## 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.

## calculate and select ball mill ball size for optimum grinding

In Grinding, selecting (calculate)the correct or optimum ball sizethat allows for the best and optimum/ideal or target grind size to be achieved by your ball mill is an important thing for a Mineral Processing Engineer AKA Metallurgist to do. Often, the ball used in ball mills is oversize just in case. Well, this safety factor can cost you much in recovery and/or mill liner wear and tear.

## finances in germany - expat guide to germany | expatica

Understanding your money management options as an expat living in Germany can be tricky. From opening a bank account to insuring your familys home and belongings, its important you know which options are right for you. To find out how you can make your money go further, read our guides to finance in Germany.

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## why use different size balls in a mill

Several years ago, Davis assumed that the rate of wear of the different sizes of balls in a ball mill was directly proportional to the weight of each ball, and he evolved a formula for calculating a balanced charge. Operators have used this formula when purchasing balls for a new mill or when reloading an old one that had been emptied for repair. The formula required that the largest ball size and the size to be rejected should be determined, and after that the other sizes were set. Stress was laid on the coarsest size, and to facilitate the use of the formula many writers have made their contribution by reporting ratio of coarsest particle size to the optimum ball size. Close adherence to this ratio has prevented giving attention to sizes and amounts of particles not falling in the category of the coarsest size.

The inadequacy of the formula and the futility of extensive experimentation for ratio determinations involving the coarsest particle size only is at once obvious when it is seen that the formula did not take into account the slow grinding rate of the finer sizes of ore and the amount present. To be sure, operators who were doing very fine grinding have sometimes altered the make-up load by using some additional small balls with the big ones, but this practice has been somewhat haphazard. Too much of the work has followed the old idea that there should be no ball present that is incapable of crushing the largest particle in the feed.

Today operators have a keener sense of the relatively large amount of work required to finish the finest sizes, so that the insufficiency of the formula is readily seen. It would have been fortunate had the formula been devised to attract more attention to the large amount of finer but unfinished particles. The formula is excellent from the basis of balance with respect to ball wear, but the literature has contained very little about the rationing of ball sizes for the best grinding of all sizes and amounts of particles extending throughout the length of the mill. Research has submitted in this matter.

It is not denied that the coarse particles have to be crushed else no fine material would accrue, but here the fact is emphasized that when crushing to 200-mesh stress should be on the selection of balls of the right size and amount to crush, say, from 100- to 200-mesh; or, when crushing to 65-mesh, the operator should judiciously load the mill for crushing from 48- to 65-mesh. If this were done, the circulating load would be relieved of the large amount of nearly finished size, and in its stead there would be some coarser material from which the classifier could more easily remove the finished size. Opposing this idea is the fact that a coarse circulating load would be undesirable in some of the recent supplementary recovery processes. However, this objection might be met by introducing a bypassing screen at the end of the ball mill.

Tests of other experimenters have been supplemented with detailed information on the optimum size of balls for grinding sized ore. Figures have been obtained that show what particular size of ball is the most efficient in crushing certain sizes of chert and dolomite. It is fortunate that this work has been done,

because it has brought out facts that would have been unsuspected otherwise. The method used here for showing what particular size of ball is best for a particular particle size of ore is to some degree unique. The reason for this is that usually such tests have been run to finish the grinding at a fine size. Those tests were as much a criterion of the work on the particle size in the finished product as of the feed, but they were not so interpreted. The tests reported in this paper are different because the first step in reduction is given the main emphasis.

As a guide in laying out this work, a mill was visualized as divided into sections. The first section had the largest media and performed the first step in grinding by reducing the particles for the second section; the second section, in turn, used smaller media to reduce the articles for the third section; and so on. This line of thought was the basis for the distribution of sizes in the ball loads already mentioned.

The ball sizes were 2.75-to 0.62-inch and the ore sizes plus 65- to plus 10-mesh. The results for chert are shown in four series in table 27 and for dolomite in five series in table 28. The ore (feed) sizes are in quotation marks because they are only nominal; their meaning is set forth in the sizing analyses under feed.

Any plan adopted would give but litle more than an approximation of the facts sought, owing to the difficulty in timing the grinding correctly. If it is desired to find the effect of balls grinding 20-mesh ore and the mill is loaded with 20-mesh material, the grinding time should be infinitely short, because fine particles are made as soon as the mill starts and if the run continues the test is of the comminuted products of the 20-mesh sample rather than that which was supplied for the test.

Extrapolation back to zero time would be desirable if it were possible. However, a very short period is unsatisfactory because the flaky particles, being the first to yield, would give a wrong impression of the sample as a whole. Long grinding periods would be useless because the particle size at the end of the run would be too far removed from the original particle size under investigation. A mean procedure had to be adopted.

The surface calculations that are given must be used guardedly, else they will be misleading. The fine particle sizes are likely to be weighted too much; when the ball size for crushing 10-mesh sizes through 14-mesh is sought, the very fine sizes should be weighted with caution.

A casual examination of each series for minimum of cumulative weights in the coarse sizes of the screen analyses probably would be a fair guide to the best ball size. But this minimum, though important of consideration, is not final, because the amount, power, and time have to be taken into account. These three quantities are resolved into tons per horsepower-hour and will be applied in table 29. Before going to that table, however, the present tables may be used to bring out a fact not commonly knownballs that were too large as well as balls that were too small failed in selective grinding. In any of the series except the last one of each table, where the largest ball sizes were not large enough, the low cumulative percentage weight of the coarse sizes is in a mean position and rises with the use of larger as well as smaller balls. Hence, it is shown that balls that were too large did nonselective grinding.

mesh size in table 27 and are shown in sizing diagrams. The percentage weights of the products from the largest, and the smallest balls are shown by broken lines. They are high in the upper part of the diagram. Their position shows that much of the coarse material was not reduced through 35-mesh. The solid line shows good selective work of the balls of optimum size.

In the study of these diagrams, it must be remembered that the main variables in the tests were ball size and that the tests were timed to give the same amount of subsieve size. The conditions imposed on the tests were entirely different from closed-circuit grinding, in which the composite feeds would have been unlike, although the new feeds might have been the same.

The nonselective grinding of the off-size balls may be explained as follows: The largest balls failed on the coarsest sizes because they did not offer a sufficient number of points of contact for the number of grains present; hence, some of the particles remained at the end of the test. Furthermore, due to the small number of points of contact of such large balls, the crushing impulse was so great that the grains that did meet it received excessive comminution and much of the subsieve size resulted.

The smallest balls had so many points of contact that the impulse at a given point was too much reduced to exert sufficient stress on the coarsest particles; hence, some of them remained without the desired reduction. However, a few that were reduced yielded grains readily comminuted by the smallest balls, and much subsieve size again resulted; hence, there was an intermediate ball size for the best work.

Table 29 will now be discussed: It is made by using the two preceding tables. It gives the amount of the coarsest size per unit of power crushed through a stated coarse but finer size. To illustrate the method of calculation, take the first test in table 27: The amount of plus 65-mesh crushed through 100-mesh is 89.563.3=26.2 parts per hundred, and by the table the ton per horsepower-hour was 0.16; hence, the tons per horsepower-hour crushed through 100-mesh was 26.2/1000.16=0.042. Similarly, in the first test in the second series 97.352.0=45.3, and 45.3/1000.186=0.084 ton per horsepower-hour through 48-mesh. Thus, table 29 has four series of tests or chert and five series for dolomite. The preferred value in each series is underscored to show what seems to be the preferable ball size. The optimum ball size for grinding closely sized particles through the limiting screen, as determined by these experiments, may be expressed in the following equation

where D is diameter of ball, d is diameter of particle to be ground, and K is a constant depending on the grindability of the ore. When D and d are expressed in inches, the value of K for chert is 55 and for dolomite is 35. This formula is of the same type as that developed by Starke. He evaluated the grind through a broader range and his dimensions are in microns.

Having selected the best ball size, it will be seen by referring to tables 27 and 28 that the preferable ball size usually gave the best capacity and efficiency. Also, the preferable ball size coincides closely with the best selective grinding, the main exception being the plus 10-mesh series in table 28. There the preferable ball size is smaller than the size for the best selective grinding. Probably the exception is due to an error in planning the plus 10-mesh series; the time periods were too long and too much grinding resulted. The spread in reduction in this series was greater than in any other series. It was intended to avoid such a broad spread in reduction. In the study of the exception and the study of the sizing analyses in the other tests an attempt has been made to gain additional information by using the Gaudin log-log method for plotting sizinganalyses, but the results were not satisfactory. It is believed, however, that the method was not expected to apply to the moderate reduction of a sized product.

Tables 27 and 28 cannot be dismissed without consideration of the variation of power throughout a test. Figure 5 is submitted for that purpose. In it the time extends from 0 to 3.5 minutes. The change in power through the grinding periods was watched in all the tests. This change is illustrated in figure 5, which deals with the plus 20-mesh size in table 28. In the discussion of this figure, what will be said about the relation of power to other factors is premised by the belief that the degree to which the balls nip the particles influences the power, and that when nipping is best the power will be the highest. The curve at the bottom of the figure shows that the 2.75-inch balls required less power than the other loads. The balls were too big for good nipping, and as the grinding continued they became relatively bigger and further power reduction resulted. Correlated with this is the fact that the grinding was poor in selection and unsatisfactory in capacity and efficiency. (It is not consistent to compare the numerical-values of capacities and efficiencies of one series in tables 27 and 28 with those of another series. The principles underlying the reason were mentioned under Sillimanite balls.)

Turning next to the deportment of the 0.62-inch balls, which were the smallest in the group, the change in power from beginning to end of the run is in a reverse order from that with the largest balls. The balls were too small for good nipping, but as comminution proceeded they became relatively larger so that nipping and power increased but did not reach the high power indicating good nipping. The selective grinding, capacity, and efficiency were again poor.

The record of the 1-inch balls is more favorable. The power was high throughout the test, indicating that a desirable mean size had been reached. The selective grinding, capacities, and efficiencies were good. This all indicates that when nipping is best the mill (when not run too fast) will do its best work. This statement is not new; the evidence is given for those who wish to weigh it.

A comprehensive examination of mills that segregate the ball sizes shows that they require mixtures containing a greater number of small balls than is supplied by the Davis ball load. This deficiency was met by using the rationed ball load, in which small balls predominated. Before going ahead, the mills will be considered.

Conical mills and cylindrical mills with grids were contemplated in introducing the new loads. Hence, these mills must be discussed before showing the tests, and they must be compared with the standard cylindrical mill.

Should the ball sizes be segregated, or should they be mixed as in the standard cylindrical mill? In the metallics industry the most effective method of segregating is to place the mills in series and use succeedingly smaller balls from first to last mill in the series. In the cement industry, dividers or grids are used to divide the long mills into sections, each of which has the appropriate size of medium. Finished material is removed at the end of each section.

With the knowledge that the cone of a conical mill functions like a grid in segregating the balls with respect to size, conical mills were built and tested. The first one was only 3 feet long. A taper of 2 inches to the foot was ample to segregate the largest balls in the big end and the smallest balls in the small end. Grinding tests in this mill with a rationed ball load were compared with the old cylindrical mill loaded with the old style ball load. A decided advantage was gained by the newer practice.

A larger conical mill was built and is shown in figure 6. It was 6 feet long and had the same taper as the smaller one. The big end was 2 feet in diameter and the small end 1 foot. The ability of the mill to segregate the balls was demonstrated by tests.

Grinding tests with several types of mills and ball loads led to the conclusion that advantages that had been gained were due more to the appropriate average size of balls than to the new design of mill. It was difficult to show that the conical mills had an outstanding advantage over the cylindrical mill. The 6-foot conical mill had a disadvantage; it induced the media to drift to the big end and pile up there so much that the balls passed through the feed entrance into the scoop. For a simple remedy a grid was placed on the feed opening to retain the load. A change was made to a cylindrical mill lined with a series of identical truncated cones. The idea was suggested by C. L. Carman, of Independence, Kans.

Although the efficiency of the long cone was good, the loss in capacity induced by the taper was marked. This may be shown by the following analysis: If the last unit section with diameter D2 = 1 foot could be speeded up to the same percent critical as the first unit section with diameter D1 = 2 feet, it would have a relatively low capacity

A 2- by 3-foot cylindrical mill was lined to employ the conical effect, but instead of having one cone it had three identical truncated cones, end to end, and apexing in the same direction. (See fig. 7.) Any cylindrical mill may be lined in this fashion by using liners tapered in thickness. If the liners are 2 feet long, a 12-foot mill would have six truncated cones, end to end. The mill would have the same capacity at the discharge end as at the feed end. In some way, at least, this would be an advantage over the long cone. The mill with truncated cones proved to be as good a sizing device as the long single cone, but when compared with the old cylindrical mill its advantage as a grinder was not marked.

Finally, a cylindrical mill with a grid was used. The grid was 1 foot from the feed end of a 2- by 3-foot cylindrical mill. Balls of 2.5 inches to 1 inch were placed in the feed-end sections and 0.75-inch balls in the discharge end. The grinding was moderately better than without the grid. Possibly the grid would have appeared to have more advantage if the feed had been coarser and the finishing finer. The

In table 30, grinding to a fine size was stressed to give the extra amount of small media in the new load a chance to work advantageously. Grinding was continuous and about 74 percent of the product passed through 200-mesh. The Davis ball load in the cylindrical mill was used first; next, the rationed ball load was used in the same mill; and finally, the rationed ball load was used in a mill having a lining of truncated cones. In selecting the Davis ball load the no. 1 load was used instead of no. 2 in accordance with the old idea that all of the balls should be of a size to crush any of the particles of ore. The free migration of the ore induced by the large, interstices would be compatible with a heavy circulating load. In the cylindrical mill the work of the rationed ball load was about 60 percent better than the Davis ball load, and when the mill which was lined with truncated cones was used there was a further gain of about 5 percent. The rationed ball load left more of the coarse sizes unfinished.

In table 31 the results of five tests with different ball loads in cylindrical, grid, and conical mills are shown. The feed was coarser than was used in table 30. The grinding in test 2 with the rationed ball load, which contained 64 percent of 0.75-inch balls, was about 44 percent more efficient than with the Davis load. The power was about 11 percent higher. If Davis ball load no. 2 instead of no. 1 had been used, the divergence in grinding results would have been reduced. In test 3, in which the grid was used to segregate the different sizes of balls, a further advantage of about 4 percent in efficiency is shown. The conical mill in test 4 increased the efficiency to 58 percent more than in test 1. The efficiency with the long (6-foot) conical mill was about the same as with the short (3-foot) one.

The validity of having graded sizes of balls to grind the ore in steps with ample provisions for a circulating load and removal of fines in each step cannot be denied, but without this quick removal of finished material the advantage was not great.

In the conical mills or in the grid mill, as used in these tests, it was difficult to set a correct feed rate. If the feed were too fast some of the coarse particles would pass the zone intended to grind them. Having passed that zone, they were likely to continue without being ground. Again, if the feed were too slow, energy would be wasted by making the fine particles remain too long with the coarse medium. Nonselective grinding and inefficiency would result.

Thus far the evidence of the efficacy of a rationed load in plant operation may be questioned because, as is shown by tables 30 and 31, the coarse sizes were not reduced as much as with the Davis load. Fear was entertained lest a circulating load might develop trouble- some characteristics. Hence, closed-circuit grinding was tried.

Rationed ball sizes were of advantage in batch and open-circuit grinding. The degree depended on the particle size of feed and product. Examination will now be made to see if the deportment of rationed sizes is satisfactory in closed-circuit grinding.

The tests were performed as shown in tables 32 and 33. In the first table dolomite B was used, and in the second the feed was chert rejects from earlier grinding tests. The procedures in the two tables have one fundamental difference; in table 32 the feed to the rationed ball load was increased on account of the extra efficiency of the rationed sizes, whereas in table 33 the feed was maintained at the same rate but the mill speed was reduced. That is, in the first table the advantage is shown by the increased amount of ore ground, and in the second the advantage is shown by the power saved. If preference is given to one of the two methods it should apply to the latter, because in it the two ball loads being compared deal with the same amount of feed, and the drag is worked under almost identical conditions. The pulp consistencies of the drag overflows were maintained at 17 percent solids.

In table 32 the drag classifier finished at a finer size when rationed sizes of balls were used. This variation is on the right side for safe conclusions about the advantage of the new ball load. With the Davis ball load, 2.95 pounds per minute were finished, and with the rationed ball load the amount was increased to 4.06 pounds perminute an increase of 37 percent. The surface tons per hour show, an increase of 45 percent in favor of the rationed ball sizes, and the surface tons per horsepower-hour show a more moderate advantage37 percent. The reason the advantage in capacity was greater than in efficiency is because of the difference in power in the two tests; the smaller balls required more power than the larger ones. The surface calculations are made from the part of the table marked section 3. There a composite feed has been calculated, so that surface calculation can be based on feed and product. However, the ultimate values would have been the same if the sizing analyses of new feed and over- flow in sections 1 and 2 had been used.

It will be seen that the circulating loads in each table are about the same, respectively. Due precaution was taken to make sure that the circulating load was balanced, about 2 hours being required after the last adjustment.

The closed-circuit set-ups are shown in figures 8 and 9. They do not include the inclined belt and weightometer formerly used. A better plan was to permit the drag sand to fall into buckets and at set intervals to pass the sand back to the new-ore belt feeder after a hurried weighing. The record of the weights obtained after decanting

superfluous water indicated the trend of the circulating load, but a more accurate estimate was made at frequent intervals by catching the ball-mill discharge in a graduate and weighing it. The weight of solids minus new feed gave the circulating load with exactness. The test was continued for a goodly period after the amount of discharge became constant.

In the two tests shown in Table 33, the overflows are nearly identical. The innovation in the manner of conducting the tests, as stated before, was to keep the new feed constant and reduce the speed of the mill containing the new ball load until the circulating load in section 2 was the same as in section 1. When the new ball load was used, the speed was reduced from 70 to 55 percent critical and the capacity was maintained. The increase in efficiency was 28 percent. The Davis ball load took 22.6 percent more power than the rationed ball load.

The comparison of different sizes of media when the mill speeds are not the same might not have been justified by the old literature, but it is justified by table 13, which shows that for speeds from 40 to 70 percent critical, inclusive, the efficiencies were almost identical when the amount of ore in the mill was the same; of course, capacity increased with speed. It is readily seen from table 33 that the capacity with the rationed ball load at 55 percent speed was about the same as with the Davis load at 70 percent speed. If the finishing could have been at 200-mesh in all the closed-circuit tests, the load of large balls would have been greatly handicapped and the load of small balls would have had a greater relative advantage. Then the difference in efficiency might have been as much as 75 percent. The grinding seems to have been a little more selective with the larger media.

By table 2 the diameter of the ball of average weight in the rationed load no. 2 was 1 inch. A load of 1-inch balls would have given about the same results but would not have permitted the study of the effect of segregation in the grid and conical mills. Furthermore, the practical application would have been doubtful. A Davis ball load with sizes from 1 to 1 inch would have done good work, but it would not have been representative of the old standard because some of the balls would have been too small to crush the largest particles.

The quantities obtained in these tests enable the mill man to get a vision of the amount of power required to do his grinding. Take, for example, the tests represented by section 1 in table 33, in which grinding was to flotation size by what may be called the ordinary ball load and the ore feed was almost 100-percent Tri-State chert through 8-mesh. Calculations show that the net energy input was 21 horsepower-hours per ton. One-third should be added for friction and motor losses, which would bring the motor input up to 28 horsepower-hours per ton of ore. An ore would have to be rich to justify the expenditure of so much additional power for grinding.

## grinding balls & rods

General statements can be made and are worthy of consideration when selecting grinding media. For the best results it has been found that the smallest diameter ball or rod which will break down the particular material to be ground is desirable since greatest surface area is obtained. From the standpoint of economy, the larger the media the higher will be the liner consumption and media consumption. The minimum size of grinding balls should be selected with caution since there will be a tendency for such balls to float out of the mill in a dense pulp (this is minimised by the use of a grate discharge mill). Also the smaller the media the quicker it will reach its reject size.

For the first stage of grinding, media will generally be in the 4 to 2 size (in some cases as high as 5). In secondary finer grinding the initial charge will begin at around 3 and in the case of balls will grade down to about . Extremely fine grinding will dictate the use of 1 and smaller balls.

Grinding media is the working part of a mill. It will consume power whether it is doing grinding work or not. The amount of work which it does depends upon its size, its material, its construction and the quantity involved. It is, therefore, advantageous to select the type of grinding media which will prove most economical, the size of media which will give the best grinding results, and the quantity of media which will just produce the grind required.

One of the economic factors of grinding is the wear of the grinding media. This is dependent upon the material used in its manufacture, method of manufacture, size of media, diameter of mill, speed of mill, pulp level maintained in the mill, rate of feed, density of pulp maintained, shape of the liner surface, nature of the feed, and the problem of corrosion.

Many shapes of grinding media have been tried over the past years, but essentially there are only two efficient types of media used. These are the spherical ball and the cylindrical rod. Other shapes are relatively expensive to manufacture and they have shown no appreciable improvement in grinding characteristics.

It will be found that a seasoned charge will provide a better grind than a new mill charge. This, of course, is impossible to determine at the offset, but after continuous operation the media charge should be checked for size and weight, and maintained at that optimum point. After the charge has been selected, replacement media should be made at the maximum size used. In some cases it has been found advantageous to add replacement media of two or more sizes, so as to maintain more closely the seasoned ratio.

As a general figure rod mills will have a void space within the charge of around 20% to 22% for new rods. In ball mills the theoretical void space is around 42% to 43%. It has been found that as grinding rods wear a 4 or 4 rod will generally break up at about 1 diameter. The smaller diameter new rods do not break up as easily and will generally wear down to about 1. In many applications it has been found, that grinding efficiency will increase if rods are removed when they reach the 1 size, and also if broken pieces of rods are removed. The Open End Rod Mill has the advantage of allowing the quick and easy removal of such rods.

It is difficult to give figures on media consumption since there are so many variables. Rods will be consumed at the rate of 0.2# per ton on soft easily ground material up to 2# per ton on harder material. Steel consumption of balls is spread out over an even greater range. Some indication as to media consumption can be obtained from power consumed in grinding. For example, balls or rods will generally wear at a rate of about 1# for each 6 or 7 kilowatt hours consumed per ton of ore. Liner consumption is generally about one-fifth of the media consumption.

We areprepared to furnish alltypes and sizes of steel rods as shown in table. Standard sizes of these rods are finest quality, high carbon, hot rolled, machine straightened steel and meet low cost, long wear requirements for use in operation of all types of rod mills.

Steel Grinding Rods are made of a special steel which breaks up without twisting when final wear occurs. This is extremely important in maintaining full grinding capacity and eliminating the difficulty of removing wire-like, worn rods which twist and bend into an inseparable and space filling mass of interlaced wires if breaking does not occur. Rods are shipped in lengths cut to suit the length of each particular customers rod mill.

Rods are to be hot rolled, hot sawed or sheared, with standard tolerance and machine straightened.
We have found that a good grade of forged steel grinding balls is generally most efficient for use with our grate discharge ball mills.

Steel balls ranging from to 5 in. in diameter are used. Rods range from 1 to 4 in. in diameter and should be 3 to 4 in. shorter than the inside mill length. Tube mills are usually fed balls smaller than 2 in., whereas 4- or 5-in. balls are more commonly used for ball-mill grinding. A much higher grinding capacity is obtained in tube mills by using steel media instead of pebbles, but in making such a conversion serious consideration must be given to the ability of the steel shell to withstand the greater loading.

Approximate ball loads can be estimated by assuming 300 lb. per cu. ft. of ball volume and a total load equivalent to 40 to 45 per cent of the mill volume. Rod loads average about 40 per cent of mill volume, and a figure of 400 to 425 lb. per cu. ft. of rod volume should be taken.

Experience indicates that rods are superior to balls for feeds in the range from to 1 in. maximum when the mill is not called upon to finish at sizes finer than 14 mesh. Balls are superior at coarser feed sizes or for finishing 1-in. feeds to 28 mesh of grind or finer because the mill can be run cataracting and the large lumps broken by hammering.

In an operating mill a seasoned charge, containing media of all sizes from that of the renewal or replacement size down to that which discharges automatic ally, normally produces better grinding than a new charge. It is inferred from this that a charge should be rationed to the mill feed, i.e., that it should contain media of sizes best suited to each of the particle sizes to be ground. Usual practice is, however, to charge a new mill with a range of sizes, based on an assumed seasoned load; thereupon to make periodic renewals, at various sizes dependent upon the character of the circulating load, until optimum grinding is obtained; and thereafter to make required renewals at the optimum size.

A coarse feed requires larger (grinding) media than a finer feed. The smaller the mesh of grind the smaller the optimum diameter of the medium. This relationship is attributed to the fact that fine product is produced most effectively by rubbing, whence maximum capacity to fine sizes is attained by maximum rubbing surface, i.e., with small balls. A practical limitation is imposed by the tendency for balls that are too small to float* out of the mill and by the high percentage of rejects when renewals are too small.

The usual materials for balls are chilled cast iron and forged steel, for rods, high- carbon steel, (0.8 to 1.0 per cent carbon) all more or less alloyed. Mild steel rods are unsuitable for the reason that they bend and kink after wearing down to a certain minimum diameter and snarl up the whole rod load. The hardened steel rods break up when they wear down and are removed at about 1 in. or left in an eventually discharge in small pieces.

If you know the price of a 3 grinding ball or what the cost of a 75mm piece of grinding ballis, you can estimate, in a relative way, the price of larger and smaller grinding media. It will serve you well when creating an operating budget.

These balls are cast alloy steel, and are made by the newly developed Payne Hot Top principle. This principle employs a rotating casting machine. This machine rotates and the molds move under the pouring spout and hot metal runs down a trough on top of the molds. Four or five molds are either filling or cooling under this stream of hot steel. By this means the heads are kept liquid, eliminating the need for risers and allowing all of the gasses to escape. For this reason the balls are solid, free from gas cavities, and show wear resistance equal to the best forged steel balls. These balls may be had in two types: a soft ball Brinnell 450+ for large diameter ball mills, and a hard ball Brinnell 600+ for small ball mills. The addition of molybdenum, chromium and manganese provides an excellent microstructure for these grinding balls. Balls are available in 4, 3, 3, 2, and 2 sizes.

## optimum choice of the make-up ball sizes for maximum throughput in tumbling ball mills - sciencedirect

The optimum composition of the make-up ball sizes in ball mills is presented.The effect of various factors was investigated via a grinding circuit simulation.Binary mixtures of two ball sizes always perform better than other mixtures.An equation is proposed for calculating the optimum composition of the make-up balls.

A grinding circuit simulation combined with ball weal law was used to determine the optimum composition of the make-up ball sizes in tumbling ball mills. It was found that the optimum composition depends on various factors, including the feed size, the product size, the mill diameter and the breakage parameters. In all cases, binary mixtures of two ball sizes (50.8mm and 25.4mm) performed better than a mixture of the three ball sizes. An equation therefore could be developed for calculating the optimum composition of the make-up balls as a function of various parameters.

## 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).

## ball mills

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