simulation of grinding circuit and the grindability test
according to Zeisel results are shown in subchapters 4.2 and 4.3 respectively.
4.1 PistonDie Tests at Different Grinding Pressures
Both samples were crushed severally at pressures ranging from 25 MPa to 200 MPa, after
which the particle size distribution analysis follows. Data obtained from the sieve analysis
and laser diffraction of materials less than 315 m were exported to Excel for plotting a
particle size distribution curve. Data from laser diffraction were combined with sieving
results.
Figure 4.1 Product PSD curves for all grinding pressures of unstressed clinker
38
Figure 4.2 Product PSD curves for all grinding pressures of stressed clinker
Since the grinding pressure acting on a particle bed controls to a high extent the fineness
of the product, the distribution curve for each of the stress levels are compared for both
clinkers in Fig 4.1 and 4.2 above. The size distribution function, Q3(x) is plotted against
the particle size, x. Both set of results show an increase in fineness as the pressure
increases. Despite the increase in quantity of fines produced in higher stress levels (175
& 200 MPa) in figure 4.1, some of the coarser particles from the initial samples are still
retained after comminution. As a result of the flawed packing within the bed, some
particles tend to have more contact than others, combined with the unequal sizes of the
particles and failure in the mineralogical structure of the individual particles, some
particles break quicker than others creating fragments that can protect the coarse,
unbroken particles. Due to this breakage and rearrangement, every confined particle bed
reaches a state where further comminution is no longer possible [62] [15]. Consequently,
the smaller particles get crushed more often during this process proving that no matter
how high the grinding pressure, there will always be particles of the initial size class in
the product [63]. This was also evident during the high stress level comminution of the
stressed clinker (figure 4.2), though much less amount of the initial large particles is still
39
present after comminution. The unstressed clinker had 29.8% initial class size (0.81 mm)
present in the product at 25 MPa while at 200 MPa, only 15.9% was present. In contrast
the stressed clinker had much lower values with 19.4% at 25 MPa and 9.2% at 200 MPa.
By observing the shape of the PSD curves, the unstressed clinker showed a general
concave upward shape across all stress levels. Though the stressed clinker showed a
milder concave upwards shape, the PSD curve at high pressures were relatively straight
bending at the ends to display its fractal features.
Figure 4.3 Comparing the product PSD curves of selected grinding pressure for
both clinkers
To compare between both clinkers, the distribution curves of grinding pressures 25, 100
and 200 MPa were plotted together. Observations show that across all pressure levels, the
stressed clinker produced significantly more fines than the unstressed clinker at the
corresponding pressure. On the other hand, at just a grinding pressure of 100 MPa, the
stressed clinker had already slightly higher quantity of fine products than unstressed
clinker had produced at the grinding pressure of 200 MPa illustrating once again that prior
stressing significantly weakens the material. As stated by Wünster [64], when a material
has been previously stressed, the particles are weakened and develop microcracks.
40
Hence, less energy input is required to reach the finished product fineness during
subsequent comminution.
Median Passing Size – x50
The median size (x50) is the given size at which point half of the sample particles are
smaller or equal this size and other half are larger. This statistical measure was employed
because it is one that is easy to understand especially with regards to particle size
distributions. Using the data, the value for x for which Q3(x) is equal to 0.5 was obtained
for each grinding pressure by linear interpolation. The x50 values thus obtained for both
clinker samples were then plotted against pressure.
Figure 4.4 Plot of X50 over pressure for both Clinkers
As seen from figure 4.4 above, both curves show x50 decreases faster at lower pressures
and wanes as the pressure increases to a point where it stagnates. At this point further
increase in pressure would probably have no further significant effect on the fineness of
the material. Comparing both samples, the x50 of the stressed clinker occurs much lower
on the mesh size scale than that of the unstressed clinker. This means that considerably
more amount of fine are produced for the stressed clinkers even at the lowest pressure.
41
Comminution Ratio (Cr)
Comminution ratio can be defined as the ratio of the initial particle size to the final particle
size. For our sample, the comminution ratio was calculated using the x50 of the original
sample and the x50 of the product as used in figure 4.4 above. Since the original sample
consisted monodisperse particles of 0.8 to 1 mm particle size range, the x50 value of initial
sample was assumed as 0.9 m. the equation for calculating Cr is given as:
Equation 19
Figure 4.5 Comminution Ratio plotted over pressure for both clinkers
As shown in figure 4.5, the comminution ratio for the stressed clinker shows a much
steeper progression as the grinding pressure increases and is much higher than the
comminution ratio of the unstressed clinker especially at higher pressures. At 25 MPa,
the comminution ration for the stressed clinker is only 20% higher than unstressed clinker
while at 200 MPa it was roughly 120% higher than the unstressed clinker. This naturally
implies that the considerably greater quantity of fines is produced with respect to the
initial sample amount of the stressed clinker than the unstressed clinker. Between the
42
highest pressures of 175 and 200 MPa, the unstressed clinker had reached a state where
higher pressures would not lead to further breakage. The stressed clinker however showed
results contrary to this probably because the fines here are produced faster which protects
the larger particles more leaving ground for further breakage at higher pressures.
Energy Absorption
Data obtained from the LabMaster computer program after each grinding cycle was
analyzed with the DIAdem software using the “ITUN script” (see appendix D) to obtain
the energy absorption required for every cycle to grind to completion. For every grinding
pressure, the energy required to grind to finish was recorded for both samples. The lowest
energy absorption values were recorded for the lower grinding pressures in both cases
and the required energy naturally increased as the pressure increased. As a result of micro
cracks which developed within particles due to previous comminution, prestressed
clinkers usually require lower energy to break down or fracture. A graph of the energy
absorption in J/g is plotted against the grinding pressure applied for each of the cycle
(Figure 4.6).
Figure 4.6 Energy Absorption for each grinding event corresponding to the
grinding pressures
43
The lowest energy recorded (2.25 J/g) was for the stressed clinker at 25 MPa grinding
pressure and this differed only slightly from the unstressed clinker with corresponding
pressure at 2.68 J/g. In the same vein, the highest energy absorption was 14.23 J/g for the
unstressed clinker at 200 MPa and this was slightly higher than that of stressed clinker
with same grinding pressure (13.44 J/g). At 175 MPa however, there was an irregularity
for both clinkers as the values for energy absorption were nearly equal with that of the
previous pressure (150 MPa). This is abnormal because of the interdependence of
grinding pressure and energy absorption [65]. Thus, at a significant increase in pressure,
the energy absorption is expected to increase accordingly. According to Reichardt &
Schönert [66] the energy absorption will increase in proportion to the pressure so far as
the volumetric solid fraction in the compacted bed does not go higher than 0.80. This
could be the reason for the anomaly recorded at 175 MPa grinding pressure considering
that the density of the sample bed is slightly higher than 0.8. Also, considering that the
products for both clinkers were finer at 175 MPa, the pressure must have been attained
which should have led to a corresponding increase in energy absorption. Since the
anomaly occurred for both clinkers, which were tested on different days, this may be an
equipment error probably with the processing of materials at 175 MPa pressure.
There is a general similar trend throughout the experiments. The stressed clinker required
less energy to complete grinding than the unstressed clinker. Though the difference in
energy requirements between both clinkers is generally low across all pressures, the
stressed clinker nevertheless always required less energy to grind. At a pressure of 150
MPa, for example, the stressed clinker has an Em of 9.2 J/g with a corresponding Cr of
3.9 while the unstressed clinker has an Em of 9.46 J/g with a Cr of 2.1 at same pressure.
Since the pressure and duration were basically the same for both clinkers, the less
resistance offered by the particles that had been prestressed accounted for the differences
in the energy absorption of both clinkers.
Compaction
From the data analyzed on DIAdem, the compaction for each grinding pressure is
obtained. The compaction for each clinker sample is plot against the corresponding
pressure as shown in figure 4.7.
44
Figure 4.7 Compression for each grinding event against the corresponding
pressures
The compaction trend for both clinkers were near similar across all pressures. The
stressed clinker showed slightly higher compaction at lowest and highest pressure levels
while the unstressed clinker was higher at 100, 125 and 150 MPa pressures. At 175 MPa
however, both clinkers might have reached a stable state where further rearrangement is
no longer possible. At this point the number of particle contact Considering that the both
samples are of same material, particle size, bulk density, and nearly same particle shape,
the particles tend to rearrange and break in the same pattern such that their fragments look
similar and have same shape. The friction losses are therefore equal since they rearrange
similarly, meaning that both systems at 200 MPa reach a nearconstant compaction. Due
to the plastic deformation of the particle contacts, however, further increase in pressure
will still cause further compaction. Because the number of particles contact here is much
higher than at the beginning, the energy still being supplied is distributed over the contacts
equally.
The energy absorption, Em is a function of the breakage, plastic deformation and
rearrangements of the particles leading to loss of friction [65] [37]. Due to the brittle
nature of cement clinker, plastic deformation in this case is negligible while breakage
varies significantly. For the unstressed clinker, it is no longer possible to overcome the
45
bonds in the particles due to the lower breakage probability in smaller particles, i.e. the
smaller particles have fewer matrix failures where breakage can occur. The stressed
clinker on the other hand has microcracks reducing its resistance against breakage.
Despite the particle bed being in a stable state, the particles still break, but as they may
not be able to rearrange, compaction must be the same. So, owing to the fact that micro
cracks also lower the resistance against breakage before the stable state is reached, it is
quite possible that the overall energy absorption is nearly the same for both clinkers.
So, while there are obvious distinctions in the x50 and Cr of both clinkers, the Em values
do not differ much.
4.2 PistonDie Grinding Circuit Tests
Using the “POLYCOM Process Guideline 2016” from thyssenkrupp Industrial Solutions
AG, the grinding circuit simulation was done to achieve 200 t/h of cement quality CEM
I 32.5 R according to DIN 1164 [67]. Data from the circuit tests are used to determine the
required dimension (scaleup) of an HPGR to grind cement of this quality industrially.
4.2.1 Grinding Circuit Simulation
The grinding circuit tests were carried out as described in section 3.2.6 till the stop
criterion was achieved. For every cycle, the data is well tabulated in order to easily detect
when the constant grinding point has been reached. This was achieved after 4 cycles for
both clinkers. The initial mass and mass in fine product are shown in the tables 4.1 and
4.2.
Since the fine products (i.e. < 100 µm) are extracted as finished product after each cycle,
the same mass of fresh material is added to the product above 100 µm in order to maintain
the 140 g initial mass before the start of every cycle.
It is interesting to note that, in line with previous results, the stressed clinker has a higher
percentage recovery of fine products than the unstressed clinker for every cycle.
46
Table 4.1 Grinding circuit data of unstressed clinker, stop criterion reached after 4
cycles
Unstressed Clinker
Cycle
1
2
3
4
m initial
in g
140,00
140,00
140,00
140,00
m after grinding
139,81
139,80
139,94
139,97
m > 100 µm
95,72
98,96
100,60
101,21
m < 100 µm
44,00
40,61
39,00
38,40
total losses
0,28
0,43
0,40
0,39
Mass recovery in fine product
in %
31,43
29,01
27,86
27,43
Difference in mass recovery

2,42
1,15
0,43
Table 4.2 Grinding circuit data of stressed clinker, stop criterion reached after 4
cycles
Stressed Clinker
Cycle
1
2
3
4
m initial
in g
140,00
140,00
140,00
140,00
m after grinding
139,80
139,88
139,57
139,79
m > 100 µm
92,62
95,98
97,13
97,45
m < 100 µm
46,98
43,72
42,38
42,19
Total losses
0,40
0,30
0,49
0,36
Mass recovery in fine product
in %
33,56
31,23
30,27
30,14
Differece in mass recovery

2,33
0,96
0,14
47
4.2.2 Particle Size Distribution Curve
After a constant grinding point has been reached, the sample from the last cycle goes
through sieve analysis. The fine product is then analysed by laser diffraction, the data
normalized and combined with that of sieve analysis for the plot of the particle size
distribution curve.
Figure 4.8 PSD curves for the grinding circuit test products of both clinkers
The PSD is plotted with the cumulative sum distribution Q3(x) over the size x. In the case
of the stressed clinker, at point Q3(x = 86 µm) is equal to 0.285. This means that particles
smaller than 86 µm account for 28.5% of the entire sample. It can be observed from figure
4.8 that a kink occurs along the 100 µm mark. This, as observed by NapierMunn [59],
usually occurs as a result of differences in grades of grain sizes analysed by sieve analysis
and by laser diffraction, leading to a kink when both sets of data are combined to produce
a curve.
The Specific surface area S of the product taken for laser diffraction was also measured
and the values which are further used in the scaleup calculations are given below.
• S; unstressed clinker = 1909 cm²/g
• S; stressed clinker = 1588 cm²/g
48
The Specific surface area S shows a distinct difference between both clinkers despite the
PSD showing quite similar distribution. The results however contradict the previous
results as it is expected that the stressed clinker, due to easier grindability should have a
larger surface area.
Energy Requirement
The energy requirement for each cycle to grind till finish is shown in table 4.3.
Table 4.3 Measured energy absorption for each grinding cycle
Cycle
Em Unstressed Clinker(J/g)
Em Stressed Clinker (J/g)
1
8.43
7.13
2
7.45
6.64
3
7.14
6.54
4
7.04
5.58
In contrast to subchapter 4.1, there is a distinct difference in Em of both clinkers. The
energy absorption decreases after every cycle as such that the lowest energy requirement
was recorded for the last cycle where the constant grinding point was reached. This is
because of the increased volume of fines in subsequent cycles. According to Tavares [68],
higher proportions of fines in HPGR products result in energy efficiency.
4.2.3 HPGR ScaleUp Using PistonDie Grindability Data
In the calculations for scaleup of HPGR, standard values for certain sizing parameters
for finish grinding as given by the “POLYCOM Process Guideline 2016” were used.
These parameters listed in table 4.4 are used at various stages of the scaleup calculations.
49
Table 4.4 Sizing parameters for HPGR ScaleUp [67]
Parameter
Sizing for Finished Grinding
Circumferential velocity (304 m2/kg Blaine)
For Blaine values of 300 – 350
m2/kg:
0.0076 Blaine + 3.96 = 1.65 m/s
Thickness of cakes / working gap, s:
maximum grain size (60 mm)
60 mm
Density of cakes,
2.75 t/m³
Density of feed,
1.98 t/m³
Lengthdiameter ratio: L/D
0.77 m
Angle of force for finished grinding, β
2.5
Throughput, m
200 t/h
Measured : stressed
Clinker
1588 cm²/g
Measured : unstressed
Clinker
1909 cm²/g
Specific Grinding Pressure,
150 MPa
Efficiency of motor & gearbox,
0.925
Calculation of Circulation Factor, U
This is an empirical throughput function of thyssenkrupp which depends on the Blaine
value.
Equation 20
For Unstressed Clinker:
For Stressed Clinker:
50
Equation 21
For Unstressed Clinker:
For Stressed Clinker:
Equation 22
For Unstressed Clinker:
For Stressed Clinker:
06
Calculation of Length & Diameter from Throughput Equation
The throughput equation is given by:
51
Equation 23
M can however be derived using the circulation factor, U thus;
Equation 24
For Unstressed Clinker:
For Stressed Clinker:
Substituting for M in equation 23 and solving for length, L, we have;
Equation 25
For Unstressed Clinker:
For Stressed Clinker:
The Diameter, D can thus be derived since the L/D ration is already given as
Hence,
For Unstressed Clinker:
For Stressed Clinker:
52
Calculation of Specific Throughput, mdot
The specific throughput differs from the throughput, M as it provides the expected
throughput in an HPGR operating with 1m length and diameter rolls running at 1ms1
peripheral speed [69]. The equation below is used for this calculation since it is more
practical for real applications.
Equation 26
For Unstressed Clinker:
For Stressed Clinker:
For finish grinding, the specific throughput should ideally fall between 220 – 250 ts/m³h
so as to prevent operational problems during processing. The values for both clinkers,
however, fall beyond this range. At 317.53 ts/m³h, the specific throughput of the
unstressed clinker is considered extremely high while that of the stressed clinker is
slightly higher at 268.61 ts/m³h. Previous studies have shown that the major factors
influencing the specific throughput is the size of the machine , which also depends on the
size distribution of the feed grains and the friction occurring internally between them [70].
In this sense, the use of finer grain feeds could provide more favourable results. Rashidi
et al. [2], however suggested that finer feeds in pilotscale HPGR could still behave
differently under compression than coarser feeds in largescale HPGRs. Ideally, in order
to minimize this machine size effect, most cost manufacturers would rather run scaleup
tests in large units despite the costs.
53
Calculation of Angle of Compression
According to Schönert [71], the angle of compression is defined as that angle at which
the normal roll pressure is increased, and the stressing of materials starts. He proposed
the equation for calculating the compression angle () in high pressure grinding which
is adopted in the POLYCOM guideline and is given below as equation 25.
Equation 27
Using the given values of the sizing parameters shown in table 4:
For Unstressed Clinker:
For Stressed Clinker:
Calculation of Grinding Force from Specific Grinding Pressure Equation
The equation for specific grinding pressure according to Schönert [71] is given in
equation 26 from the process guideline. This equation explains that the fineness of the
product depends on the grinding pressure acting on the particle bed and enables the
comparability of grinding forces at different roll sizes.
Equation 28
54
However, the grinding pressure, for the circuit tests were preset at 150 MPa. This
value can thus be substituted for in the equation and the solving for the grinding force, F.
Equation 29
For Unstressed Clinker:
For Stressed Clinker:
Calculation of Specific Grinding Force
The specific grinding force, Fsp is described as the average force that is applied on a
projected area of the grinding rolls [2]. According to Schönert [5], an increase in specific
grinding force would lead to increase in the rate at which finer products are generated at
a diminishing rate. Having already determined the grinding force, the specific grinding
force, Fsp can be deduced using equation 29.
Equation 30
For Unstressed Clinker:
For Stressed Clinker:
55
Calculation of Power Consumption
The amount of power required to drive the roll is determined by the force, F and the angle
of force, β. The angle of force determines the point where the grinding force is applied
on the roll and as such should be low (less than the nip angle) so as to apply the grinding
force efficiently on the particle bed [2]. From the POLYCOM guideline, the forceacting
angle, β is given as 2.5 and the circumferential velocity for 304 m2/kg Blaine is 1.65 m/s.
Thus, the equation for power consumption (shaft) is given as:
Equation 31
For Unstressed Clinker:
For Stressed Clinker:
Applying the efficiency, of the motor and gearbox, the counter power
consumption, Pz is calculated from equation 31.
Equation 32
For Unstressed Clinker:
For Stressed Clinker:
56
This gives the power of electrical drive by calculating the power consumed through the
shaft in relation to the empirical factor.
Energy Absorption
Energy absorption can be described as the energy consumed by mass/volume of the
sample particles while undergoing compaction with the exception of the energy due to
elastic expansion of the particle bed during unloading. Consequently, energy absorption
is said to be a measure of stressing intensity on a particle bed [72]. A decrease in energy
absorption at any given grinding force could be put into effect by an increase in the
specific throughput. As such energy absorption can be calculated using equation 32.
Equation 33
For Unstressed Clinker:
For Stressed Clinker:
Calculations show the stressed clinker to have a higher energy absorption at 9.43 KWh/t
while the unstressed has a value 7.34 KWh/t. This result is not logical. The Blaine values
measured in subchapter 4.2 leads to this problem where grinding of the stressed clinker
seems to be worse with regards to machine size, power and energy consumption than the
unstressed clinker. The underlying error most probably lies in the determination of the
Blaine values. The Blaine determination method is deemed comparative rather than
absolute. The Blaine measurement gives only an averaged single figure. Considering two
samples where one has more fines than the other but also has more coarse particles, the
Blaine may not be the best representation value of fineness here, as the values would fall
within the same range. The stressed clinker in this case most likely had a similar
57
occurrence where the finer particles protected more of the larger ones leading to a
measured Blaine that’s higher than the unstressed clinker.
4.3 BallMill Grindability Test According to Zeisel
As detailed in section 3.2.5, grindability tests according to Zeisel were carried out for
both clinkers. After every grinding cycle, the Blaine is measured. Since the target Blaine
value is 3040 cm²/g (standard for index cement CEM I 32.5 R), the test for each sample
was ended once a Blaine value of over 3000 cm²/g was achieved. Data from the Blaine
apparatus is calculated on Excel and then used to plot a graph of specific energy
consumption against Specific surface (Blaine). The Blaine value generally increases as
the specific energy consumption increases. From the recorded excel data, the stressed
clinker required 5 cycles to achieve a Blaine of 3560 cm²/g with a specific energy
consumption of 56.32 kWh/t while the unstressed clinker required 6 cycles to get to 3370
cm²/g Blaine with a specific energy consumption of 62.75 kWh/t.
From the graph, the equation of the slope was determined from which the energy
requirement for grinding to Blaine 3040 cm2/g can be calculated.
Figure 4.9 Zeisel grindability plot of specific energy consumption over Blaine for unstressed clinker
58
Figure 4.10 Zeisel grindability plot of specific energy consumption over Blaine
for stressed clinker
Using the Zeisel data, the energy consumption can be calculated for any selected fineness,
with the aid of the approximation function. Since the target of this study is the index
cement CEM I 32.5 R with an average fineness of 3040 cm²/g, the energy requirements
for both clinkers are calculated accordingly. The specific energy consumption, Em,z
calculated from the slopes of both graphs is given as 53.03 kWh/t for the unstressed
clinker and 44.12 kWh/t for the stressed clinker. This result is in contrast to grinding
circuit tests where the stressed clinker required higher energy to grind. However, in
comparison to the HPGR system, the energy consumption for the ball mill is almost five
times higher regardless of which clinker considered. These values were combined with
empirical functions from Zisselmar to determine the length and diameter of a ballmill
required to grind 200 t/h of the cement, CEM I 32.5 R according to DIN 1164.
59
4.3.1 Ball Mill ScaleUp Using Zeisel Data
Zisselmar [73] developed this scaleup approach using grindability data from Zeisel tests.
Using this approach, the empirical scaleup functions from his study were adopted for
this work. From the experiment carried out, the relationship between the energy
requirement and the mill diameter, D are required for the scaleup of the mill size and
other parameters. Standard parameters according to Zisselmar [73] used in the scaleup
calculation are listed in table 4.5 below. The value of 6.0 for the factor, C () was selected
to correspond with the filling ratio and the ball size as shown in table 4.6.
Table 4.5 Sizing Parameters for Ball Mill ScaleUp adopted from [73]
Parameter
Sizing for Finished Grinding
Density of grinding media (steel balls),
7.85 t/m³
Uniform ball size
35 mm
Factor, C (
)
6.0
Filling ratio of grinding media, φ
0.4
Porosity of grinding media bulk, ε
0.4
Lengthdiameter ratio: L/D
3
Relative speed, η
0.75 or ¾
Throughput, m
200 t/h
60
Table 4.6 Factor C(φ) [kW/(t.
m)] as related to mill loading factor and type of
grinding media [73]
Filling ratio of grinding media ()
0.1
0.2
0.3
0.4
0.5
Type of grinding mill
Flintstone
9.8
9.0
8.1
7.0
5.7
Ball mill > 40mm
8.8
9.1
7.3
6.3
5.2
Ball mill < 40mm
8.5
7.8
7.0
6.0
5.0
Calculation of R90 using the RRSB Function
The R90 represents the percentage quantity of particles larger than 90 µm and therefore
left on the 90 µm sieve as residue. The index cement CEM I 32.5 R has a particle size
distribution that can be described as an RRSB distribution having the slope dimension, m
of 0.9 and a position parameter, x63.2 of 24.8. The R90 is calculated using the RRSB
function because these data exactly describe the particle size distribution of the cement.
The equation for the RRSB function is used as shown in equation 13 (section 3.2.3),
substituting for the slope, position parameter, and x = 90.
R90 has a value of 4.1% and is further used in the calculation of the transfer factor, ft.
61
RSSB Test
Considering the use of RRSB function in scaleup calculations for this study, a test was
done to see if the distribution of clinker sample used matches that of the RRSB function.
Using the RRSB constants for CEM I 32.5 R, where position parameter x63.2 and slope m
are equal to 24.8 µm and 0.9 respectively, the curve for RRSB distribution is plotted
together with the product distribution to determine if the PSD curve for ground clinker
fits the pattern (figure 4.11).
The PSD of the clinker sample clearly does not fit with the RRSB R90 distribution for
CEM I 32.5 R. Despite the results from this test, the RRSB was still used in the scaleup
calculations. This is done solely because in the cement industry, air classifiers are used,
and these classifiers operate in line with the RRSB function [57].
Figure 4.11 RRSB test: comparison of the PSD of ground clinker with the RRSB
distribution
Since the product does not fit with the R90 distribution parameters, the clinker product is
tested with other parameters for a possible match. The position parameter x63.2 and slope
m are then set as 36.93 µm and 0.99 respectively. The plot of the product distribution and
the RRSB distribution using the new parameters are shown in figure 4.12 below.
62
Figure 4.12 RRSB test: comparison of the PSD of clinker product with new
parameters of the RRSB R² distribution
As is evident from the graph, the residuals fit fine with the new parameters (R²=0,991).
The clinker product thus fits with RRSB using the m and x63.2 parameters (0,99; 36µm).
Calculation of Factor of Transfer, ft and Ball Mill Energy Consumption, Em,BM
The relation of the factor of transfer, ft to the energy requirements from Zeisel and ball
mill test is expressed in the equation below.
Equation 34
Where Em,BM is the energy consumption required in a ball mill to grind clinker to same
fineness (3040 cm2/g) and A, B & C are constants with the values 6.83, 0.165 & 0.43
respectively.
In order to solve for the transfer factor, ft, the equation is derived as:
63
Equation 35
For Unstressed Clinker:
For Stressed Clinker:
The transfer factor, ft is then substituted in equation 33 to calculate Em,BM.
Equation 36
For Unstressed Clinker:
For Stressed Clinker:
Thus, the grinding of both clinkers in a ball mill would require an energy consumption
49.05 kWh/t and 44.22 kWh/t for the unstressed and stressed clinkers respectively. A
significantly lower amount of energy is required for the stressed clinker in comparison.
64
Calculation of Mass of the Grinding Media
The following equations are considered in the derivation of final equation for the
calculation of mass of the grinding media. Empirical parameters from table 4.5 are
applied.
Mill Volume
Equation 37
Volume of grinding media
Equation 38
Porosity of grinding media bulk
Equation 39
Filling ration of grinding media
Equation 40
Using the interrelationship between equations 36 through 39, the equation for mass of
the grinding media, is obtained thus:
Finally:
Equation 41
For Unstressed Clinker:
For Stressed Clinker:
65
Calculation of Length, L, Diameter, D and Speed, n of the Ball Mill
The speed, n of the ball mill can be derived from the equations for the critical speed and
relative speed.
Equation 42
Equation 42 is valid if D >> Dball
Bearing in mind that the relative speed, is a ratio of speed to critical speed, , the
equation for speed, n is therefore derived thus:
Equation 43
First, the Diameter, D has to be deduced. Considering the equations for diameter
calculation:
Equation 44
In order to substitute the unknown for known variables, equations 40 and 42 are combined
in equation 43 to derive a more viable equation for D from which further calculations are
made.
Equation 45
66
For Unstressed Clinker:
For Stressed Clinker:
m
The L/D ratio was determined to have a value of 3 (table 4.5). Hence the length, L off the
ball mill would be 3 times the diameter, D.
For Unstressed Clinker:
For Stressed Clinker:
Since the diameter, D has been calculated, this can be substituted in equation 42 to
calculate the speed, n.
For Unstressed Clinker:
For Stressed Clinker:
67
Calculation of the Power Consumption, P
In relation to equations by Blanc and Eckardt, the power consumption can be obtained by
multiplying the energy requirement, with the desired throughput, m to give the
equation:
Equation 46
For Unstressed Clinker:
For Stressed Clinker:
The unstressed clinker has a higher power consumption requirement than the stressed
clinker.
4.4 Discussion
The results from the experimental tests all show significant differences between the
stressed and unstressed clinkers. The PSD analyses showed that at corresponding
pressures the stressed clinker had a higher amount of fine product. The scaleup
calculations, however, show that contrary to expectations the energy requirement in
HPGR scaleup is higher with the stressed clinker (9.43 kWh/t) than with the unstressed
clinker (7.34 kWh/t). According to Fuerstenau et al., [17], when a bed has been
comminuted generating interparticle stresses which creates internal flaws within the
particles, energy efficiency is enhanced in subsequent comminution events. Energy
efficiency however depends on a number of parameters including L/D ratio, reduction
ratio, throughput and the fineness of both the feed and product. The higher energy and
power consumption for the grinding of the stressed clinker is observed to be a
consequence of the Blaine values which are abnormal and illogical. Another possibility
for the abnormal results could be the reduction ratio. This refers to the dimensionless ratio
of the feed median size to the fine product median size [37]. At low reduction ratios,
68
HPGRs are more energy efficient but this efficiency diminishes as the reduction ratio
increases [17]. This occurs because the fine particles produced during comminution
impede the breakage of coarser particles thereby causing an isostaticlike pressure field
to form around the coarse particles leading to an increase in energy requirement [74]. To
increase the reduction ratio, the pressure must then be increased generally leading to
inefficient comminution as evident in figures 4.1 and 4.2.
On the other hand, the scaleup of ball mill showed a significantly lower energy
requirement for the stressed clinker in contrast to the unstressed clinker. The power
consumption for the stressed clinker was calculated to be 8994 kW while that of the
unstressed clinker is 10,790 kW. Since the stressed clinker had undergone comminution
prior to ball milling, the method is similar to hybrid comminution. Despite the observed
efficiency of the hybrid method, the efficiency of the ball mill is still affected by the size
of the grinding media as well as the fact that selection of optimum ball size is strongly
associated to the particle size [17].
In comparing HPGR and Ball mill using scaleup results from both sets of data, HPGR is
seen to be way more energy efficient in comminution with Em values of 7.34 kWh/t and
9.43 kWh/t as compared to 49.05 kWh/t and 44.22 kWh/t in the ball mill for the unstressed
and stressed clinkers respectively. This result falls in line with previous research reviewed
in the literature section. Considering that comminution is a major part of the mineral
processing industry, the slightest gain in efficiency during comminution could not only
make a huge difference in the operational cost of a processing plant but also help conserve
resources and maintain sustainability.
69
5 Summary and Conclusion
In addition to the main study on the influence of multiple stressing on cement clinker
comminution, this research work also looks at the sustainability of cement plants by
investigating the energy efficiency of the HPGR and ball mill techniques.
In particle comminution at different grinding pressures using the pistondie press, results
from eight different cycles in line with past literature showed that increase in pressure led
to an increase in product fineness. The direct comparison between the prestressed and
unstressed clinker was made to evaluate the effect of multiple stressing on clinker
comminution. The particle size distribution showed that the stressed clinker produced
more fines at every grinding pressure. Further analyses were made involving the plot of
the comminution ration, x50 and energy absorption against pressure. Comminution ration
and x50 both distinctly showed that the stressed clinker product had considerably more
fines than the unstressed clinker. The Em however, showed only a slight difference in
energy efficiency though the unstressed clinker required more energy to grind to finish.
Further using the pistondie press, simulation of grinding circuit was carried out at a
constant pressure of 150 MPa. Results show that a constant grinding point was reached
after 4 cycles for both clinkers and there was constant reduction in the energy absorption
for every cycle after the first grinding. The stressed clinker generally required less energy
to complete each cycle. The fourth cycle had the least energy absorption at 5.58 J/g while
the last cycle for the unstressed clinker had an energy absorption of 7.04 J/g. The PSD
curve however showed only some difference between both clinkers though the stressed
clinker had the higher proportion of fines.
The results for the grinding circuit tests were used in the scaleup calculations for HPGR
employing empirical functions by thyssenkrupp.
Further grindability tests according to Zeisel were carried out and the results obtained
were used for ball mill scaleup calculations. The scaleup was done for the grinding of
200 t/h of the cement CEM I 32.5 R, hence parameters were selected accordingly. For the
ball mill scaleup, empirical parameters from the Zisselmar were used.
Comparison between scaleup results of both HPGR and ball mill are shown in table 5.1.
For the purpose of sustainability and energy efficiency, HPGR comminution showed
much more favourable results in terms of power and energy efficiency.
70
Table 5.1 Comparing the major parameters calculated from scaleup of HPGR &
Zeisel tests
PARAMETERS
HPGR
BALL MILL
Unstressed
Clinker
Stressed
Clinker
Unstressed
Clinker
Stressed
Clinker
Diameter (m)
1.87
2.21
1.72
1.64
Length (m)
1.44
1.70
5.97
4.91
Power (kW)
1467.5
1886.11
10790
8994
Energy Consumption (kWh/t)
7.34
9.43
49.05
44.22
Throughput (t/h)
1411.8
1668.9
200
200
Specific Throughput (ts/m3h)
317.53
265.61


Scaleup results showed that the ball mill required energy input of 44.22 kWh/t when the
stressed clinker is being considered while HPGR required 9.43 kWh/t. For the HPGR
scaleup however, the stressed clinker showed an