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# ball mill for limestone grinding power calculation

## calculation of power consumption for ball mills and grinding

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## bond work index (energy equation) - grinding & classification circuits - metallurgist & mineral processing engineer

I am dealing with the calculation of Bond Work Index. The flowsheet is attached. I have calculated primary ball mill bond index but for the calculation of second ball mill bond index I got trouble. In a bond energy equation, where should I select tonnage ? and where should I pick P(80), F(80) values ? Thanks in advance.

First stage, will be broken into two parts as well, you use a Bond rod mill work index for the coarse component of the ore (+2.1 mm) and the Bond ball mill work index for the fine component (-2.1 mm). It would look like this:

E is the specific energy consumption, kWh/tonne, F80 is the feed size to the primary BM; T80 is the transfer size (prim mill product size), P80 is the final product (cyclone overflow). The following "efficiency factors" may also apply, but they must be greater than 1.0 otherwise use 1.0: EF2 is the open-circuit correction factor, EF4 is the oversize feed factor, EF5 is the fine product factor.

You will not get a circulating load prediction from a Bond calculation. The assumption is that your secondary circuit is "efficient", whatever that might mean. Typically this means circulating loads of 250%, but can go to over 400% for maximum classification efficiency.

Thank you sir, but I have calculated all of the stream tonnage and size distributions. However, my only confusion is while computing the second ball mill bond index, in which stream should I take P(80),F(80) and the tonnage for mill power estimation ? For example, for P(80), should I use hydrocyclone overflow or second mill product or whatever and also for F(80 should I select hydrocyclone underflow or whatever, and for tonnage which I use in mill energy calculation should I use fresh feed tonnage, circulation load or any other ?

Thank you sir, but I have calculated all of the stream tonnage and size distributions. However, my only confusion is while computing the second ball mill bond index, in which stream should I take P(80),F(80) and the tonnage for mill power estimation ? For example, for P(80), should I use hydrocyclone overflow or second mill product or whatever and also for F(80 should I select hydrocyclone underflow or whatever, and for tonnage which I use in mill energy calculation should I use fresh feed tonnage, circulation load or any other ?

The key: in a closed circuit ball mill circuit, you put a "black box" over the whole secondary circuit. Ignore the hydrocyclone underflow and the secondary mill product, those are internal to the black box. You only care what feed enters the secondary circuit (which is the primary mill product) and what product exits the secondary circuit (the hydrocyclone overflow).

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## ball mill parameter selection & calculation - power, critical speed | jxsc

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The production capacity of the ball mill is determined by the amount of material required to be ground, and it must have a certain margin when designing and selecting. There are many factors affecting the production capacity of the ball mill, in addition to the nature of the material (grain size, hardness, density, temperature and humidity), the degree of grinding (product size), the uniformity of the feeding material, and the portion of loaded, , and the mill structure (the mill barrel length, diameter ratio, the number of bins, the shape of the partition plate and the lining plate). It is difficult to theoretically determine the productivity of the mill. The grinding mills production capacity is generally calculated based on the newly generated powder ore of less than 0.074 mm (-200 mesh). V Effective volume of ball mill, m3; G2 Material less than 0.074mm in product accounts for the percentage of total material, %; G1 Material less than 0.074mm in ore feeding accounts for 0.074mm in the percentage of the total material, %; qm Unit productivity calculated according to the new generation grade (0.074mm), t/(m3.h). The values of qm are determined by experiments or are calibrated in production with similar ore physical properties and the same equipment and working conditions. When there is no test data and production calibration value, it can be calculated by formula (1-3). Di1- Standard mill diameter, m; K4 feed size and product size coefficient of mill. G3 G4 The production capacity of existing or experimental mills with newly designed and parameters (feed size or product size calculated according to the new generation 0.074mm level) is shown in Table 1-6. The values of G1 and G2 above should be calculated according to actual data. If there is no actual data, they can be selected according to tables 1-7 and 1-8.

When the filling rate of grinding medium is less than 35% in dry grinding operation, the power can be calculated by formula (1-7). n - mill speed, r/min; G - Total grinding medium, T; - Mechanical efficiency, when the center drive, = 0.92-0.94; when the edge drive, = 0.86-0.90.

\ Critical Speed_ When the ball mill cylinder is rotated, there is no relative slip between the grinding medium and the cylinder wall, and it just starts to run in a state of rotation with the cylinder of the mill. This instantaneous speed of the mill is as follows: N0 - mill working speed, r/min; Kb speed ratio, %. There are many layers of grinding media in the mill barrel. It is assumed that the media will be concentrated in one layer, called the polycondensation layer, so that the grinding media of this layer will be in the maximum drop, i.e. the calculating speed of the mill when the total impact energy is the largest nj. Therefore, it is theoretically deduced that the reasonable working speed is The working speeds of various mills are shown in Table 1-10. Table 1-10 Working speeds of various mills

In production practice, there are many factors affecting the motion state of grinding media. Therefore, the appropriate working speed should be selected according to the actual situation. In determining the actual working speed of the mill, the influences of the mill specifications, production methods, liner forms, grinding media types, filling rate, physical and chemical properties of the ground materials, particle size of the grinding materials and grinding fineness of the products should be taken into account. The actual working speed of the mill should be determined by scientific experiments, which can reflect the influence of these factors more comprehensively.

Ball loading capacity The volume of the grinding medium is the percentage of the effective volume of the mill, which is called the filling rate of the grinding medium. The size of filling directly affects the number of shocks, the area of grinding and the load of grinding medium in the grinding process. At the same time, it also affects the height of the grinding medium itself, the impact on the material and the power consumption. A kind of The ball loading capacity of the mill can be calculated according to the formula (1-14). Gra Quantity of Grinding Medium, T. Rho s loose density of grinding medium, t/m3. Forged steel balls; P=s=4.5-4.8t/m3 cast steel balls P=4.3-4.6t/m3; rolling steel balls P=6.0-6.8t/m3; steel segments P=4.3-4.6t/m3_-filling ratio of grinding medium, When wet grinding: lattice ball mill pi = 40% 45%; overflow ball mill phi = 40%; rod mill phi = 35%. Dry grinding: When material is mixed between grinding media, the grinding medium expands, and when dry grinding is adopted, the material fluidity is relatively poor, material flow is hindered by abrasive medium, so filling rate is low, and the filling rate is between 28% and 35%. The pipe mill is 25%-35%. The void fraction of grinding medium_k=0.38-0.42 and the quality of crushed material accounts for about 14% of the quality of grinding medium.

Size and Proportion of Grinding Medium In the ball mill, the size and proportion of steel balls have a great influence on the productivity and working efficiency of the mill. For coarse and hard materials, larger steel balls should be selected, for fine and brittle materials, with smaller diameter steel balls, the impact times of steel balls in the mill increase with the decrease of ball diameter, and the grinding between balls increases. The clearance is dense with a decrease of spherical diameter. Therefore, it is better to choose the ball with a larger mass and smaller diameter (loose density) as the grinding medium. The size of the ball mainly depends on the particle size of the material to be ground, and the diameter and speed of the mill can be considered appropriately. Formula (1-15) is an empirical formula for spherical diameter and feed size. dmax The maximum diameter of steel ball, mm; amax the maximum size of feeding granularity, mm. After calculating the maximum steel ball diameter, the steel ball ratio in the mill can be calculated with reference to Fig. 2-1 (suitable for cement mill, other mills can refer to). After choosing the maximum diameter and minimum diameter of steel balls according to technological requirements, material properties, mill specifications and various parameters, and then matching grade, using curves, the accumulative percentage of the mass of each corresponding steel balls loaded into the mill can be found, the actual percentage of the mass can be calculated, and the loading quality of steel balls at all levels can be obtained. According to the production practice of production enterprises, the relationship between ball diameter and material size is shown in Table 1-11. A kind of Steel balls are gradually worn out in the process of grinding materials. The wear of drop steel ball is related to its impact force. The wear of grinding steel balls is related to the surface area of steel balls. In general, the steel ball in the grinder has both impact and abrasion effects, so the wear is proportional to the n power of the diameter of the steel ball, and the value of n is between 2 and 3. Table 1-11 The Relation between Steel Ball Diameter and Material Size

The quality and surface area of forged steel balls of various sizes are shown in Table 1-12. A kind of Because of the wear of steel balls in the mill production process, in order to keep the mill stable. Steel balls need to be added regularly. The maximum diameter of additional steel balls is still determined by the method mentioned above. In addition to the addition of additional steel balls, several smaller diameter steel balls should be added according to production experience.

## ball mill design/power calculation

The basic parameters used in ball mill design (power calculations), rod mill or anytumbling millsizing are; material to be ground, characteristics, Bond Work Index, bulk density, specific density, desired mill tonnage capacity DTPH, operating % solids or pulp density, feed size as F80 and maximum chunk size, productsize as P80 and maximum and finally the type of circuit open/closed you are designing for.

In extracting fromNordberg Process Machinery Reference ManualI will also provide 2 Ball Mill Sizing (Design) example done by-hand from tables and charts. Today, much of this mill designing is done by computers, power models and others. These are a good back-to-basics exercises for those wanting to understand what is behind or inside the machines.

W = power consumption expressed in kWh/short to (HPhr/short ton = 1.34 kWh/short ton) Wi = work index, which is a factor relative to the kwh/short ton required to reduce a given material from theoretically infinite size to 80% passing 100 microns P = size in microns of the screen opening which 80% of the product will pass F = size in microns of the screen opening which 80% of the feed will pass

Open circuit grinding to a given surface area requires no more power than closed circuit grinding to the same surface area provided there is no objection to the natural top-size. If top-size must be limited in open circuit, power requirements rise drastically as allowable top-size is reduced and particle size distribution tends toward the finer sizes.

A wet grinding ball mill in closed circuit is to be fed 100 TPH of a material with a work index of 15 and a size distribution of 80% passing inch (6350 microns). The required product size distribution is to be 80% passing 100 mesh (149 microns). In order to determine the power requirement, the steps are as follows:

The ball mill motorpower requirement calculated above as 1400 HP is the power that must be applied at the mill drive in order to grind the tonnage of feed from one size distribution. The following shows how the size or select thematching mill required to draw this power is calculated from known tables the old fashion way.

The value of the angle a varies with the type of discharge, percent of critical speed, and grinding condition. In order to use the preceding equation, it is necessary to have considerable data on existing installations. Therefore, this approach has been simplified as follows:

A = factor for diameter inside shell lining B = factor which includes effect of % loading and mill type C = factor for speed of mill L = length in feet of grinding chamber measured between head liners at shell- to-head junction

Many grinding mill manufacturers specify diameter inside the liners whereas othersare specified per inside shell diameter. (Subtract 6 to obtain diameter inside liners.) Likewise, a similar confusion surrounds the length of a mill. Therefore, when comparing the size of a mill between competitive manufacturers, one should be aware that mill manufacturers do not observe a size convention.

In Example No.1 it was determined that a 1400 HP wet grinding ball mill was required to grind 100 TPH of material with a Bond Work Index of 15 (guess what mineral type it is) from 80% passing inch to 80% passing 100 mesh in closed circuit. What is the size of an overflow discharge ball mill for this application?

## calculation of energy required for grinding in a ball mill - sciencedirect

The Bond work index, Wi, as an indicator of the grindability of raw materials is not a material constant but rather it changes with change of size of the grinding product. Therefore, in practice we can expect some difficulties and errors when the energy consumption is determined according to this formula in the case when, for a given size of grinding product, the value of the work index Wi, which is determined by experiments, is not known.

This problem is considered in this paper and some solutions are put forward. Experiments were made on copper ore, andesite and limestone, and it was found that the change of the mass passing a test screen G could be related to the aperture size Pk of the screen by the formula: G=K1Pk. The grinding-product size, P, in a Bond ball mill, which is given by the aperture size which passes 80% of the grinding product as a function of the aperture size of the test screen Pk, can be expressed by the formula P=PkK2.

## energy use of fine grinding in mineral processing | springerlink

Fine grinding, to P80 sizes as low as 7m, is becoming increasingly important as mines treat ores with smaller liberation sizes. This grinding is typically done using stirred mills such as the Isamill or Stirred Media Detritor. While fine grinding consumes less energy than primary grinding, it can still account for a substantial part of a mills energy budget. Overall energy use and media use are strongly related to stress intensity, as well as to media size and quality. Optimization of grinding media size and quality, as well as of other operational factors, can reduce energy use by a factor of two or more. The stirred mills used to perform fine grinding have additional process benefits, such as polishing the mineral surface, which can enhance recovery.

Fine grinding is becoming an increasingly common unit operation in mineral processing. While fine grinding can liberate ores that would otherwise be considered untreatable, it can entail high costs in terms of energy consumption and media use. These costs can be minimized by performing adequate test work and selecting appropriate operating conditions. This paper reviews fine grinding technology, research, and plant experience and seeks to shed light on ways in which operators can reduce both operating costs and the environmental footprint of their fine grinding circuit.

This paper will begin by giving an overview of fine grinding and the equipment used. It will then discuss energyproduct size relationships and modeling efforts for stirred mills in particular. The paper will go on to cover typical test work requirements, the effect of media size, and the contained energy in media. In closing, specific case studies will be reviewed.

Grinding activities in general (including coarse, intermediate, and fine grinding) account for 0.5pct of U.S. primary energy use, 3.8pct of total U.S. electricity consumption, and 40pct of total U.S. mining industry energy use. Large energy saving opportunities have been identified in grinding in particular.[1]

TableI shows a very large disparity between the theoretical minimum energy used in grinding and the actual energy used. More interestingly, a fairly large difference remains even between Best Practice grinding energy use and current energy use. This suggests that large savings in grinding energy (and associated savings in maintenance, consumables, and capital equipment needed) could be obtained by improving grinding operations.

As fine grinding is typically used on regrind applications, the feed tonnages to fine grinding circuits are small compared to head tonnages, typically 10 to 30tph. However, the specific energies are often much larger than those encountered in intermediate milling and can be as high as 60kWh/t. Total installed power in a fine grinding circuit can range from several hundred kW to several MW; for example, the largest installed Isamill has 3MW installed power.[3] This quantity is small compared to the power used by a semi-autogenous mill and a ball mill in a primary grinding circuit; a ball mill can have an installed power of up to 15MW, while installed power for a SAG mill can go up to 25MW. However, the energy used for fine grinding is still significant. Moreover, as this paper seeks to demonstrate, large energy reduction opportunities are frequently found in fine grinding.

Grinding can be classified into coarse, intermediate, and fine grinding processes. These differ in the equipment used, the product sizes attained, and the comminution mechanisms used. The boundaries between these size classes must always be drawn somewhat arbitrarily; for this paper, the boundaries are as given in TableII. As shown in the table, coarse grinding typically corresponds to using an AG or SAG mill, intermediate grinding to a ball mill or tower mill, and fine grinding to a stirred mill such as an Isamill or Stirred Media Detritor (SMD). Of course, various exceptions to these typical values can be found.

In fine grinding, a material with an F80 of less than 100m is comminuted to a P80 of 7 to 30m. (P80s of 2m are at least claimed by equipment manufacturers.) The feed is typically a flotation concentrate, which is reground to liberate fine particles of the value mineral.

The three modes of particle breakage are impact; abrasion, in which two particles shear against each other; and attrition, in which a small particle is sheared between two larger particles or media moving at different velocities. In fine grinding, breakage is dominated by attrition alone.[4] In stirred mills, this is accomplished by creating a gradient in the angular velocity of the grinding media along the mills radius.

Fine grinding is usually performed in high-intensity stirred mills; several manufacturers of these stirred mills exist. Two frequently used stirred mills include the Isamill, produced by Xstrata Technology, and the SMD, produced by Metso (Figure1). A third mill, the KnelsonDeswik mill (now the FLS stirred mill), is a relative newcomer to the stirred milling scene, having been developed through the 1990s and the early 2000s.[5] In all these mills, a bed of ceramic or sand is stirred at high speed. Ceramic media sizes in use range from 1 to 6.5mm.

The Isamill and the SMD have very similar grinding performance. Grinding the same feed using the same media, Nesset et al.[7] found that the Isamill and SMD had very similar specific energy use. Gao et al.[8] observed that an Isamill and SMD, grinding the same feed with the same media, produced very similar product particle size distributions (PSDs). This similarity in performance has also been observed in other operations.

Nevertheless, there are important differences. In the Isamill, the shaft is horizontal and the media are stirred by disks, while in the SMD, the stirring is performed by pins mounted on a vertical shaft. In an SMD, the product is separated from the media by a screen; the Isamill uses an internal centrifugation system. This means that the screens in an SMD constitute a wear part that must be replaced, while for the Isamill, the seals between the shaft and body constitute important wear parts. Liner changes and other maintenance are claimed by Xstrata Technology to be much easier than in an SMD: While an SMDs liner is removed in eight parts, the Isamills liner can be removed in two pieces, with the shell sliding off easily.[3] The KnelsonDeswik mill is top stirred and can therefore be considered to be similar to an SMD.[5]

An important difference among the Isamill, the SMD, and the KnelsonDeswik mill is that of scale. The largest Isamill installed at time of writing had 3MW of installed power; an 8MW Isamill is available, but appears not to have yet been installed.[3] The largest SMD available has 1.1MW of installed power; one 1.1-MW SMD has been installed. The next largest size SMD has 355kW of installed power.[6] Thus, several SMDs are often installed for a fine grinding circuit, while the same duty would be performed by a single Isamill. SMDs are typically arranged in series, with the product of one becoming the feed for the other. This has the advantage that each SMD in the line can have its media and operating conditions optimized to the particle size of its particular feed. The largest installed power in a KnelsonDeswik mill is 699kW[5]; this places it in an intermediate position between the 355-kW and 1.1-MW SMDs.

In 2012, FLSmidth reported that it had acquired the KnelsonDeswik mill; the mill is now known as the FLSmidth stirred mill. An FLSmidth stirred mill will be installed to perform a copper concentrate regrind in Mongolia.[9] It is speculated that the mill will continue to be scaled up under its new owners to allow it to effectively compete against the SMD and Isamill.

Gravity-induced stirred (GIS) mills include the Tower mill, produced by Nippon Eirich, and the Vertimill, produced by Metso. Grinding to below 40m in GIS mills or ball mills is usually not recommended. In their product literature, Metso give 40m as the lower end of the optimal P80 range for Vertimills.[6] At lower product sizes, both tower mills and ball mills will overgrind fines. At Mt. Isa Mines, a GIS mill fed with material of F80 approximately 50m lowered the P80 size by only 5 to 10m, at the same time producing a large amount of fines.[10] Similarly, in ball mills, it is known that grinding finer than approximately 40m will result in overgrinding of fines as well as high media consumption. However, it must be noted that the product size to which a mill can efficiently grind depends on the feed material, the F80, and media type and size. A Vertimill has been used to grind to sizes below 10m.[11]

The phenomenon of overgrinding is largely the result of using media that are too large for the product size generated. The smallest ball size typically charged into ball mills and tower mills is inch (12.5mm), although media diameters as small as 6mm have been used industrially in Vertimills.[11]

In a laboratory study by Nesset et al.,[7] a GIS mill charged with 5-mm steel shot, and with other operating conditions similarly optimized, achieved high energy efficiencies when grinding to less than 20m. This appears to qualitatively confirm the notion that fine grinding requires smaller media sizes. In the case of the Nesset study, the power intensity applied to the laboratory tower mill was lowthat is, the shaft was rotated slowly in order to obtain this high efficiency, leading to low throughput. This suggests that charging GIS mills with small media may not be practicable in plant operation.

Millpebs have been used as grinding media to achieve fine grinding in ball mills. These are 5- to 12-mm spherical or oblong cast steel pellets, charged into ball mills as a replacement of, or in addition to, balls. While Millpebs can give significantly lower energy use when grinding to finer sizes, they also can lead to high fines production and high media use.

Millpebs were tested for fine grinding at the Brunswick concentrator. The regrind ball mills at the concentrator used 25-mm slugs to produce a P80 of 28m. In one of the regrind mills, the slugs were replaced by Millpebs; these were able to consistently maintain a P80 of 22m while decreasing the power draw by 20pct. However, media use increased by 50pct and the production of fines of less than 16m diameter increased by a factor of 5.[12] The observed drop in specific energy may be due to the fact that Millpebs had smaller average diameters than the slugs and so were more efficient at grinding to the relatively small product sizes required. It is therefore unclear whether the performance of Millpebs would be better than that of conventional 12-mm steel balls. To the best of the authors knowledge, no performance comparison between Millpebs and similarly sized balls has been performed.

A host of other technologies exist to produce fine grinding, including jet mills, vibrating mills, roller mills, etc. However, none of these technologies has reached the same unit installed power as stirred mills. For example, one of the largest vibrating mills has an installed power of 160kW.[13] Therefore, these mills are considered as filling niche roles and are not treated further in this review. A fuller discussion of other fine grinding technologies can be found in a review by Orumwense and Forssberg.[14]

Neese et al.[15] subjected 50- to 150-m sand contaminated with oil to cleaning in a stirred mill in the laboratory. The mill operated at low stress intensities: A low speed and small-size media (200- to 400-m quartz or steel beads) were used. These conditions allowed the particles to be attrited without being broken. As a result, a large part of the oil contaminants was moved to the 5-m portion of the product. This treatment may hold promise as an alternative means of processing bituminous sands, for example, in northern Alberta.

The Albion process uses ultrafine grinding to enhance the oxidation of sulfide concentrates in treating refractory gold ores.[16] In the process, the flotation concentrate is ground to a P80 of 10 to 12m. The product slurry is reacted with oxygen in a leach tank at atmospheric pressure; limestone is added to maintain the pH at 5 to 5.5. The leach reaction is autothermal and is maintained near the slurry boiling point. Without the fine grinding step, an autoclave would be required for the oxygen leaching process. It is hypothesized that the fine grinding enhances leach kinetics by increasing the surface area of the particles, as well as by deforming the crystal lattices of the particles.

Numerous researchers, for example, Buys et al.,[17] report that stirred milling increases downstream flotation recoveries by cleaning the surface of the particles. The grinding media used in stirred mills are inert, and therefore corrosion reactions, which occur with steel media in ball mills, are not encountered. Corrosion reactions change the surface chemistry of particles, especially with sulfide feeds, and hamper downstream flotation.

Further increases in flotation recoveries are obtained by limiting the amount of ultrafine particles formed; stirred mills can selectively grind the larger particles in the feed with little increase in ultrafines production. Ultrafine particles are difficult to recover in flotation.

In intermediate grinding to approximately 75m, the Bond equation (Eq. [1]) is used to relate feed size, product size, and mechanical energy applied. Below 75m, correction factors can be applied to extend its range of validity.[4]

No general work index formula governing energy use over a range of conditions, like the Bond equation for intermediate grinding, has yet been found for the fine grinding regime. Instead, the work-to-P80 curve is determined in the laboratory for each case. The energy use usually fits an equation of the form

Signature plot (specific energy vs P80 curve) for Brunswick concentrator Zn circuit ball mill cyclone underflow; F80=63m. The plots give results for grinding the same feed using different mills and media. After Nesset et al.[7]

Values for the exponent k have been found in the range 0.7 to 3.5, meaning that the work to grind increases more rapidly as grind size decreases than in intermediate grinding. The specific energy vs product size curve has a much steeper slope in this region than in intermediate grinding.

The values of k and A are specific to the grinding conditions used in the laboratory tests. Changes in feed size, media size distribution, and in other properties such as media sphericity and hardness can change both k and A, often by very large amounts. Media size and F80 appear to be the most important determinants of the signature plot equation.

The connections (if any) between k and A and various operating conditions remain unknown. Because of the relatively recent advent of stirred milling in mineral processing, fine grinding has not been studied to the same extent as grinding in ball mills (which of course entail much larger capital and energy expenditures in any case). One of the research priorities in the field of stirred milling should be the investigation of the effects of F80 and media size on the position of the signature plots. If analogous formulas to the Bond ball mill work formula and the Bond top ball size formula can be found, the amount of test work required for stirred milling would be greatly reduced.

Larson et al.[19] found that when specific energy is plotted against the square of the percent particles in the product passing a given size (a proxy for particle surface area), a straight line is obtained. This is demonstrated in Figure3.

In contrast to the conventional signature plot, this function gives zero energy at the mill feed. It is therefore hypothesized that if a squared function plot is obtained by test work for one feed particle size, the plot for another feed particle size can be obtained simply by changing the intercept of the line while keeping the slope the same. Therefore, the squared function plot allows the effect of changes in both F80 and P80 to be modeled.

While the Squared Function Plot is intriguing, experimental validation of its applicability has not yet been published. It nevertheless remains an interesting topic for further investigation and if validated may be used in the future as an alternative measure of specific energy.

A similar analysis has been performed by Musa and Morrison,[21] who developed a model to determine the surface area within each size fraction of mill product. They defined a marker size below which 70 to 80pct of the product surface area was contained; the marker size thus served as a proxy for surface area production. Specific energy use was then defined as kWh of power per the tonne of new material generated below the marker size. Musa and Morrison found that by defining specific energy in this way, it was possible to accurately predict the performance of full-scale Vertimills and Isamills from laboratory tests.

Blecher and coworkers[22,23] found that stress intensity combines the most important variables determining milling performance. Stress intensity for a horizontal stirred mill, with media much harder than the mineral to be ground, is defined as in Eq. [4].

Note that the stress intensity is strongly sensitive to changes in media diameter (to the third power), is less sensitive to stirrer tip speed (to the second power), and is relatively insensitive to media and slurry density.

For vertical stirred mills such as the SMD and tower mill, both SIs and SIg are non-zero. For horizontal stirred mills such as the Isamill, net gravitational SI is zero due to symmetry along the horizontal axis. Therefore, for horizontal stirred mills, only SIs need be taken into consideration.

Kwade and coworkers noted that, at a given specific energy input, the product P80 obtainable varies with stress intensity and passes through a minimum. Product size at a given energy input can be viewed as a measure of milling efficiency; therefore, milling efficiency reaches a maximum at a single given stress intensity. This idea was experimentally validated by Jankovic and Valery (Figure 4).[25]

The stress intensity is defined by parameters that are independent of mill size or type. According to Jankovic and Valery,[25] once the optimum SI has been determined in one mill for a given feed, the same SI should also be the point of optimum efficiency in any other mill treating that feed. Therefore, the optimum SI need only be determined in one mill (e.g., a small test mill); the operating parameters of a full-scale mill need only be adjusted to produce the optimum SI.

Stress frequency multiplied by stress intensity is equal to mill power; therefore, stress intensity could in theory be used to predict mill specific energy. However, to the authors knowledge, a comprehensive model linking stress intensity, stress frequency, and specific energy has not yet been developed. Therefore, there is not yet any direct link between stress intensity and specific energy.

The definition of SIs as given in Eq. [4] is valid only for cases where the grinding media are much harder than that of the material ground (for example, the grinding of limestone with glass beads). Becker and Schwedes[26] determined that, in a collision between media and a mineral particle, the fraction of energy transferred to the product is given by Eq. [6]:

To maintain high efficiency in milling, the media must be chosen so as to be much harder (higher Youngs modulus) than the product material, keeping E p,rel close to unity. Where the Youngs modulus of the product is similar to that of the media, much of the applied energy goes into deformation of the media instead of that of the particle to be ground. The energy used to deform the media is lost, lowering the amount of energy transferred to the product. This fact explains why steel media, with a relatively low Youngs modulus, tend to perform poorly in stirred milling, even though the media are much more dense than silica or alumina media.

The previous sections indicated that stress intensity is independent from individual millsi.e., the optimal stress intensity when using Mill A will also be the optimal stress intensity when using Mill B. However, this does not seem to be the case when actually scaling up mills.

Four-liter Isamills are commonly used for grindability test work. It can be assumed that operating parameters of the test mill (including media type, media size, and slurry density) are adjusted so far as possible to give the optimum SI. These parameters are then used in the full-scale mill as well. However, the 4-L test mills have a tip speed of approximately 8m/s, while full-scale Isamills have tip speeds close to 20m/s.[27] If the same media size, media density, and slurry density are used in the test mill as in the full-scale mill, the stress intensity of the full-scale mill will be approximately 6.25 times larger than that of the test mill. This implies that the full-scale mill is operating outside of the optimum SI and will be grinding less efficiently. That is to say that the operating point of the full-scale mill will be above the signature plot determined by test work.

In reality, however, the operating points of full-scale stirred mills are generally found to lie on the signature plots generated in test work.[19] Therefore, the full-scale mills and test mills have the same milling efficiency, even though the full-scale mill operates at a different stress intensity than the test mill.

This question remains unresolved. One possible answer arises from the observation that two of the P80 vs SI curves in Figure4 appear to have broad troughs, covering almost an order of magnitude change in SI. In this case, even a sixfold increase in SI might not create a noticeable difference in performance, considering experimental and measurement error.

Product size vs stress intensity at three different specific energies for a zinc regrind. Note optimum stress intensity at which the lowest product size is reached. Figure used with permission from Jankovic and Valery[25]

The SMD test unit appears from photographs to have a bed depth of around 30cm, while the full-scale SMD355 has a bed depth of approximately one meter. This represents a change in the gravitational stress intensity of almost two orders of magnitude. As has been previously noted, however, laboratory and full-scale SMDs scale-up with a scale-up factor of approximately unity, with no apparent change in the optimum stress intensity. This observation suggests that the gravitational stress intensity, SIg, is unimportant in SMDs compared to the stirring stress intensity, SIs. By contrast, in GIS mills, where full-size units have bed depths of ten meters or more, gravitational stress intensity can be expected to be much more important in full-size units than in test units, adding a complicating factor to GIS mill scale-up.

Factorial design experiments were performed by Gao et al.[28] and Tuzun and Loveday[29] to determine the effect of various operating parameters on the power use of laboratory mills. Power models were determined giving the impact of different parameters as power equations with linear and nonlinear terms. The derived models did not appear to be applicable to mills other than the particular laboratory units being studied.

In ball milling, the Bond ball mill work index can be used to determine specific energy at a range of feed and product sizes. The Bond top size ball formula can be used to estimate the media size required. No such standard formulas exist in fine grinding. Energy and media parameters must instead be determined in the laboratory for every new combination of operating conditions such as feed size, media size, and media type.

For the Isamill, test work is usually performed with a 4-L bench-scale Isamill. Approximately 15kg of the material to be ground is slurried to 20pct solid density by volume. The slurry is then fed through the mill and mill power is measured. The products PSD is measured, additional water is added if needed, and the material is sent through the mill again. This continues until the target P80 is reached; typically, there will be 5 to 10 passes through the mill. The test work will produce a signature plot and media consumption data as the deliverables.

In contrast to laboratory-scale testing for ball mills and AG/SAG mills, test work results for stirred mills can be used for sizing full-size equipment with a scale-up factor close to one. Larson et al.[19,20] found a scale-up factor for the Isamill of exactly 1, while Gao et al.[8] imply that the scale-up factor for SMDs is 1.25.

A common error in test work is using monosize media (e.g., fresh 2-mm media loaded into in the mill) as opposed to aged media with a distribution of particle sizes. The aged media will grind the smaller feed particles more efficiently. Therefore, using fresh media will give a higher specific energy than in reality.[30]

Another pitfall is coarse holdup in the mill. If the mill is not sufficiently flushed, coarse particles will be kept inside the mill. The mill product then appears finer than it in reality is. This leads to lower estimates of specific energy than reality.[19]

In ball milling, the product particle size distribution (PSD) can usually be modeled as being parallel to the feed PSD on a log-linear plot.[4] When grinding to finer sizes in ball mills, the parallel PSDs mean that large amounts of ultrafine particles are produced. This consumes a large amount of grinding energy while producing particles which are difficult to recover in subsequent processing steps such as flotation.

As shown in the figure, at the left end of the graph, the product PSD is very close to the feed PSD; at the right, the two PSDs are widely spaced. This indicates that the mill is efficiently using its energy to break the top size particles and is spending very little energy on further grinding of fine particles. Thus, the overall energy efficiency of the fine grinding can be expected to be good. As a bonus, the tighter PSD makes control of downstream processes such as flotation easier.

In an experimental study, Jankovic and Sinclair subjected calcite and silica to fine grinding in a laboratory pin stirred mill, a Sala agitated mill (SAM), and a pilot tower mill. The authors found that for each mill, the PSD of the product was narrower (steeper) than that of the feed. In addition, when grinding to P80s below approximately 20m in any of the three mills tested, the PSD became more narrow (as measured by P80/P20 ratio) as the P80 decreased. (When the width of the PSD was calculated using an alternative formula, the PSD was only observed to narrow with decreasing P80 when using the pin stirred mill.) The authors concluded that the width of the PSD was strongly affected by the material properties of the feed, while not being significantly affected by the media size used.[32]

In stirred milling, the most commonly used media are ceramic balls of 1 to 5mm diameter. The ceramic is usually composed of alumina, an alumina/zirconia blend, or zirconium silicate. Ceramic media exist over a wide range of quality and cost, with the lower quality/cost ceramic having a higher wear rate than higher quality/cost ceramic. Other operations have used sand as media, but at the time of writing, only two operations continue to use sand.[8,27,33] Mt Isa Mines has used lead smelter slag as media; however, it is now using sand media.[10,27] Mt Isa is an exception in its use of slag, as a vast majority of operations do not have a smelter on-site to provide a limitless supply of free grinding media. However, in locations where slag is available, it should be considered as another source of media.

Media use in fine grinding is considered to be proportional to the mechanical energy applied. Typical wear rates and costs are given in TableIII and Figure6; these figures can of course vary significantly from operation to operation.

Contained energy refers to the energy required to produce and transport the media, and is distinct from the mechanical (electrical) energy used to drive the mill. Hammond and Jones estimated the contained energy in household ceramics (not taking account of transportation).[39] Hammond and Jones estimates range from 2.5 to 29.1MJ/kg, with 10MJ/kg for general ceramics and 29MJ/kg for sanitary ceramics. Given that ceramic grinding media require very good hardness and strength, especially compared to household ceramics, it is appropriate to estimate its contained energy at the top end of Hammond and Jones range, at 29MJ/kg.

Using 29MJ/kg for the contained energy of ceramic media and a wear rate of 35g/kWh of mechanical energy gives a contained energy consumption of 0.28kWh contained per kWh of mechanical energy applied. A wear rate of 7g/kWh gives a contained energy consumption of 0.06kWh contained per kWh of mechanical energy applied. Therefore, 6 to 20pct of the energy use in fine grinding using ceramic media can be represented by contained energy in the grinding media itself.

Sand media have much lower contained energy than ceramic media as the media must simply be mined or quarried rather than manufactured. Hammond and Jones report a contained energy of 0.1MJ/kg. Blake et al.[36] reported that switching a stirred mills media from sand to ceramic results in a mechanical energy savings of 20pct. Therefore, using sand rather than ceramic media would produce savings in contained energy, but would cost more in mechanical energy. Likewise, Davey[40] suggests that poor-quality media will increase mechanical energy use in stirred milling. It is speculated that this is due to the lower sphericity of sand media. On the other hand, the work of Nesset et al.[7] suggests that the energy use between ceramic and sand media of the same size is the same. Slag media, where a smelter is on-site, would probably have the lowest contained energy consumption of the different media types. There is very little transportation, and for accounting purposes, almost no energy has gone into creating the media as the granulated slag is a by-product of smelter operation.

Becker and Schwedes[41] point out that with poor-quality media, a significant part of the product will consist of broken pieces of media, which will affect the measured product PSD. Clearly, more information on the relationships between contained energy in media and media wear rates is desirable.

Of the different operating parameters for stirred mills, media size probably has the biggest influence on overall energy consumption. The appropriate media size for a mill appears to be a function of the F80 and P80 required. The grinding media must be large enough to break up the largest particles fed to the mill and small enough to grind the material to the product fineness desired. As demonstrated by the experience of Century mine, an inappropriate media size choice can result in energy consumption double that of optimum operation.[8]

In their laboratory study, Nesset et al.[7] varied a number of operating parameters for stirred mills and identified media size as having the largest impact on energy use. It was also noted that the trials which produced the sharpest product PSD were also the ones which resulted in the lowest specific energy use.

Gao et al.[8] report that at Century mine, the grinding media in SMDs performing regrind duty were changed from 1 to 3mm. This resulted in a drop in energy use of approximately 50pct; the signature plot shifted significantly downward (Figure7).

Figure8 shows the product PSD for laboratory SMD tests using 1- and 3-mm media. The PSD for the test using 1-mm media shows that the SMD produced a significant amount of fines (20pct below 4m). The mill also had difficulty breaking the top size particlesthe 100pct passing size appears to be almost the same for both the feed and the product. In contrast, the PSD using 3-mm media shows less fines production (20pct below 9m) and effective top size breakage, with all the particles above 90m broken. This is in line with the observation of Nesset et al.[7] that low energy use is associated with tight product size distributions.

Gao et al.[38] tested copper reverberatory furnace slag (CRFS, SG 3.8) and heavy media plant rejects (HMPR, SG 2.4) in a laboratory stirred mill at two sizes: 0.8/+0.3mm, and 1.7/+0.4mm. For both CRFS and HMPR, the smaller size media gave a lower specific energy than the larger size media. At the same size, both CRFS and HMPR had similar specific energy use. However, the CRFS ground the material much faster than HMPR. Possibly, this was due to its higher density.

Data on F80, P80, and media size were compiled from the literature in order to allow benchmarking against existing operations. The sources are listed in Table IV. F80 and P80 were plotted against media size; the results are given in Figure9.

F80 plotted against media size (blue diamonds); P80 plotted against media size (red crosses). Century UFG=Century ultrafine grind; Century Regr.=Century regrind. Data are taken from Case studies table (Color figure online)

It can be seen from the figure that as the P80 achieved decreases, the media size does as well, from 3mm to achieve 45m to 1mm to achieve under 10m. The F80 decreases with media size in a similar way, from 90m at 3mm to 45m at 1mm. Dotted lines have been added to Figure7 to define the region of operation of mills; these delimit a zone in which the stirred mill can be expected to operate efficiently.

In general, for a particular media size, limits on both F80 and P80 must be respected. For example, the figure suggests that a mill operating with an F80 of 100m should use 3-mm media, while a mill grinding to below 10m would need to use 1-mm media. To reduce a feed of 90m F80 to 10m P80, Figure9 suggests that comminution be done in two stages (two Isamills or SMDs in series) for optimal efficiency. The first stage would grind the feed from 90m to perhaps 45m using 3-mm media, while the second would grind from 45 to 10m using 1- or 2-mm media.

A number of opportunities exist to reduce the energy footprint of fine grinding mills. There are no general formulas, such as the Bond work formula and Bond top size ball formula in ball milling, to describe the performance of stirred mills. Therefore, improvement opportunities must be quantified by performing appropriate test work.

In addition to obtaining the signature plot, the specific energy as a function of new surface area should be determined during test work. This could be done either by the method of Larsen or by that of Musa and Morrison. Defining specific energy as a function of new surface area may constitute a superior means of predicting the performance of full-scale mills, as opposed to defining specific energy as a function of feed tonnage.

Media size should be chosen with care. It is recommended that test work be done with several media sizes in order to locate the stress intensity optimum. Media size can be benchmarked against other operations using Figure9.

There are indications that lower-quality media, apart from degrading faster, require more mechanical energy for grinding due to factors such as lower sphericity. It is recommended to perform test work using media of different quality to determine the effect of media quality on energy use. Slag and sand media may also be considered. Subsequently, a trade-off study involving media cost, electricity cost, improvement in energy efficiency, and contained energy in media should be performed to identify the best media from an economic and energy footprint standpoint.

D. Rahal, D. Erasmus, and K. Major: KnelsonDeswick Milling Technology: Bridging the Gap Between Low and High Speed Stirred Mills, Paper presented at the 43rd Canadian Mineral Processors Meeting, Ottawa, 2011.

Metso: Stirred milling: Vertimill grinding mills and Stirred Media Detritor (product brochure), 2013, available at http://www.metso.com/miningandconstruction/MaTobox7.nsf/DocsByID/F58680427E2A748F852576C4005210AC/\$File/Stirred_Mills_Brochure-2011_LR.pdf, accessed April 21, 2013.

J. Nesset, P. Radziszewski, C. Hardie, and D. Leroux: Assessing the Performance and Efficiency of Fine Grinding Technologies, Paper presented at the 38th Canadian Mineral Processors Meeting, Ottawa, 2006.

FLSmidth: Acquisition enhances our precious metals offerings, 2012, FLSmidth eHighlights April 2012, available at http://www.flsmidth.com/en-US/eHighlights/Archive/Minerals/2012/April/Acquisition+enhances+our+precious+metals+offerings, accessed 17 April 2013.

S. Buys, C. Rule, and D. Curry: The Application of Large Scale Stirred Milling to the Retreatment of Merensky Platinum Tailings, Paper presented at the 37th Canadian Mineral Processors Meeting, Ottawa, 2005.

D. Curry, M. Cooper, J. Rubenstein, T. Shouldice, and M. Young: The Right Tools in the Right Place: How Xstrata Nickel Australasia Increased Ni Throughput at Its Cosmos Plant, Paper presented at the 42nd Canadian Mineral Processors conference, Ottawa, 2010.

G. Davey: Fine Grinding Applications Using the Metso Vertimill Grinding Mill and the Metso Stirred Media Detritor (SMD) in Gold Processing, Paper presented at the 38th Canadian Mineral Processors Meeting, Ottawa, 2006.

## ball mill for grinding calcium carbonate - calcium carbonate ball mill

Ball mill grinder is usually used to grind crushed materials, such as ores, chemicals, ceramic raw material and others. This article mainly talks about ball mill for grinding calcium carbonate. Ground calcium carbonate powder is in greater demand worldwide in various industries. Turnkey calcium carbonate ball mill plant is popular, for ball mill is an essential equipment for grinding calcium carbonate in great capacity. With constant upgrades, Daswell ball mill for grinding calcium carbonate has become more cost-efficient, durable and reliable. Paired with classifier, ball mill for grinding calcium carbonate can produce fine ground calcium carbonate powder D97(5-22m) and even ultra fine GCC powder with high capacity. Daswell machinery offers provides customized high quality ball mill and classifier equipment which work best for your calcium carbonate plant.

Daswell machinery is a serious player in calcium carbonate powder making industry. Daswell has successfully delivered several turnkey ground calcium carbonate projects around the world. Except for designing and planning, Daswell also provides complete set of realiable and durable ground calcium carbonate equipment. And ball mill combined with classifier is the central part of calcium carbonate production line. According to customers needs, Daswell ball mill for grinding calcium carbonate can come in different diameter and be paired with primary or secondary classifier. Daswell calcium carbonate ball mill machine is made of high grade steel which is durable to work long time with easy maintenance. Besides, Daswell ball mill machine for calcium carbonate is also the symbol of high technology, which consumes less energy and produce quality finished ground calcium carbonate powder.

Ball mill is a hollow cylinder which rotates about its axis. The axis can be horizontal or be at some angle to the horizontal. The shell of ball mill can be made of strong steel and coated with refractory materials. Ball mill is partially filled with free moving media balls which can be made of steel, stainless steel, ceramic or rubber. And the media balls are in different sizes: smaller grinding balls for fine calcium carbonate and larger media balls for coarse calcium carbonate. For the internal side, the inner wall of the ball mill is often lined with abrasive-resistant materials such as steel or rubber. And the length and diameter of ball mill grinder for calcium carbonate can come in different sizes according to production capacity.

Industrial ball mill machine for ground calcium carbonate often can operate continuously. And the raw material such as limestone or marble is fed from one end and discharged from another end. When the calcium carbonate ball mill starts to rotate under the function of drive, the media balls inside the ball mill will be lifted and then impacted against the calcium carbonate material bed. Through constant rotation, the raw material in the ball mill will be ground to medium and fine sizes. And then the ground calcium carbonate will be transported pneumatically to classifier. In the classifier, while the calcium carbonate powder of required sizes will be transported to product silo, the coarse ones will be returned to ball mill with feed material.

Ball mill and classifier often work together for calcium carbonate process. Although ball mill grinder for calcium carbonate can grind calcium carbonate material to medium and fine particle sizes, to meet customers needs of consistent fine and ultra fine GCC powder, calcium carbonate ball mill must work together with primary and even secondary classifiers. After the grinding process in calcium carbonate ball mill, the ground calcium carbonate will be transported to classifier pneumatically. The air flow in classifier will then transfer fine calcium carbonate powder to product silo, while the coarse calcium carbonate will return to ball mill together with feed material. For ultra fine ground calcium carbonate powder, a secondary classifier can be installed, forming a series circus with the primary classifier. In all, to produce uniform fine and ultra fine calcium carbonate powder in large quantity, calcium carbonate ball mill and classifying production line is the most suitable solution. Please fill the form below to get free quotes. We will reply in 24 hours. Product Model: Your Name(required): Your Email(required): Your Tel: Your country: Your Company: Your Message(required):

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