- Email: [email protected]
Load behaviour in the Hicom nutating mill
Minerals Engineering, Vol. 11, No. 10, pp. 979-988, 1998
Pergamon 0892-6875(98)00084-3
© 1998 Published by Elsevier Science Lid All rights reserved 0892-6875/98/$ w see front matter
LOAD BEHAVIOUR IN THE HICOM NUTATING MILL
P.Q. NESBIT and M.H. MOYS School of Process and Materials Engineering, University of the Witwatersrand, PO Wits 2050, Johannesburg, South Africa. E-mail: [email protected] (Received 27 April 1998; accepted 24 June 1998)
ABSTRACT The Hicom nutating mill is a high intensity compact grinding mill of novel design. It is an adaptation of the centrifugal mill concept, but unlike the centrifugal mill, it's grinding chamber geometry and motion can only be adequately described in three dimensions. This has prompted an investigation into the load behaviour characteristics of the Hicom mill. Measurements of the Hicom mill's load behaviour have been made using conductivity and force probes passing through the shell of the mill. The results have shown that the load behaviour is unique and that existing two-dimensional load behaviour models for centrifugal mills are inadequate to describe the Hicom mill's load behaviour. The uniqueness of the Hicom mill's load behaviour is believed to be as a result of the vertical acceleration component of the chamber wall and base acting on the load. © 1998 Published by Elsevier Science Ltd. All rights reserved Keywords Comminution, modelling, process instrumentation
INTRODUCTION The Hicom nutating mill [ 1,2] is a relatively new concept and has only recently been used in commercial applications. A Hicom 120 mill has now been operating in a diamond recovery plant for over a year in the South African marine diamond industry, where it is reducing the volume of diamond bearing feed which reports to x-ray sorting equipment, without damage to the diamonds. A second plant is being commissioned for BHP Diamonds' Lac de Gras project in Canada, and is scheduled for operation later this year. Apart from its application in the treatment of diamondiferous ore, Hicom mills have been designed to mill ores to fine particle sizes (< 10 microns) cost-effectively. The Hicom mill is an adaptation of the centrifugal mill and the similarity between the two types of mills has resulted in proposed models for the Hicom mill [3,4] being based on existing centrifugal mill models. This assumption is the natural starting point for the development of a load behaviour model as the load behaviour of the centrifugal mill has been investigated, modelled analytically [5-7] and computationally using the Discrete Element Method (DEM) [8,9].
Presented at Corarainution "98, Brisbane, Australia, February 1998
979
980
p.Q. Nesbit and M. H. Moys
Modelling and measurement of mill load behaviours is essentially to increase our understanding of the fundamental behaviour of mill loads. This increased understanding will lead to better mill models, which will in turn lead to better mill design, control and process operation. A measurement technique based on the use of conductivity probes passing through the mill shell [10,11] was applied to rotary mills and gives an accurate measurement of the load orientation. It has been used for the development of mill power models and control strategies in industrial tumbling mills [12,13]. A problem with the conductivity sensor is that it indicates only the presence of slurry on the probes and gives no indication of the mass of the load above the probe, which can result in uncertainties in the analysis of the data. Another load sensing technique is the measurement of forces on mill liners [14]. This technique provides a quantitative measurement of the load and can be directly related to load mass, liner and media wear and power draw of the mill. These two techniques have furthered our understanding of mill load behaviours and provided information that is relevant for mill model development and verification. This paper discusses the measurements made of the Hicom mill's load behaviour using conductivity and force probes and the applicability of the two-dimensional Discrete Element Method (2D DEM) centrifugal mill model for the Hicom mill.
HICOM NUTATING M I L L The Hicom 90 mill, which is the pilot plant scale Hicom mill, is shown schematically in Figure 1. It uses a conical shaped grinding chamber, which is attached to a special rolling beating and drive arrangement. This design results in the chamber axis intersecting with the nutation axis at the stationary nutation point. The chamber motion results from the rotation of the chamber axis about the nutation axis. This motion is similar to that of a conical pendulum where the top is stationary and the bottom describes a circle instead of swinging in the plane. As is shown in Figure 1, the Hicom mill presents a stationary feed throat, allowing for feed material to be introduced from the top by a conventional feed hopper. This arrangement has the advantage over the centrifugal mill that experienced material handling problems when used on a continuous basis.
L
. . . . .
•
Electric motor
J
t
Feed chute
Spring coupling
Nutation point D
•
Nutafion axis Grinding chamber Services pack
Chamber axis II !
o
o
a
o
8
!
Fig. 1 The Hicom 90 mill.
i
!
Load behaviour in the hicom nutating mill
981
The Hicom mill, however, maintains the advantages of the centrifugal mill by operating with high acceleration fields and with high power densities (2500kW/m3 is typical of normal operation) to produce an intense grinding action. This intense grinding action results in rapid breakage rates per unit mill volume of 50 to 100 times that of conventional tumbling mills, which makes the mill suitable for rapid autogenous reduction and fine grinding processes. The novel design of the Hicom mill requires that the chamber motion be described in three dimensions. Figure 2 shows the motion of a point P fixed on the mill chamber from the top (x,y plane) and side (x,z plane) views. The radius of nutation or eccentricity is denoted by e, the chamber diameter by D, the nutation angle by rl and the nutation speed by co (rad/s). From the top view the base will appear as an ellipse with its major axis rotating with speed to, coinciding with the x-axis at t=0, T/2 and the y-axis at t=T/4, 3T/4.
~
..-
., f : 2
....
!
Y _...
Base att=T/4
- ~ " - - ~
Base at t=0
i
~'s %
Base
i
at
~-/:~-
~
".
. . . .
I ~
I
Base at t=3T/4
/
Patholehamberaxis
I
!
!
Chamber axisat
Chamber base at
t=T/4,3T/4 t=T/2
\
~
~t~I.T//4,3T/4
l
D/2
~
P~0
Fig.2 Motion of a fixed point P on mill chamber.
982
p.Q. Nesbit and M. H. Moys
During a single nutation cycle the mill chamber axis will subscribe a circle on the x,y plane of diameter 2E and point P will follow an elliptical path. The ellipse created by the path of point P will have a minor axis of e, a major axis of r' and be tilted at an angle of o~ to the x-axis. The motion of point P is unique, but it can be shown that all other points on the chamber cross section follow similar paths to P but are out of phase with P by an angle of cot. The dynamic analysis of the chamber reveals that a point on the outer diameter of the chamber base will experience a vertical acceleration of approximately 25% of the horizontal acceleration as shown in Figure 3. The influence of the vertical acceleration vectors on the load behaviour is not accounted for in 2D centrifugal mill models as these mills do not possess this vertical acceleration component. This acceleration component will have a significant effect on the load behaviour and it is important to quantify it for the optimisation of future designs of the Hicom mill.
13g mill axis I/Jlz--axis (nutationaxis)a, =~ L g vector (maximum centrifugal
T
D/2 i
a, = -13g
I,
I
I
I
~
•
t /a,:,0: ~
mill base
I I Fig.3 Vertical acceleration vectors on base of mill.
E X P E R I M E N T A L EQUIPMENT AND M E T H O D Two techniques are being used for the measurement of the load behaviour. The first technique uses conductivity probes. The conductivity probes were two screws imbedded in the rubber liners and separated by 5mm. The first screw is connected through a 10kfl resistor to a ±12 volt square wave power supply. The use of alternating current prevents any polarisation of the probes from taking place. The second screw is connected to ground. If a conductive fluid passes over the probe a change in the measured probe voltage occurs. This change in voltage provides information about the position of the load in the mill as a function of time. Eight conductivity probes were inserted into the liners of the grinding chamber as shown in Figure 4. The probes were sampled consecutively at an overall rate of 740 Hz, which at a mill speed of 960 rpm gives an eight degree resolution of the load position for each probe. The data was sampled using a 12 bit analogto-digital converter.
Load behaviourin the hicom nutating mill
983
The experiments were all performed in batch mode. The variables under consideration were: load volume( 35%, 45% & 55%); ball type( steel & ceramic); ball size (6ram & 16mm); liner geometry( smooth & ribbed) and finally water content(0.21 to 3.41 in increments of 0.41).
I
11 56
I
÷
8J
Fig.4 Eight axial conductivity probes. The second technique of load measurement uses a tri-axial force sensor as illustrated in Figure 5. The force sensor is mounted on the outside of the mill chamber with the force probe protruding through the shell wall. The sensor consists of three piezoelectric ceramics arranged in an equilateral triangle and clamped between two pre-stressing plates and the foot of the probe. Any force that is applied to the probe head produces voltage responses from the three piezoelectric ceramics. These responses are then filtered using a force sensor model to provide the three axial forces. A force sensor has been mounted on the bottom of the chamber (approximately where conductivity probe 4 is positioned in Figure 4). The probe was fitted with a circular head 3mm thick and 18ram in diameter. The mill was run with a 45% load volume of ceramic balls.
984
P.Q. Nesbitand M. H. Moys RESULTS AND DISCUSSION
The conductivity data allows for the determination of the load position as a function of time and mill position. To simplify the analysis of the conductivity data and to allow for easy visual comparison with the 2D DEM simulations it was required to display the data using a geometrical technique. The technique used divides the data up into several probability levels. Contour lines are then determined over the surface of the mill chamber for each conductivity level by interpolating between the probes. Each contour line then gives a probability of the load being in contact with the walls. The contour lines are then plotted together with the loci of the probes to produce a load orientation plot, as shown in Figure 6 (the shaded areas indicate where the load is in contact with the base of the mill with varying probability). This technique provides a "photograph" of the load position at a particular time. The mill position is such that the g-vector (maximum centrifugal acceleration vector) is pointing downwards (corresponding to the time t=3T/4 in Figure 3).
Chamber shell f
Mounting bolt _ ~ ~
~
Liner
"~
Probe head PI
I=
/
Force probe
.I
1 pl
p2
its3
~fJ
• .~
~___--~
Probe foot m PiezoelectriCceramic
Fh
Q
®
Top view
®!
,, Pre-stress bolt
Fig.5 Tri-axial force sensor. A load orientation plot of the nutating mill with 45% load volume of ceramic balls wetted with 0.2~ of water (approximately 2% of the load volume) is depicted in Figure 6. The load orientation plot shows some
Load behaviour in the hicom nutating mill
985
interesting features. Firstly, two separate loads (1 and 2 in Figure 6) are observed. It is believed that the first load is a pool of water moving in front of the ceramic ball mass. The second load, believed to be the ball mass, forms a spiral shape on the base of the chamber, indicating that contact with the load on the base takes place in the right half of the chamber. Thirdly, this load is in contact with the chamber walls between probes three and four, which indicates that the load lies predominantly in the bottom half of the chamber. SIDE VIEW II channels
l ~ u t a t i / /
I Ia x i s
7t 31/ J~
x i
.
II
Mill axis
k
c o n d u c d v i t y levels
d
high Fig.6
I I
low
Load orientation diagram of HiCom mill with 45% load volume of ceramic balls and 0.21 water (Q - quadrant).
This picture of the load contact in the Hicom mill is compared to the load plot of a centrifugal mill, under similar operating conditions, as predicted by the 2D DEM. The 2D DEM predicts that the load should be in contact with the walls of the mill in the second quadrant of the chamber, the conductivity measurements show that the load is in contact in the upper parts of the mill chamber wall equally spread between quadrant one and two. There is some similarity between the two load contacts on the walls of the mill and this does indicate some similarity between the two mills' load behaviours. However, Figure 7 shows a very different picture for the shape of the load on the base of the Hicom mill. The Hicom mill shows that virtually no load is measured in the second quadrant where the DEM predicts that most of the load should be.
2D DEM model
HiCom nutating mill
Fig.7 Comparison of 2D DEM with conductivity measurements from the Hicom mill.
986
P.Q. Nesbit and M. H. Moys
An explanation of this phenomenon requires an understanding of the motion of the base. The vertical acceleration of the base at point 1 is zero, whilst the velocity is a maximum. At point two the velocity is zero whilst the acceleration is at its maximum. This indicates that where the base is moving upwards it has contact with the load and when it moves downwards it does not have contact with the load. Thus it is shown that the load is in contact with the mill base which is moving upwards and is thus experiencing a vertical force. The wails in quadrant two are moving downwards and this is where part of the load is observed, thus the walls of the mill in quadrant two are applying a downward vertical force onto the load. It is known that the vertical acceleration of the chamber at the edge of the mill base is approximately 25% that of the horizontal acceleration and the conductivity data shows that the load is positioned where this vertical motion is taking place. The effect that this will have on the Hicom mill's load behaviour is unknown. It is further investigated with the measurement of forces in the mill. The results from the force sensor are shown in Figure 8. The normal force is that force exerted by the load normal to the surface of the chamber. The normal force measurement indicates that the load exerts a pressure of approximately 0.16MPa on the chamber walls at this position. The tangential force is the force exerted by the load tangential to the surface of the mill in a horizontal direction. The axial force is the force exerted by the load on the surface of the mill wall in a vertical direction. It is seen that the axial force is approximately half of the tangential force in the first set of peaks and only about 25-30% in the second set of peaks. There is some variation in the data, which is probably as a result of the probe head design and the natural variations that would occur in the load itself. However, this result does indicate that the mill chamber wall is exerting a vertical force on the load of the Hicom mill. It is believed that these vertical forces are responsible for the observed discrepancies between the 2D DEM simulations and the conductivity results from the Hicom mill.
50 45 40 35 z 30 • 25 o,0 15
normal \
-
'J^/
4
~"
~"
0
~
0.05 Fig.8
j~
one nutation / ' °'''6'a',,,I,,,,,-, n
/
rl* .
axial
.
w
0.07
0.09
time (a)
0.1t
0.13
0.15
Three axial forces measured from the Hicom mill operating with a 45% load volume of ceramic balls.
One complicating problem with the conductivity probes is that they are a poor indicator of load depth. This has created uncertainties in the data, as it becomes impossible to say whether we are observing a ball load or merely a water slick. This is particularly troublesome on the base of the mill where it is possible that the observed conductivity changes could be as a result of a thin pool of water. This is one of the reasons for the development of the force probe as these uncertainties will be eliminated.
Loadbehaviourin the hicomnutatingmill
987
CONCLUSIONS AND FUTURE WORK Eight conductivity probes have been inserted into the liners of the Hicom mill and measurements made of the load behaviour under various operating conditions. The results show a load in contact with the walls of the chamber that is significantly different to that predicted by the 2D DEM model for centrifugal mills. It is believed that the vertical acceleration component of the Hicom mill, which does not occur in the centrifugal mill, is responsible for the differences in the observed load behaviours. This belief is confirmed by the measurements of a tri-axial force sensor which has been mounted through the Hicom mills chamber wall. It shows that there is a vertical force component of significance being experienced by the load. Thus the influence of the vertical acceleration component on the load in the chamber is shown to be significant and that the modelling of the Hicom mill's load behaviour with 2D centrifugal mill models has limitations for the Hicom mill. The measurement of force exerted by the load on the mill liners is to be continued with the mounting of five tri-force sensors arrangement axially. The data from these measurements is to be compared with the results from the 3D DEM model for the Hicom mill, which is to be completed shortly by the South African Council of Mining Technology (Mintek). Furthermore, power draw is to be measured and compared to the predictions of the 3D DEM. With the success of this program new liner geometries will be designed and modelled using the 3D DEM to try and optimise the performance of the Hicom mill. ACKNOWLEDGEMENTS This work was sponsored by the C H Warman Group and it's divisions: Hicom International (Australia), Warman Research and Development (RSA) and M.D.Research (Australia). The permission granted to publish this paper by the Group is gratefully acknowledged. REFERENCES .
2. 3. 4. 5. 6. 7. 8. 9. 10. 11.
12.
Boyes, J.M., High Intensity Centrifugal Milling - A Practical Solution. Int. J. Min. Proc., 1988, 22, 413--430. Boyes, J.M., Performance Testing of a New High Intensity Centrifugal Mill. XIV Int. Min. Proc. Congress. Stockholm, Sweden, 1988, 135. Hoyer, D.I. & Boyes, J.M., The High-Intesity Nutating MiI1-A Batch Ball Milling Simulator. Minerals Eng. 1990, 3(1/2), 35-51. Hoyer, D.I., Power Consumption in Centrifugal and Nutating Mills Minerals Engng. 1992, 5(6), 671--684. Bradley, A.A., Some Principles of Centrifugal Milling, Third European Symposium on Comminution, Cannes, 1971, Weinheim, Vedag Chemie, 1972, 705-723. Hoyer, D.I., A Study of the Behaviour of the Centrifugal Mill. Ph.D. Thesis, 1984, Natal Univ., S.Africa. Hoyer, D.I., Particle Trajectories and Charge Shapes in Centrifugal Milling. Int. Conf. On Recent Advances in Minerals Sciences and Technology, Mintek, S.Africa, 1984, 401--409. Mishra, B.K. & Rajamani, R.K., The Discrete Element Method for the Simulation of Ball Mills. Appl. Math. Modelling, 1992, 16, 598-604. Inoue, T. & Okaya, K., Grinding Mechanisms of Centrifugal Mills. 8~ European Symposium on Comminution, Stockholm, Sweden, 1994, pp.431-440. Vermeulen, L.A., Ohlson De Fine, M.J. & Schakowski, F., Physical information from the inside of a Rotary Mill. J. S. Africa. Inst. Min. Metall., 1984, 84(8), 247-253. Moys, M.H., Measurement of Slurry Properties and Load Behaviour in Grinding Mills. IFAC Applied Measurements in Mineral and Metallurgical Processing, Sommer, G. ed., S. Africa, 1988, 3-9. Van Nierop, M.A. & Moys, M.H., The Effect of Overloading and Premature centrifuging on the Power of an Autogenous Mill. J. S. African Inst. Min. Metall., 1997, 97(7), 313-317.
988 13.
14.
P.Q. Nesbitand M. H. Moys Marklund, U. & Oja, J., Optimisation of an Autogenous Grinding Circuit through Mill Filling Measurement and Multivariate Statistical Analysis. SAG Conf., Vancouver, Canada, 1996, pp.617-631. Moys, M.H. & Skorupa, J., Measurement of the Radial and Tangential Forces Exerted by the Load on a Liner in a Ball Mill, as a Function of Load Volume and Mill Speed. Int. J. Min. Proc., 1993, 37, 239-256.
Correspondence on papers published in Minerals Engineering is invited, preferably by email to [email protected], or by Fax to +44-(0)1326-318352
Pergamon 0892-6875(98)00084-3
© 1998 Published by Elsevier Science Lid All rights reserved 0892-6875/98/$ w see front matter
LOAD BEHAVIOUR IN THE HICOM NUTATING MILL
P.Q. NESBIT and M.H. MOYS School of Process and Materials Engineering, University of the Witwatersrand, PO Wits 2050, Johannesburg, South Africa. E-mail: [email protected] (Received 27 April 1998; accepted 24 June 1998)
ABSTRACT The Hicom nutating mill is a high intensity compact grinding mill of novel design. It is an adaptation of the centrifugal mill concept, but unlike the centrifugal mill, it's grinding chamber geometry and motion can only be adequately described in three dimensions. This has prompted an investigation into the load behaviour characteristics of the Hicom mill. Measurements of the Hicom mill's load behaviour have been made using conductivity and force probes passing through the shell of the mill. The results have shown that the load behaviour is unique and that existing two-dimensional load behaviour models for centrifugal mills are inadequate to describe the Hicom mill's load behaviour. The uniqueness of the Hicom mill's load behaviour is believed to be as a result of the vertical acceleration component of the chamber wall and base acting on the load. © 1998 Published by Elsevier Science Ltd. All rights reserved Keywords Comminution, modelling, process instrumentation
INTRODUCTION The Hicom nutating mill [ 1,2] is a relatively new concept and has only recently been used in commercial applications. A Hicom 120 mill has now been operating in a diamond recovery plant for over a year in the South African marine diamond industry, where it is reducing the volume of diamond bearing feed which reports to x-ray sorting equipment, without damage to the diamonds. A second plant is being commissioned for BHP Diamonds' Lac de Gras project in Canada, and is scheduled for operation later this year. Apart from its application in the treatment of diamondiferous ore, Hicom mills have been designed to mill ores to fine particle sizes (< 10 microns) cost-effectively. The Hicom mill is an adaptation of the centrifugal mill and the similarity between the two types of mills has resulted in proposed models for the Hicom mill [3,4] being based on existing centrifugal mill models. This assumption is the natural starting point for the development of a load behaviour model as the load behaviour of the centrifugal mill has been investigated, modelled analytically [5-7] and computationally using the Discrete Element Method (DEM) [8,9].
Presented at Corarainution "98, Brisbane, Australia, February 1998
979
980
p.Q. Nesbit and M. H. Moys
Modelling and measurement of mill load behaviours is essentially to increase our understanding of the fundamental behaviour of mill loads. This increased understanding will lead to better mill models, which will in turn lead to better mill design, control and process operation. A measurement technique based on the use of conductivity probes passing through the mill shell [10,11] was applied to rotary mills and gives an accurate measurement of the load orientation. It has been used for the development of mill power models and control strategies in industrial tumbling mills [12,13]. A problem with the conductivity sensor is that it indicates only the presence of slurry on the probes and gives no indication of the mass of the load above the probe, which can result in uncertainties in the analysis of the data. Another load sensing technique is the measurement of forces on mill liners [14]. This technique provides a quantitative measurement of the load and can be directly related to load mass, liner and media wear and power draw of the mill. These two techniques have furthered our understanding of mill load behaviours and provided information that is relevant for mill model development and verification. This paper discusses the measurements made of the Hicom mill's load behaviour using conductivity and force probes and the applicability of the two-dimensional Discrete Element Method (2D DEM) centrifugal mill model for the Hicom mill.
HICOM NUTATING M I L L The Hicom 90 mill, which is the pilot plant scale Hicom mill, is shown schematically in Figure 1. It uses a conical shaped grinding chamber, which is attached to a special rolling beating and drive arrangement. This design results in the chamber axis intersecting with the nutation axis at the stationary nutation point. The chamber motion results from the rotation of the chamber axis about the nutation axis. This motion is similar to that of a conical pendulum where the top is stationary and the bottom describes a circle instead of swinging in the plane. As is shown in Figure 1, the Hicom mill presents a stationary feed throat, allowing for feed material to be introduced from the top by a conventional feed hopper. This arrangement has the advantage over the centrifugal mill that experienced material handling problems when used on a continuous basis.
L
. . . . .
•
Electric motor
J
t
Feed chute
Spring coupling
Nutation point D
•
Nutafion axis Grinding chamber Services pack
Chamber axis II !
o
o
a
o
8
!
Fig. 1 The Hicom 90 mill.
i
!
Load behaviour in the hicom nutating mill
981
The Hicom mill, however, maintains the advantages of the centrifugal mill by operating with high acceleration fields and with high power densities (2500kW/m3 is typical of normal operation) to produce an intense grinding action. This intense grinding action results in rapid breakage rates per unit mill volume of 50 to 100 times that of conventional tumbling mills, which makes the mill suitable for rapid autogenous reduction and fine grinding processes. The novel design of the Hicom mill requires that the chamber motion be described in three dimensions. Figure 2 shows the motion of a point P fixed on the mill chamber from the top (x,y plane) and side (x,z plane) views. The radius of nutation or eccentricity is denoted by e, the chamber diameter by D, the nutation angle by rl and the nutation speed by co (rad/s). From the top view the base will appear as an ellipse with its major axis rotating with speed to, coinciding with the x-axis at t=0, T/2 and the y-axis at t=T/4, 3T/4.
~
..-
., f : 2
....
!
Y _...
Base att=T/4
- ~ " - - ~
Base at t=0
i
~'s %
Base
i
at
~-/:~-
~
".
. . . .
I ~
I
Base at t=3T/4
/
Patholehamberaxis
I
!
!
Chamber axisat
Chamber base at
t=T/4,3T/4 t=T/2
\
~
~t~I.T//4,3T/4
l
D/2
~
P~0
Fig.2 Motion of a fixed point P on mill chamber.
982
p.Q. Nesbit and M. H. Moys
During a single nutation cycle the mill chamber axis will subscribe a circle on the x,y plane of diameter 2E and point P will follow an elliptical path. The ellipse created by the path of point P will have a minor axis of e, a major axis of r' and be tilted at an angle of o~ to the x-axis. The motion of point P is unique, but it can be shown that all other points on the chamber cross section follow similar paths to P but are out of phase with P by an angle of cot. The dynamic analysis of the chamber reveals that a point on the outer diameter of the chamber base will experience a vertical acceleration of approximately 25% of the horizontal acceleration as shown in Figure 3. The influence of the vertical acceleration vectors on the load behaviour is not accounted for in 2D centrifugal mill models as these mills do not possess this vertical acceleration component. This acceleration component will have a significant effect on the load behaviour and it is important to quantify it for the optimisation of future designs of the Hicom mill.
13g mill axis I/Jlz--axis (nutationaxis)a, =~ L g vector (maximum centrifugal
T
D/2 i
a, = -13g
I,
I
I
I
~
•
t /a,:,0: ~
mill base
I I Fig.3 Vertical acceleration vectors on base of mill.
E X P E R I M E N T A L EQUIPMENT AND M E T H O D Two techniques are being used for the measurement of the load behaviour. The first technique uses conductivity probes. The conductivity probes were two screws imbedded in the rubber liners and separated by 5mm. The first screw is connected through a 10kfl resistor to a ±12 volt square wave power supply. The use of alternating current prevents any polarisation of the probes from taking place. The second screw is connected to ground. If a conductive fluid passes over the probe a change in the measured probe voltage occurs. This change in voltage provides information about the position of the load in the mill as a function of time. Eight conductivity probes were inserted into the liners of the grinding chamber as shown in Figure 4. The probes were sampled consecutively at an overall rate of 740 Hz, which at a mill speed of 960 rpm gives an eight degree resolution of the load position for each probe. The data was sampled using a 12 bit analogto-digital converter.
Load behaviourin the hicom nutating mill
983
The experiments were all performed in batch mode. The variables under consideration were: load volume( 35%, 45% & 55%); ball type( steel & ceramic); ball size (6ram & 16mm); liner geometry( smooth & ribbed) and finally water content(0.21 to 3.41 in increments of 0.41).
I
11 56
I
÷
8J
Fig.4 Eight axial conductivity probes. The second technique of load measurement uses a tri-axial force sensor as illustrated in Figure 5. The force sensor is mounted on the outside of the mill chamber with the force probe protruding through the shell wall. The sensor consists of three piezoelectric ceramics arranged in an equilateral triangle and clamped between two pre-stressing plates and the foot of the probe. Any force that is applied to the probe head produces voltage responses from the three piezoelectric ceramics. These responses are then filtered using a force sensor model to provide the three axial forces. A force sensor has been mounted on the bottom of the chamber (approximately where conductivity probe 4 is positioned in Figure 4). The probe was fitted with a circular head 3mm thick and 18ram in diameter. The mill was run with a 45% load volume of ceramic balls.
984
P.Q. Nesbitand M. H. Moys RESULTS AND DISCUSSION
The conductivity data allows for the determination of the load position as a function of time and mill position. To simplify the analysis of the conductivity data and to allow for easy visual comparison with the 2D DEM simulations it was required to display the data using a geometrical technique. The technique used divides the data up into several probability levels. Contour lines are then determined over the surface of the mill chamber for each conductivity level by interpolating between the probes. Each contour line then gives a probability of the load being in contact with the walls. The contour lines are then plotted together with the loci of the probes to produce a load orientation plot, as shown in Figure 6 (the shaded areas indicate where the load is in contact with the base of the mill with varying probability). This technique provides a "photograph" of the load position at a particular time. The mill position is such that the g-vector (maximum centrifugal acceleration vector) is pointing downwards (corresponding to the time t=3T/4 in Figure 3).
Chamber shell f
Mounting bolt _ ~ ~
~
Liner
"~
Probe head PI
I=
/
Force probe
.I
1 pl
p2
its3
~fJ
• .~
~___--~
Probe foot m PiezoelectriCceramic
Fh
Q
®
Top view
®!
,, Pre-stress bolt
Fig.5 Tri-axial force sensor. A load orientation plot of the nutating mill with 45% load volume of ceramic balls wetted with 0.2~ of water (approximately 2% of the load volume) is depicted in Figure 6. The load orientation plot shows some
Load behaviour in the hicom nutating mill
985
interesting features. Firstly, two separate loads (1 and 2 in Figure 6) are observed. It is believed that the first load is a pool of water moving in front of the ceramic ball mass. The second load, believed to be the ball mass, forms a spiral shape on the base of the chamber, indicating that contact with the load on the base takes place in the right half of the chamber. Thirdly, this load is in contact with the chamber walls between probes three and four, which indicates that the load lies predominantly in the bottom half of the chamber. SIDE VIEW II channels
l ~ u t a t i / /
I Ia x i s
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Load orientation diagram of HiCom mill with 45% load volume of ceramic balls and 0.21 water (Q - quadrant).
This picture of the load contact in the Hicom mill is compared to the load plot of a centrifugal mill, under similar operating conditions, as predicted by the 2D DEM. The 2D DEM predicts that the load should be in contact with the walls of the mill in the second quadrant of the chamber, the conductivity measurements show that the load is in contact in the upper parts of the mill chamber wall equally spread between quadrant one and two. There is some similarity between the two load contacts on the walls of the mill and this does indicate some similarity between the two mills' load behaviours. However, Figure 7 shows a very different picture for the shape of the load on the base of the Hicom mill. The Hicom mill shows that virtually no load is measured in the second quadrant where the DEM predicts that most of the load should be.
2D DEM model
HiCom nutating mill
Fig.7 Comparison of 2D DEM with conductivity measurements from the Hicom mill.
986
P.Q. Nesbit and M. H. Moys
An explanation of this phenomenon requires an understanding of the motion of the base. The vertical acceleration of the base at point 1 is zero, whilst the velocity is a maximum. At point two the velocity is zero whilst the acceleration is at its maximum. This indicates that where the base is moving upwards it has contact with the load and when it moves downwards it does not have contact with the load. Thus it is shown that the load is in contact with the mill base which is moving upwards and is thus experiencing a vertical force. The wails in quadrant two are moving downwards and this is where part of the load is observed, thus the walls of the mill in quadrant two are applying a downward vertical force onto the load. It is known that the vertical acceleration of the chamber at the edge of the mill base is approximately 25% that of the horizontal acceleration and the conductivity data shows that the load is positioned where this vertical motion is taking place. The effect that this will have on the Hicom mill's load behaviour is unknown. It is further investigated with the measurement of forces in the mill. The results from the force sensor are shown in Figure 8. The normal force is that force exerted by the load normal to the surface of the chamber. The normal force measurement indicates that the load exerts a pressure of approximately 0.16MPa on the chamber walls at this position. The tangential force is the force exerted by the load tangential to the surface of the mill in a horizontal direction. The axial force is the force exerted by the load on the surface of the mill wall in a vertical direction. It is seen that the axial force is approximately half of the tangential force in the first set of peaks and only about 25-30% in the second set of peaks. There is some variation in the data, which is probably as a result of the probe head design and the natural variations that would occur in the load itself. However, this result does indicate that the mill chamber wall is exerting a vertical force on the load of the Hicom mill. It is believed that these vertical forces are responsible for the observed discrepancies between the 2D DEM simulations and the conductivity results from the Hicom mill.
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Three axial forces measured from the Hicom mill operating with a 45% load volume of ceramic balls.
One complicating problem with the conductivity probes is that they are a poor indicator of load depth. This has created uncertainties in the data, as it becomes impossible to say whether we are observing a ball load or merely a water slick. This is particularly troublesome on the base of the mill where it is possible that the observed conductivity changes could be as a result of a thin pool of water. This is one of the reasons for the development of the force probe as these uncertainties will be eliminated.
Loadbehaviourin the hicomnutatingmill
987
CONCLUSIONS AND FUTURE WORK Eight conductivity probes have been inserted into the liners of the Hicom mill and measurements made of the load behaviour under various operating conditions. The results show a load in contact with the walls of the chamber that is significantly different to that predicted by the 2D DEM model for centrifugal mills. It is believed that the vertical acceleration component of the Hicom mill, which does not occur in the centrifugal mill, is responsible for the differences in the observed load behaviours. This belief is confirmed by the measurements of a tri-axial force sensor which has been mounted through the Hicom mills chamber wall. It shows that there is a vertical force component of significance being experienced by the load. Thus the influence of the vertical acceleration component on the load in the chamber is shown to be significant and that the modelling of the Hicom mill's load behaviour with 2D centrifugal mill models has limitations for the Hicom mill. The measurement of force exerted by the load on the mill liners is to be continued with the mounting of five tri-force sensors arrangement axially. The data from these measurements is to be compared with the results from the 3D DEM model for the Hicom mill, which is to be completed shortly by the South African Council of Mining Technology (Mintek). Furthermore, power draw is to be measured and compared to the predictions of the 3D DEM. With the success of this program new liner geometries will be designed and modelled using the 3D DEM to try and optimise the performance of the Hicom mill. ACKNOWLEDGEMENTS This work was sponsored by the C H Warman Group and it's divisions: Hicom International (Australia), Warman Research and Development (RSA) and M.D.Research (Australia). The permission granted to publish this paper by the Group is gratefully acknowledged. REFERENCES .
2. 3. 4. 5. 6. 7. 8. 9. 10. 11.
12.
Boyes, J.M., High Intensity Centrifugal Milling - A Practical Solution. Int. J. Min. Proc., 1988, 22, 413--430. Boyes, J.M., Performance Testing of a New High Intensity Centrifugal Mill. XIV Int. Min. Proc. Congress. Stockholm, Sweden, 1988, 135. Hoyer, D.I. & Boyes, J.M., The High-Intesity Nutating MiI1-A Batch Ball Milling Simulator. Minerals Eng. 1990, 3(1/2), 35-51. Hoyer, D.I., Power Consumption in Centrifugal and Nutating Mills Minerals Engng. 1992, 5(6), 671--684. Bradley, A.A., Some Principles of Centrifugal Milling, Third European Symposium on Comminution, Cannes, 1971, Weinheim, Vedag Chemie, 1972, 705-723. Hoyer, D.I., A Study of the Behaviour of the Centrifugal Mill. Ph.D. Thesis, 1984, Natal Univ., S.Africa. Hoyer, D.I., Particle Trajectories and Charge Shapes in Centrifugal Milling. Int. Conf. On Recent Advances in Minerals Sciences and Technology, Mintek, S.Africa, 1984, 401--409. Mishra, B.K. & Rajamani, R.K., The Discrete Element Method for the Simulation of Ball Mills. Appl. Math. Modelling, 1992, 16, 598-604. Inoue, T. & Okaya, K., Grinding Mechanisms of Centrifugal Mills. 8~ European Symposium on Comminution, Stockholm, Sweden, 1994, pp.431-440. Vermeulen, L.A., Ohlson De Fine, M.J. & Schakowski, F., Physical information from the inside of a Rotary Mill. J. S. Africa. Inst. Min. Metall., 1984, 84(8), 247-253. Moys, M.H., Measurement of Slurry Properties and Load Behaviour in Grinding Mills. IFAC Applied Measurements in Mineral and Metallurgical Processing, Sommer, G. ed., S. Africa, 1988, 3-9. Van Nierop, M.A. & Moys, M.H., The Effect of Overloading and Premature centrifuging on the Power of an Autogenous Mill. J. S. African Inst. Min. Metall., 1997, 97(7), 313-317.
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14.
P.Q. Nesbitand M. H. Moys Marklund, U. & Oja, J., Optimisation of an Autogenous Grinding Circuit through Mill Filling Measurement and Multivariate Statistical Analysis. SAG Conf., Vancouver, Canada, 1996, pp.617-631. Moys, M.H. & Skorupa, J., Measurement of the Radial and Tangential Forces Exerted by the Load on a Liner in a Ball Mill, as a Function of Load Volume and Mill Speed. Int. J. Min. Proc., 1993, 37, 239-256.
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