ball mill c capacity formula in australia

ball mill design/power calculation

ball mill design/power calculation

The basic parameters used inball mill design (power calculations), rod mill or anytumbling millsizingare; 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 modelsand others.These are a good back-to-basics exercises for those wanting to understand what is behind or inside the machines.

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 motorpowerrequirement 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:

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.

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

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 - an overview | sciencedirect topics

ball mill - an overview | sciencedirect topics

The ball mill accepts the SAG or AG mill product. Ball mills give a controlled final grind and produce flotation feed of a uniform size. Ball mills tumble iron or steel balls with the ore. The balls are initially 510 cm diameter but gradually wear away as grinding of the ore proceeds. The feed to ball mills (dry basis) is typically 75 vol.-% ore and 25% steel.

The ball mill is operated in closed circuit with a particle-size measurement device and size-control cyclones. The cyclones send correct-size material on to flotation and direct oversize material back to the ball mill for further grinding.

Grinding elements in ball mills travel at different velocities. Therefore, collision force, direction and kinetic energy between two or more elements vary greatly within the ball charge. Frictional wear or rubbing forces act on the particles, as well as collision energy. These forces are derived from the rotational motion of the balls and movement of particles within the mill and contact zones of colliding balls.

By rotation of the mill body, due to friction between mill wall and balls, the latter rise in the direction of rotation till a helix angle does not exceed the angle of repose, whereupon, the balls roll down. Increasing of rotation rate leads to growth of the centrifugal force and the helix angle increases, correspondingly, till the component of weight strength of balls become larger than the centrifugal force. From this moment the balls are beginning to fall down, describing during falling certain parabolic curves (Figure 2.7). With the further increase of rotation rate, the centrifugal force may become so large that balls will turn together with the mill body without falling down. The critical speed n (rpm) when the balls are attached to the wall due to centrifugation:

where Dm is the mill diameter in meters. The optimum rotational speed is usually set at 6580% of the critical speed. These data are approximate and may not be valid for metal particles that tend to agglomerate by welding.

The degree of filling the mill with balls also influences productivity of the mill and milling efficiency. With excessive filling, the rising balls collide with falling ones. Generally, filling the mill by balls must not exceed 3035% of its volume.

The mill productivity also depends on many other factors: physical-chemical properties of feed material, filling of the mill by balls and their sizes, armor surface shape, speed of rotation, milling fineness and timely moving off of ground product.

where b.ap is the apparent density of the balls; l is the degree of filling of the mill by balls; n is revolutions per minute; 1, and 2 are coefficients of efficiency of electric engine and drive, respectively.

A feature of ball mills is their high specific energy consumption; a mill filled with balls, working idle, consumes approximately as much energy as at full-scale capacity, i.e. during grinding of material. Therefore, it is most disadvantageous to use a ball mill at less than full capacity.

The ball mill is a tumbling mill that uses steel balls as the grinding media. The length of the cylindrical shell is usually 11.5 times the shell diameter (Figure 8.11). The feed can be dry, with less than 3% moisture to minimize ball coating, or slurry containing 2040% water by weight. Ball mills are employed in either primary or secondary grinding applications. In primary applications, they receive their feed from crushers, and in secondary applications, they receive their feed from rod mills, AG mills, or SAG mills.

Ball mills are filled up to 40% with steel balls (with 3080mm diameter), which effectively grind the ore. The material that is to be ground fills the voids between the balls. The tumbling balls capture the particles in ball/ball or ball/liner events and load them to the point of fracture.

When hard pebbles rather than steel balls are used for the grinding media, the mills are known as pebble mills. As mentioned earlier, pebble mills are widely used in the North American taconite iron ore operations. Since the weight of pebbles per unit volume is 3555% of that of steel balls, and as the power input is directly proportional to the volume weight of the grinding medium, the power input and capacity of pebble mills are correspondingly lower. Thus, in a given grinding circuit, for a certain feed rate, a pebble mill would be much larger than a ball mill, with correspondingly a higher capital cost. However, the increase in capital cost is justified economically by a reduction in operating cost attributed to the elimination of steel grinding media.

In general, ball mills can be operated either wet or dry and are capable of producing products in the order of 100m. This represents reduction ratios of as great as 100. Very large tonnages can be ground with these ball mills because they are very effective material handling devices. Ball mills are rated by power rather than capacity. Today, the largest ball mill in operation is 8.53m diameter and 13.41m long with a corresponding motor power of 22MW (Toromocho, private communications).

Planetary ball mills. A planetary ball mill consists of at least one grinding jar, which is arranged eccentrically on a so-called sun wheel. The direction of movement of the sun wheel is opposite to that of the grinding jars according to a fixed ratio. The grinding balls in the grinding jars are subjected to superimposed rotational movements. The jars are moved around their own axis and, in the opposite direction, around the axis of the sun wheel at uniform speed and uniform rotation ratios. The result is that the superimposition of the centrifugal forces changes constantly (Coriolis motion). The grinding balls describe a semicircular movement, separate from the inside wall, and collide with the opposite surface at high impact energy. The difference in speeds produces an interaction between frictional and impact forces, which releases high dynamic energies. The interplay between these forces produces the high and very effective degree of size reduction of the planetary ball mill. Planetary ball mills are smaller than common ball mills, and are mainly used in laboratories for grinding sample material down to very small sizes.

Vibration mill. Twin- and three-tube vibrating mills are driven by an unbalanced drive. The entire filling of the grinding cylinders, which comprises the grinding media and the feed material, constantly receives impulses from the circular vibrations in the body of the mill. The grinding action itself is produced by the rotation of the grinding media in the opposite direction to the driving rotation and by continuous head-on collisions of the grinding media. The residence time of the material contained in the grinding cylinders is determined by the quantity of the flowing material. The residence time can also be influenced by using damming devices. The sample passes through the grinding cylinders in a helical curve and slides down from the inflow to the outflow. The high degree of fineness achieved is the result of this long grinding procedure. Continuous feeding is carried out by vibrating feeders, rotary valves, or conveyor screws. The product is subsequently conveyed either pneumatically or mechanically. They are basically used to homogenize food and feed.

CryoGrinder. As small samples (100 mg or <20 ml) are difficult to recover from a standard mortar and pestle, the CryoGrinder serves as an alternative. The CryoGrinder is a miniature mortar shaped as a small well and a tightly fitting pestle. The CryoGrinder is prechilled, then samples are added to the well and ground by a handheld cordless screwdriver. The homogenization and collection of the sample is highly efficient. In environmental analysis, this system is used when very small samples are available, such as small organisms or organs (brains, hepatopancreas, etc.).

The vibratory ball mill is another kind of high-energy ball mill that is used mainly for preparing amorphous alloys. The vials capacities in the vibratory mills are smaller (about 10 ml in volume) compared to the previous types of mills. In this mill, the charge of the powder and milling tools are agitated in three perpendicular directions (Fig. 1.6) at very high speed, as high as 1200 rpm.

Another type of the vibratory ball mill, which is used at the van der Waals-Zeeman Laboratory, consists of a stainless steel vial with a hardened steel bottom, and a single hardened steel ball of 6 cm in diameter (Fig. 1.7).

The mill is evacuated during milling to a pressure of 106 Torr, in order to avoid reactions with a gas atmosphere.[44] Subsequently, this mill is suitable for mechanical alloying of some special systems that are highly reactive with the surrounding atmosphere, such as rare earth elements.

A ball mill is a relatively simple apparatus in which the motion of the reactor, or of a part of it, induces a series of collisions of balls with each other and with the reactor walls (Suryanarayana, 2001). At each collision, a fraction of the powder inside the reactor is trapped between the colliding surfaces of the milling tools and submitted to a mechanical load at relatively high strain rates (Suryanarayana, 2001). This load generates a local nonhydrostatic mechanical stress at every point of contact between any pair of powder particles. The specific features of the deformation processes induced by these stresses depend on the intensity of the mechanical stresses themselves, on the details of the powder particle arrangement, that is on the topology of the contact network, and on the physical and chemical properties of powders (Martin et al., 2003; Delogu, 2008a). At the end of any given collision event, the powder that has been trapped is remixed with the powder that has not undergone this process. Correspondingly, at any instant in the mechanical processing, the whole powder charge includes fractions of powder that have undergone a different number of collisions.

The individual reactive processes at the perturbed interface between metallic elements are expected to occur on timescales that are, at most, comparable with the collision duration (Hammerberg et al., 1998; Urakaev and Boldyrev, 2000; Lund and Schuh, 2003; Delogu and Cocco, 2005a,b). Therefore, unless the ball mill is characterized by unusually high rates of powder mixing and frequency of collisions, reactive events initiated by local deformation processes at a given collision are not affected by a successive collision. Indeed, the time interval between successive collisions is significantly longer than the time period required by local structural perturbations for full relaxation (Hammerberg et al., 1998; Urakaev and Boldyrev, 2000; Lund and Schuh, 2003; Delogu and Cocco, 2005a,b).

These few considerations suffice to point out the two fundamental features of powder processing by ball milling, which in turn govern the MA processes in ball mills. First, mechanical processing by ball milling is a discrete processing method. Second, it has statistical character. All of this has important consequences for the study of the kinetics of MA processes. The fact that local deformation events are connected to individual collisions suggests that absolute time is not an appropriate reference quantity to describe mechanically induced phase transformations. Such a description should rather be made as a function of the number of collisions (Delogu et al., 2004). A satisfactory description of the MA kinetics must also account for the intrinsic statistical character of powder processing by ball milling. The amount of powder trapped in any given collision, at the end of collision is indeed substantially remixed with the other powder in the reactor. It follows that the same amount, or a fraction of it, could at least in principle be trapped again in the successive collision.

This is undoubtedly a difficult aspect to take into account in a mathematical description of MA kinetics. There are at least two extreme cases to consider. On the one hand, it could be assumed that the powder trapped in a given collision cannot be trapped in the successive one. On the other, it could be assumed that powder mixing is ideal and that the amount of powder trapped at a given collision has the same probability of being processed in the successive collision. Both these cases allow the development of a mathematical model able to describe the relationship between apparent kinetics and individual collision events. However, the latter assumption seems to be more reliable than the former one, at least for commercial mills characterized by relatively complex displacement in the reactor (Manai et al., 2001, 2004).

A further obvious condition for the successful development of a mathematical description of MA processes is the one related to the uniformity of collision regimes. More specifically, it is highly desirable that the powders trapped at impact always experience the same conditions. This requires the control of the ball dynamics inside the reactor, which can be approximately obtained by using a single milling ball and an amount of powder large enough to assure inelastic impact conditions (Manai et al., 2001, 2004; Delogu et al., 2004). In fact, the use of a single milling ball avoids impacts between balls, which have a remarkable disordering effect on the ball dynamics, whereas inelastic impact conditions permit the establishment of regular and periodic ball dynamics (Manai et al., 2001, 2004; Delogu et al., 2004).

All of the above assumptions and observations represent the basis and guidelines for the development of the mathematical model briefly outlined in the following. It has been successfully applied to the case of a Spex Mixer/ Mill mod. 8000, but the same approach can, in principle, be used for other ball mills.

The Planetary ball mills are the most popular mills used in MM, MA, and MD scientific researches for synthesizing almost all of the materials presented in Figure 1.1. In this type of mill, the milling media have considerably high energy, because milling stock and balls come off the inner wall of the vial (milling bowl or vial) and the effective centrifugal force reaches up to 20 times gravitational acceleration.

The centrifugal forces caused by the rotation of the supporting disc and autonomous turning of the vial act on the milling charge (balls and powders). Since the turning directions of the supporting disc and the vial are opposite, the centrifugal forces alternately are synchronized and opposite. Therefore, the milling media and the charged powders alternatively roll on the inner wall of the vial, and are lifted and thrown off across the bowl at high speed, as schematically presented in Figure 2.17.

However, there are some companies in the world who manufacture and sell number of planetary-type ball mills; Fritsch GmbH (www.fritsch-milling.com) and Retsch (http://www.retsch.com) are considered to be the oldest and principal companies in this area.

Fritsch produces different types of planetary ball mills with different capacities and rotation speeds. Perhaps, Fritsch Pulverisette P5 (Figure 2.18(a)) and Fritsch Pulverisette P6 (Figure 2.18(b)) are the most popular models of Fritsch planetary ball mills. A variety of vials and balls made of different materials with different capacities, starting from 80ml up to 500ml, are available for the Fritsch Pulverisette planetary ball mills; these include tempered steel, stainless steel, tungsten carbide, agate, sintered corundum, silicon nitride, and zirconium oxide. Figure 2.19 presents 80ml-tempered steel vial (a) and 500ml-agate vials (b) together with their milling media that are made of the same materials.

Figure 2.18. Photographs of Fritsch planetary-type high-energy ball mill of (a) Pulverisette P5 and (b) Pulverisette P6. The equipment is housed in the Nanotechnology Laboratory, Energy and Building Research Center (EBRC), Kuwait Institute for Scientific Research (KISR).

Figure 2.19. Photographs of the vials used for Fritsch planetary ball mills with capacity of (a) 80ml and (b) 500ml. The vials and the balls shown in (a) and (b) are made of tempered steel agate materials, respectively (Nanotechnology Laboratory, Energy and Building Research Center (EBRC), Kuwait Institute for Scientific Research (KISR)).

More recently and in year 2011, Fritsch GmbH (http://www.fritsch-milling.com) introduced a new high-speed and versatile planetary ball mill called Planetary Micro Mill PULVERISETTE 7 (Figure 2.20). The company claims this new ball mill will be helpful to enable extreme high-energy ball milling at rotational speed reaching to 1,100rpm. This allows the new mill to achieve sensational centrifugal accelerations up to 95 times Earth gravity. They also mentioned that the energy application resulted from this new machine is about 150% greater than the classic planetary mills. Accordingly, it is expected that this new milling machine will enable the researchers to get their milled powders in short ball-milling time with fine powder particle sizes that can reach to be less than 1m in diameter. The vials available for this new type of mill have sizes of 20, 45, and 80ml. Both the vials and balls can be made of the same materials, which are used in the manufacture of large vials used for the classic Fritsch planetary ball mills, as shown in the previous text.

Retsch has also produced a number of capable high-energy planetary ball mills with different capacities (http://www.retsch.com/products/milling/planetary-ball-mills/); namely Planetary Ball Mill PM 100 (Figure 2.21(a)), Planetary Ball Mill PM 100 CM, Planetary Ball Mill PM 200, and Planetary Ball Mill PM 400 (Figure 2.21(b)). Like Fritsch, Retsch offers high-quality ball-milling vials with different capacities (12, 25, 50, 50, 125, 250, and 500ml) and balls of different diameters (540mm), as exemplified in Figure 2.22. These milling tools can be made of hardened steel as well as other different materials such as carbides, nitrides, and oxides.

Figure 2.21. Photographs of Retsch planetary-type high-energy ball mill of (a) PM 100 and (b) PM 400. The equipment is housed in the Nanotechnology Laboratory, Energy and Building Research Center (EBRC), Kuwait Institute for Scientific Research (KISR).

Figure 2.22. Photographs of the vials used for Retsch planetary ball mills with capacity of (a) 80ml, (b) 250ml, and (c) 500ml. The vials and the balls shown are made of tempered steel (Nanotechnology Laboratory, Energy and Building Research Center (EBRC), Kuwait Institute for Scientific Research (KISR)).

Both Fritsch and Retsch companies have offered special types of vials that allow monitoring and measure the gas pressure and temperature inside the vial during the high-energy planetary ball-milling process. Moreover, these vials allow milling the powders under inert (e.g., argon or helium) or reactive gas (e.g., hydrogen or nitrogen) with a maximum gas pressure of 500kPa (5bar). It is worth mentioning here that such a development made on the vials design allows the users and researchers to monitor the progress tackled during the MA and MD processes by following up the phase transformations and heat realizing upon RBM, where the interaction of the gas used with the freshly created surfaces of the powders during milling (adsorption, absorption, desorption, and decomposition) can be monitored. Furthermore, the data of the temperature and pressure driven upon using this system is very helpful when the ball mills are used for the formation of stable (e.g., intermetallic compounds) and metastable (e.g., amorphous and nanocrystalline materials) phases. In addition, measuring the vial temperature during blank (without samples) high-energy ball mill can be used as an indication to realize the effects of friction, impact, and conversion processes.

More recently, Evico-magnetics (www.evico-magnetics.de) has manufactured an extraordinary high-pressure milling vial with gas-temperature-monitoring (GTM) system. Likewise both system produced by Fritsch and Retsch, the developed system produced by Evico-magnetics, allowing RBM but at very high gas pressure that can reach to 15,000kPa (150bar). In addition, it allows in situ monitoring of temperature and of pressure by incorporating GTM. The vials, which can be used with any planetary mills, are made of hardened steel with capacity up to 220ml. The manufacturer offers also two-channel system for simultaneous use of two milling vials.

Using different ball mills as examples, it has been shown that, on the basis of the theory of glancing collision of rigid bodies, the theoretical calculation of tPT conditions and the kinetics of mechanochemical processes are possible for the reactors that are intended to perform different physicochemical processes during mechanical treatment of solids. According to the calculations, the physicochemical effect of mechanochemical reactors is due to short-time impulses of pressure (P = ~ 10101011 dyn cm2) with shift, and temperature T(x, t). The highest temperature impulse T ~ 103 K are caused by the dry friction phenomenon.

Typical spatial and time parameters of the impactfriction interaction of the particles with a size R ~ 104 cm are as follows: localization region, x ~ 106 cm; time, t ~ 108 s. On the basis of the obtained theoretical results, the effect of short-time contact fusion of particles treated in various comminuting devices can play a key role in the mechanism of activation and chemical reactions for wide range of mechanochemical processes. This role involves several aspects, that is, the very fact of contact fusion transforms the solid phase process onto another qualitative level, judging from the mass transfer coefficients. The spatial and time characteristics of the fused zone are such that quenching of non-equilibrium defects and intermediate products of chemical reactions occurs; solidification of the fused zone near the contact point results in the formation of a nanocrystal or nanoamor- phous state. The calculation models considered above and the kinetic equations obtained using them allow quantitative ab initio estimates of rate constants to be performed for any specific processes of mechanical activation and chemical transformation of the substances in ball mills.

There are two classes of ball mills: planetary and mixer (also called swing) mill. The terms high-speed vibration milling (HSVM), high-speed ball milling (HSBM), and planetary ball mill (PBM) are often used. The commercial apparatus are PBMs Fritsch P-5 and Fritsch Pulverisettes 6 and 7 classic line, the Retsch shaker (or mixer) mills ZM1, MM200, MM400, AS200, the Spex 8000, 6750 freezer/mill SPEX CertiPrep, and the SWH-0.4 vibrational ball mill. In some instances temperature controlled apparatus were used (58MI1); freezer/mills were used in some rare cases (13MOP1824).

The balls are made of stainless steel, agate (SiO2), zirconium oxide (ZrO2), or silicon nitride (Si3N). The use of stainless steel will contaminate the samples with steel particles and this is a problem both for solid-state NMR and for drug purity.

However, there are many types of ball mills (see Chapter 2 for more details), such as drum ball mills, jet ball mills, bead-mills, roller ball mills, vibration ball mills, and planetary ball mills, they can be grouped or classified into two types according to their rotation speed, as follows: (i) high-energy ball mills and (ii) low-energy ball mills. Table 3.1 presents characteristics and comparison between three types of ball mills (attritors, vibratory mills, planetary ball mills and roller mills) that are intensively used on MA, MD, and MM techniques.

In fact, choosing the right ball mill depends on the objectives of the process and the sort of materials (hard, brittle, ductile, etc.) that will be subjecting to the ball-milling process. For example, the characteristics and properties of those ball mills used for reduction in the particle size of the starting materials via top-down approach, or so-called mechanical milling (MM process), or for mechanically induced solid-state mixing for fabrications of composite and nanocomposite powders may differ widely from those mills used for achieving mechanically induced solid-state reaction (MISSR) between the starting reactant materials of elemental powders (MA process), or for tackling dramatic phase transformation changes on the structure of the starting materials (MD). Most of the ball mills in the market can be employed for different purposes and for preparing of wide range of new materials.

Martinez-Sanchez et al. [4] have pointed out that employing of high-energy ball mills not only contaminates the milled amorphous powders with significant volume fractions of impurities that come from milling media that move at high velocity, but it also affects the stability and crystallization properties of the formed amorphous phase. They have proved that the properties of the formed amorphous phase (Mo53Ni47) powder depends on the type of the ball-mill equipment (SPEX 8000D Mixer/Mill and Zoz Simoloter mill) used in their important investigations. This was indicated by the high contamination content of oxygen on the amorphous powders prepared by SPEX 8000D Mixer/Mill, when compared with the corresponding amorphous powders prepared by Zoz Simoloter mill. Accordingly, they have attributed the poor stabilities, indexed by the crystallization temperature of the amorphous phase formed by SPEX 8000D Mixer/Mill to the presence of foreign matter (impurities).

how to size a ball mill -design calculator & formula

how to size a ball mill -design calculator & formula

A) Total Apparent Volumetric Charge Filling including balls and excess slurry on top of the ball charge, plus the interstitial voids in between the balls expressed as a percentage of the net internal mill volume (inside liners).

B) Overflow Discharge Mills operating at low ball fillings slurry may accumulate on top of the ball charge; causing, the Total Charge Filling Level to be higher than the Ball Filling Level. Grate Discharge mills will not face this issue.

C) This value represents the Volumetric Fractional Filling of the Voids in between the balls by the retained slurry in the mill charge. As defined, this value should never exceed 100%, but in some cases particularly in Grate Discharge Mills it could be lower than 100%. Note that this interstitial slurry does not include the overfilling slurry derived from the difference between the Charge and Ball Filling.

D) Represents the so-called Dynamic Angle of Repose (or Lift Angle) adopted during steady operation by the top surface of the mill charge (the kidney) with respect to the horizontal. A reasonable default value for this angle is 32, but may be easily tuned to specific applications against any available actual power data.

The first step in mill design is to determine the power needed to produce the desired grind in the chosen ore. The most used equation, for this purpose, is the empirical Bond equation (Bond, 1960, 1961; Rowland and Kjos, 1978).

In this equation, E is the specific energy required for the grind, and F80 and P80 are the sizes in micrometers that 80% of the weight passes of the mill feed and product respectively. The parameter Wi, known as the work index of the ore, is obtained from batch bench tests first devised by Bond (1961). The power calculated on using equation 1, (Bond, 1961; Rowland and Kjos, 1978), relates to:

1) Rod milling a rod mill with a diameter of 2.44 meters, inside new liners, grinding wet in open circuit. 2) Ball milling a ball mill with a diameter of 2.44 meters, inside new liners, grinding wet in open circuit.

When the grinding conditions differ from these specified conditions, efficiency factors (Rowland and Kjos, 1978) have to be used in conjunction with equation 1. In general, therefore, the required mill power is calculated using the following equation

where n is the number of efficiency factors, EFi, used and fo is the feed rate of new ore to the mill. The power calculated from equation 2 can be looked up in published tables (Rowland and Kjos, 1978) and the correct mill size and type can be selected.

The philosophy in the development of the MRRC grinding simulation package was to build interactive software that could be used as an inexpensive means of providing a semi-quantitative check on a grinding mill design. In addition the software is designed to slot in to a general mineral processing package now undergoing development at the MRRC.

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