bond work index - an overview | sciencedirect topics

bond work index - an overview | sciencedirect topics

The Bond work index is not solely a material constant but is influenced by the grinding conditions. For example, the finer the grind size desired, the higher is the kWh/t required to grind to that size. Magdalinovic [38] measured the Bond work index of three ore types using different test screen sizes. He produced a correlation between the mass of test screen undersize per revolution, G, and the square root of the test screen size, D:

The constant K2 is also dependent on ore type and ranged from 1.4 to 1.5. A regression of Magdalinovics data including the feed 80% passing size gives an average value of 1.485 for K2. If we extend this relationship to any sample of screened material then this gives an approximate estimate of the 80% passing size as 67.3% of the top size. This compares with a value of 66.7% of the 99% passing size obtained from data in Table3.3.

Using Magdalinovics method, from the results of a Bond work index test at a single test screen size, the constants K1 and K2 can be calculated and from these values, the work index at any test screen size can be estimated.

An alternative approach to determine the effect of closing screen size on the Bond ball mill work index (BWi), in the absence of extensive test work, is to use computer simulation. The batch grinding process has been modelled using the sizemass balance approach (Austin [37], Chapter11) and if we can do this, then we can effectively simulate the Bond ball mill work index test. Yan and Eaton [39] measured the selection function and breakage distribution parameters for the Austin grinding model and demonstrated the BWi simulation with soft and medium/hard ore samples. The measured BWi was 14.0 and 6.6kWh/t for the medium/hard and soft ore, respectively, at a closing screen size of 106 m compared with the simulated values of 13.2 and 5.6kWh/t.

The ability to simulate the Bond work index test also allows examination of truncated ball mill feed size distributions on the work index. For grinding circuits where the feed to a ballmill is sent directly to the classifier and the cyclone underflow feeds the ball mill (see Figure3.10), a question arises as to whether this practice will alter the ball mill work index (BWi) of the material being ground and hence have an impact on the energy used in the mill for grinding. Some might conclude that a higher percentage of coarse material in the mill feed will increase the amount of material that needs to be ground to produce the end product and hence it will affect the BWi. Others, in the absence of contrary evidence, assume that there is no change in the work index. Figure3.11 shows the typical circuit represented by the standard Bond work index correlation and Figure3.10 represents the scalped or truncated feed case.

The procedure for the work index test bases the BWi value on the calculation of new fines generated in the test. This means that the fraction of fines in the feed should not influence the test result significantly, if at all. For example, for a sample with 20% of 300 m material in the feed, if this is not scalped out of the fresh feed, then the mill charge, at 250% circulating load will contain 0.2/3.5 or 5.7% of 300 m in the mill charge compared with 0% for a scalped fresh feed, at a closing screen of 300 m. This should not have a great influence on the production of new fines unless the test was carried out in a wet environment and the fines contained a high percentage of clays to affect the viscosity of the grind environment. Thus for a Bond test (dry test), the difference between the scalped and unscalped BWi result is expected to be minor. In a plant operation where the environment is wet and clays are present, a different result may be observed.

Tests carried out to confirm this have clouded the water a little. Three rock types were tested with scalped and unscalped feeds with two samples showing higher BWi values for the scalped ore and the other sample showing a lower value [40].

In the work index test simulation, it is easy to change the closing screen size to examine the effect on the BWi. The results of such a simulation are shown in Figure3.12 where the simulated test was performed at different closing screen sizes and different scalping sizes. This shows that for scalping sizes at or below the closing screen size of the test, the BWi values are not affected. The scalping size of zero refers to the un-scalped mill feed. For scalped screen sizes above the closing screen size, the BWi values start to increase. The increase in BWi is more pronounced at the larger closing screen sizes. At a closing screen size of 300 m and a scalped size of 600 m, the increase in BWi is 4%.

Another outcome of the simulation is the effect of the closing screen size on the work index. As the closing size decreases, the ore must be ground finer, using more energy and producing a higher work index. Further simulations at even larger closing screen sizes show the BWi to increase. This dip in BWi with closing screen size has been observed experimentally, as shown in Figure3.13, with the minimum in BWi occurring at different closing screen sizes for different rock types [41,42].

Bond impact crushability work index (CWi) (Bond, 1963) results reported for iron ores vary from hard iron ore (17.7kWh/t) to medium hardness iron ore (11.3kWh/t) and friable iron ore (6.3kWh/t) (Table 2.11; Clout et al., 2007). The CWi for hard iron ores typically overlaps with those reported for BIF (taconite) iron ores while the range in values in Table 2.11 covers that for different types of iron ores and materials reported earlier by Bond (1963), with some relevant data in Table 2.12.

The most widely used parameter to measure ore hardness is the Bond work index Wi. Calculations involving Bonds work index are generally divided into steps with a different Wi determination for each size class. The low energy crushing work index laboratory test is conducted on ore specimens larger than 50mm, determining the crushing work index (WiC, CWi or IWi (impact work index)). The rod mill work index laboratory test is conducted by grinding an ore sample prepared to 80% passing 12.7mm ( inch, the original test being developed in imperial units) to a product size of approximately 1mm (in the original and still the standard, 14 mesh; see Chapter 4 for definition of mesh), thus determining the rod mill work index (WiR or RWi). The ball mill work index laboratory test is conducted by grinding an ore sample prepared to 100% passing 3.36mm (6 mesh) to product size in the range of 45-150m (325-100 mesh), thus determining the ball mill work index (WiB or BWi). The work index calculations across a narrow size range are conducted using the appropriate laboratory work index determination for the material size of interest, or by chaining individual work index calculations using multiple laboratory work index determinations across a wide range of particle size.

To give a sense of the magnitude, Table 5.1 lists Bond work indices for a selection of materials. For preliminary design purposes such reference data are of some guide but measured values are required at the more advanced design stage.

A major use of the Bond model is to select the size of tumbling mill for a given duty. (An example calculation is given in Chapter 7.) A variety of correction factors (EF) have been developed to adapt the Bond formula to situations not included in the original calibration set and to account for relative efficiency differences in certain comminution machines (Rowland, 1988). Most relevant are the EF4 factor for coarse feed and the EF5 factor for fine grinding that attempt to compensate for sizes ranges beyond the bulk of the original calibration data set (Bond, 1985).

The standard Bond tumbling mill tests are time-consuming, requiring locked-cycle testing. Smith and Lee (1968) used batch-type tests to arrive at the work index; however, the grindability of highly heterogeneous ores cannot be well reproduced by batch testing.

Berry and Bruce (1966) developed a comparative method of determining the hardness of an ore. The method requires the use of a reference ore of known work index. The reference ore is ground for a certain time (T) in a laboratory tumbling mill and an identical weight of the test ore is then ground for the same time. Since the power input to the mill is constant (P), the energy input (E=PT) is the same for both reference and test ore. If r is the reference ore and t the ore under test, then we can write from Bonds Eq. (5.4):

Work indices have been obtained from grindability tests on different sizes of several types of equipment, using identical feed materials (Lowrison, 1974). The values of work indices obtained are indications of the efficiencies of the machines. Thus, the equipment having the highest indices, and hence the largest energy consumers, are found to be jaw and gyratory crushers and tumbling mills; intermediate consumers are impact crushers and vibration mills, and roll crushers are the smallest consumers. The smallest consumers of energy are those machines that apply a steady, continuous, compressive stress on the material.

A class of comminution equipment that does not conform to the assumption that the particle size distributions of a feed and product stream are self-similar includes autogenous mills (AG), semi-autogenous (SAG) mills and high pressure grinding rolls (HPGR). Modeling these machines with energy-based methods requires either recalibrating equations (in the case of the Bond series) or developing entirely new tests that are not confused by the non-standard particle size distributions.

Variability samples must be tested for the relevant metallurgical parameters. Ball mill design requires a Bond work index, BWi, for ball mills at the correct passing size; SAG mill design requires an appropriate SAG test, for example, SPI (Chapter 5). Flotation design needs a valid measure of kinetics for each sample, including the maximum attainable recovery and rate constants for each mineral (Chapter 12). Take care to avoid unnecessary testing for inappropriate parameters, saving the available funds for more variability samples rather than more tests on few samples. Remember that it must be possible to use the measured values for the samples to estimate the metallurgical parameters for the mine blocks in order to describe the ore body, and these estimates will be used in process models to forecast results for the plant. Always include some basic mineralogical examination of each sample.

The expression for computing the power consumption (P) derived theoretically by Rose and English [9] involved the knowledge of Bonds work index (Wi). To evaluate the work index they considered the maximum size in the feed and also the maximum size of particles in the discharge from the crusher. To determine the size through which 80% of the feed passed, they considered a large database relating the maximum particle size and the undersize. From the relation it was concluded that F80 was approximately equal to 0.7 times the largest size of particle. Taking the largest size of the particle that should be charged to a jaw crusher as 0.9 times the gape, F80 was written as

Also, to establish the P80 from the largest product size, Rose and English considered that the largest particle size discharged from the bottom of the crusher would occur at the maximum open set position and hence

For operating a jaw crusher it is necessary to know the maximum power required consistently with the reduction ratio and the gape and closed side settings. The maximum power drawn in a system will occur at the critical speed. Thus for maximum power, Q in Equation (4.51) is replaced with QM from Equation (4.19) to give

The largest size of ore pieces mined measured 560mm (average) and the smallest sizes averaged 160mm. The density of the ore was 2.8t/m3. The ore had to be crushed in a C-63 type jaw crusher 630 440. At a reduction ratio of 4, 18% of the ore was below the maximum size required. Determine:1.the maximum operating capacity of the crusher,2.the optimum speed at which it should be operated.

Finally, a look should be taken at coal elasticity, hardness and strength. However, a particular matter of importance which arises from those consideration is the ease of coal grinding, an important step in whatever coal preparation efforts for further processing. The more fundamental material properties are covered reasonably by Berkowitz (1994), so the discussion here will be limited to coal grindability. For that purpose, use is made of two different indices, both determined experimentally with the material to be ground. One is the Hardgrove grindability index and the other the Bond work index.

The Hardgrove index is determined using the ASTM method D 40971. It involves grinding 50g of the material, e.g. coal, of specified size (1630 mesh cut) in a specified ball-and-race mill for 60 revolutions. The amount of 200 mesh material is measured (w grams) and the index is defined as I = 13+ 6.93w. Thus, the higher the index, the easier is the grinding task. This method loosely assumes that the specific energy consumed is proportional to the new surface generated, following the concept of Rittingers law of comminution.

Berkowitz (1994 p.96) gives a generalized variation of the Hardgrove index with coal rank. According to the variation, anthracites are hard to grind, bituminous coals the easiest, and the subbituminous more difficult, with lignites down to the same low index level as anthracites. It is suggested that the decrease in the index below daf coal of 85% is caused by plastic deformation and aggregation of the softer coal particles, hence reducing the 200 mesh fraction generated by the grinding test.

The Bond work index (Bond, 1960) is based on Bonds law, which states that the energy consumed is proportional to the 1.5 power of particle size rather than the square of Rittingers law. Accordingly, the energy consumed in reducing the particle size from xF to xp (both measured as 80% undersize) is given by

We should note that the higher the value of the work index, the more difficult it is to grind the material. A compilation of data is available, for example, in Perrys Chemical Engineers Handbook (Perry et al., 1984). For coal, one average value is given, with Ei = 11.37 for = 1.63. Bonds law is useful because of the extensive comparative database.

Interestingly, Hukki (1961) offers a Solomonic settlement between the different grinding theories (rather than laws). A great deal of additional material related to grinding, or size reduction, comminution, is available in handbooks, e.g. by Prasher (1987) and research publications in journals such as Powder Technology. A very brief overview of grinding equipment is given in Section 1.5.3.

Rock fragmentation is a consequence of unstable extension of multiple cracks. Theoretically, rock fragmentation is also a facture mechanics problem. Two major differences between rock fracture and rock fragmentation are that (1) rock fragmentation deals with many cracks, but rock fracture deals with only one or a few, and (2) rock fragmentation concerns the size distribution of the fragments produced, but rock fracture does not. There are two important factors in rock fragmentation: (1) total energy consumed and (2) size distribution of fragments. In a study on crushing and grinding, fracture toughness has been taken as a key index similar to the Bond Work Index. Due to many cracks dealt with, rock fragmentation is a very complicated and difficult fracture problem. To achieve a good fragmentation, we need to know how the energy is distributed, which factors influence energy distribution, what is the size distribution, and so on. In practice such as mining and quarrying, it is of importance to predict and examine size distribution so as to make fragmentation optimized by modifying the blast plan or changing the fragmentation system. About size distribution, there are a number of distribution functions such as Weibulls distribution function [11], Cunninghams Kuz-Ram model [12], and the Swebrec function [13]. In engineering practice, how to develop a feasible and simple method to judge rock fragmentation in the field is still a challenging but significant job and will be in the future.

Although the fracture toughness of a rock is very important in rock fracture, the strengths of the rock are also useful in rock engineering. In the following we will see that the strengths and fracture toughness of a rock have a certain relation with each other, partly because of a similar mechanism in the micro-scale failure.

Bong's Work Index is used in Bong's law of comminution energy. It states that the total work useful in breakage is inversely proportional to the length of the formed crack tips and directly proportional to the square root of the formed surface:

where W is the specific energy expenditure in kilowatt-hours per ton and dp and df are the particle size in microns at which 80% of the corresponding product and feed passes through the sieve; CB is a constant depending on the characteristics of materials; and Sp and Sf are the specific surface areas of product and initial feed, respectively. Wi is called Bond's Work Index in kilowatt-hours per ton. It is given by the empirical equation:

where P1 is the sieve opening in microns for the grindability test, Gb.p. (g/rev) is the ball mill grindability, dp is the product particle size in microns (80% of product finer than size P1 passes) and df is the initial feed size in microns (80% of feed passes). A standard ball mill is 305mm in internal diameter and 305mm in internal length charged with 285 balls, as tabulated in Table 2.1. The lowest limit of the total mass of balls is 19.5Kg. The mill is rotated at 70 rev/min. The process is continued until the net mass of undersize produced by revolution becomes a constant Gb.p in the above equation.

To investigate the influence of the coal type on the stampability factor K, stamping tests with eight different coals (C1C8 in Table11.1) were carried out, using the Hardgrove grindability index (HGI) as a measure for the material dependency. The grindability is broadly defined as the response of a material to grinding effort. It can be interpreted as the resistance of the material against particularization. It is not an absolutely measurable physical property of the material. Generally, grindability can be determined either based on product constant fineness method (Bond work index Wi) or on constant useful grinding work method (HGI). The correlation between HGI and Wi can be described by the formula (11.5):

HGI is influenced by the petrographic composition of coal. HGI was developed to find a relationship between petrographic properties and strength of coal particles thus aiming to interpret the coking behavior of coals (Hardgrove 1932). HGI correlates to VM content, and the relationship is empirically specified for most of the hard coals and given with VM from 10% to 38% (db) by Eqs. (11.6) and (11.7):

For the execution of each test, further coal property parameters, particle size distribution and moisture content, as well as the height of fall of the stamp and the number of stamping steps were kept constant, so that the only parameter varied was the coal rank characterized by HGI.

The obtained data of each test was analyzed as described above to calculate the stampability factor K. A higher value for the HGI is equivalent to a lower resistance to stamping, i.e., a better stampability. The determined values of the stampability factor K are plotted against HGI in Fig.11.12.

tablet manufacturing: the ultimate guide - saintytec

tablet manufacturing: the ultimate guide - saintytec

A hammer mill will use in air mechanical impact force in the transformation of bulky material to smaller uniform particles. The key variable that the machine uses in controlling size of the particles include screen size and rotor speed. Feed throat and geometry will also play a major role.

The dry granulation machine depends on certain factors to produce the right size of particles. Some of the factors are roller speed, roll design, feed rate, particle size, die diameter and tooling features among others.

Instead of electricity, the mixer uses air bubbles or air compression for mixing or homogenizing or mixing powders. It has a mixing silo and a central conveying tube for spreading and mixing materials. It also has a housing cone with aerators around it.

Slugging Technique involves the compression of powder particles into large and flat tablets. You may use a tablet press or a rotary press. You will employ the use of a hammer mill to mill the resultant compact.

Roller compaction technique involves passing the ingredients through counter rotating rollers. The ingredients will consolidate and densify into a solid mass. Depending on the machine, you can get dense flakes or briquettes.

You will measure and weigh appropriate quantities of the ingredients. Make sure that the active ingredients and the excipients are in a finely divided form. If not, you have to reduce the size of the particles.

You will mix all the ingredients in a powder mixer until you achieve a uniform mix of the powder. At this stage, you will add half amount of the lubricants to the process. It will enhance the process of powder flow in the slugging process and prevent sticking of compressed powders.

In this stage you will compress the tablets into large flat pallets or tablets. This is the pre-compression process and the compacts that you will get are slugs. You might decide to use the roller compaction techniques or the slugging technique.

Weight variation from one tablet to another may cause a great challenge in the manufacturing process. You should ensure that the weight issue is not a problem because it is the genesis of solving other defects.

This type of packaging is good for very strong tablets that cannot break easily. You will place the tablets in a bottle which is the primary package. After that, you will cover the bottle with a lid which acts as the secondary package.

These tests focus on the content or in vitro release of the active ingredients. You must make sure that the content on the ingredient list should match the content of the tablets. Apart from that, the content of the tablets should conform to all the requirements of the official test.

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what particle size range does ball mill grinding produce?

what particle size range does ball mill grinding produce?

Ball Mill The ball mill has been around for eons. There are many shapes and sizes and types. There is a single enclosed drum-type where material is placed in the drum along with a charge of grinding media. These can be in various shapes, and typically they are balls. There is a whole science in the size of the starting material versus the ball size, shape material of construction and charge percentage of grinding media. All of these variables affect particle size, shape, and grinding efficiency. This type of grinding is very good for abrasive materials to prevent contamination. The grinding media as well as the interior surfaces of the mill can be lined with abrasion resistant materials suited to the material being ground. In some cases, it can even be the material being ground. However, the batch type system is not a very efficient means of grinding. There is a variety of ball mill that is a continuous process versus a batch process. It has an external classifier which returns the oversized material to the ball mill for further milling. This system is much more efficient in the grinding ability, but it is much more difficult to line the entire system with wear parts to grind an abrasive material.

Ball mill grinding is one method of crushing ore to an appropriate size fraction.Specifically, ore is put into a large receptacle (a drum) and then it rotates slowly around.Inside the receptacle, there are balls, usually made of metal, that as the ore is rotated around the revolving drum the ore is crushed as the balls rise and fall.The drum has a slight tilt to it, from one end to the other so that the ore slowly works its way to discharging end.The trick or art to all of this is to rotate the drum at a distinct rpm and the balls are harder than the ore so as to efficiently crush the continuous stream of ore to the desired size at the discharge end.

The ball mill is a key piece of equipment for grinding crushed materials, and it is widely used in production lines for powders such as cement, silicates, refractory material, fertilizer, glass ceramics, etc. as well as for ore dressing of both ferrous and non-ferrous metals. The ball mill can grind various ores and other materials either wet or dry. There are two kinds of ball mill, grate type and overfall type due to different ways of discharging material. There are many types of grinding media suitable for use in a ball mill, each material having its own specific properties and advantages. Key properties of grinding media are size, density, hardness, and composition.

The grinding chamber can also be filled with an inertshield gasthat does not react with the material being ground, to prevent oxidation or explosive reactions that could occur with ambient air inside the mill.

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).

ball mills - an overview | sciencedirect topics

ball mills - an overview | sciencedirect topics

A ball mill is a type of grinder used to grind and blend bulk material into QDs/nanosize using different sized balls. The working principle is simple; impact and attrition size reduction take place as the ball drops from near the top of a rotating hollow cylindrical shell. The nanostructure size can be varied by varying the number and size of balls, the material used for the balls, the material used for the surface of the cylinder, the rotation speed, and the choice of material to be milled. Ball mills are commonly used for crushing and grinding the materials into an extremely fine form. The ball mill contains a hollow cylindrical shell that rotates about its axis. This cylinder is filled with balls that are made of stainless steel or rubber to the material contained in it. Ball mills are classified as attritor, horizontal, planetary, high energy, or shaker.

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.

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 the movement of particles within the mill and contact zones of colliding balls.

By the rotation of the mill body, due to friction between the mill wall and balls, the latter rise in the direction of rotation until a helix angle does not exceed the angle of repose, whereupon the balls roll down. Increasing the rotation rate leads to the growth of the centrifugal force and the helix angle increases, correspondingly, until the component of the weight strength of balls becomes larger than the centrifugal force. From this moment, the balls are beginning to fall down, describing certain parabolic curves during the fall (Fig. 2.10).

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 remain attached to the wall with the aid of centrifugal force is:

where Dm is the mill diameter in meters. The optimum rotational speed is usually set at 65%80% of the critical speed. These data are approximate and may not be valid for metal particles that tend to agglomerate by welding.

where db.max is the maximum size of the feed (mm), is the compression strength (MPa), E is the modulus of elasticity (MPa), b is the density of material of balls (kg/m3), and D is the inner diameter of the mill body (m).

The degree of filling the mill with balls also influences the 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 30%35% of its volume.

The productivity of ball mills depends on the drum diameter and the relation of drum diameter and length. The optimum ratio between length L and diameter D, L:D, is usually accepted in the range 1.561.64. The mill productivity also depends on many other factors, including the physical-chemical properties of the feed material, the filling of the mill by balls and their sizes, the armor surface shape, the speed of rotation, the milling fineness, and the timely moving off of the ground product.

where D is the drum diameter, L is the drum length, b.ap is the apparent density of the balls, is the degree of filling of the mill by balls, n is the revolutions per minute, and 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, that is, during the grinding of material. Therefore, it is most disadvantageous to use a ball mill at less than full capacity.

Milling time in tumbler mills is longer to accomplish the same level of blending achieved in the attrition or vibratory mill, but the overall productivity is substantially greater. Tumbler mills usually are used to pulverize or flake metals, using a grinding aid or lubricant to prevent cold welding agglomeration and to minimize oxidation [23].

Cylindrical Ball Mills differ usually in steel drum design (Fig. 2.11), which is lined inside by armor slabs that have dissimilar sizes and form a rough inside surface. Due to such juts, the impact force of falling balls is strengthened. The initial material is fed into the mill by a screw feeder located in a hollow trunnion; the ground product is discharged through the opposite hollow trunnion.

Cylindrical screen ball mills have a drum with spiral curved plates with longitudinal slits between them. The ground product passes into these slits and then through a cylindrical sieve and is discharged via the unloading funnel of the mill body.

Conical Ball Mills differ in mill body construction, which is composed of two cones and a short cylindrical part located between them (Fig. 2.12). Such a ball mill body is expedient because efficiency is appreciably increased. Peripheral velocity along the conical drum scales down in the direction from the cylindrical part to the discharge outlet; the helix angle of balls is decreased and, consequently, so is their kinetic energy. The size of the disintegrated particles also decreases as the discharge outlet is approached and the energy used decreases. In a conical mill, most big balls take up a position in the deeper, cylindrical part of the body; thus, the size of the balls scales down in the direction of the discharge outlet.

For emptying, the conical mill is installed with a slope from bearing to one. In wet grinding, emptying is realized by the decantation principle, that is, by means of unloading through one of two trunnions.

With dry grinding, these mills often work in a closed cycle. A scheme of the conical ball mill supplied with an air separator is shown in Fig. 2.13. Air is fed to the mill by means of a fan. Carried off by air currents, the product arrives at the air separator, from which the coarse particles are returned by gravity via a tube into the mill. The finished product is trapped in a cyclone while the air is returned in the fan.

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).

Modern ball mills consist of two chambers separated by a diaphragm. In the first chamber the steel-alloy balls (also described as charge balls or media) are about 90mm diameter. The mill liners are designed to lift the media as the mill rotates, so the comminution process in the first chamber is dominated by crushing. In the second chamber the ball diameters are of smaller diameter, between 60 and 15mm. In this chamber the lining is typically a classifying lining which sorts the media so that ball size reduces towards the discharge end of the mill. Here, comminution takes place in the rolling point-contact zone between each charge ball. An example of a two chamber ball mill is illustrated in Fig. 2.22.15

Much of the energy consumed by a ball mill generates heat. Water is injected into the second chamber of the mill to provide evaporative cooling. Air flow through the mill is one medium for cement transport but also removes water vapour and makes some contribution to cooling.

Grinding is an energy intensive process and grinding more finely than necessary wastes energy. Cement consists of clinker, gypsum and other components mostly more easily ground than clinker. To minimise over-grinding modern ball mills are fitted with dynamic separators (otherwise described as classifiers or more simply as separators). The working principle is that cement is removed from the mill before over-grinding has taken place. The cement is then separated into a fine fraction, which meets finished product requirements, and a coarse fraction which is returned to mill inlet. Recirculation factor, that is, the ratio of mill throughput to fresh feed is up to three. Beyond this, efficiency gains are minimal.

For more than 50years vertical mills have been the mill of choice for grinding raw materials into raw meal. More recently they have become widely used for cement production. They have lower specific energy consumption than ball mills and the separator, as in raw mills, is integral with the mill body.

In the Loesche mill, Fig. 2.23,16 two pairs of rollers are used. In each pair the first, smaller diameter, roller stabilises the bed prior to grinding which takes place under the larger roller. Manufacturers use different technologies for bed stabilisation.

Comminution in ball mills and vertical mills differs fundamentally. In a ball mill, size reduction takes place by impact and attrition. In a vertical mill the bed of material is subject to such a high pressure that individual particles within the bed are fractured, even though the particles are very much smaller than the bed thickness.

Early issues with vertical mills, such as narrower PSD and modified cement hydration characteristics compared with ball mills, have been resolved. One modification has been to install a hot gas generator so the gas temperature is high enough to partially dehydrate the gypsum.

For many decades the two-compartment ball mill in closed circuit with a high-efficiency separator has been the mill of choice. In the last decade vertical mills have taken an increasing share of the cement milling market, not least because the specific power consumption of vertical mills is about 30% less than that of ball mills and for finely ground cement less still. The vertical mill has a proven track record in grinding blastfurnace slag, where it has the additional advantage of being a much more effective drier of wet feedstock than a ball mill.

The vertical mill is more complex but its installation is more compact. The relative installed capital costs tend to be site specific. Historically the installed cost has tended to be slightly higher for the vertical mill.

Special graph paper is used with lglg(1/R(x)) on the abscissa and lg(x) on the ordinate axes. The higher the value of n, the narrower the particle size distribution. The position parameter is the particle size with the highest mass density distribution, the peak of the mass density distribution curve.

Vertical mills tend to produce cement with a higher value of n. Values of n normally lie between 0.8 and 1.2, dependent particularly on cement fineness. The position parameter is, of course, lower for more finely ground cements.

Separator efficiency is defined as specific power consumption reduction of the mill open-to-closed-circuit with the actual separator, compared with specific power consumption reduction of the mill open-to-closed-circuit with an ideal separator.

As shown in Fig. 2.24, circulating factor is defined as mill mass flow, that is, fresh feed plus separator returns. The maximum power reduction arising from use of an ideal separator increases non-linearly with circulation factor and is dependent on Rf, normally based on residues in the interval 3245m. The value of the comminution index, W, is also a function of Rf. The finer the cement, the lower Rf and the greater the maximum power reduction. At C = 2 most of maximum power reduction is achieved, but beyond C = 3 there is very little further reduction.

Separator particle separation performance is assessed using the Tromp curve, a graph of percentage separator feed to rejects against particle size range. An example is shown in Fig. 2.25. Data required is the PSD of separator feed material and of rejects and finished product streams. The bypass and slope provide a measure of separator performance.

The particle size is plotted on a logarithmic scale on the ordinate axis. The percentage is plotted on the abscissa either on a linear (as shown here) or on a Gaussian scale. The advantage of using the Gaussian scale is that the two parts of the graph can be approximated by two straight lines.

The measurement of PSD of a sample of cement is carried out using laser-based methodologies. It requires a skilled operator to achieve consistent results. Agglomeration will vary dependent on whether grinding aid is used. Different laser analysis methods may not give the same results, so for comparative purposes the same method must be used.

The ball mill is a cylindrical drum (or cylindrical conical) turning around its horizontal axis. It is partially filled with grinding bodies: cast iron or steel balls, or even flint (silica) or porcelain bearings. Spaces between balls or bearings are occupied by the load to be milled.

Following drum rotation, balls or bearings rise by rolling along the cylindrical wall and descending again in a cascade or cataract from a certain height. The output is then milled between two grinding bodies.

Ball mills could operate dry or even process a water suspension (almost always for ores). Dry, it is fed through a chute or a screw through the units opening. In a wet path, a system of scoops that turn with the mill is used and it plunges into a stationary tank.

Mechanochemical synthesis involves high-energy milling techniques and is generally carried out under controlled atmospheres. Nanocomposite powders of oxide, nonoxide, and mixed oxide/nonoxide materials can be prepared using this method. The major drawbacks of this synthesis method are: (1) discrete nanoparticles in the finest size range cannot be prepared; and (2) contamination of the product by the milling media.

More or less any ceramic composite powder can be synthesized by mechanical mixing of the constituent phases. The main factors that determine the properties of the resultant nanocomposite products are the type of raw materials, purity, the particle size, size distribution, and degree of agglomeration. Maintaining purity of the powders is essential for avoiding the formation of a secondary phase during sintering. Wet ball or attrition milling techniques can be used for the synthesis of homogeneous powder mixture. Al2O3/SiC composites are widely prepared by this conventional powder mixing route by using ball milling [70]. However, the disadvantage in the milling step is that it may induce certain pollution derived from the milling media.

In this mechanical method of production of nanomaterials, which works on the principle of impact, the size reduction is achieved through the impact caused when the balls drop from the top of the chamber containing the source material.

A ball mill consists of a hollow cylindrical chamber (Fig. 6.2) which rotates about a horizontal axis, and the chamber is partially filled with small balls made of steel, tungsten carbide, zirconia, agate, alumina, or silicon nitride having diameter generally 10mm. The inner surface area of the chamber is lined with an abrasion-resistant material like manganese, steel, or rubber. The magnet, placed outside the chamber, provides the pulling force to the grinding material, and by changing the magnetic force, the milling energy can be varied as desired. The ball milling process is carried out for approximately 100150h to obtain uniform-sized fine powder. In high-energy ball milling, vacuum or a specific gaseous atmosphere is maintained inside the chamber. High-energy mills are classified into attrition ball mills, planetary ball mills, vibrating ball mills, and low-energy tumbling mills. In high-energy ball milling, formation of ceramic nano-reinforcement by in situ reaction is possible.

It is an inexpensive and easy process which enables industrial scale productivity. As grinding is done in a closed chamber, dust, or contamination from the surroundings is avoided. This technique can be used to prepare dry as well as wet nanopowders. Composition of the grinding material can be varied as desired. Even though this method has several advantages, there are some disadvantages. The major disadvantage is that the shape of the produced nanoparticles is not regular. Moreover, energy consumption is relatively high, which reduces the production efficiency. This technique is suitable for the fabrication of several nanocomposites, which include Co- and Cu-based nanomaterials, Ni-NiO nanocomposites, and nanocomposites of Ti,C [71].

Planetary ball mill was used to synthesize iron nanoparticles. The synthesized nanoparticles were subjected to the characterization studies by X-ray diffraction (XRD), and scanning electron microscopy (SEM) techniques using a SIEMENS-D5000 diffractometer and Hitachi S-4800. For the synthesis of iron nanoparticles, commercial iron powder having particles size of 10m was used. The iron powder was subjected to planetary ball milling for various period of time. The optimum time period for the synthesis of nanoparticles was observed to be 10h because after that time period, chances of contamination inclined and the particles size became almost constant so the powder was ball milled for 10h to synthesize nanoparticles [11]. Fig. 12 shows the SEM image of the iron nanoparticles.

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.

In spite of the traditional approaches used for gas-solid reaction at relatively high temperature, Calka etal.[58] and El-Eskandarany etal.[59] proposed a solid-state approach, the so-called reactive ball milling (RBM), used for preparations different families of meal nitrides and hydrides at ambient temperature. This mechanically induced gas-solid reaction can be successfully achieved, using either high- or low-energy ball-milling methods, as shown in Fig.9.5. However, high-energy ball mill is an efficient process for synthesizing nanocrystalline MgH2 powders using RBM technique, it may be difficult to scale up for matching the mass production required by industrial sector. Therefore, from a practical point of view, high-capacity low-energy milling, which can be easily scaled-up to produce large amount of MgH2 fine powders, may be more suitable for industrial mass production.

In both approaches but with different scale of time and milling efficiency, the starting Mg metal powders milled under hydrogen gas atmosphere are practicing to dramatic lattice imperfections such as twinning and dislocations. These defects are caused by plastics deformation coupled with shear and impact forces generated by the ball-milling media.[60] The powders are, therefore, disintegrated into smaller particles with large surface area, where very clean or fresh oxygen-free active surfaces of the powders are created. Moreover, these defects, which are intensively located at the grain boundaries, lead to separate micro-scaled Mg grains into finer grains capable to getter hydrogen by the first atomically clean surfaces to form MgH2 nanopowders.

Fig.9.5 illustrates common lab scale procedure for preparing MgH2 powders, starting from pure Mg powders, using RBM via (1) high-energy and (2) low-energy ball milling. The starting material can be Mg-rods, in which they are processed via sever plastic deformation,[61] using for example cold-rolling approach,[62] as illustrated in Fig.9.5. The heavily deformed Mg-rods obtained after certain cold rolling passes can be snipped into small chips and then ball-milled under hydrogen gas to produce MgH2 powders.[8]

Planetary ball mills are the most popular mills used in scientific research for synthesizing MgH2 nanopowders. In this type of mill, the ball-milling media have considerably high energy, because milling stock and balls come off the inner wall of the 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.

In the typical experimental procedure, a certain amount of the Mg (usually in the range between 3 and 10g based on the vials volume) is balanced inside an inert gas atmosphere (argon or helium) in a glove box and sealed together with certain number of balls (e.g., 2050 hardened steel balls) into a hardened steel vial (Fig.9.5A and B), using, for example, a gas-temperature-monitoring system (GST). With the GST system, it becomes possible to monitor the progress of the gas-solid reaction taking place during the RBM process, as shown in Fig.9.5C and D. The temperature and pressure changes in the system during milling can be also used to realize the completion of the reaction and the expected end product during the different stages of milling (Fig.9.5D). The ball-to-powder weight ratio is usually selected to be in the range between 10:1 and 50:1. The vial is then evacuated to the level of 103bar before introducing H2 gas to fill the vial with a pressure of 550bar (Fig.9.5B). The milling process is started by mounting the vial on a high-energy ball mill operated at ambient temperature (Fig.9.5C).

Tumbling mill is cylindrical shell (Fig.9.6AC) that rotates about a horizontal axis (Fig.9.6D). Hydrogen gas is pressurized into the vial (Fig.9.6C) together with Mg powders and ball-milling media, using ball-to-powder weight ratio in the range between 30:1 and 100:1. Mg powder particles meet the abrasive and impacting force (Fig.9.6E), which reduce the particle size and create fresh-powder surfaces (Fig.9.6F) ready to react with hydrogen milling atmosphere.

Figure 9.6. Photographs taken from KISR-EBRC/NAM Lab, Kuwait, show (A) the vial and milling media (balls) and (B) the setup performed to charge the vial with 50bar of hydrogen gas. The photograph in (C) presents the complete setup of GST (supplied by Evico-magnetic, Germany) system prior to start the RBM experiment for preparing of MgH2 powders, using Planetary Ball Mill P400 (provided by Retsch, Germany). GST system allows us to monitor the progress of RBM process, as indexed by temperature and pressure versus milling time (D).

The useful kinetic energy in tumbling mill can be applied to the Mg powder particles (Fig.9.7E) by the following means: (1) collision between the balls and the powders; (2) pressure loading of powders pinned between milling media or between the milling media and the liner; (3) impact of the falling milling media; (4) shear and abrasion caused by dragging of particles between moving milling media; and (5) shock-wave transmitted through crop load by falling milling media. One advantage of this type of mill is that large amount of the powders (100500g or more based on the mill capacity) can be fabricated for each milling run. Thus, it is suitable for pilot and/or industrial scale of MgH2 production. In addition, low-energy ball mill produces homogeneous and uniform powders when compared with the high-energy ball mill. Furthermore, such tumbling mills are cheaper than high-energy mills and operated simply with low-maintenance requirements. However, this kind of low-energy mill requires long-term milling time (more than 300h) to complete the gas-solid reaction and to obtain nanocrystalline MgH2 powders.

Figure 9.7. Photos taken from KISR-EBRC/NAM Lab, Kuwait, display setup of a lab-scale roller mill (1000m in volume) showing (A) the milling tools including the balls (milling media and vial), (B) charging Mg powders in the vial inside inert gas atmosphere glove box, (C) evacuation setup and pressurizing hydrogen gas in the vial, and (D) ball milling processed, using a roller mill. Schematic presentations show the ball positions and movement inside the vial of a tumbler mall mill at a dynamic mode is shown in (E), where a typical ball-powder-ball collusion for a low energy tumbling ball mill is presented in (F).

particle size distribution of grinding mill products

particle size distribution of grinding mill products

Size analyses of mineral products are usually made by screening with a set of sieves having mean apertures arranged in the Tyler scale, which is a geometric progression with a constant ratio equal to the square root of two. For this reason it is convenient to represent particle size as a logarithmic function of the particle diameter

The variable, x, may be defined as the logarithm to the base s of the ratio of the particle diameter to the reference diameter, d. The inverse of the transformation given in equation 1 is given by equation 2:

where yi is the weight fraction in the size interval between xi-l and xi; N is the total number of size intervals. If the reference diameter is equal to the maximum sieve aperture represented in the screen analysis and this is taken as the axis for the first moment, xo is zero and the first moment is the value of x corresponding to the mean particle size:

These higher moments contain the essential information concerning the form of the distribution function; that is, they are parameters that measure various aspects of the way in which the weight fraction is distributed about the mean. The second moment, or variance, measures the width of the distribution; the third moment measures the skewness or asymmetry; the fourth moment measures the kurtosis or peakedness; etc. Obviously, higher moments are increasingly dependent on values of the weight fraction remote from the mean which represent only a small fraction of the sample. For this reason, moments beyond the fourth are usually not considered. The third and fourth moments are usually represented as dimensionless ratios with respect to the second moment:

Moment analysis is a well-established method for analyzing and characterizing statistical distribution. Quoting from one of the standard treatises in mathematical statistics: For all ordinary purposes, therefore, a knowledge of the moments, when they exist, is equivalent to a knowledge of the distribution function: equivalent, that is, in the sense that it should be possible theoretically to exhibit all the properties of the distribution in terms of the moments.The procedures that have been developed for computation of moments and deriving distribution functions that best fit the data are fully discussed in a book by Elderton which has recently been published in a new edition. The application of moment analyses to particle size distribution data is discussed in a previous paper by the author.

When uniform sized samples of cryptocrystalline quartz were crushed by impact in a drop-weight machine, the reduction in size, as measured by the change in the mean value of x, was found to follow the relationship in equations 8 and 9

Equation 8 is an empirical relationship derived by multiple regression analyses of various combinations of independent variables from the data on the impact crushing experiments. The logarithms of E, the impact energy per unit weight of mineral, and d0, the initial mean particle diameter, gave the greatest decrease in variance between the observed and expected values. The threshold energy, Eo, which is the energy corresponding to zero size reduction, varies approximately inversely as the diameter of the particle being crushed.

Analyses of other data obtained by Hukki, using a double pendulum apparatus for impact crushing, gave slightly larger values for the coefficients in equations 8 and 9 and the exponent of do was slightly larger than one. If the exponent of do is assumed to be unity, the equation derived for the combined data from the Hukki and Bureau of Mines experiments gives the equations 10 and 11

These equations represent a best fit of data from 39 experiments on impact crushing of quartz particles ranging in size from .156 to 5.75 cm in diameter. The standard error for x is .387 as compared with 1.192 for the observed data.

The form of the distribution curve was found to be primarily a function of the size reduction. The distribution function of the initial uniform sample is a delta function. As soon as any size reduction occurs, there is a transfer of material to a wide range of sizes thereby increasing the dispersion. The change in distribution is asymetric since crushing transfers material only to the finer sizes, and so the skewness, as measured by 1, initially has a very large value. In other words, as a uniform sample is progressively decreased in size, there is a progressive increase in dispersion as measured by 2 and a decrease in skewness as measured by 1.

These changes are shown in Figure 1 which depicts the changes in distribution that occur in size distribution when quartz samples are subjected to increasing impact energy. As size reduction proceeds, the effect of the initial uniform distribution is gradually obliterated and both ant! tend to approach steady values. The variance tends to approach a steady value of 18 which corresponds to a standard deviation of 4.25 or a little more than four intervals in the Tyler sieve scale. The skewness levels off at a value between 1.6 and 1.8.

The manner in which energy is employed in a ball mill to effect size reduction is much more complex than in simple impact crushing. The application of energy in a drop-weight machine is similar to that occurring in a stamp mill, in which a considerable size reduction is produced by a single impact of relatively high energy input. In a tumbling mill, such as a ball mill, the size reduction occurs by repeated application of kinetic energy of less intensity by impact and rolling action of a large number of crushing media, in certain circumstances an appreciable amount of size reduction may occur by abrasion.

A series of studies has been made at the University of California in Berkeley on the grinding of dolomite in a ball mill. These tests were made in a specially designed mill in which the input energy can be measured.

A series of impact crushing experiments was made on a sample of the same dolomite used by Berlioz. The results of those experiments are summarized in Table 1. The results of these experiments permit comparison of the size reduction by impact and by ball mill grinding for the same energy input. Differences in the behavior of the particle size distribution may also be observed.

A comparison of the size reduction by impact and ball mill grinding is shown in figure 2. The ball mill experiments show the size reduction versus energy input for 7 series of experiments in which the weight of dolomite was 660, 1320, 1980, 2640, 3300, 3960, and 5420, respectively. The charge was composed of equal portions of -7 +8 and -8 +10 size fractions. The ball load was 455 stainless steel balls one inch in diameter, having a total weight of 30 kg. The particle size distribution was observed after 20, 40, 60, 80, 100, 150, 200 and 300 ball mill revolutions. The energy input was calculated from the net torque (corrected for the torque for the empty mill) and the number of revolutions.

For light ball loads the ball mill is less efficient as might be expected. As the load exceeds 1980 gm it has no influence on size reduction. The relationship between size reduction and input for optimum grinding in the ball mill is represented by the solid curve. The corresponding relationship for crushing by impact is represented by broken lines.

It is evident, as might be expected, that for moderate size reduction (x<5) the input energy is utilized much more effectively in the drop-weight machine than in the ball mill. For example, reduction to one-half of the original particle size requires about 4-3 kg cm per gm by impact as compared to 18.5 kg-cm by ball mill; that is, the energy requirements are less than 25 percent as much for impact crushing as for ball milling. For great size reduction the application of energy by a single impact becomes less effective so that there would be no advantage in applying more impact energy than would be required for about a four-fold reduction of particle diameter; this is equivalent to x = k. The energy required would be about percent that required for an equivalent size reduction in the ball mill.

The change in particle size distribution during ball milling is shown by the graphs of the variance and skewness in Figure 3. Here again, the points representing variance for those experiments with light ball mill loads show a noticeable divergence from those for optimum loading. The skewness is not affected by the load.

The differences in distribution between the products from the ball mill and those from impact crushing can be observed by comparing the solid lines, which represent the ball mill products, with the broken lines, which represent the products from the drop-weight experiments. The greatest difference is in the variance. The products from the ball mill show considerably greater dispersion over the size range and this dispersion develops sooner as the mean size is decreased. On the other hand, the skewness decreases earliest for impact crushing. The differences in size distribution are essentially difference in degree of dispersion and asymmetry. Actually there is a surprising similarity in the evolution of the distribution from uniform particle size to a typical skewed bell-shaped curve as the size is reduced whether by the ball mill or impact crushing.

The comminution process may be represented mathematically in terms of a set of state variables that define the mean size and size distribution of the feed to and product from a grinding machine. Three variables are required to specify the particulate state of the mineral undergoing size reduction; these variables define quantitatively the mean particle size, degree of dispersion and asymmetry of the distribution. Such a set of variables may be calculated by moment analysis of the screen analysis of the aggregate being studied. Conversely, if the mean, variance, and skewness of a size distribution are known, a gamma distribution function may be derived that will approximate the weight fraction in any given size range.

When a sized fraction of particles is subjected to comminution, the size distribution undergoes progressive change characterized by a steady increase in the variance or second moment and an abrupt decrease in skewness or third moment. As size reduction proceeds further, both the variance and skewness approach steady values and the form of the distribution becomes more and more stable.

dem-pbm approach to predicting particle size distribution in tumbling mills | springerlink

dem-pbm approach to predicting particle size distribution in tumbling mills | springerlink

Tumbling mills using balls as grinding media are used extensively in the mining and cement industries to produce fine powders; however, it is well known that the process of size reduction is highly energy-intensive. For this reason, much of todays comminution research is aimed at understanding grinding mechanisms, by estimating power draft and modeling milling circuits using the discrete element method (DEM). DEM predicts individual particle trajectories, the distribution of energy and contact forces at each collision, lifter wear and power draw. This paper presents a prediction of the discharge particle size distribution using three components, mass balance model (sometimes referred to as a population balance model, PBM), impact energy distribution of the mill obtained from the simulation of the charge motion using DEM and breakage characteristics of particles determined from drop-ball tests DEM simulation of the charge of a tumbling mill was done using the code MinProSim 1.0 to obtain impact spectra at different operative conditions. Then, thepopidation balance model (PBM), based on impact energy distribution, was used to predict the final particle size distribution in a batch mill and compared with experimental data. It is demonstrated that the DEM-PBM approach allows a reliable solution to predict particle size distribution for tumbling mills. Ideally, the model has to predict size distribution for any operational condition and feed characteristic; however, it has been shown that predictions include some degree of error.

Datta, A., and Rajamani, R.K., 2002, A direct approach of modeling batch grinding in ball mills using population balance principles and impact energy distribution, International Journal of Mineral Processing, Vol. 64, pp. 181200.

Mishra, B.K., 2003, A review of computer simulation of tumbling mills by the discrete element method Part II - Practical applications, International Journal of Mineral Processing, Vol. 71, pp. 95112.

Rajamani, R.K., Agrawala, S., and Mishra, B.K., 1993, Mill scale up: ball collision frequency and collision energy density in laboratory and plant-scale mills, Proceedings of the 18th International Mineral Processing Congress, Sydney, Australia, pp. 103109.

Prez-Alonso, C.A., Delgadillo, J.A. DEM-PBM approach to predicting particle size distribution in tumbling mills. Mining, Metallurgy & Exploration 30, 145150 (2013). https://doi.org/10.1007/BF03402260

dem investigation of energy distribution and particle breakage in tumbling ball mills - sciencedirect

dem investigation of energy distribution and particle breakage in tumbling ball mills - sciencedirect

This work investigates the grinding process in tumbling ball mills using a discrete element method (DEM) based model. Binary particles are used to represent grinding balls and ground powders, respectively. Three forms of energy inside mills, collision energy, dissipated energy and maximum impact energy, are investigated and linked to particle breakage. By linking the energy information with population balance models, the evolution of product size with grinding time is predicted and the results are compared with the experimental data from the literature. The results indicate that the collision energy is more directly linked with particle breakage and can predict the product size reasonably well without adjustment. Other two energies can also be used for size prediction but the selection function needs to be carefully calibrated. The effects of operation conditions such as rotation speed and loadings of grinding balls and ground material are also investigated.

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