In grinding, operating Efficiency compares the operating work index of a comminution machine to the Bond work index from bench scale crushing and grindability tests or/and pilot plant tests. Economic Efficiency is comparing the income from production to the planned income from production.

Energy as consumed in comminution machines and the required energy as determined, from bench scale laboratory or pilot plant tests to perform the required size reduction are the key factors in determining the operational efficiency of comminution machines.

Bond Work Indicies obtained from bench scale crushability and grindability tests or from pilot plant tests are used in the Bond Equation to determine the energy required to produce the required size reduction in comminution circuits. The Bond Equation as found in reference 5 is:

W = kwh per short ton. Wi = Work Index determined from crushing and grinding tests. P = The size in microns (micrometers) that 80% of the product is finer than. F = The size in microns (micrometers) that 80% of the feed is finer than.

When accurate mill ore feed rate in dry tons per hour, mill power draw in kilowatts, and mill feed and product size analyses in microns are available the Bond Equation can be used to measure the operation of comminution machines, reporting it as operating work index. The equation for operating work index as given in the paper Tools of Power Power (6) is

Wio = Operating Work Index as kwh per either short ton or metric tonne. W = Measured power in kwh per either short ton or metric ton. P = The size in microns (micrometers) that 80% of the product is finer than. F = The size in microns (micrometers) that 80% of the feed is finer than.

W as calculated using the Bond Equation can be converted to kwh per metric tonne by multiplying it by 1.102. If the measured power for the operating data used in the operating work index equation is given as kwh per metric tonne then the calculated operating work index is power per metric tonne.

Fred Bond defined Work Index as The comminution parameter which expresses the resistance of material to crushing and grinding. Numerically the Work Index is the kwh per short ton required to reduce the material from theoretically infinite feed size to 80 percent passing 100 microns. Wi and Wio both fit Fred Bonds definition for Work Index. Operating work indices can be compared to work indices from bench and pilot scale tests run on samples of circuit feed taken for the same time period, as the operating data. By definition, both work indices cover exactly the same amount of size reduction, namely from an infinite feed size to a product size of 80% passing 100 microns.

When (Wio/Wi)x100 is less than 100 this indicates the circuit, based upon this comparison, is operating efficiently. When it is greater than 100 this indicates the circuit is operating inefficiently. A large difference, either low or high, could indicate that the two work indicies are not on the same basis. For operating efficiency calculations, it is necessary that the efficiency factors are applied so that both work indices, used in the comparison, are on the same basis.

Operating efficiency, based upon using operating work indices, is also a useful tool in comparing the variations in grinding mill operations such as: mill speed, mill size, size of grinding media, mill discharge arrangements, liner designs etc.

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.

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

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

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

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

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

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

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

DISCLAIMER: Material presented on the 911METALLURGIST.COM FORUMS is intended for information purposes only and does not constitute advice. The 911METALLURGIST.COM and 911METALLURGY CORP tries to provide content that is true and accurate as of the date of writing; however, we give no assurance or warranty regarding the accuracy, timeliness, or applicability of any of the contents. Visitors to the 911METALLURGIST.COM website should not act upon the websites content or information without first seeking appropriate professional advice. 911METALLURGY CORP accepts no responsibility for and excludes all liability in connection with browsing this website, use of information or downloading any materials from it, including but not limited to any liability for errors, inaccuracies, omissions, or misleading statements. The information at this website might include opinions or views which, unless expressly stated otherwise, are not necessarily those of the 911METALLURGIST.COM or 911METALLURGY CORP or any associated company or any person in relation to whom they would have any liability or responsibility.

You can read all the details of this now Biblical grinding power requirement calculation formula in Fred Bonds original paper. You can also review the step-by-step Bond Work Index Test Procedure I posted here.

For any circuit, whether a crushing circuit, a rod mill, or a closed ball mill circuit, the Work Index always means the equivalent amount of energy to reduce one ton of the ore from a very large size to 100 um.

The sample was received crushed appropriately for the ball mill test. Ball Mill Grindability Testwas conducted by standard practice using 100-mesh (150 pm) closingscreens.The ball mill work index is shown below.

Any improvement in the accuracy of commercial comminution calculations under the Third Theory must be accomplished either by increased precision in energy input measurements, or by a better evaluation of the total new crack length produced, as indicated by the feed and product size distributions. Since at the present time feed and product sizes are approximated solely by the microns 80% passes, the most promising opportunity for increased accuracy lies in consideration of their plotted size distribution characteristics. This paper shows how more accuracy can be obtained over an increased range of feed and product sizes from size distribution studies.

where W is the work input required in kilowatt hours per short ton to grind from 80% passing F microns to 80% passing P microns, and Wi is the work index, or the grinding resistance parameter. It represents the energy input required in kilowatt hours to reduce a short ton from theoretically infinite feed size to 80% passing 100 microns. This simple equation has been extremely useful in analyzing and grinding operations, and in predicting the performance of new installations.It can be written in the following form:

The work index Wi can be determined from plant operations and from laboratory ball mill grindability, rod mill grindability, and impact crushing tests. The laboratory test results are used to check the efficiency of commercial operations and to compute the proper machine sizes for new installations.

where Pi is the opening in microns of the sieve mesh tested, and Gbp is the net grams of mesh undersize produced per revolution of the 12 x 12 test ball mill. The closed circuit 80% passing size P averages P1/log 20 for all sizes larger than 150 mesh. For 150 mesh the average P value is 76 microns, for 200 mesh it is 50, for 270 mesh it is 32.3, and for 325 mesh it is 26.7. These average values can be used when P cannot be determined from screen analyses.

where Sg is the specific gravity and C is the impact crushing strength of the twin pendulum weights in foot-pounds per inch of rock thickness. No size distribution measurements are made in the impact test.

The trend of the particle size distribution line is shown by plotting its screen analysis in, such a manner that a complete homogeneous crushed or ground product will form a straight line; any curvature then indicates a natural or induced grain size. Semi-log paper is used with the percent cumulative retained plotted on the vertical logarithmic scale Y. Straight lines which each represent one mesh sieve size of P1 microns are drawn radiating from the upper left hand corner of the plot; each crosses the 20% retained, or 80% passing, line at w = 10/P1 where w is the horizontal lineal X value at Y = 20. The total work input to the sample in KWH/ton divided by the work index Wi is w. The straight plotted distribution line follows the exponential equation:

The exposure ratio Er is the quantity that expresses the line trend, or the fine size distribution. Er equals X2/W where X2 is the value of x at the top of the chart with Y = 100%. It has the following relationship to b.

When the exposure ratio Er is zero only one particle size is present and there has been no exposure of fines to the grinding media. The fines present increase as Er increases, and when Er is unity b is infinite.

When natural or induced grain sizes cause the plotted distribution line to curve in the region of 80% passing, the straight line determining Er is drawn through w at the average slope from Y = 10 to Y = 40, or is estimated to avoid the curvature. The exposure, ratio of the feed is Erf and that of the product is Erp.

It is apparent that the specific work input required, as represented by the new crack length Cr produced in centimeters per cc of solid (Crp Crf), will be decreased at large product sizes and will increase at fine product sizes when Crf and Erf are increased. In this case the work index Wi will increase as the product size P becomes smaller. Conversely, when the feed contains little fines and Erf and Crf are small, the work index will increase as P increases. These conditions are largely responsible for the observed work index variations at different product sizes which were formerly thought to require an exponent different from .

In a recent publication fifteen different ores each had grindability tests made at 28, 35, 48, 65 and 100 mesh, with many work index variations at the different product sizes. These tests are used here to develop empirical equations from which the work index at different product sizes can be computed from a grindability test at one size. In each of the 15 ores the data from the grindability test at 48 mesh alone were used to calculate the Wi values at 28, 35, 65, and 100 mesh, and these were compared with the actual values obtained by testing. In the calculation the exposure ratio Erp of each mesh product size was considered to be that determined by testing at 48 mesh, and Crp was determined from that value and the average P for each mesh size.

However, an equation is desired which uses the exposure ratios and does not require calculation of the crack lengths, Eq. (8) was derived to give the work index Wi at any 80% passing product size P from the work index Wio found from a single grindability test with a product size Po and exposure ratios Erf and Erp. It is

The work index values calculated from Eq. (7) and Eq. (8) are listed in Table I. Comparison with the actual Wi values shows that Eq. (8) is slightly more accurate than Eq. (7), and it is much simpler to use. Eq. (8) is suitable for determining the work index at various product sizes from one ball mill grindability test made at product size Po. It can be checked by grindability tests made at other product sizes.

The exposure ratio of the prepared minus 6 mesh feed Erf is regularly somewhat larger than that of the closed circuit product Erp, and Eq. (8) indicates that when Erf/Erp equals 1.29 the work index continues constant at all product sizes. When Erf/Erp is greater than 1.29, the work index increases as the product size decreases, and when Erf/Erp is less than 1.29 the work index decreases.

When Wi100 is calculated by Eq. (9) from the data at 48 mesh for each of the 15 ores listed, then Wip found by Eq. (10) for each of these ores at 28, 35, 65, and 100 mesh is essentially the same as the Wi value found from Eq. (8).

Comparison of the Wi100 values from Eq. (9) for different ores furnishes a measure of the relative grindability unaffected by size distribution differences; and comparison of the Wi100 values for the same ore calculated from the data at different mesh sizes gives a measure of the actual experimental errors involved in testing, plus any error in measuring the plotted Er values, and any error resulting from natural grain sizes causing curved plotted lines.

The standard work index Wi100 values calculated from Eq. (9) for each ore at each mesh size are included in Table I. Comparison for each ore shows a reasonable agreement among the tests made at various mesh sizes, and indicates that Eq. (9) and Eq. (10) can be used with confidence. The data show that the ball mill grindability tests at 28 mesh are somewhat less accurate than the others; this is expected because of the low ratio of reduction and the short retention time in the mill, when grinding prepared minus 6 mesh feed.

The total crack length Cr in centimeters per cubic centimeter of solids is most conveniently found from log-log charts prepared from a previously published table. However, in the absence of these chart the crack length of a crushed or ground product can be calculated for any 80% passing size P in microns and any exposure ratio Er by the following equation:

In the standard ball mill and rod mill grindability tests the specific crack lengths of the product Crp and of the feed Crf are found from their Erp, P, Erf, and F values. Where Y is the cumulative fraction of the feed retained on the mesh size tested the centimeters of new crack length produced per mill revolution are found from:

The average useful work input to the standard ball mill is 65 joules/Rev. with 115 joules/Rev. to the rod mill. The crack energy Ce of the sample tested is found by dividing joules/Rev. by Cm/Rev. The standard work index can then be found by transposing Eq. (16) and solving for Wi100.

In commercial grinding mills the operating work index is found by Eq. (19). However, when exposure ratios of the feed and product are obtained by plotting the screen analyses, their specific crack lengths Crf and Crp can be found. This furnishes the crack energy Ce in joules/Cm from:

The standard work index Wi100 can then be found from transposed Eq. (16). Comparison with the plant operating work index at product size P may show that the coefficients .018 and .014 in the last term of Eq. (9) should be altered slightly for the commercial grind. With the proper coefficients Eq. (9) can be used to evaluate the plant grinding operation at different product sizes with considerable accuracy.

The determination of the Bond work index (BWI) on finer samples.Accurate determination of the (BWI) is essential for the proper design plant.Suggested equation for determination BWI on finer samples.The error is smaller than 2.5%.

The Bond work index (BWI) is a well-known method used when selecting comminution equipment, to evaluate the grinding efficiency and to calculate the required grinding power. Although considered an industry standard, Bond did not fully define that procedure, and therefore significant discrepancies in test results can sometimes be obtained due to some undefined steps in the method. One of these cases is the initial sample size for grinding, why it must be the initial sample size of 3.35mm, and whether it is possible to determine the BWI on samples of finer classes. In practice, it is possible to find materials whose size is finer than 3.35mm. This paper examines the determination of the BWI on finer samples and proposes an equation for the determination of the BWI on finer samples.

Burns, R.S., and Erskine J.G., 1983, Experience with large diameter ball mills at Bougainville Copper Limited, Proceedings, Mini Symposium, Grinding Performance Of Large Ball Mills II, SME/ AIME fall meeting, Salt Lake City, UT, pp. 4153.

Rowland, C.A., 1973, Comparison of work indices calculated from operating data with those from laboratory test data, Proceedings Tenth International Minerals Processing Congress, The Institution of Mining and Metallurgy, London, UK, pp. 4761.

Rowland, C.A., 1978, Determination and use of operating work indices in controlled grinding circuitsA proposed concept, Mill Operators Conference and Exhibit, Northwestern Branch, Australasian Institution of Mining and Metallurgy, Mt. Isa, Queensland Australia, June.

Rowland, C.A., 1982, Selection of rod mills, ball mills, pebble mills, and regrind mills, in Design and Installation of Comminution Circuits, Andrew L. Mular and Gerald V. Jergensen, eds., SME, Chapter 23, pp. 393438.

Rowland, C.A., 1988, Large ball mills length and diameter, Proceedings XVI International Minerals Processing Congress, K.S. Forssberg, ed., Elsevier, Amsterdam, The Netherlands, Vol. 1, Part A, pp. 281292.

Rowland, C.A., 1989, Testing for selection of autogenous and semi-autogenous grinding mills and circuits, in Advances in Autogenous and Semiautogenous Grinding Technology Andrew L. Mular and Gordan E. Agar, eds., University of British Columbia, Vancouver, British Columbia, Canada, Vol. 1, pp. 4759.

Rowland, C.A., and Kjos, D.M., 1997, Rod and ball mills, Comminution Practices, S. Komar Kawatra, ed., SME, Chapter 39, pp. 319338 (Originally published in Minerals Process Plant Design, 1978, A.L. Mular and R.B. Bhappu, eds., Chapter 12, pp. pp238278).

Hi, As Alex told you: The crushing work index you calculated appears mostly correct. The only correction factor that might affect the calculation is to correct for the efficiency of the motor -- the work index is based on motor output (pinion) power, whereas the measurement of motor power is usually based on motor input power. I have attached a calculation of operating work index that includes the motor efficiency correction, and the result is WiO=22.4 (compared to your 21.5). This correction is minor and can probably be ignored.

The Bond crushing work index test (sometimes called the "impact work index" test) is noisy, and the difference you observed is perfectly reasonable. The paper by Angove & Dunne (1997) reports a standard deviation in crushing work index tests across laboratories as 4.5. The laboratory CWi value of 27.4 (metric) is almost within 4.5 units of the 22.4 value I calculated, so what you are observing is probably the natural variation in the crushing test.

So there is nothing wrong with your calculation, and the variation between the laboratory test and your observation of the operating crusher is within the normal range of variation for this calculation. It appears normal to me -- this is a noisy test, unfortunately.

Did you see http://www.911metallurgist.com/blog/bond-abrasion-index-vs-bond-work-index and http://www.911metallurgist.com/blog/bond-impact-crushing-work-index-procedure-and-table-of-crushability + http://www.911metallurgist.com/blog/rod-mill-work-index-table

DISCLAIMER: Material presented on the 911METALLURGIST.COM FORUMS is intended for information purposes only and does not constitute advice. The 911METALLURGIST.COM and 911METALLURGY CORP tries to provide content that is true and accurate as of the date of writing; however, we give no assurance or warranty regarding the accuracy, timeliness, or applicability of any of the contents. Visitors to the 911METALLURGIST.COM website should not act upon the websites content or information without first seeking appropriate professional advice. 911METALLURGY CORP accepts no responsibility for and excludes all liability in connection with browsing this website, use of information or downloading any materials from it, including but not limited to any liability for errors, inaccuracies, omissions, or misleading statements. The information at this website might include opinions or views which, unless expressly stated otherwise, are not necessarily those of the 911METALLURGIST.COM or 911METALLURGY CORP or any associated company or any person in relation to whom they would have any liability or responsibility.

Related Equipments

Copyright © 2021 Ecaystone Machinery All rights reserved sitemap Privacy Policy