UNTIL THE THIRD THEORY OF COMMINUTION of Work Index method of determining crushing and grinding mill size was introduced, there was no way of accurately figuring the most applicable, most economical size of crushing and grinding mill.

Naturally, with little or no factual operating data correlated in useful form, it was easy enough, even for the most experienced, to arrive at an incorrect size of crusher or grinding mill, especially when a slightly smaller unit carried an advantage in initial investment.

The Work Index method, frequently referred to as the Bond* method, is based on extensive field operating data and equally extensive laboratory data covering wide varieties of materials, ranges of reduction sizes and types of equipment.The correlation of all this factual material enabled the establishment of a consistent common factor, known as the Work Index, for accurately determining crushing and grinding mill sizes.

Knowing the Work Index, one has but to apply the proper given equation to determine the power input required. The calculated power input in turn enables you to select the proper crusher or grinding mill unit. Selection of various sizes of machines is made from the power requirements listed in equipment manufacturers published bulletins. The following example will help clarify the above procedure.

Assume a capacity of 2000 short tons of average material per day. A Work Index of 13 over the entire size range. A feed 80% passing 3 and a final desired product of 80% passing 100 mesh. These, then, work out as follows:

By referring to equipment manufacturers bulletin on crushers, Fig. 1, a crusher producing 80% passing 3/4 requires a close side setting of approximately 5/8. Since the selected crusher capacity must be in excess of 143 tons per hour, the next higher figure (159) is chosen. The 159 indicates a 548 crusher size with 1 eccentric throw. With 1-in. eccentric throw, the motor hp allowed on the crusher is a maximum of 125. However, since only 90.3 hp is required for this average material, a 100-hp motor is sufficient.

Fig. 2, taken from manufacturers bulletin, lists horsepower requirements and Rod Mill sizes. The calculatedpower input or horsepower in the above example is 316. Therefore, a 350-hp motor is required and this in turn indicates that an 812 (8 x 12) Rod Mill is required.

For your convenience, this manual lists over 1200 work indexes. Table I lists the Work Indexes alphabetically by company and deposit. Table II lists the Work Indexes alphabetically by materials. Table III lists the average Work Indexes alphabetically by different types of materials. In the event these 1200 listings of Work Indexes do not include the particular one that applies to your particular material, you can readily determine it, since the WorkIndex expresses the resistance or a material to crushing and grinding and the relative efficiency of any machine.

Let W represent the work input in Kwhr/T, F the feed size or diameter in microns of the square hole which 80% of the feed passes, P the product size or microns which 80% of the product passes, and Rr the reduction ratio F/P. To find the Work Index (IF/) use Equation 1.

The 80% passing size in microns is a convenient term for expressing the fineness of a crushed or ground product. It is also a convenient base for calculating the reduction ratio and the work required for reduction. It is readily found by plotting the percent passing on log-log paper, as in Fig. 5, to determine the size distribution curve.

When the size distribution curves of the feed and product are parallel, the reduction ratio remains constant for all particle sizes, and the Work Index calculated from the 80% passing size is equivalent to that calculated on the basis of any other selected percent passing size.

Small differences between the slopes of the plotted feed and product lines have only a slight effect on the Work Index, proportional to the square root of the effect upon the surface areas. However, when the feed has had the fines removed the feed size is changed and the Work Index may be considerably in error. In cases where a crusher feed is scalped by passing over a grizzly screen, with openings equal to or smaller than the crusher openings, the tonnage and size distribution of the fines removed are rarely known. It is preferable, therefore, to consider the feed to the grizzly as being equivalent to the feed to the crusher and calculate the Work Index on this basis.

Several methods (2) have been used to correct the calculated Work Index for large differences between the product and feed slopes, when plotted as in Fig. 5. A newer method is the use of the average reduction ratio Rra. This can be obtained by averaging the reduction ratios at 90, 70, 50, 30 and 10% passing. The reduction ratio, at any percent passing, can be obtained quickly. Place a piece of the log- log paper (the same as used in plotting) along the percent passing line as indicated by the dotted lines A and B, Fig. 5. With point A coinciding with 100 on the micron scale and B coinciding with 773 on the same scale, 7.73 is the reduction ratio at that percent passing.

The Work Index values listed in Table I and II apply directly to a wet grinding overflow type rod mill 7.5 feet in diameter in open circuit; and to a wet grinding overflow type ball mill 7.5 feet in diameter in closed circuit with a rake classifier at 250% circulating load, and with 80% or more of the feed passing 4 mesh. Correction factors should be applied for over-size feed and other operating conditions which change the grinding efficiency. When Work Index values at several different product sizes are available (see Tables I and II), the value nearest the actual product size should be used. The Work Index represents the total work input necessary in installations of average efficiency.How to Find Work Index From Impact Crushing Tests

The Work Index is found from the first stage of the wet open circuit grinding tests (1) by multiplying the grinding index Iw by 0.0082, and from the first stage of the dry open circuit grinding tests by multiplying the dry grinding index Id by 0.00546.

The Work Index is found from the second stage of the wet open circuit grinding tests(1) by multiplying the grinding index IIw by 0.0022, and from the second stage of the dry open circuit grinding tests by multiplying the dry grinding index IId by 0.00147. The second stage dry open circuit grinding tests may show an increased Work Index because of ball coating, and are not reliable if ball coating exists.

The Work Index can be calculated by Equation 1 from commercial crushing or grinding data or from pilot mill tests, and compared with the listed Work Indexes in Tables I and II to obtain the relative mechanical efficiency.

In cases where the capacity is found to vary more than this amount, some condition causing inefficient operation should be suspected. These may include packing in a crusher, oversize feed or improper ball and rod sizes in a tumbling mill, and coating dry in grinding.

Impact crushing tests, as well as rod mill and ball mill grindability tests, can be made at cost by thewww.911metallurgist.com Laboratories. To run a proper test, a representative sample of 50 pounds minimum is required. The sample for an impact crushing test should be no finer than 2. The sample for a rod mill grindability test should be no finer than 80% passing 0.5, and the sample for a ball mill grindability test should be no finer than 80% passing 6 mesh.

FRED C. BOND Special Engineer with Allis-Chalmers Mfg. Co. Standard Grindability Tests Tabulated, Trans. AIME (1949) vol. 183, page 313, TP 2180, Mining Technology, July 1947. FRED C. BONDThe Third Theory of Comminution, Trans. AIME, TP 3308B, Mining Engineering, May 1952.

The grinding circuit is among your largest capital investments and greatest operating costs. SGS can reduce your risk by combining different test procedures and design methodologies to ensure that you optimize this critical part of your plant.

Our philosophy is to first determine the variability of your ore using rigorous comminution testing, including Bond tests for ball and rod mills. We conduct a small number of expensive tests that require a larger sample size, such as the Bond Ball Mill Grindability Test. The results are used to calibrate a large number of less expensive tests that require only a small sample, such as the Modbond Grindability Test.

Similar to a Comparative Work Index, this test is an open circuit dry batch grindability test run in the standard Bond Ball Mill for a set time. It can be used at mesh sizes from 65 to 200 mesh (normally 100 mesh). The test requires calibration against the standard Bond Ball Mill Work Index test to estimate the Work Index. It is used to show the orebody hardness profile and to predict throughput in a ball mill circuit.

SGS created the Modbond grindability test and has a large proprietary database. The small sample size enables many tests to be conducted, resulting in extensive variability information that our experts use to efficiently design your grinding circuit.

Where W = Net power consumption in kWh/t Wi = Bond work index (either Imperial or Metric units) P= The 80% passing size of the ground product in m F = The 80% passing size of the feed in m

The test determines the Bond Impact Work Index which is used with Bonds Third Theory of Comminution to calculate net power requirements when sizing crushers*. It is also used to determine the required open-side settings (jaw crushers and gyratory crushers) or closed-side settings (cone crushers) for a given product size.

WhereOss = Open-side setting in inches Css = Closed-side settings in inches Ecc = Eccentric throw in inches P80 = Aperture through which 80% of the product will pass. Wi = Work Index

The impact apparatus consists of two pendulum-mounted hammers, mounted on two bicycle wheels so as to strike equal blows simultaneously on opposite sides of each rock specimen. The height that the pendulum is raised is increased until the energy is sufficient to break the specimen.

The test determines the Bond Rod Mill Work Index which is used with Bonds Third Theory of Comminution to calculate net power requirements when sizing ball mills*. Various correction factors may have to be applied.

A specimen preparation approach is demonstrated to be effective in achieving filler particles dispersion.Filler particle's morphological indices are well characterized.Filler particles are found to have significant effects on rheological properties of mastics.Correlation degrees between morphological features of filler and rheological properties of mastic are studied.

The primary objective of this study was to investigate the feasibility of the dispersion of fillers dispersion as individual particles and evaluate the effects of the morphological characteristics of filler particles on the rheological properties of asphalt mastics at high and medium temperatures. For a given source and filler, three various filler particle sizes produced from different crushers (i.e., a jaw crusher, an impact crusher and a ball grinding mill) were obtained, namely, F1 (P200-R300: passing a 200-mesh and retained by a 300-mesh sieve), F2 (P400-R500) and F3 (P800-R1000). The binary image particle analysis system was employed to acquire the morphological characteristics of filler particles such as form factor, angularity and surface texture. By applying multiple stress creep and recovery (MSCR) tests at high temperature and time sweep (TS) tests at medium temperature, the rheological properties of asphalt mastics prepared with different filler particle sizes were also investigated. Furthermore, the correlations between the morphological characteristics of filler particles and the high/medium-temperature properties of asphalt mastics were studied by grey relational analysis (GRA) method. Results showed that the proposed new approach to sample preparation was demonstrated to be effective in achieving filler particle dispersion. The GRA demonstrated that the rheological properties of asphalt mastics at high and medium temperatures were significantly affected by the morphological characteristics of the filler particles. Percent recovery (R) and fatigue law fitting coefficients (A and B) were more sensitive to porosity, angularity index, average diameter, aspect ratio and fractal dimension but less sensitive to feature roughness, roundness, convexity ratio, density and specific surface area. In terms of non-recoverable creep compliance (Jnr), the sensibility was apparently reversed, with the reference sequence Jnr presenting less susceptibility to porosity, angularity index, average diameter, aspect ratio and fractal dimension. The GRA results can inform engineers regarding the selection of filler particles that produce asphalt mastics with desired performance characteristics, such as specific rutting resistance and fatigue failure.

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The control of a milling operation is a problem in imponderables: from the moment that the ore drops into the mill scoop the process becomes continuous, and continuity ceases only when the products finally come to rest at the concentrate bins and on the tailing dams. Material in process often cannot be weighed without a disturbance of continuity; consequently, mill control must depend upon the sampling of material in flux. From these samples the essential information is derived by means of analyses for metal content, particle size distribution, and content of water or other ingredient in the ore pulp.

The following formulas were developed during a long association not only with design and construction, but also with the operation of ore dressing plants. These formulas are herein the hope that they would prove of value to others in the ore dressing industry.

Pulp densities indicate by means of a tabulation the percentages of solids (or liquid-to-solid ratio) in a sample of pulp. This figure is valuable in two waysdirectly, because for each unit process and operation in milling the optimum pulp density must be established and maintained, and indirectly, because certain important tonnage calculations are based on pulp density.

As used in these formulas the specific gravity of the ore is obtained simply by weighing a liter of mill pulp, then drying and weighing the ore. With these two weights formula (2) may be used to obtain K, and then formula (1) to convert to S, the specific gravity. A volumetric flask of one liter capacity provides the necessary accuracy. In laboratory work the ore should be ground wet to make a suitable pulp. This method does not give the true specific gravity of the ore, but an apparent specific gravity which is more suitable for the intended purposes.

A mechanical classifier often receives its feed from a ball mill and produces (1) finished material which overflows to the next operation and (2) sand which returns to the mill for further size-reduction. The term circulating load is defined as the tonnage of sand that returns to the ball mill, and the circulating load ratio is the ratio of circulating load to the tonnage of original feed to the ball mill. Since the feedto the classifier, the overflow of the classifier, and the sand usually are associated with different proportions of water to solid, the calculation of circulating load ratio can be based on a pulp density formula.

Example: A mill in closed circuit with a classifier receives 300 dry tons of crude ore per day, and the percentages of solid are respectively 25, 50, and 84% in the classifier overflow, feed to classifier, and sand, equivalent to L: S ratios of 3.0, 1.0, and 0.190. Then the circulating load ratio equals

A more accurate basis for calculation of tonnage in a grinding circuit is the screen analysis. Samples of the mill discharge, return sand, and the classifier overflow are screen sized, and the cumulative percentages are calculated on several meshes. Let:

The efficiency of a classifier, also determined by means of screen analyses, has been defined as the ratio, expressed as percentage, of the weight of classified material in the overflow to the weight of classifiable material in the feed. Overflow having the same sizing test as the feed is not considered classified material. Let:

When no other method is available an approximation of the tonnage in a pulp stream or in a batch of pulp can be quickly obtained by one of these methods. In the dilution method water is added to astream of pulp at a known rate, or to a batch of pulp in known quantity, and the specific gravity of the pulp ascertained before and after dilution.

In both cases Dx and D2 are dilutions (tons of water per ton of ore) before and after addition of water. These are found from the specific gravities of the pulp, by formulas (4) and (6) or directly by the use of the tabulation on these of Pulp Density Tables.

The Pulp Density Tables were compiled to eliminate the many complicated calculations which were required when using other pulp density tables. The total tank volume required for each twenty-four hour period of treatment is obtained in one computation. The table gives a figure, in cubic feet, which includes the volume of a ton of solids plus the necessary volume of water to make a pulp of the particular specific gravity desired. Multiply this figure by the number of dry tons of feed per twenty-four hours. Then simply adjust this figure to the required treatment time, such as 16, 30, 36, 72 hours.

In the chemical method a strong solution of known concentration of common salt, zinc sulphate, or other easily measured chemical is added to the flowing pulp at a known rate, or to a batch of pulp in known quantity. The degree of dilution of this standard solution by pulp water is ascertained by chemical analysis of solution from a filtered sample, and the tonnage of ore is then calculated from the percentage solid. This method is impractical for most purposes, but occasionally an exceptional circumstance makes its employment advantageous. It has also been suggested as a rapid and accurate method of determining concentrate moistures, but in this application the expense is prohibitive, since ordinary chemicals of reasonable cost are found to react quickly with the concentrate itself.

With the above chart the per cent solids or specific gravity of a pulp can be determined for ores where gravities do not coincide with those in the Pulp Density Tables.This chart can also be used for determining the specific gravity of solids, specific gravity of pulps, orthe per cent solids in pulp if any two of the three are known.

These are used to compute the production of concentrate in a mill or in a particular circuit. The formulas are based on assays of samples, and the results of the calculations are generally accurate as accurate as the sampling, assaying, and crude ore (or other) tonnage on which they depend.

The simplest case is that in which two products only, viz., concentrate and tailing, are made from a given feed. If F, C, and T are tonnages of feed r on-centrate, and tailing respectively; f, c, and t are the assays of the important metal; K, the ratio of concentration (tons of feed to make one ton of concentrate); and R, the recovery of the assayed metal; then

When a feed containing, say, metal 1 and metal z, is divided into three products, e.g., a concentrate rich in metal 1, another concentrate rich in metal z, and a tailing reasonably low in both l and z, several formulas in terms of assays of these two metals and tonnage of feed can be used to obtain the ratio of concentration, the weights of the three products, and the recoveries of 1 and z in their concentrates. For simplification in the following notation, we shall consider a lead-zinc ore from whicha lead concentrate and a zinc concentrate are produced:

The advantages of using the three-product formulas (20-25) instead of the two-product formulas (14-19), are four-fold(a) simplicity, (b) fewer samples involved, (c) intermediate tailing does not have to be kept free of circulating material, (d) greater accuracy if application is fully understood.

In further regard to (d) the three-product formulas have certain limitations. Of the three products involved, two must be concentrates of different metals. Consider the following examples (same as foregoing, with silver assays added):

In this example the formula will give reliable results when lead and zinc assays or silver and zinc assays, but not if silver and lead assays, are used, the reason being that there is no concentration of lead or silver in the second concentrate. Nor is the formula dependable in a milling operation, for example, which yields only a table lead concentratecontaining silver, lead, and zinc, and a flotation concentrate only slightly different in grade, for in this case there is no metal which has been rejected in one product and concentrated in a second. This is not to suggest that the formulas will not give reliable results in such cases, but that the results are not dependablein certain cases one or more tonnages may come out with negative sign, or a recovery may exceed 100%.

To estimate the number of cells required for a flotation operation in which: WTons of solids per 24 hours. RRatio by weight: solution/solids. LSpecific gravity, solution. SSpecific gravity, solids. NNumber of cells required. TContact time in minutes. CVolume of each cell in cu. ft.

Original feed may be applied at the ball mill or the classifier. TTons of original feed. XCirculation factor. A% of minus designated size in feed. B% of minus designated size in overflow. C% of minus designated size in sands. Circulating load = XT. Where X = B-A/A-C Classifier efficiency: 100 x B (A-C)/A (B-C)

Original feed may be applied at theball mill or the primary classifier. TTons of original feed. XPrimary circulation factor. YSecondary circulation factor. A% of minus designated size in feed. B% of minus designated size in primary overflow. C% of minus designated size in primary sands. D% of minus designated size in secondary overflow. E% of minus designated size in secondary sands. Primary Circulating Load = XT. Where X = (B-A) (D-E)/(A-C) (B-E) Primary Classifier Efficiency: 100 xB (A C)/A (B C) Secondary Circulating Load = YT. Where Y = (D-B)/(B-E) Secondary Classifier Efficiency: 100 xD (B-E)/B (D E) Total Circulating Load (X + Y) T.

Lbs. per ton = ml per min x sp gr liquid x % strength/31.7 x tons per 24 hrs.(26) Solid reagents: Lbs. per ton = g per min/31.7 x tons per 24 hrs.(27) Example: 400 ton daily rate, 200 ml per min of 5% xanthate solution Lbs. per ton = 200 x 1 x 5/31.7 x 400 = .079

Generally speaking, the purpose of ore concentration is to increase the value of an ore by recovering most of its valuable contents in one or more concentrated products. The simplest case may be represented by a low grade copper ore which in its natural state could not be economically shipped or smelted. The treatment of such an ore by flotation or some other process of concentration has this purpose: to concentrate the copper into as small a bulk as possible without losing too much of the copper in doing so. Thus there are two important factors. (1) the degree of concentration and (2) the recovery ofcopper.

The question arises: Which of these results is the most desirable, disregarding for the moment the difference in cost of obtaining them? With only the information given above the problem is indeterminate. A number of factors must first be taken into consideration, a few of them being the facilities and cost of transportation and smelting, the price of copper, the grade of the crude ore, and the nature of the contract between seller and buyer of the concentrate.

The problem of comparing test data is further complicated when the ore in question contains more than one valuable metal, and further still when a separation is also made (production of two or more concentrates entirely different in nature). An example of the last is a lead-copper-zinc ore containing also gold and silver, from which are to be produced. (1) a lead concentrate, (2) a copper concentrate, and (3) a zinc concentrate. It can be readily appreciated that an accurate comparison of several tests on an ore of this nature would involve a large number of factors, and thatmathematical formulas to solve such problems would be unwieldy and useless if they included all of these factors.

The value of the products actually made in the laboratory test or in the mill is calculated simply by liquidating the concentrates according to the smelter schedules which apply, using current metal prices, deduction, freight expense, etc., and reducing these figures to value per ton of crude ore by means of the ratios of concentration.

The value of the ore by perfect concentration iscalculated by setting up perfect concentrates, liquidating these according to the same smelter schedulesand with the same metal prices, and reducing theresults to the value per ton of crude ore. A simple example follows:

The value per ton of crude ore is then $10 for lead concentrate and $8.50 for zinc, or a total of $18.50 per ton of crude ore. By perfect concentration, assuming the lead to be as galena and the zinc as sphalerite:

The perfect grade of concentrate is one which contains 100% desired mineral. By referring to the tables Minerals and Their Characteristics (pages 332-339) it is seen that the perfect grade of a copper concentrate will be 63.3% when the copper is in the form of bornite, 79.8% when in the mineral chalcocite, and 34.6% when in the mineral chalcopyrite.

A common association is that of chalcopyrite and galena. In concentrating an ore containing these minerals it is usually desirable to recover the lead and the copper in one concentrate, the perfect grade of which would be 100% galena plus chalcopyrite. If L is the lead assay of the crude ore, and C the copper assay, it is easily shown that the ratio of concentration of perfect concentration is:

% Pb in perfect concentrate = K perfect x L.(30) % Cu in perfect concentrate = K perfect x C..(31) or, directly by the following formula: % Pb in perfect concentrate = 86.58R/R + 2.5.(32) where R represents the ratio:% Pb in crude ore/% Cu in crude ore Formula (32) is very convenient for milling calculations on ores of this type.

by (29) K perfect = 100/5.775+2.887 = 11.545 and % Pb in perfect concentrate = 11.545 x 5 = 57.7% and % Cu in perfect concentrate = 11.545 x 1 = 11.54% or, directly by (32), % Pb = 86.58 x 5/5 + 2.5 = 57.7%

Occasionally the calculation of the grade of perfect concentrate is unnecessary because the smelter may prefer a certain maximum grade. For example, a perfect copper concentrate for an ore containing copper only as chalcocite would run 79.8% copper, but if the smelter is best equipped to handle a 36% copper concentrate, then for milling purposes 36% copper may be considered the perfect grade.

Similarly, in a zinc ore containing marmatite, in which it is known that the maximum possible grade of zinc concentrate is 54% zinc, there would be no point in calculating economic recovery on the basis of a 67% zinc concentrate (pure sphalerite). For example, the following assays of two zinc concentrates show the first to be predominantly sphalerite, the second marmatite:

The sulphur assays show that in the first case all of the iron is present as pyrite, and consequently the zinc mineral is an exceptionally pure sphalerite. This concentrate is therefore very low grade, from the milling point of view, running only 77.6% of perfect grade.On the other hand, the low sulphur assay of concentrate B shows this to be a marmatite, for 10% iron occurs in the form of FeS and only 2.5% iron as pyrite. The zinc mineral in this case contains 55.8% zinc, 10.7% iron, and 33.5% sulphur, and clearly is an intermediate marmatite. From the milling point of view cencentrate B is high grade, running 93% of perfect grade, equivalent to a 62% zinc concentrate on a pure sphalerite.

The term Mesh is used to describe the size of an abrasive particle. In some instances, such as withAluminum Oxide GritorSilicon Carbide Grit, a single number is used. This does not mean every particle in that product is exactly that size but rather than mesh size indicator is approximately the mean or average size of the range of particles in that grade. In other instances, such as withWalnut Shell GritorGlass Beads, two numbers are used. This indicates that all of the particles in that grade of product are within that range of mesh sizes.

U.S. Mesh Size (or U.S. Sieve Size) is defined as the number of openings in one square inch of a screen. For example, a 36 mesh screen will have 36 openings while a 150 mesh screen will have 150 openings. Since the size of screen (one square inch) is constant, the higher the mesh number the smaller the screen opening and the smaller the particle that will pass through. Generally US Mesh is measured using screens down to a 325 mesh (325 openings in one square inch).

Sometimes the mesh size of a product in noted with either a minus (-) or plus (+) sign. These signs indicate that the particles are either all smaller than (-) or all larger than (+) the mesh size. For example, a product identified as -100 mesh would contain only particles that passed through a 100 mesh screen. A +100 grade would contain particles that did not pass through a 100 mesh screen. When a grade of product is noted with a dash or a slash is indicates that the product has particle contained within the two mesh sizes. For example, a 30/70 or 30-70 grade would only have particles that are smaller than 30 mesh and larger than 70 mesh.

The terms Mesh and Grit are often confused. The terms can be used interchangeably when referring to abrasive grit. A 60 mesh Aluminum Oxide can also correctly be termed a 60 grit Aluminum Oxide. In practical terms, identifying a specific abrasive product with the term 60 Mesh would normally indicate that the product has a median size of the openings on a 60 mesh screen. The term 60 Grit more accurately identifies the particle size distribution of the product but the difference in terminology is insignificant for industry purposes. See our blog post Mesh vs. Grit for more detail.

The chart below shows the approximate size in inches and microns for various mesh sizes. These values are generally accepted as accurate but are approximates because the thickness of the wire used to make a specific screen will vary the number of openings in the one square inch. A micron is one-millionth of a meter or one-twenty-five thousandths of an inch. Most grades below 325 mesh are indicated by the micron size as these sizes are not manufactured using screens.

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