## mill critical speed calculation

In this experiment the overall motion of the assembly of 62 balls of two different sizes was studied. The mill was rotated at 50, 62, 75 and 90% of the critical speed. Six lifter bars of rectangular cross-section were used at equal spacing. The overall motion of the balls at the end of five revolutions is shown in Figure 4. As can be seen from the figure, the overall motion of the balls changes with the mill speed inasmuch as the shoulder height shifts with the speed and the charge pressure reduced with the speed. At the highest speed the outer layer of discs tends to stick to the wall, showing a tendency to centrifuge.

The effect of mill speed on energy input was studied in a mill of 0.3-m diameter and 0.25-m long with 40% charge filling. The total charge weight was 54 kg. The variation in torque with speed is shown in Figure 5. It is seen from the figure that the energy input increases with mill speed and then drops off; this behavior is also observed in laboratory experiments.

Figure 3 shows the trajectory of a disc as the face angle of the lifter bars decreases. The speed of the mill was kept at 63% of the critical speed. The face angle was varied from 90 to 111 degrees for the three types of configuration 1, 2 and 4, as shown in the figure. Also, the height of the lifter bar in configuration 3 was changed to observe the trajectory. It was observed that the ball trajectories could be controlled by the face angle and the height of the lifter bars.

A smoothly lined mill consisting of 24 elements (walls) with 45% ball filling was simulated. The behavior of the charge was studied by changing the coefficient of friction at the wall. Three different disc sizes of equal proportion were used. The mill was rotated at 63% of the critical speed. The position of the balls at the end of five revolutions is shown in Figure 2. It is seen that, using a low coefficient of friction at the walls, balls tend to flow down the surface of the charge, and a toe begins to form. As the friction at the wall increases, cataracting motion is observed. A comparison of the energy input shows that for a coefficient of friction of 0.9 the energy input is about 1.5 times higher than for a coefficient of friction of 0.2.

## sagmilling.com .:. mill critical speed determination

The "Critical Speed" for a grinding mill is defined as the rotational
speed where centrifugal forces equal gravitational forces at the mill
shell's inside surface. This is the rotational speed where balls will
not fall away from the mill's shell.

Enter the width of a mill shell liner. Note this is not the width of a lifter! You may use the
Mill Liner Effective Width
calculation to determine this value. The mill critical speed will be calculated based on the diameter (above) less twice this shell liner width.

## ball mills

Ball Mills
What Are These Machines and How Do They Work?
Short flash video at bottom of page showing batch ball mill grinding in lab.
May have to click on browser "Allow Active X blocked content" to play
A Ball Mill grinds material by rotating a
cylinder with steel grinding balls, causing the balls to fall back into the cylinder and onto the material to be ground. The rotation is usually between
4 to 20 revolutions per minute, depending upon the diameter of the mill. The larger the diameter, the slower the rotation. If the peripheral
speed of the mill is too great, it begins to act like a centrifuge and the balls do not fall back, but stay on the perimeter of the mill.
The point where the mill becomes a centrifuge is called the "Critical Speed", and ball mills usually operate at 65% to 75% of the critical speed.
Ball Mills are generally used to grind material 1/4 inch and finer, down to the particle size of 20 to 75 microns.
To achieve a reasonable efficiency with ball mills, they must be operated in a closed system, with oversize material
continuously being recirculated back into the mill to be reduced. Various classifiers, such as screens, spiral classifiers,
cyclones and air classifiers are used for classifying the discharge from ball mills.
This formula calculates the critical
speed of any ball mill. Most ball mills operate most efficiently between 65% and 75% of their critical speed.
Photo of a 10 Ft diameter by 32 Ft
long ball mill in a Cement Plant.
Photo of a series of ball mills in a Copper Plant,
grinding the ore for flotation.
Image of cut away ball mill, showing material
flow through typical ball mill.
Flash viedo of Jar Drive and Batch Ball Mill grinding ore for testing
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## ball mill critical speed

A Ball Mill Critical Speed(actually ball, rod, AG or SAG) is the speed at which thecentrifugal forces equal gravitational forces at the mill shells inside surface and no balls will fall from its position onto the shell.

The mill speed is typically defined as the percent of the Theoretical Critical Speed, often abbreviated as %Cs.
The Theoretical Critical Speed (Cs) of rotation is the speed (in RPM) at which an infinitely small particle will cling to the inside of the liners for a complete revolution. The percent of critical speed is the ratio (expressed as a percentage) of the actual mill speed and the Theoretical Critical Speed of that mill. The critical speed of a rotating mill is the RPM at which a grinding medium will begin to centrifuge, namely will start rotating with the milland therefore cease to carry out useful work.

Ball and SAG Mills are driven in practice at a speed corresponding to 60-81% of the critical speed, the choice of speed being influenced by economical considerations. Within that range the power is nearly proportional to the speed.

## mill speed - an overview | sciencedirect topics

Medium-speed mills are smaller than low-speed units and are generally of the vertical spindle construction. The speed of the grinding section of these mills is usually 75225rpm. They operate on the principles of crushing and attrition. Pulverization takes place between two surfaces, one rolling on top of the other. Primary air causes coal feed to circulate between the grinding elements, and when coal becomes fine enough to be airborne, the finished product is conveyed to the burners or the classifier. Medium-speed mills require medium to high maintenance, but their power consumption is low.

In the ball-and-race mill (Fig. 13.3), balls are held between two races, much like a large ball bearing. The top race or grinding ring remains stationary while the bottom race rotates. As the coal is ground between large diameter balls and the ring, the balls are free to rotate on all axes and therefore remain spherical.

The grinding elements of a roll-and-race mill consist of three equally spaced, spring-loaded heavy conical (Fig. 13.4) or toroidal rolls (Fig. 13.5) suitably suspended inside near the periphery. These rolls travel in a concave grinding ring or bowl (with heavy armoring). The main drive shaft turns the table supporting the grinding ring, which in turn transmits the motion to the rolls. There is no metal-to-metal contact between grinding elements, since each roller rests on a thick layer of coal. Thus the maintenance is minimized.

Mills with conical rolls are known as bowl mills. As the coal is ground between large diameter rolls and the bowl, rolls revolve about their own axes, and the grinding bowl revolves about the axis of the mill.

During normal operation the mill speed tends to vary with mill charge. According to available literature, the operating speeds of AG mills are much higher than conventional tumbling mills and are in the range of 8085% of the critical speed. SAG mills of comparable size but containing say 10% ball charge (in addition to the rocks), normally, operate between 70 and 75% of the critical speed. Dry Aerofall mills are run at about 85% of the critical speed.

The breakage of particles depends on the speed of rotation. Working with a 7.32m diameter and 3.66m long mill, Napier-Munn etal. [4] observed that the breakage rate for the finer size fractions of ore (say 0.1mm) at lower speeds (e.g., 55% of the critical speed) was higher than that observed at higher speeds (e.g., 70% of the critical speed). For larger sizes of ore (in excess of 10mm), the breakage rate was lower for mills rotating at 55% of the critical speed than for mills running at 70% of the critical speed. For a particular intermediate particle sizerange, indications are that the breakage rate was independent of speed. The breakage ratesize relation at two different speeds is reproduced in Figure9.7.

Mills operating below 75rpm are known as low-speed mills. Low-speed units include ball or tube or drum mills, which normally rotate at about 1525rpm. Other types of mills, e.g., ball-and-race and roll-and-race mills, that generally fall into the medium-speed category may also be included in this category provided their speed is less than 75rpm.

Tube mills (Figure 4.9), also known as ball mills, are usually a drum-type construction or a hollow cylinder with conical ends and heavy-cast wear-resistant liners, less than half-filled with forged alloy-steel balls of mixed size. This is a very rugged piece of equipment, where grinding is accomplished partly by impact, as the grinding balls and coal ascend and fall with cylinder rotation, and partly by attrition between coal lumps inside the drum.

Primary air is circulated over the charge to carry the pulverized coal to classifiers. In this type of mill pulverized coal exits from the same side of the mill that solid coal and air enter. In some designs entry of solid coal air and exit of pulverized coal are provided at each end of the mill. Both ends of the mill are symmetrical in nature. Consequently, each mill is served by two coal feeders.

Reliability of this type of mill is very high and it requires low maintenance. The disadvantages of this type of mill are high power consumption, larger and heavier construction, greater space requirement, etc. To pulverize coal of high rank and low grindability, ball/tube mills are preferred because they can achieve high fineness, required for proper burning, and maintain high availability.

Dick and Lenard (2005) conducted cold rolling experiments on low-carbon steel strips, using progressively rougher rolls in a STANAT two-high variable speed mill. The strips were lubricated by O/W emulsions, delivered at a rate of 3l/m.

Five kinds of roll surfaces were prepared. In the first instance, the rolls were ground in the traditional manner to a surface roughness of approximately Ra=0.3m in the direction around and along the roll. The next surfaces were prepared by sand blasting, expected to create a random roughness direction. Using Blasto-Lite glass beads BT-11 resulted in a surface roughness nearly identical to that of the ground rolls, Ra=0.35m. The next surface was prepared using larger glass beads of grit #24, creating a randomly oriented surface, approximately Ra=0.91m. Following this, using #60 Lionblast oxide grit resulted in surface roughness of 1.31m and using BEI Pecal EG 12, another oxide grit, created surface roughness of approximately 1.76m.

Three lubricants, supplied by Imperial Oil, were used in an O/W emulsion. Walzoel M3 is a low-viscosity, high-VI oil with synthetic ester lubricity agents and phosphorus-containing antiwear agents. Its kinematic viscosity of 8.65mm2/s at 40C and 2.34mm2/s at 100C. Kutwell 40 is a medium-viscosity and medium-VI paraffinic oil with sodium sulphonate surfactant and antirust additives, and no lubricity ester or antiwear agents with a viscosity of 37mm2/s at 40C. Oil FSG is a high-viscosity, high-VI oil with natural ester lubricity agents and zinc- and phosphorus-containing antiwear agents. Its viscosity is 185mm2/s at 40C and 16.75mm2/s at 100C. The supplier estimates the droplets to be between 5 and 10m in size.

The results indicate that the roll separating forces depend on the roughness of the work roll in a very significant manner, as shown in Figure 9.30. Two sets of data are given in Figure 9.30, both for high reduction. The empty symbols indicate the forces at low rolling speeds, while the full symbols indicate the same at higher rolling velocities. The forces increase almost in a linear fashion as the roll roughness is increasing. The speed effect is also observable from Figure 9.30 and as above, under most conditions the forces drop as the speed increases.

In a recent manuscript Lenard (Lenard, 2004), dealing with cold rolling of 6061-T6 aluminium alloy strips, using a low-viscosity mineral seal oil and progressively rougher work rolls, the slopes of the roll forceroll roughness plots indicated sudden increases of the slope at approximately 1m Ra. These changes revealed the relative contributions of the adhesive and ploughing forces to friction and indicated that the effect of ploughing overwhelms that of adhesion. While it is possible that increasing the roll roughness beyond 1.76m Ra would lead to similar behaviour, no comparable observations can be made in the present study and within the range of the parameters, as no sudden changes of the slopes are demonstrated. The different observations result from the significant differences of the viscosities of the lubricants used. In the study of Lenard (2004) the mineral seal oils viscosity was 4.4mm2/s while in the present study the lightest oils viscosity is twice that. The low viscosity created a very low film thickness and the sharp asperities of the sand-blasted work roll must have pierced through the film as soon as contact was established at the entry. In the present work, the sharp asperities must also have pierced the oil particles but because of the higher viscosities, these likely have occurred later and to a lesser extent. Trijssenaar (2002) discusses the mechanisms that may cause continuous oil films: the coalescence and the break-up of the oil droplets and concludes that break-up is not likely to occur because of the low Weber numbers present during cold rolling. In the presence of the sharp edges of the asperities, created by the sand blasting process, the surface tension of the droplets may be overcome by the piercing action of the edges, leading to the creation of thin oil films.

During grinding, particles fracture when the applied stresses exceed the particle strength globally (massive fracture) or locally (fine wear debris is considered to be formed by attrition). The rate of particle size reduction increases with frequency of stress application and magnitude of the stress. However, particle size reduction rate typically decreases during the grinding process, for example, due to the increase in fracture resistance of the smaller particles.1

Impact energy depends on the specific mill design. It increases with mill speed, density and size of milling media (ball, rod, etc.). High impact energy is required to produce fine powders. However, very high mill speeds could lead to high wear of the balls inducing high contamination, excessive heating and lower powder yields.

The size of the milling media (typically 20:1 for ball:powder diameter) also influences size, morphology and microstructure of the powder. To produce fine powders, it is recommended to mill in several steps while reducing successively the milling media size, as one milling step usually induces a particle size reduction of about factor 10.

An increase in ball to powder ratio increases the impact frequency and the total energy consumption per second while the average impact energy per collision decreases. Typical values of this ratio range from 5 to 30. For the amorphisation of a powder this ratio may approach 100.

Additives (surface-active agents or process control agent (PCA) and lubricant) are used to nullify autohesion (Van der Waals forces) and so inhibit agglomeration, to reduce welding (atomic bonding) and/or to lower the surface tension of the material (proportional to the energy required to create new surfaces). Their aims are to shorten milling times and/or to produce finer powdersbb0010bb0010bb0010.1,5 The most widely used PCAs are alcohols, stearic acid and ethyl acetate.1 Small amounts of these additives remain in the powder and are responsible for contamination in C, H and/or O, which can reach 0.5 to 3wt%.4

Crushing and grinding equipment is available that can reduce particles in size from coarse (tens of centimeters) to very fine (submicron). The discussion here will be limited to grinding in the finer sizes, e.g., millimeters to micrometers and less. It should also be noted that the reduction ratio (feed size:product size) is limited for most machines and seldom exceeds about 10:1. In order to achieve higher reduction ratios, it is usually necessary to grind in stages.

Equipment suitable for fine grinding of brittle solids such as ceramic powders generally falls into one of several classes. Important examples include media mills, impact mills, and fluid-energy mills.

Media mills are the most widely used machines for fine grinding of powders. These machines contain individual loose grinding elementsthe grinding mediawhich can consist of balls, rods, pebbles, beads, etc. The action of the mill leads to motion of the media elements, which collide with each other and with the walls of the grinding chamber. Grinding occurs when particles are caught, nipped, in these collisions. Depending on the mechanisms used to induce media motion, this class of machines can be further subdivided into tumbling mills, vibratory mills, and stirred mills.

For each of these, the breakage characteristics are determined by the frequency of media collisions and by the energy associated with each collision. Collision frequencies depend on the motion of the mill and the number of media elements contained in it. The collision energy is also related to mill motion as well as to the mass of the individual elements. It follows that smaller media provide increased collision frequency but reduced breakage energy associated with each collision. As a consequence, breakage rates in media mills typically exhibit the kind of pattern illustrated in Fig. 3. For a fixed size of media, the rates initially increase with particle size because a greater volume is stressed in each collision. For very small particles impacted by coarse media the impact energy is sufficient to ensure breakage, while in the case of coarse particles the impact energy may be insufficient and only a fraction of such impacts will lead to breakage. Efficient operation of media mills depends on the proper matching of the media size to the size of the particles being ground. Size ratios of about 20:1 (media:particles) generally appear to be appropriate. Media density determines the impact energy and thereby the location of the maximum in the breakage ratesize relationship. Using a range of media sizes can extend the range of particle sizes that can be ground effectively. However, in order to obtain a large reduction ratio, it is usually best to grind in stages using progressively finer media in different mills or in different compartments of a continuous mill.

Since media mills generally operate by applying compressive stresses to particles, the relationships between breakage parameters and particle size tend to follow very similar patterns for different machines and operating conditions. Actual magnitudes, of course, vary substantially. For batch grinding systems, the set of breakage rates and breakage distributions for the different particle sizes present (or that can be produced) can be used to predict product size distributions as a function of grinding time. In the case of continuous grinding, additional information on the transport of particles through the mill is needed. Procedures for making such predictions are beyond the scope of this article and are well documented in the modern grinding literature (see the Bibliography). However, a useful, though very approximate, relationship that can be derived from a simplified treatment of the breakage process is that the required grinding time varies roughly with the reciprocal of the desired product size. Specifically:

The grinding energy in a properly designed media mill with appropriately sized media is usually sufficient to ensure massive fracture of the particles. However, the grinding action does not normally include high-speed impacts, so the breakage distributions typically take the form shown by curve I in Fig. 1.

Tumbling mills are the simplest and most commonly used type. Typically they consist of a horizontal cylinder, partially filled with the media and rotated about its horizontal axis, as illustrated in Fig. 4. Essentially, these mills operate by raising the media through rotation of the mill and allowing them to fall back under gravity. Thus the grinding energy is supplied by, and therefore limited by, gravity. The motion of the media is also controlled by gravity. As the rotational speed is increased, the motion changes from a cascading type where individuals roll and bounce over each other, to the cataracting condition which involves projection of media out of the bed after which they remain in free flight for a period before falling back into the bed. Eventually, a speed is reached at which the outer layers of media begin to centrifuge. This is known as the critical speed of the mill and it can be calculated, by equating gravity and centrifugal forces, from

where Nc is the critical speed (rpm), g is the gravitational constant, D is the mill diameter, and d is the media diameter. Tumbling mills are normally operated at about 7080% of the critical speed, which corresponds to maximum power input and is probably related to the transition between the cascading and cataracting regimes.

Media filling levels of about 50% of the mill volume are common in batch grinding; somewhat lower levels are required in continuous mills to allow for feed and discharge of powder. Powder loading is generally considered to be optimum when the voids in the media bed are just filled, i.e., the bulk volume of powder should be about 40% of the bulk volume of the media. Lower loadings allow too much direct mediamedia contact and wear while higher levels favor cushioning of mediamedia impacts and energy loss in rearrangement of particles. Fine grinding is very often carried out wet using slurry concentrations of up to 40% solids by volume. Wet grinding is generally considered to be more efficient than dry grinding, probably because of improved dispersion of the particles and reduced tendency for aggregation of fines. Grinding aids, typically surface-active agents, are available commercially for both wet and dry grinding. They probably function by improving particle dispersion.

Because of their wide application, design and scale-up criteria for tumbling mills are well established and standard test procedures, such as the well-known Bond Test, are available for evaluating specific materials. Tumbling media mills are quite effective for grinding to sizes in the 1050m range, but often require inordinately long grinding times for size reduction into the micron range.

Centrifugal mills are, for the most part, a special case of tumbling-media mills, the difference being the addition of a centrifugal component to increase the effective gravitational force. The typical arrangement involves a planetary type of motion in which the mill shell rotates about its own axis, which is itself rotated about a central axis. In effect, the mill is equivalent to a simple tumbling mill operating in a centrifugal, rather than a gravitational field. In contrast to conventional tumbling mills, rotational speeds, which determine media collision frequency, are not limited by the onset of centrifugation when the centrifugal force due to rotation of the shell equals or exceeds that of gravity (i.e., at the critical speed). As the mill speed increases, the effective gravitational force also increases. Provided the ratio of mill speed to orbital speed falls within a specified range, determined by the geometry of the planetary system, media motion in the mill is essentially independent of the actual speed. Practical operating speeds are limited only by mechanical design constraints. The principal advantage of centrifugal mills is that substantially higher grinding forces can be obtained than with the conventional types, even with small mills and fine media. Consequently, mill capacity is substantially increased and grinding can be extended to finer sizes. The main disadvantages are in mechanical design and questions of reliability. For these reasons, centrifugal mills have found only rather limited applications in commercial-scale grinding.

Stirred-media mills generally consist of a cylindrical, stationary vessel filled almost completely by grinding media and agitated by means of an internal impeller. In contrast to the tumbling mills, in which shearing of the media bed and, consequently, the grinding action is largely confined to the surface layers of the bed, the entire charge in a stirred mill is in motion at all times. As a result, the inherent capacity of these mills is significantly higher than that of their conventional counterparts. Mills agitated at low speeds are usually oriented vertically since the grinding force relies, to some extent, on gravity. In high-speed mills, centrifugal forces dominate over gravity and orientation is more a matter of convenience. For the most part, the grinding energy is derived from the kinetic energy of the media. Increasing the agitation rate increases both the media collision frequency and the impact energy, which leads to higher breakage rates and also extends the range of particle sizes that can be broken. Because of the high energies involved, stirred mills using fine media are especially suitable for grinding into submicron size ranges. As with the other kinds of media mills, careful matching of the media size to the size of the particles being ground can be critical to efficient operation. Powder loading so as just to fill the void space between the media elements is appropriate for these mills also. Wet grinding is normal, both to ensure particle dispersion and to assist in the removal of the excess heat developed in the process. For grinding to very fine sizes, it is common practice to circulate the slurry through a heat exchanger. Ceramic liners, agitators, and media can be used to minimize contamination due to wear.

Vibratory mills use oscillatory motion of the mill shell to agitate the media. As for the stirred mills, the active grinding zone encompasses the entire mill volume. The grinding energy is supplied by the inertia of the media and is not limited by gravity. In principle, high energy can be supplied to quite fine media, making these devices attractive for ultrafine grinding applications. By very careful matching of media size, powder size, and energy input (based on vibrational amplitude and frequency) it should be possible to achieve quite high grinding efficiencies. Unfortunately, mechanical design for reliability and low maintenance is not simple. Problems in these areas have tended to limit their large-scale application.

Impact mills induce particle breakage by collision with moving parts of the machine itself. A widely used example is the hammer mill which typically consists of a set of hammers rotating, usually at high speed, in a cylindrical case as shown schematically in Fig. 5. The shell of the case generally takes the form of a grate through which product particles can exit the mill. Breakage can result from direct impact between particles and hammers, by shearing of large particles between the hammers and the grate, or by particleparticle collisions in the highly turbulent environment of the mill. The classifying action of the grate is limited to quite coarse particles and product sizes are typically considerably finer than the grate opening size.

Impact velocities in hammer mills are normally very high which leads to fine breakage distributions of the form shown as curve II in Fig. 1. Because of the high impact velocities employed, large particles are broken very effectively. At finer sizes, however, breakage is probably limited by aerodynamic factors; entrainment of the particles tends to reduce the probability of impact as well as the severity of those impacts that do occur. As a consequence, high-speed, mechanical-impact mills are ideal for reducing a relatively coarse feed to a considerably finer size in a single stage. They cannot, however, be used to reduce a complete batch of material into the micron size range.

Fluid-energy mills, also known as jet mills, rely on collisions in a stream of particles entrained in a high-velocity fluid, typically air or steam, to effect breakage. In the pancake type, the particle-laden stream is injected through peripheral jets into a flat, cylindrical chamber at extremely high velocity. The highly turbulent environment so generated leads to high-velocity impacts between particles and with the walls of the chamber. The systems are generally designed so as to remove fine particles with the fluid while coarser material is retained for further breakage. An alternative arrangement is the opposed jet type in which particles enter the chamber through jets arranged in direct opposition to each other, the idea being to promote breakage by particleparticle collisions rather than by impact against chamber walls. Designs of this kind are intended to reduce contamination due to wear of machine surfaces.

Fluid-energy mills are commonly used to produce particles in the 110m size range. Product size distributions are often relatively narrow which may be due in part to the loss of extremely fine (submicron) material in the product collection system.

This case study illustrates the impact of changes in contamination control showing how condition monitoring was used in association with improved filtering to reduce environmental effects through reductions in the disposal of consumables and scrap product. Increased profitability, through increased reliability, is also a consequential benefit.

Ding [15] reports on developments at the No-Twist Finishing Mill, at the BHP Steelworks in Newcastle, Australia. The mill contains 63 gear sets, 99 rolling element bearings and 43 assorted bearings. The system had been found to fail without warning due to its high operating speed. A comprehensive lubricant assessment programme was implemented to improve performance. The programme included: viscosity measurement, assessment of oxidation and additive depletion, assessment of solid particle contamination, spectrometric analysis and ferrography. It was found that 82% of oil samples were outside target levels and there were high levels of abrasive wear.

Improved filtering was implemented and over a period of 3 years a change of filter specification from >30 m to 6 urn allowed a speed increase in the plant from 46 ms-1 to 120 ms-1 accompanied by a significant reduction in bearing failure. (See figure 2.)

These outcomes highlight the relationship between contamination control and bearing life extension. Solid particle contamination control is an often-overlooked aspect of the oil analysis condition monitoring strategy. Not only can the mill speed increased substantially after the improvements, but the number of bearing failures has also been reduced. The environmental impact of monitoring the contamination levels has thus lead to a reduction in the replacement of failed bearings, reducing the off-site environmental impact of the bearing manufacturing, but also, reducing the additional power demand and disposal of maintenance consumables associated with the task of a bearing change.

Penton [16] reports an interview with the plant's Reliability Engineer which describes how monitoring solid particle levels highlighted an issue with short element life on the tissue mill bearing oil filters.

Owing to a lack of monitoring and trending of metrics, the fact that the filters in use on the mill were blinding every 3 days was overlooked for several years. It had not occurred to the operations staff responsible for the changing of these filters that there was an issue. However, through a proactive monitoring programme, the solid particle levels were found to be exceptionally high. The short filter element life came to light during the investigation, and the root cause was found to be the fact that the tank had a problem with high levels of contaminant ingress. This was rectified and the filters now last in excess of six months, with a subsequent annual saving of 10,000. More importantly, the environmental impact of the filter disposal has been reduced, both on-site and off-site.

The third case study is drawn from Tutuka Power Station which operates in South Africa [17]. It was put into full commercial operation in 1990 and during the first year of its operation a study was conducted to improve machine reliability and reduce lubricant consumption. Several areas of the station were investigated.

The coal pulverisers use steel balls to pulverise coal prior to burning. Each pulveriser has a lubrication system supporting main bearings, drive motor bearings and main drive gearing. Initially reliability problems were encountered as a result of contamination by coal dust and ash. With the implementation of condition monitoring, proactive lubrication management and improvements in sealing of bearings, the average lubricant drain interval was increased from the suppliers recommendation of 4000 hours to 27,968 hours. These actions led to an annual reduction in the disposal of lubricating oil of 43,684 litres.

The successful action on the coal pulverisers led to changes in the practices being used elsewhere in this parts of the plant. For example, the lubrication systems for six high capacity fans and an air heater were also modified by the implementation of portable offline filtering allowing re-use of 5,940 litres of oil until oil testing indicated it has become unfit for use.

Accumulated of savings 13,879 litres of waste oil per boiler mill were achieved through all improvements in practice leading to a total saving of 499,648 litres of oil for the 36 boiler mills on the site in an operating period of just over 3 years.

Cattaert [17] reports further that by implementing other monitoring programmes and (unspecified) improvements in the turbine lubricating system lubricant losses have also been reduced in this area of the station.

Lubricants are replaced by both schedule and condition based practice. Improvements in practice have resulted in a reduction in the use of lubricant under both forms of approach. Condition based lubricant usage has fallen by 79%, while schedule based lubricant consumption has fallen by 77%.

The savings made in lubricant disposal at the station make a significant contribution to reducing environmental contamination as well as offering economic advantage including: savings in manpower, outage and consumables.

Comminution consumes the largest part of the energy used in mining operations, from 30 to 70% (Radziszewski, 2013b; Nadolski et al., 2014). This has consequently drawn most of the sustainability initiatives designed to reduce energy consumption in mining, including, for example, the establishment of CEEC (Coalition for Eco-efficient Comminution, www.ceecthefuture.org) and GMSG (Global Mining Standards Guidelines Group, www.globalminingstandards.org).

One approach is to ask if all the ore needs fine grinding, where the bulk of the energy is consumed. Certainly in the case of low grade ores, much of the gangue can be liberated at quite coarse size and its further size reduction would represent inefficient expenditure of comminution energy (Chapter 1). This provides an opportunity for ore sorting, for example (Chapter 14). Lessard et al. (2014) provide case studies showing the impact on comminution energy of including ore sorting on crusher products ahead of grinding. Similar in objective, the development of coarse particle flotation technologies (Chapter 12) aims to reduce the mass of material sent to the fine grinding (liberation) stage.

This still leaves the question of how efficiently the energy is used in comminution. It is common experience that significant heat is generated in grinding (in particular) and can be considered a loss in efficiency. However, it may be that heat is an inevitable consequence of breakage. Capturing the heat could even be construed as a benefit (Radziszewski, 2013b).

A fundamental approach to assessing energy efficiency is to compare input energy relative to the energy associated with the new surface created. This increase in surface energy is calculated by multiplying the area of new surface created (m2) by the surface tension expressed as an energy (J m2). On this basis, efficiency is calculated to be as little as 1% (Lowrison, 1974). This may not be an entirely fair basis to evaluate as we suspect that some input energy goes into deforming particles and creating micro-cracks (without breakage) and that the new surface created is more energetic than the original surface, meaning the surface tension value may be underestimated. In addition, both these factors may provide side-benefits of comminution. Rather than this comparison as a basis, other measures use a comparison against a standard.

Single particle slow compressive loading is considered about the most energy efficient way to comminute. Comparing to this basis, Fuerstenau and Abouzeid (2002) found that ball milling quartz was about 15% energy efficient. From theoretical reasoning, Tromans (2008) estimated the energy associated with breakage by slow compression and showed that relative to this value the efficiency of creating new surface area could be as high as 26%, depending on the mineral.

Nadolski et al. (2014) propose an energy benchmarking measure based on single particle breakage. A methodology derived from the JK Drop-weight Test is used to determine the limiting energy required for breakage, termed the essential energy. They derive a comminution benchmark energy factor (BEF) by dividing actual energy consumed in the comminution machine by the essential energy. They make the point that the method is independent of the type of equipment, and can be used to include energy associated with material transport as well to assess competing circuit designs.

This is obtained for a comminution device using Eq. (5.4), by measuring W (the specific energy being used, kWh t1), F80 and P80 and solving for Wi as the operating work index, WiO. (Note that the value of W is the power applied to the pinion shaft of the mill. Motor input power thus has to be converted to power at the mill pinion shaft output by applying corrections for electrical and mechanical losses between the power measurement point and the shell of the mill.) The ratio of laboratory determined work index to operating work index, Wilab:WiO, is the measure of efficiency relative to the standard: for example, if Wilab:WiO <1, the unit or circuit is using more energy than predicted by the standard test, that is, it is less efficient than predicted. Values of Wilab:WiO obtained from specific units can be used to assess the effect of operating variables, such as mill speed, size of grinding media, type of liner, etc. Note, this means that the Bond work index has to be measured each time the comparison is to be made. An illustration of the use of this energy efficiency calculation is provided by Rowland and McIvor (2009) (Example 5.2).

a.A survey of a SAG-ball mill circuit processing ore from primary crushing showed size reduction of circuit (SAG) feed F80 of approximately 165,000m to flotation circuit feed (cyclone overflow) P80 of 125m. The total specific energy input for the two milling stages was 14.6kWh t1. Calculate the operating work index for the circuit.b.Circuit feed samples taken at the same time were sent for Bond work index testing. The rod mill test gave RWilab of 14.5kWh t1 and a ball mill work index BWilab of 13.8kWh t1. Accepting that the rod mill work index applies to size reduction of the circuit feed down to the rod mill test product P80 of 1050m and that the ball mill work index applies from this size to the circuit product size, calculate the standard Bond energy for the circuit.c.Calculate the combined Wilab and the relative efficiency, Wilab:Wio. What do you conclude?

A survey of a SAG-ball mill circuit processing ore from primary crushing showed size reduction of circuit (SAG) feed F80 of approximately 165,000m to flotation circuit feed (cyclone overflow) P80 of 125m. The total specific energy input for the two milling stages was 14.6kWh t1. Calculate the operating work index for the circuit.

Circuit feed samples taken at the same time were sent for Bond work index testing. The rod mill test gave RWilab of 14.5kWh t1 and a ball mill work index BWilab of 13.8kWh t1. Accepting that the rod mill work index applies to size reduction of the circuit feed down to the rod mill test product P80 of 1050m and that the ball mill work index applies from this size to the circuit product size, calculate the standard Bond energy for the circuit.

a.The appropriate form of Eq. (5.4) is:14.6=10Wio(11251165000)Wio=16.8(kWht1)b.Bond energy for both size reduction stages is:From rod mill test:W=1014.5(110501165000)W=4.1(kWht1)From ball mill test:W=1013.8(112511050)W=8.1(kWht1)Therefore predicted total is: WT=12.2kWh t1c.The combined test work index for this ore, WilabC is given by:12.2=10WilabC(11251165000)WilabC=14.0(kWht1)and, thus:WilabCWio=14.016.8=0.83(or83%)This result indicates the circuit is only 83% efficient compared to that predicted by the Bond standard test.

The procedure has the virtue of simplicity and the use of well recognized formulae. Field studies have shown the ratio can vary as much as 35% from unity (some circuits will operate at greater efficiency than the Bond energy predicts). Rowland and McIvor (2009) discuss some of the limitations of the method. They note that the size distributions from AG/SAG milling can be quite unlike those from rod and ball mills on which the technique originated; and, beyond giving a measure of efficiency, it does not provide any specific indication of the causes of inefficiency. In the case of ball mill-classifier circuits functional performance analysis does provide a tool to identify which of the two process units (or both) may be the source of inefficiency.

McIvor (2006, 2014) has provided an intermediate level (i.e., between the simple lumped parameter work index of Bond, and the highly detailed computerized circuit modeling approach) to characterize ball mill-cyclone circuit performance.

Classification System Efficiency (CSE) is the percentage of coarse size (typically with reference to the P80) material occupying the mill and can be calculated by taking the average of the percentage of coarse material in the mill feed and mill discharge. As this also represents the percentage of the mill energy expended on targeted, coarse size material, it is directly proportional to overall grinding circuit efficiency and production rate. Circuit performance can then be expressed in the Functional Performance Equation for ball milling circuits, which is derived as follows.

Define fines as any product size material, and coarse as that targeted to be further ground, the two typically differentiated by the circuit target P80. For any grinding circuit, the production rate of new, product size material or fines (Production Rate of Fines, PRF) must equal the specific grinding rate of the coarse material (i.e., fine product generated per unit of energy applied to the coarse material) times the power applied to the coarse material:

A measure of the plant ball mills grinding efficiency is the ratio of the grinding rate of the coarse material in the plant ball mill compared to the grinding rate, or grindability, of the same coarse material (g rev1) as measured in a standardized test mill set up. That is:

This is a simple yet insightful expression of how a ball mill-cyclone circuit generates new product size material. Rate of production is a direct function of the material grindability, as well as the amount of power provided by the mill. It is also a direct function of two separate and distinct efficiencies that are in play. Each of these efficiencies is specifically related to certain physical design and operating variables, which we can manipulate. The terms in the equation are generated by a circuit survey. Thus, the Functional Performance Equation provides understanding and opportunity for plant ball mill circuit optimization.

It is also noteworthy that the complement to CSE is the fraction of mill energy being used on unnecessary further grinding of fines. Such over-grinding is often detrimental to downstream processing and thus an important motivator to achieve high CSE, even beyond its impact on grinding circuit efficiency.

The coal-milling product is pulverized fuel PF containing grains with a different size (polydisperse product). The degree of comminution can be defined using the Rx =f(x) function referred to as the pulverized material grain-size characteristic. Parameter Rx denotes the mass content of the dust specimen particles, which are bigger than size x. So-defined contents can be determined easily by sieving (so-called sieve analysis), and quantity Rx represents the cumulative percentage retained on a sieve with a mesh diameter equal to x. To describe the PSD, a cumulative percentage Dx of particles that are smaller than the size x is also used. It is obvious that the relation between Rx and Dx is

Joining the points given by the sieve analysis and plotted onto the Rx x system, a graphic characteristic is obtained. In order to describe the distribution of product, obtained from milling minerals by means of mills used in boiler technology, the model of Rosin-Rammler-Sperling-Bennett (RRSB) is used:

where Rx [%] is the content of grains bigger than x in m, b is the comminution number, and n is the uniformity (polydispersity) number. The formula was supplemented with an equation that introduced the interdependence between b and n

As a result, the PSD governed by the RRSB law can be determined unequivocally by giving the material retained amount on two sieves. The polydispersity number n characterizes the degree of uniformity of the product grains. For n=, the product would be composed of particles with an identical size (monodisperse pulverized material). The polydispersity number depends on the type of the mill (especially - the classifier) and the kind of milled coal. In Polish hard coal installations n0.71.6. Lower values correspond to high-speed pulverizers, e.g., fan mills, while higher ones are observed in low and medium speed mills. Reconstructions of mills and classifiers to meet NOx emission limits are made to produce finer particles with increased n values. This strongly affects the PSD of RRSB particles (Table5.1). The average particle diameter dp and the specific surface area Fp of the particles, resulting from PSD, have a large impact on the combustion process, radiation heat transfer, as well as on slagging, fouling, and fly-ash erosion. As n decreases, dp also decreases, while Fp of the milling product increases. The diameter dp is associated with Fp according to the equation

which means that a higher furnace loss will arise if the boiler is fired with PF with a lower value of n. Raising the polydispersity number is also beneficial regarding energy for the same value of R0.09, less energy is required to obtain product with a higher value of n.

The comminution number b or the grain size xm corresponding to it characterize the degree of the product comminution. The higher the value of b (or lower the value of xm) at a given polydispersity number, the greater the degree of material comminution and the larger the unit surface area expressed in m2/kgdust.

There is a need to describe the relationship between the capacity of the mill and the properties of the milled material. Appropriate methods are based on various comminution theories, the most common of which are Rittingers [2], Kicks [3] and Bonds [4].

The commonly used method to evaluate the grindability of coal in medium speed pulverizers is the Hardgrove Grindability Index (HGI) [5]. The HGI test is based on Rittingers theory. It allows to predict the mill output, performance and energy requirements, and (qualitatively) also the particle size distribution after milling [6]. As the value of HGI increases, the capacity of the mill increases as well. Numerous experiences show that if the HGI test is a good indicator of milling performance for medium speed mills when grinding coal, it is poor for other materials such as biomass. Another disadvantage of HGI is that the tester is a batch device and does not reflect the continuous grinding process.

Broad dissemination of biomass burning in PF boilers caused the search for other indicators better reflecting the comminution of such materials [79]. The studies show that in this case better results give the methods based on Bonds theory.

By the term quality of pulverized coal is understood its fineness (cumulative percentage retained R0.09 and R0.20 or other assumed pair of Rx values) in conjunction with its homogeneity described by the uniformity (polydispersity) number n. The quality described in this way obviously results from PSD, which is a continuous function (Weibull distribution).

The problem of optimizing the quality of the pulverized coal has long been the subject of research because of its importance for the operating costs of the power unit. This resulted in a variety of recommendations [1214]. However, they have now lost validity because of economic changes and the emergence of restrictions on NOx and CO2 emissions. Another method, in the form of an algorithm based on economic criteria and taking into account the variations of the power unit load as well as the durability and the output of pulverizers, is presented in Ref. [1]. The data in the algorithm are obtained from tests of pulverizers of a 650t/h PF boiler (OP650) in a Polish power plant. On the basis of these studies, relationships were derived between the fineness of the produced pulverized fuel and operating parameters, the efficiency of the boiler and parameters of the milling system, e.g., energy consumption of the mill and its fan. The influence of variation of excess air in the boiler on the maximum grain size that can burn at an acceptable unburned combustibles level is also shown. The analysis of the impact of the composition of the mineral part of the Polish hard coals to the abrasion of mills was made.

Based on the measurements carried out and the actual periods between overhauls of mills of the boiler under investigation, which were determined during the operation, a correlation was found to determine the abrasive wear rate of the elements of ring-ball mills with a nominal output of 33t/h (type MKM33). The following function was determined for this particular set of data:

The optimization described in Ref. [1] is an effective tool for a quantitative assessment of the most favorable conditions of the mill-furnace system operation in the case of the tested power plant. The proposed algorithm could also be used for other PF boilers provided that measurements were performed to select functions based on the measuring data appropriately.

For installations with other types of pulverizers, the general form of the algorithm (made in the form of the MS Excel spreadsheet) remains the same. However, functions derived for MKM33 mills have to be replaced with other resulting from respective research.

Further development of the described method should allow the automation of settings of blades in static classifiers of pulverizers or rotational speed in dynamic ones. It can be included in online monitoring of the boiler thermo-flow parameters, in a similar way to that presented in Ref. [15]. An additional improvement in optimization accuracy can be provided by online monitoring of the particle size of the pulverized fuel [1619].

The optimization results depend not only on PSD, but also on other parameters of influence. The diagrams in Fig.5.2 and Fig.5.3 show the difference in total costs related to fuel and comminution process. A higher NCV value, which reduces fuel consumption, allows the boiler to operate at high loads using only three mills, while with a reduced NCV value four mills are required. However, the low NCV fuel is cheaper what affects the costs.

Taking into account significant share of maintenance cost in the total cost, economic optimization allows to choose the option of replacing parts that are susceptible to wear by choosing for example between coal piping made of cast ductile iron, carbon steel, and ceramic lined elements.

The type of fuel is another important impact parameter. Even hard (bituminous) coal has many varieties with different petrography, especially when comparing coals from the northern and southern hemispheres. For example, in Ref. [20] it was shown that German coal contained 20%30% inertinite, while South African 66%71% with similar Vdaf content. High inertinite coal requires a higher ignition temperature and burns slowly. Therefore, the replacement of German coal with South African coal requires its finer pulverizing.

Simple stainless steel, glass-lined, or even mild steel vessels, fitted with a suitable stirrer, are more than adequate for the production of solvent-based primers. These vessels will often be fitted with internal or external heating elements and water-cooled condensers, so that, for example, polymeric ingredients can be more readily dissolved at temperatures close to the reflux temperature of the solvent or solvent blend. This procedure is also valid for solvent-based structural adhesives.

If water-based primers are being manufactured, then the situation is slightly more involved. The use of water means that only glass-lined or stainless steel vessels can be used for the final stage of mixing. In many instances, solid raw materials will not be supplied as a water-based solution or dispersion and, hence, the first stage of any manufacturing process requires suitable solution/dispersions to be made. This is often achieved using a conventional bead mill (Fig. 13.43), where bead size, bead volume, temperature, pump rate, solids content, pH, and so on, all have to be optimized.

This is best carried out using statistical experimental design techniques,15,16 optimizing the process conditions against the critical parameter of resultant particle size distribution. Once the variables to be studied have been identified, an experimental design can be created. This is usually a standard quadratic model, which can fit nonlinear data. The experimental designs produced allow several variables to be studied at once, which enables a wide area of experimental space to be mapped. This enables interactions to be identified and areas of optimum performance to be found.

The resultant matrix of experiments comprises a series of trials with each chosen variable set at high, low, or intermediate values; replication of some trials is used to assess error; other parameters are held at a constant value.

Data analysis then fits a polynomial equation to the collected data. The magnitudes of the coefficient estimates in the equation indicate the importance of the variables. This equation can be simply viewed as a multidimensional French curve to illustrate the relationship between variables and responses. Those coefficient estimates with statistical significance are highlighted and are used to select the axes for contour plots.

Bishopp et al.17 show a contour plot, or response curve, for the variation in bead size and pump rate against the D0.9 value for the particle size (D0.9 is the particle size, in m, below which 90% of the particles fall); constants are bead volume at 75% and mill speed at 4000 rpm.

Contour plots allow the relationship between significant variables and responses to be visualized. These plots resemble topographical maps in that contour lines are drawn on a two dimensional plane to represent the surface of a response variable. This allows a highly visual, easily interpreted picture to be used to understand the process or system being studied. Thus, in the example given in Ref. 17, it is very clear that the lowest particle size is achieved using intermediate bead dimensions and that it is essentially independent of pump rate.

Low-viscosity pastes can usually be manufactured using simple stirrers to disperse and/or dissolve the raw materials. However, as the viscosity increases so does the need to use high-shear stirrers such as toothed-bladed stirrers, planetary mixers, and/or Z-blade mixers.

Insoluble powders, which can include blowing agents for foaming adhesives, curatives, fillers, and so on, can be predispersed in any liquid polymer or resin present, thoroughly wetted out using a conventional two-roll paint mill and then added as an intimate dispersion to the main mix.

Other techniques such as mixing under vacuum or under a nitrogen blanket might be necessary should incorporated air prove a problem or, as is the case with isocyanate resins and some aliphatic amines where the raw materials are reactive with moisture in the air.

In essence, there are two methods of manufacturing film adhesives: from solution or from a melt. In the first case, the film has to be cast and the solvent has to be removed in a continuous operation. In the second case, as there is no solvent to be removed, the matrix has to be melted and then cast into film; this is the so-called hot melt film technique.

The initial stage, in either case, is to produce the fully formulated matrix; the solvent-based system can use similar equipment as is used to manufacture primers and the hot-melt route would use the same sort of plant as is used for the high-viscosity pastes except that the capability of heating and then cooling the matrix during the mixing cycle will be required.

Film casting also gives rise to, essentially, two different procedures. When preparing films from solvent-based matrices, the actual equipment used can be dependent on the final areal film weight. Low areal weights, for example, 50100 g/m2, can utilize conventional reverse roll coating of a continuous film onto a backing paper. This would pass straight into an air-circulating oven whose various zones would be set to drive off the residual solvent without leading to skinning or blistering of the final film. For areal weights more than 100 g/m2, lower weight films can be laminated together through nip rollers or a suitable metering device; for example, a doctor knife-over-table or knife-over-roll technique can produce film at the correct weight, which can then be dried as before.

When 100% solid matrices are employed, manufacture of the film is simplified because no solvents have to be removed, but, nevertheless, highly specialized equipment has to be used. Figure 13.44 shows a schematic representation for a batch process in which the mixed formulation is metered, at a suitable elevated temperature, under a doctor knife to produce the final film.

Using the hot-melt approach, it is possible to mix and cast the adhesive film as a continuous operation. Here, the individual raw materials are fed into a conventional screw extruder, are mixed under controlled temperature conditions, and are then pumped out into a reverse-roll coating machine that can produce film adhesives from as low as 50 g/m2 up to about 1800 g/mm2. The schematic representation of such a process is shown in Fig. 13.45.

Mention has already been made of Redux 775, the first structural adhesive film. Its manufacturing process has not changed since 1954. A film of phenolic resole is cast under a doctor knife, a considerable excess of the Polyvinyl Fluoride (PVF) powder is curtain coated onto the phenolic film, and the excess is then removed. Two of these half-webs are then laminated together to produce the final film adhesive. This is shown schematically in Fig. 13.46, and Fig. 13.47 shows the slightly modified original 1954 film-making equipment.

## analysis of power draw in ball mills by the discrete element method - sciencedirect

Ball mills, like other comminution devices, consume large amounts of energy. Mill operators often have to assess the power draft of mills for an entirely different set of operating conditions or for a reconfigured circuit. It is shown that the power draft can be accurately predicted from analysis of the motion of the charge. The motion of the charge is rigorously simulated with a numerical technique known as Discrete Element Method (DEM). In this technique, the coordinates and velocities of each individual ball are computed from a knowledge of forces arising when balls collide with each other and with mill shell and lifter walls. First, simulation results on a wide range of ball mills are compared with available experimental data. Then the power draft predictions as a function of a few operating variables are shown. The unique feature of this method is that the mill power can be predicted for a mixture of ball sizes, different lifter geometry and lifter spacing, which is absent in other methods proposed in the literature.

Les broyeurs billes, comme dautres appareils de comminution, consommenme grande quantit denergie. Les oprateurs de broyeurs ont souvent valueda demande de courant de broyeurs ayant un ensemble compltement diffrent de conditions doprations ou dun circuit reconfigur. On montre qu partir de lanalyse du mouvement de lacharge, lon peut prdire prcisment la demande de courant. Le mouvement de la charge est simul rigoureusement par un technique numrique connue sous le nom de mthode des lments finis (MEF). Par cette techniquen calcule les coordonnes et la vlocit de chaque bille individuelle, partir de donnaissance des forces qui se produisent lorsque les billes entrent on collision loanes avec les autres et avec le revtement du broyeur et les parois deeames. En premier lieu, les rsultats de la simulation dun grand nombre de broyeurs billes sont compars avec les donnes exprimentales disponibles. Ensuite, on montre les prdictions de demande de courant en fonction de quelques variables dopration. La caractristique unique de cette mthode est que lon peut prdire le courant broyeur pour un mlange de taille de billes et pour diffrentes gomtries des cames diffrents espacements, ce qui manque chez dautres mthodes proposes dans la littrature.