Testing Plant Equipment:In order to determine, among other things, the operating conditions of the ball-mill when working on this rock, a test mill of about 300 T. daily capacity was erected at Duluth, Minn. The fine-crushing plant contains a Hardinge 8-ft. by 22-in. (2.4-m. by 55.8-cm.) conical mill, a 6- by 27-ft. (1.8 by 8.2-m.) Dorr duplex bowl-type classifier, a 4-ft. (1.37-m.) standard Akins classifier, and the auxiliary machinery necessary to handle the products. Each machine is driven by an individual motor, each of which is provided with meters for measuring the power required. Over 150 tests have been made in the ball-mill, varying in duration from a few hours to several weeks, in every case being continued until operating conditions became steady. The plant is so constructed that good samples of all products can be secured, both by automatic samplers and by hand. An apron feeder governs the feed rate and the tonnage is checked in every test. Water is metered into the circuit and every precaution is taken to make the data accurate and reliable.

It is a little hard to secure a basis upon which to compare crushing results. Neither Kicks nor Rittingers law of crushing is of much use in this case. This is evident when it is considered that the average size of a particle finer than 200 mesh is a matter of opinion, and that in this crushing problem practically all the ore must be crushed to pass a 200-mesh screen. The comparisons have therefore been made on the basis of kilowatt-hours per ton of material finer than 200 mesh actually produced. This, of course, does not give a scientifically exact basis for comparison, but since only the material below 200 mesh is considered finished product, in this case this is a suitable method for comparison.

On the eastern end of the Mesabi Range, in Northern Minnesota, is a large formation of siliceous rock which contains bands and fine grains of magnetite. The magnetite comprises about 35 per cent, of the rock, the remainder being chiefly quartzite and iron silicates. The rock has a specific gravity of 3.4, a hardness of 7, and is extremely tough.

This large deposit was located early in the history of the Minnesota iron-ore industry but has not been utilized because of its low percentage of iron as compared with the other Mesabi ores, and because of the difficulty and expense of any milling treatment that would concentrate the iron. An investigation, begun about 3 years ago, shows that the magnetite is finely disseminated throughout the entire formation and that there are bands or lenses of higher- and of lower-grade material, in which the magnetite and silicate are intimately mixed. As a result, the scheme of milling adopted must include a fine-crushing plant. As it is necessary to crush to 200 mesh in order to produce the desired grade of product, the fine crushing is one of the largest items of expense and for this reason has been given detailed study. It is the purpose of this paper to present some of the results of the work on fine crushing, as to both theory and practice.

Previous to fine crushing the part of the rock that contains little or no magnetite can be discarded by magnetic concentrators after each reduction in size in the dry-crushing plant. This makes it possible to fine-crush a minimum of rock and also establishes the feed to the ball-mill as below in. The fine-crushing problem, then, consists simply in crushing the rock from in. to 200 mesh at the minimum expense.

Feed rate, variable from 3 to 18 T. per hr. Ball load, 28,000 lb. of 5-, 4-, 3-, and 2-in. balls. Speed, 19.7 r.p.m. Ball-mill power, 88 kw. Feed, minus in., containing 6.52 per cent, minus 200-mesh material. Amount of solids, about 50 per cent.

Fig. 1 shows graphically that the tonnage of minus 200-mesh material produced varies directly with the tonnage fed to the mill. There is undoubtedly some limit to this relation, but there seems to be no indication of it at 18 T. per hr. Some of the conclusions drawn from this test are that: (a) The ball-mill is naturally a machine of very large capacity; (b) if it is not possible to deliver a large tonnage of original feed to the mill, a closed circuit should be provided so that the mill may crush its own oversize.

The results of these tests also are shown in Fig. 1. It is interesting to note that the curve showing tons per hour of minus 200-mesh material does not tend to flatten out as the tonnage to the mill is increased. The power per ton is also continually decreasing. It is, of course, impossible to state how much further this condition will continue, but it seems evident that it will continue for tonnages considerably beyond 15 T. per hr. As the two curves are slowly converging, at some large tonnage the amount of minus 200-mesh material produced per kilowatt-hour will be the same for either open- or closed-circuit crushing. The real advantage then gained by the closed-circuit system lies in the fact that the product consists of particles much more uniform in size. Although the average reduction in both systems may be the same, the closed-circuit will deliver a product in which the maximum-size particle will be much nearer the average size than will the open-circuit system.

(a) For equal tonnages of original feed, the closed-circuit crushing system produces the greater tonnage of minus 200-mesh material per kilowatt-hour, (b) For equal tonnages of original feed, the closed- circuit system of crushing shows the greater average reduction, (c) There is no indication that the mill was operated at, or even near, a tonnage that would give the greatest number of tons of minus 200-mesh material per kilowatt-hour. (d) Closed-circuit crushing will always have the advantage over open-circuit crushing, in that the maximum-size particle produced will be much nearer the average size. This is a desirable condition since the size of the balls making up the charge must be computed on the maximum-size particles in the feed rather than the average size.

Feed rate, 7.37 T. per hr. Ball-mill power, 108 kw. Classifier, Dorr duplex bowl-type. Feed, minus -in. ore. Ball load, 28,000 lb. of 2- and 2 3/8-in. balls. Amount of solids, about 70 per cent. Speed, 23.8 r.p.m.

There were 5.63 T. of minus 200-mesh material actually produced per hour and 19.2 kw.-hr. per ton of minus 200-mesh material produced were required. The classifier delivered 33 T. of sand per hour. The total ball-mill feed was therefore 40.37 T. per hr. or 550 per cent, of the original feed.

In the first stage, 9.11 T. of minus 200-mesh material were produced per hour and 11.98 kw.-hr. were required for each ton of minus 200-mesh material produced. The classifier delivered 32 T. of sand per hour. The total feed to the mill was therefore 47.31 T. per hr. or 308 per cent, of the original feed. The classifier overflow was reclassified, most of the material below 200 mesh being discharged from the crushing circuit while the sands were fed to the second stage. In this stage 3.73 T. of minus 200-mesh material were produced per hour and 28.9 kw.-hr. were required for each ton of minus 200-mesh material produced.

The classifier delivered 5 T. of sand per. hour. The total feed to the ball-mill was therefore 11.54 T. per hr. or 179 per cent, of the original feed. It was evident that the ball-mill was greatly underloaded in this test, but so much trouble developed in the classifier, due to the tendency of the sands to slip down the slopes, that a more rapid feed was not attempted at this time. The classifier had been set at a slope of 1 in. per ft. (125 mm. per m.) and conditions were such that the slope could not be decreased. It was impossible also to use the bowl overflow at this flat slope without rebuilding the classifier. At the present writing this work has not been completed. It seems certain, however, that the ball-mill will crush to 200 mesh a considerably greater tonnage when the proper classification is provided. Since in previous tests the mill has crushed 7 T. per hr. from in. to 200 mesh, it seems possible that it will crush at least 8 T. per hr. from 48 to 200 mesh.

Comparing single- and double-stage crushing on the basis of these two tests, it appears that the single-stage crushing produces a ton of minus 200-mesh material for 19.2 kw.-hr. while double-stage crushing produces a ton of minus 200-mesh material for 16.8 kw.-hr. These figures, though, do not show the real relative efficiencies of the two systems, for the second stage of the two-stage system was so obviously underloaded. The conclusions drawn from these tests are that (a) two-stage crushing shows a greater efficiency than single-stage, (b) two-stage crushing is much more flexible and offers greater possibilities for improvement than does single stage. In addition, a considerable amount of tailing can be discarded between the stages.

Test No. 12 shows a production of 6.3 T. of minus 200-mesh material per hour, which is 17.15 kw.-hr. per ton of this material actually produced. Test No. 150 shows a production of 8.07 T. of minus 200-mesh material per hour, which is 13.10 kw.-hr. per ton of this material actually produced. These two tests clearly indicate the superiority of small balls. It is instructive to compare the classifier sands in these two tests (see Table 0).

It appears that the small balls produced a much more uniform sand than did the large balls. The evident crowding of material at certain sizes is almost entirely absent in the small-ball test. Since this classifier sand is composed of the particles of ore that have passed through the mill at least once without being crushed, it appears that the large balls

reduce the coarse particles very readily but have trouble in crushing the finer particles. On the other hand, the small balls appear to crush all particles equally well. From this it would seem to be possible, by an analysis of the classifier sands, to determine whether or not the balls are too large or too small for the work they are doing. If the screen analysis of the sands is crowded on the upper end, the balls are too small; if it is crowded at the approximate size of the overflow, the balls are too large. The best results have been obtained when the screen analysis of the sands is about uniform between the size of the original feed and the size of the overflow.

In the tests shown in Table 9, in which balls of 2-, 2-, and 1-in. diameter (63.5, 50.8, and 38.1 mm.) were used, the tonnage also being increased, the effect of a change in speed is much more marked.

mill was unable to handle the coarse ore. The obvious conclusion is that either the speed of the mill should be increased slightly or balls of a little larger diameter should be used. At 23.8 r.p.m. the sands were nearly uniform and at this speed the mill showed the greatest efficiency.

(a) If the balls are large or the speed of the mill is high, crowding will appear at the finer sizes in the classifier sands. (b) If the balls are small or the speed is low, crowding will appear at the coarser sizes in the classifier sands. (c) The indications are that best efficiency is obtained when the screen analysis of the sands shows a minimum of crowding at any size. This statement has not been proved conclusively, however.

In view of these conclusions and the test data at hand, it is interesting to outline the manner in which a fine-crushing plant may be designed. In this discussion, the following limitations are imposed:

(a) The first cost of the plant must not be excessive. (b) Since the experiments were made with a Hardinge mill and a Dorr classifier, these are given first consideration herein, although not necessarily the best adapted for the work to be done. (c) The plant is to receive a feed and deliver a final product approximately as shown in Table 11.

The flow sheet shown in Fig. 2 has been designed to meet these requirements. Its most conspicuous feature is the large number of classifiers; possibly there are too many, but in all tests the limiting factor has been the capacity of these machines. It is estimated that the capacity of this plant will be 720 T. per day, receiving a feed and delivering a product as shown. The plant will require 344 kw. at the switchboard, which Will be 11.5 kw.-hr. per ton of ore crushed, or 14 kw.-hr. per ton of minus 200-mesh material actually produced. This is not an extremely low figure as better results have been obtained many times in the tests.

The 720 T. per day, or 30 T. per hr., of original feed will divide to the various units in the following manner: Each first-stage ball-mill will crush 15 T. per hr. to minus 48 mesh. This 15 T. will pass into the Simplex bowl-type classifier, where 10 T. will overflow as finished product; the 5 T. of sand, with the 5 T. of sand from the second Simplex bowl-type classifier, will constitute the feed to the second-stage ball-mill. The test data indicate that this can be accomplished with one classifier in closed circuit with each ball-mill. By adding the second classifier, as shown, it is expected that the tonnage can be increased at least 25 per cent. In order to maintain this feed rate, it will be necessary to maintain carefully the proper ball charge in each mill. A slight increase or decrease in the average size of the balls making up the charge will cause a large loss in efficiency and a corresponding reduction in tonnage.

If balls 3 in. (76.2 mm.) in diameter are fed to the first-stage mills and if all balls less than 2 in. (50.8 mm.) in diameter are removed from the mills regularly, the average size of the balls forming the working charge will be 2.499 in. (63.47 mm.), which is about the size indicated in the tests as giving the best results. The working ball charge in the mill will be as shown in Table 12.

Suppose that once every week the mills are stopped and all balls less than 2 in. in diameter are removed. If the ball wear is 2 lb. per ton of ore crushed, this will amount to 720 lb. (326.5 kg.) per day for each mill. This is actual wear and takes no account of the small balls that are removed. Then, since the working charge is to comprise balls from 3 in. (76.2 mm.) to 2 in. (50.8 mm.) in diameter, the amount of wear secured from each ball will be 2.89 lb. (1.31 kg.) and the 720 lb. of wear per day will be taken care of by the reduction in diameter of 249 balls per day from 3 in. to 2 in. It will then be necessary actually to charge 249 three-inch balls, or 1020 lb. (462.6 kg.) per day.

It is evident that some of the minus 2-in. balls that will be removed after seven days will be smaller than others. It may be computed by methods hereinafter described that the smallest ball will be 1.92 in. (48.7 mm.) in diameter. Then if 249 three-inch balls are charged at the beginning of each day, at the end of each day 249 balls will have been worn to a diameter of less than 2 in. At the end of seven days there will be 1743 balls of diameter between 2 and 1.92 in., which will weigh 1995 lb. (904.9 kg.) and will be removed from the mill. As the operation of each of the first-stage mills will consist in charging 249 three-inch balls each day, the mill charge will gain in weight each day until at the end of seven days it will have gained 1995 lb. and will therefore weigh 29,995 lb. At the end of the seven days, however, the 1995 lb. of balls smaller than 2 in. will be removed, leaving the original 28,000 lb. working charge, as at the beginning of the week.

Since in this flow sheet there are two first-stage mills, there will be formed 3990 lb, (1809.8 kg.) of balls per week of average diameter 1.96 in. (49.7 mm.). These 3990 balls will be used up each week in the daily charges of balls to the second-stage mill. In order to have a balanced condition, it will be necessary to charge these balls at the same rate as that at which they are made, or 498 balls per day. These 498 balls, weighing 571 lb. (259 kg.), will constitute the daily charge to the second-stage mill. This mill is to handle 240 tons of ore per day and the steel consumption at 2 lb. (0.9 kg.) per ton will be 480 lb. (217 kg.) per day. Since 498 balls, weighing 571 lb., are to be added to the mill each day, 498 balls weighing 91 lb. (41 kg.) should be removed each day. These 498 balls will weigh 0.1827 lb. (0.08 kg.) each and will be 1.06 in. (26.9 mm.) in diameter. At regular intervals all balls less than 1 in. in diameter should be removed from the second-stage mill.

If the ball charge in the second-stage mill is screened once a month, there will be 14,940 balls less than 1 in. in diameter to remove. The smallest ball will be 0.85 in. (21.59 mm.) in diameter and the largest ball will be 1 in. The total weight of the balls removed at the end of the month will be 1825 lb. (824.8 kg.). The removal of this weight of small balls will again produce the original charge that is shown in the above screen analysis. Of course, if the ball wear is not 2 lb. per ton, as assumed, these figures will not hold. However, as soon as the correct ball wear is found, it will be possible to determine by this method the exact figures that will make it possible to maintain the proper ball charge and the balance between the different mills at all times. As a result in the design of this fine-crushing plant, provision should be made for sizing the ball charges of the first-stage mills each week and of the second-stage mill each month. It can then be done with a very small amount of lost time.

The chief advantages in this flow sheet are: Good efficiency as to the power expended; large tonnage for the capital invested; and flexibility. By adjusting the overflow end of the classifier in the first stage, the load can be balanced perfectly between the two crushing stages.

In the endeavor to determine the best working conditions for the ball-mill, a detailed mathematical study was made of the action of the ball charge. While the data taken from a properly conducted test are convincing, an engineer sometimes prefers a mathematical proof. Test data contain a large personal factor, not only of manipulation but also of the person reporting the results. In the case of ball-mill crushing the amount of available data is enormous and, by careful selection, nearly any statement can be proved. For this reason, a consideration which is entirely theoretical and devoid of any personal element would seem to be desirable and instructive.

It is evident that the ball inside a revolving mill must act according to some exact regulating force which governs its every motion. There are three important variables to consider: the speed of the mill, its size, and the size of the ball charge, and it will be the aim of this discussion to show the relation existing between these variables.

Any loose charge piled up in a cone will assume a certain definite critical angle, usually called the angle of repose. If more of the charge is added to the top of the cone, this will be increased in size but the same critical angle will be maintained. This is what happens inside a mill revolving at very low speeds. The charge is tilted until the critical angle is reached, after which the balls simply roll down the slope to the lower side of the mill. This critical angle is affected but slightly by a change in the speed of the mill, up to a certain point; the increase in speed simply increases the rapidity with which the charge is raised to the top of the incline. In this condition the balls are in contact with one another except as they may bounce in rolling down the slope of the charge; also, the balls must roll down the incline at the same rate, pounds per hour, at which they are raised to the top. Then, with a mill half full of balls, any particular ball will roll down the incline something less than twice per revolution of the mill.

As the speed of the mill is slowly increased, the time required to bring the ball back to the top of the pile is diminished, but the time required by it in rolling down remains practically the same. It would seem then that the whole problem of crushing would resolve itself into getting the balls to the top of the heap fast enough. This would be true if it were not for centrifugal force and inertia. As the speed of the mill is increased these two forces grow very rapidly in importance.

Consider the forces acting on a particle p, Fig. 3, in contact with the lining of the mill. The centrifugal force c acts to press it against the lining while w1, a component of the weight w, acts to pull it away fromthe lining. Then if 1 is the angle between the vertical axis and the radius op, w1 = w cos 1. It is possible for c to be greater than, equal to, or less than w1 or w cos 1 for as 1 decreases w1 increases. Then c w cos 1 = f1, and f1 may be positive, negative or zero. If f1 is positive the particle will be held against the lining of the mill. As 1 decreases f1 decreases and if, when is zero, f1 is still positive, it is evident that the particle will maintain its contact with the mill lining throughout a complete revolution.

If f1 becomes zero for some value of 1 the particles below p1, having a greater angle , will be held against the lining of the mill by a positive force f. In other words, as the mill rotates, the force with which a particle p is held in position decreases until it reaches zero. At this point the particle is being pushed on by the particles below it and is free to move in a path governed by this initial velocity and gravity. The path it takes will, of course, be parabolic. Then when the angle is such that f is zero, the particle p will leave off contact with the mill and start on a parabolic path. In this position c = w cos .

The centrifugal force c = wv/rg, where w = weight of particle; v = initial velocity; r = radius; and g = 32.2 ft. per sec. per sec. Also the initial velocity of the particle is its velocity in the circular path, or v = 2rn in which n = speed of mill in revolutions per second. Then by substitution in the formula c = w cos ,

From this equation it is evident that an increase in either the speed of the mill or its radius will cause a decrease in the angle and the parabolic path will not start until the particle is carried farther around in the direction of rotation. At any speed n,

in which k = 1.226n. Then at constant speed, the particle p nearer the center of the circle than p1 will start on its parabolic path from a larger angle , or as r decreases increases, the relation between r and given in equation (2) always holding true when is the angle at which the parabolic path starts. Equation (2), then, is really the equation of the curve above which all particles are following the parabolic path and below which all particles are following the circular path.

From equation (1) n = g cos /4r and if the radius is considered as the constant, must decrease as n increases. Since the minimum value of is zero, when cos = 1, the speed has reached a point above which c is always greater than w cos (Fig. 3), and the particle will cling to the lining of the mill throughout the complete cycle. Then the speed at which any particle of radius r will cling is given by the equation n =g/4r in which n is in revolutions per second and r is in feet. If the speed is in revolutions per minute the equation will become

This equation shows the critical speed N at which the particle of radius r will cling to the lining of the mill or to the next outer layer of particles of radius greater than r. If N is sufficiently large, r will be sufficiently small to include all of the balls in the mill and the mill will rotate as a flywheel with no relative motion between the particles in the charge. Table 14 shows the speed at which the first particle will cling to the lining of the mill.

Below the critical speed given in equation (3), the particle of radius r will reach the critical angle a and will then start on its parabolic path. The next consideration is to determine where the particle p1 will strike the lining of the mill at the end of its parabolic path.

The simultaneous solution of these two equations will give the co-ordinates of the point d, where the two curves intersect. Substituting the value of y from the equation of the parabola in the equation of the circle and then simplifying, the following equations are secured:

These are the coordinates of the point d, at which the particle p1 will strike at the end of its parabolic path. From the above solution, it is seen that there are, in general, four points of intersection between the two curves. In this case, however, only one of these intersections requires consideration, the other three being zero. This is a very important fact, for if this condition did not exist the paths of travel of the various particles would cross and recross one another, resulting in a large friction loss above the pulp level in the mill and the performance of little or no crushing.

It is now possible to draw the outline of the charge in the mill under operating conditions. Consider an 8-ft. mill running at 24 r.p.m. From equation (2) cos = 1.226 x 24 x r/3600 = 0.1962r, which is the equation of a circle of radius 0.408/n. The center is then vertical axis 0.408/n units above the center of the mill. From this the value of in Table. 15 can be computed:

From the values of r and a, the curve aO, Fig. 5, can be drawn, which is the dividing line between the parabolic path and the circular path of the particles. Then by use of equations (4) and (5) it is possible to find any number of points on the curve cd. This may be done more simply by drawing the circle through the point e and then measuring a distance z to a vertical line which will intersect the circle at the desired point f as in Fig. 5. For this purpose, the corresponding values of x are added to the preceding table.

It is then possible to draw the line Od, which is the dividing line between the parabolic path and the circular path for all particles of the charge. The complete cycle of any particle p is then seen to be from e to f along the parabolic path, and then from f to e along the circular path. From Fig. 5 it is evident that the particle p acts exactly as though it were in a mill of radius r, the lining of which is the layer of particles of radius next larger than r.

From Fig. 5 it is evident that when a has increased beyond a certain large value, the parabolic paths of the balls near the center of the mill will overlap, thus causing interference. The balls will then be striking together at a point so near the maximum pulp level that little or no effective crushing can be done. It is thus obvious that the size of the charge should be so regulated that this interference shall not occur. It appears from Fig. 5 that this limiting condition occurs when x is a minimum, or is equal to its largest negative value.

Then since x = 4r sin a cos a r sin a, or eliminating r by use of the equation, r = g/4n cos a, x = g/n (sin a cos a sin a cos a). dx = g/n(cos4 a 3 sin a cos a cos a + sin a). For maximum and minimum values of x, dx = 0. Thus 4 cos4 a 7/2 cos2 a + = 0; whence cos a = 0.8925 and 0.2801, and a = 2649 and 7344 (7)

The larger result is obviously the one desired, the smaller one being the value that makes x a maximum. From this it appears that the largest charge that can be used in the mill without definite interference between the particles is when angle a2 = 7344 and 2 = 13112. If the inner radius of the charge, corresponding to a2 = 7344, is r2, then cos 7344 = 1.226nr2 or r2 = 0.2283/n which is the smallest value that r2 should have at any speed.

In order to determine at what angle a the maximum effective blow will be delivered by the particle when it strikes the surface of the mill, it is necessary to find the resultant velocity of the particle relative to the lining of the mill. Fig. 6 shows the resultant velocities and their components.

Vp = velocity of point on parabola; Vc = velocity of point on mill; Vt = component of Vp in direction of Ve, with mill stationary; Vm = component of VP in direction of Vc, with mill revolving; Vr = component of Vp perpendicular to Vc; = angle between Vc and VP; Vt = velocity that produces blow; or the velocity of particle relative to lining of mill.

It has been shown that the initial velocity of any particle when it started on its parabolic path is given by the equation V = rg cos a. This is the velocity in the circular path of a particle of radius r. The velocity of any point on the parabola is given by the equation

In order to determine the angle it is necessary to find the angle at which the circle and parabola intersect. This is done by computing the slopes of the tangents to both curves at this point and then the angle between these tangents. As the slope of the tangent is the first derivative of the equation of the curve, the slope of the tangent to the circle is

Thus when a = 5444 the balls are striking with maximum velocity relative to the circular path in which they travel. Since the whole charge, near ao, may be considered as being concentrated at the radius of gyration, it would seem that the most effective conditions would be obtained by placing r (equation 9) equal to the radius of gyration of the charge. Since the radius of gyration is equal to r1 + r2/2 when r1 is the radius of the mill and r2 is the inner radius of the charge, then

The value of K given by this equation is the relation between r1 and r2 which should exist for best operating conditions and is really the measure of the quantity of the charge. This equation then gives the proper relation between the size of the charge, the size of the mill and its speed. It is the fundamental equation of the ball-mill and shows the relations mentioned on page 264.

Equations (12) to (16) all depend on the value of K, which is the real measure of the quantity of the charge. It is now necessary to get a better idea of the exact relation between K and the volume of the charge. In order to do this the cycle of the charge must be known.

This means that when the mill is running at the proper speed for the ball charge, then the charge is passing through 1.444 cycles per revolution, and each ball in the charge strikes, on the average, 1.444 blows per revolution.

Equation (18) states that the balls spend 56.65 per cent, of the time in the circular path. Then it is apparent that 56.65 per cent, of the total charge is always in the circular path. In other words, the volume of the charge between r1 and r2 (Fig. 5) is only 56.65 per cent, of the total charge, the remaining 43.35 per cent, being spread out over the rest of the mill and following the parabolic path.

The exact analytical determination of the variation in the volume of the total charge as K varies is very complicated and will not be gone into here. A very close approximation can be made, however, by use of the equation,

in which P is the fractional part of the entire volume of the mill that is occupied by the charge when the mill is stationary. It should be noted that the charge will contain a considerable proportion of voids. These are, of course, included in the space occupied by the charge.

From equation (8) it appears that Vb = 16kgr 32kgr4 + 16k5gr6, but the kinetic energy e = wv/2g, or in this case, e = w(8kr 16k3r4 + 8k5r6), which is the energy possessed by any particle of weight w, and radius r, at the end of its parabolic path, which is available for the purpose of crushing ore. Then the total energy possessed by the particles of radius between r1 and r2 is expressed by the equation,

In this equation, if W is the entire weight of the charge, then E represents the foot-pounds of energy delivered each time the charge passes through one cycle. Then since there are 1.444 cycles per revolution, and n = 0.8158/r1 41 + k rev. per sec., the number of foot-pounds per second is represented by the equation,

This formula gives the power output and therefore input to the mill when the weight of the charge is W, in pounds, the radius of the mill is r1, in feet, and the value of K and the speed N are as given by formulas (20) and (13). In other words, formula (22) gives the power required to operate the mill at the most efficient speed for any ball charge. In Table 16 the horsepower required has been computed for certain operating conditions: Any table or set of curves covering all conditions would be too large and complicated to include in this paper; the formulas may, however, be applied to any particular condition.

The actual application of the formulas to a definite problem may be instructive. Consider an 8 by 6-ft. cylindrical mill charged with 28,000 lb. (12,700 kg.) of steel balls. If the balls are made of steel weighing 500 lb. per cu. ft., and are all of one size, it may be shown that the charge will weigh 74.05 per cent, of 500 lb., or 370.25 lb. per cu. ft. The charge will then occupy 28,000 370.25 = 75.6 cu. ft. (2.14 cu. m.) of space in the mill. The factor 75.05 per cent, is derived on the assumption that the spheres are equal; in the case of a mill, the space being limited and the balls not of one size, 65 per cent, is probably more nearly correct. Using this factor, the charge would weigh 325 lb. per cu. ft., and would therefore occupy 86 cu. ft. (2.23 cu. m.). The volume of an 8 by 6-ft. mill is 301 cu. ft. (8.5 cu. m.), hence the charge occupies 28.6 per cent, of the total volume. From formula (20), when the charge occupies 28.6 per cent, of the volume of the mill, the factor K is 0.770. The speed of the mill, by formula (13), is 21.75 r.p.m., and the power, by formula (22), is 181.5 hp. Angle a will then be given by formula (15):

From these results and formula (2), which gives other values of r for various values of a, it is possible to plot the outline of the charge, as is shown in Fig. 7. The particular path of any ball can be plotted by use of equation (3a).

r = radius to any particle p. r1 = radius of mill. r2 = inner radius of charge. R = radius of gyration of charge near ao. a = angle from vertical to r. a1 = angle from vertical to r1 a2 = angle from vertical to r2. ar = angle from vertical to R. = angle from horizontal to r. 1 = angle from horizontal to r1. 2 = angle from horizontal to r2. n = speed of mill in rev. per sec. N = speed of mill in rev. per min. N1 = critical speed of mill in rev. per min. Vb = relative velocity of particle at od, ft. per sec. w = weight of portion of charge, lb. W = weight of entire charge, lb. P = fraction of mill volume occupied by charge. g = a constant = 32.2 ft. per sec. per sec. k = a constant = 4n/g = 1.226n. K = a constant = r2/r1 H = height of charge in mill at rest. E = kinetic energy, foot-pounds. Cn = cycles per revolution. re = radius of circle oa.

By use of these equations, with any given set of conditions, it is possible to determine the geometrical shape of the charge in the mill, the horsepower absorbed by it, the velocity of the blow struck by any ball, and the number of blows struck by any ball. The equations show also the relation that should exist between speed, diameter of mill and size of charge in order to secure the maximum theoretical efficiency.

In order to observe how closely theory and practice agree, a small model mill 3 in. (76.2 mm.) in diameter and 2 in. (50.8 mm.) long was made, having a bearing at only one end so that the other could be closed by a piece of glass through which the action of the charge could be observed. The method of comparison consisted in introducing a weighed charge of fine sand, computing the best operating speed, and drawing the outline of the charge according to the preceding theory. The mill was then operated at this speed, and photographed. The comparison between the photograph and the drawing shows how closely theory and practice agree. No accurate data as to the power required could be secured on this small model. A number of these photographs and the corresponding drawings are shown.

The similarity between the photograph of the mill in actual operation and the theoretical drawing is very striking, especially when, the mill contains a large charge. When the charge is small, the difference appears greater; this is because all interference between the particles causes them to fall into the open space near the center of the mill. The photographs could not be made to show clearly the fact that these particles were accidental; it is apparent, however, when actually watching the mill run, that the particles in the central space are only occasional, as compared with the outer band. While the results of interference are more evident in the small charge than in the large one, the actual amount of interference is greater in the large charge than in the small. This is evident when the cause of this interference is considered.

The curve a-b (Fig. 5) shows the boundary line between the circular and the parabolic paths. Each particle, as it passes the line a-b, starts on its parabolic path in a direction perpendicular to the radius of the

mill through that point. It is evident that the perpendicular to the radius at p would intersect the perpendicular to the radius at a if it were produced far enough. If the two particles considered are closer together than a and p on the curve a-b, the intersection between the lines of initial direction are closer to the points considered. If the two points are adjacent on the curve a-b, it is apparent that the intersection will be

very close to the points and will, in fact, take the form of a slight crowding action between the particles. The result of this will be a slight deformation of the curve through which the particle travels. This will be just as prominent in a small charge as in a large one, although the results will be more apparent in the small charge.

It may also be shown that when the size of the charge exceeds 0.4 the volume of the mill, there will be a tendency for the particles near the center of the mass to crowd one another. This is, however, not at all serious and could probably never be detected in operation, but as previously stated, when the mill is filled beyond 0.64 of its volume, the interference becomes quite important and the mill probably could not be made to operate efficiently when more than 0.6 full.

It appears from the photographs that there is a certain amount of movement between the particles at the end of the parabolic path which causes the actual parabolic path to end sooner than the theoretical path. This motion between the particles is due to the fact that each particle must change its direction of travel and move at about right angles to its original path. This change in direction requires time and reacting forces; if the force is small the time will be long and the agitation great. If the force is large the time will be small and the agitation small. Therefore, when the mill speed is low, this zone of agitation is wide, as shown in Fig. 14. In this agitation zone grinding is done by attrition, but above it, the crushing is done by impact.

While these photographs and drawings were made to illustrate the action of the particles in the charge of a 3-in. mill, they also show the action in mills of any size when operated at the most efficient speed, as given by formula (13). In Table 17, the speeds have been computed for various sizes of mills and charges. In each case, the illustration that shows the position of the charge for the particular operating condition is indicated

In Figs. 14, 15, 16 and 17, the effects of high and low speeds are shown. In all of these photographs the mill was 0.4 full, the operation at the proper speed being shown in Fig. 11. Table 18 shows the speed at which the charge in mills of various diameters would appear as illustrated.

In this whole discussion, only the force of gravity and centrifugal force have been considered. In a mill containing water and ore as well as balls, the force of adhesion is to be considered. This force not only tends to hold the balls and ore together but also tends to hold them against the lining of the mill. Just how important this force may be under ordinary operating conditions is hard to say. It was shown, however, in the little model mill, that adhesion tended to hold the particles together in their parabolic paths and almost entirely eliminated the accidental particles that fall near the center of the mass. It is impossible to apply the results secured in a small mill to a large mill in this respect, however, as adhesion varies inversely with the size of the particles considered.

Adhesion also varies with the moisture, so the mill operator has a convenient means of controlling this force so as to produce the best results. The amount of moisture in the pulp for best efficiency will vary with the nature of the ore, the nature of the ball charge, and the nature of the mill. With a mill charge of large steel balls, adhesion will not affect the operating conditions to any considerable extent unless the pulp is made very thick. The tendency would then be for the balls to stick to the lining and revolve with it.

It is very important to prevent slipping between the charge and the lining of the mill; the tendency to slip is much smaller with large charges than with small ones. If the friction between the charge and the lining of the mill is not great enough to carry the particles up to the curve a-b, the efficiency of the mill will be very greatly reduced and the lining of the mill will be rapidly worn away. Flat sides will also appear on the balls and the cycle of the charge will be slow and irregular. In an open-trunnion discharge mill, the pulp will not flow from the mill regularly but will come in pulsations. Lifters or roughened liners are therefore desirable, as they insure a greater coefficient of friction.

A. L. Blomfield, Colorado Springs, Colo, (written discussion). I congratulate the author on bringing out a paper of real service to the profession. His contention of uniform size in balls is borne out by my own experience; in coarse crushing at the Golden Cycle in 6 by 6-ft. (1.8 by 1.8-m.) ball-mills we unquestionably gain by screening out the small balls once or twice a month. The point of gaging the ball size to be used by the uniformity of screen sizing is of particular interest.

The necessity of sufficient return feed from classifier to the ball-mill is sound and clearly shown. In connection with this, I wish two further points had been gone into as thoroughly: (1) The effect of the quality of classification. In general, it is true that the smaller the per cent, of undersize in the feed the more effective is the mills work. This is true on a bucking board, in tube-mills, ball-mills, and grinding pans. Given the possibility of returning a full-feed load to any mill, it has been my experience that the effective work in the grinder is almost proportional to the quality of the return feed. (2) Again speaking generally, the shorter the tube-mill the greater is the quantity of return feed necessary to keep it loaded. The classification thus keeps the oversize in the mill more free from finished product and thus the crushing more efficient. It is very easy to overload any long mill with too much return feed. The authors tests were made on an 8-ft. by 22-in. Hardinge. This type is capable of handling very large return feeds. I would like to hear Mr. Davis views on the best length of mill, given the diameter.

Dealing with feeds to fine grinders: At the mill of the Great Fingall Cons. M. Co., in 1906, we found that the 5-ft. grinding pan gave the greatest tonnage in closed circuit, grinding a feed 8+20 mesh to 20 mesh when the feed was slightly over twice the effective work done, and that the effective work was almost directly proportional to the efficiency of classification.

I note the large number of classifiers in his flow sheet and agree that it is clearly demonstrated that sufficient classifier capacity should be installed, as they cost very little to run. Two 6-ft. classifiers to the ball-mill could probably be replaced by one 12-ft. quadruplex machine, though possibly the only gain would be a saving in first cost.

H. A. White, P. O. Dersley, Transvaal (written discussion). The fact that the author makes no reference to the work of others on the same subject, I think, must be attributed to the neglect of the usual distinction between ball and tube mills, which is founded upon the presence of special lifting devices in the ball mill. The paper really deals with tube-mill theory, upon which quite a lot of work has been done. The most accessible reference will probably be Richards Ore Dressing, (Vol. III, p. 1336), but I will specially refer to my own papers in the Journal of the Chemical, Metallurgical & Mining Society of South Africa (Vol. V, p. 290 and Vol. XV, p. 176), where very much the same ground is covered.

It may be interesting to compare the results obtained by an independent handling of the same problem. The critical speed obtained is very, slightly different owing to the value of g, which, of course, is not everywhere the same, author has omitted to note the fact that his diameter of mill must be reduced by the average diameter of balls used in order to make the theoretical particle correspond with the actual balls and, of course, only the inside diameter of the lined tube is meant.

The directions for drawing the parabolic curve of flight might be very much simplified by using the relation between the angle of impact and the angle of departure, which I discovered in 1905 and the author has proved on p. 269. The author notes that the locus of points of departure is a semicircle but does not observe that the locus of points of impact is a trisectrix. The maximum of x, when only one layer of balls is considered (the outside layer), is obviously r and the angle of departure is 30 from the vertical.

In order to calculate the maximum value of the blow struck, the author uses the second order effects beside the principal one due to the height of fall of the balls from the vertex of the parabola. The author thus derives a value of 0.5775 for cos a, this value is identical with that found for the maximum height of fall, as might have been anticipated, but the derivation of the latter is very much simpler. He does not notice that the path in this case is through the center of the mill.

The author deviates from exact methods and uses the idea of center of gyration in place of summation of various layers of balls and no doubt the approximation is sufficiently close if K were independently known; but to ascertain K the assumption is made that the average of the whole charge passes through the same cycle as the particle at the radius of gyration, and as the inner layers have a much shorter cyclic time than the outer and there are also many fewer balls, this assumption is much less accurate. In fact, the authors figure of average number of cycles per revolution (1.444) may vary from more than 1.5 to less than 1.2, in accordance with the speed and loading of the tube. However, if correction is made of tube diameter, as previously mentioned, the final results are not very far out.

Of importance is the question of maximum efficiency to be got out of any tube and the load for that efficiency; but though the author gives the best speed for any load he does not indicate which load and speed give maximum efficiency. A further important question in actual running plants is the maximum capacity that may be gotten out of any tube, and as the efficiency is not widely affected this latter maximum may be the most important. These points may be well illustrated from the Witwatersrand practice with standard tube mills 5 ft. 6 in. by 22 ft. The effective diameter inside linings, allowing 2 in. for pebbles used is put at 59 in. and the speed for maximum efficiency is 27.96 r.p.m. with a load about 45 per cent., while the maximum capacity is attained at 32.2 r.p.m. with a load 3 in. above the center.

These theoretical deductions and some others of interest were confirmed by observation of a working model of 7 ft. diameter, the full account of which will be found in the papers mentioned. I have to thank the author for the exceedingly clear manner in which his paper is arranged and for the able paragraphs on ball wear which should be of great practical use.

All Grinding Mill & Ball Mill Manufacturers understand the object of the grinding process is a mechanical reduction in size of crushable material. Grinding can be undertaken in many ways. The most common way for high capacity industrial purposes is to use a tumbling charge of grinding media in a rotating cylinder or drum. The fragmentation of the material in that charge occurs through pressure, impact, and abrasion.

The choice of mill design depends on the particle size distribution in the feed and in the product wanted. Often the grinding is more economic when executed in a primary step, followed by a secondary step, giving a fine size product.

C=central trunnion discharge P=peripheral discharge R=spherical roller trunnion bearing, feed end H=hydrostatic shoe bearing, feed end R=spherical roller trunnion bearing, discharge end K=ring gear and pinion drive

Type CHRK is designed for primary autogenous grinding, where the large feed opening requires a hydrostatic trunnion shoe bearing. Small and batch grinding mills, with a diameter of 700 mm and more, are available. These mills are of a special design and described on special request by allBall Mill Manufacturers.

The different types of grinding mills are based on the different types of tumbling media that can be used: steel rods (rod mills), steel balls (ball mills), and rock material (autogenous mills, pebble mills).

The grinding charge in a rod mill consists of straight steel rods with an initial diameter of 50-100 mm. The length of the rods is equal to the shell length inside the head linings minus about 150 mm. The rods are fed through the discharge trunnion opening. On bigger mills, which need heavy rods, the rod charging is made with a pneumatic or manual operated rod charging device. The mill must be stopped every day or every second day for a few minutes in order to add new rods and at the same time pick out broken rod pieces.

As the heavy rod charge transmits a considerable force to each rod, a rod mill can not be built too big. A shell length above 6100 mm can not be recommended. As the length to diameter ratio of the mill should be in the range of 1,2-1,5, the biggest rod mill will convert maximum 1500 kW.

Rod mills are used for primary grinding of materials with a top size of 20-30 mm (somewhat higher for soft materials). The production of fines is low and consequently a rod mill is the right machine when a steep particle size distribution curve is desired. A product with 80% minus 500 microns can be obtained in an economical manner.

The grinding charge in a ball mill consist of cast or forged steel balls. These balls are fed together with the feed and consequently ball mills can be in operation for months without stopping. The ball size is often in the diameter range of 20-75 mm.

The biggest size is chosen when the mill is used as a primary grinding mill. For fine grinding of e.g. sands, balls can be replaced by cylpebs, which are heat treated steel cylinders with a diameter of 12-40 mm and with the same length as the diameter.

Ball mills are often used as secondary grinding mills and for regrinding of middlings in concentrators. Ball mills can be of the overflow or of the grate discharge type. Overflow discharge mills are used when a product with high specific surface is wanted, without any respect to the particle size distribution curve. Overflow discharge mills give a final product in an open circuit. Grate discharge mills are used when the grinding energy shall be concentrated to the coarse particles without production of slimes. In order to get a steep particle size distribution curve, the mill is used in closed circuit with some kind of classifier and the coarse particles known as classifier underflow are recycled. Furthermore, it should be observed that a grate discharge ball mill converts about 20% more energy than an overflow discharge mill with the same shell dimensions.

Ball mill shells are often furnished with two manholes. Ball mills with small balls or cylpebs can produce the finest product of all tumbling mills. 80% minus 74 microns is a normal requirement from the concentrators.The CRRK series of wet grinding ball mills are tabulatedbelow.

No steel grinding media is used in a fully autogenous mill. When choosing primary autogenous grinding, run of mine ore up to 200-300 mm in size is fed to the mill. When using a crushing step before the grinding, the crusher setting should be 150-200 mm. The feed trunnion opening must be large enough to avoid plugging. The biggest pieces in the mill are important for the size reduction of middle size pieces, which in their turn are important for the finer grinding. Thus the tendency of the material to be reduced in size by pressure, impact, and abrasion is a very important question when primary autogenous grinding is proposed.

When autogenous grinding is used in the second grinding step, the grinding media is size-controlled and often in the range of 30-70 mm. This size is called pebbles and screened out in the crushing station and fed to the mill in controlled proportion to the mill power. The pebble weight is 5-25% of the total feed to the plant, depending on the strength of the pebbles. Sometimes waste rock of high strength is used as pebbles.

Pebble mills should always be of the grate discharge type. The energy that can be converted in a mill depends on the total weight of the grinding charge. Consequently, pebble mills convert less power per mill volume unit than rod and ball mills.

High quality steel rods and balls are a considerable part of the operating costs. Autogenous grinding should, therefore, be considered and tested when a new plant shall be designed. As a grinding mill is built to last for decades, it is more important to watch the operation costs than the price of the mill installation. The CRRK series of wet grinding pebble mills are tabulated below.

Wet grinding is definitely the most usual method of grinding minerals as it incorporates many advantages compared to dry grinding. A requirement is, however, that water is available and that waste water, that can not be recirculated, can be removed from the plant without any environmental problems. Generally, the choice depends on whether the following processing is wet or dry.

When grinding to a certain specific surface area, wet grinding has a lower power demand than dry grinding. On the other hand, the wear of mill lining and grinding media is lower in dry grinding. Thus dry grinding can be less costly.

The feed to a dry grinding system must be dried if the moisture content is high. A ball mill is more sensitive to clogging than a rod mill. An air stream through the mill can reduce the moisture content and thus make a dry grinding possible in certain applications.

Due to the hindering effect that the ball charge gives to the material flow in dry grinding, the ball charge is not more than 28-35% of the mill volume. This should be compared with 40-45% in wet grinding. The expression used for this phenomenon is that the charge in a dry grinding mill is swollen.

Big dry grinding ball mills are often two-compartment mills, with big balls in the first compartment and small balls or cylpebs in the second one. An extra grate wall is used to separate the two charges.

The efficiency of wet grinding is affected by the percentage of solids. If the pulp is too thick, the grinding media becomes covered by too thick a layer of material, which hinders grinding. The opposite effect may be obtained if the dilution is too high, and this may also reduce the grinding efficiency. A high degree of dilution may sometimes be desirable in order to suppress excessive slime formation.

The specific power required for a certain grinding operation, usually expressed in kWh/ton, is a function of both the increase in the specific surface of the material (expressed in cm/cm or cm/g) and of the grinding resistance of the material. This can be expressed by the formula

where c is a material constant representing the grinding resistance, and So and S are the specific surfaces of the material before and after the grinding operation respectively. The formula is an expression of Rittingers Law which is shown by tests to be reasonably accurate up to a specific surface of 10,000 cm/cm.

When the grinding resistance c has been determined by trial grinding to laboratory scale, the net power E required for each grinding stage desired may be determined by the formula, at least as long as Rittingers Law is valid. If grinding is to be carried out not to a certain specific surface S but to a certain particle size k, the correlation between S and k must be determined. The particle size is often expressed in terms of particle size at e.g. 95, 90 or 80% quantity passing and is denoted k95, k90 or k80.

where E =the specific power consumption expressed in kWh/short ton. Eo = a proportionality and work factor called work index k80p = particle size of the product at 80% passage (micron) k80f =the corresponding value for the raw material (micron)

The value of Eo is a function of the physical properties of the raw material, the screen analyses of the product and raw material respectively, and the size of the mill. The value for easily-ground materials is around 7, while for materials that have a high grinding resistance the value is around 17.

Eo is correlated to a certain reduction ratio, mill diameter etc. Corrections must be made for each case. The simplest method of calculating the specific power consumption is test grinding in a laboratory mill, and comparison of the results with a known reference material. The sample is ground in batches for 3, 6,12 minutes, a screen analysis is carried out after each period, after which the specific surface is determined. A good estimate of the grinding characteristics of the sample can be obtained by comparison of the specific surfaces with corresponding values for the reference material.

When the net power required has been determined, an allowance is made for mechanical losses. The gross power requirement thus arrived at, should with a satisfactory margin be utilised by the mill selected.

The critical speed of a rotating mill is the RPM at which a grinding medium will begin to centrifuge, namely will start rotating with the mill and therefore cease to carry out useful work. This will occur at an RPM of ncr, which may be determined by the formula

where D is the inside diameter in meters of the mill. Mills are driven in practice at a speed corresponding to 60-80% of the critical speed, the choice of speed being influenced by economical considerations. Within that range the power is nearly proportional to the speed.

The charge volume in the case of rod and ball mills is a measure of the proportion of the mill body that is filled by rods or balls. When the mill is stationary, raw material and liquid should fill the voids between the grinding media, in order that these should be fully utilized.

Maximum mill efficiency is reached at a charge volume of approximately 55%, but for a number of reasons 45-50% is seldom exceeded. The efficiency curve is in any case quite flat about the maximum. In overflow mills the charge volume is usually 40%, while there is a greater choice in the case of grate discharge mills.

For coarse grinding in rod mills, the rods used have a diameter of 50-100 mm and their lengths are approx. 150 mm below the effective inside shell length. Rods will break when they have been worn down to about 20 mm and broken rods must from time to time be taken out of the mill since otherwise they will reduce the mill capacity and may cause blockage through piling up. The first rod charge should also contain a number of rods of smaller diameter.

It may be necessary to charge the mill with rods of smaller diameter when fine grinding is to be carried out in a rod mill. Experience shows that the size of the grinding media should bear a definite relationship to the size of both the raw material and the finished product in order that optimum grinding may be achieved. The largest grinding media must be able to crush and grind the largest pieces of rock, while on the other hand the grinding media should be as small as possible since the total active surface increases in inverse proportion to the diameter.

A crushed mineral whose largest particles pass a screen with 25 x 25 mm apertures shall be ground to approx. 95% passing 0.1 mm in a 2.9 x 3.2 m ball mill of 35 ton charge weight. In accordance with Olewskis formula

Grinding media wear away because of the attrition they are subjected to in the course of the grinding operation, and in addition a continuous reduction in weight takes place owing to corrosion. The rate of wear will in the first place depend on the abrasive properties of the mineral being ground and naturally also on the hardness of the grinding media themselves.

The wear of rods and balls is usually quoted in grammes per ton of material processed (dry weight) and normal values may lie between 100 and 1500 g/ton. Considerably higher wear figures may however be experienced in fine wet grinding of e.g. very hard siliceous sand.

A somewhat more accurate way of expressing wear is to state the amount of gross kWh of grinding power required to consume 1 kg of grinding media. A normal value in wet grinding is 15 kWh/kg.The wear figures in dry grinding are only 10-30 % of the above.

where c is a constant which, inter alia, takes into consideration the mean slope a of the charge, W is the weight in kp of the charge n is the RPM Rg is the distance in metres of the centre of gravity from the mill centre

W for rod and ball mills shall be taken as the weight of the rod or ball charge, i.e. the weight of the pulp is to be ignored. For pebble mills therefore W is to be calculated on the basis of the bulk weight of the pebbles.

It should be pointed out that factor c in the formula is a function of both the shape of the inner lining (lifter height etc.) and the RPM. The formula is however valid with sufficient accuracy for normal speeds and types of lining.

The diagram gives the values of the quantity Rg/d as a function of the charge volume, the assumption being that the charge has a plane surface and is homogeneous, d is the inside diameter of the mill in metres. The variation of the quantity a/d, where a is the distance between the surface of the charge and the mill centre, is also shown in the same figure.

In order to keep manufacturing costs at a minimum level, Morgardshammar has a series of standard mill diameters up to and including 6.5 m. Shell length, however, can be varied and tailor made for each application. The sizes selected are shown on the tables on page 12-13 and cover the power range of 200-5000 kW.

Shells with a diameter of up to about 4 m are made in one piece. Above this dimension, the shell is divided into a number of identical pieces, bolted together at site, in order to facilitate the transport. The shell is rolled and welded from steel plate and is fitted with welded flanges of the same material. The flanges are machined in order to provide them with locating surfaces fitting into the respective heads. The shells of ball and pebble mills are provided with 2 manholes with closely fitting covers. The shells have drilled holes for different types of linings.

Heads with a diameter of up to about 4 m are integral cast with the trunnion in one piece. Above this diameter the trunnion is made as a separate part bolted to the head. The head can then be divided in 2 or 4 pieces for easy transport and the pieces are bolted together at site. The material is cast steel or nodular iron. The heads and the trunnions have drilled holes for the lining.

Spherical roller (antifriction) bearings are normally used. They offer the most modern and reliable technology and have been used for many years. They are delivered with housings in a new design with ample labyrinth seals.

For very large trunnions or heavy mills, i.e. for primary autogenous grinding mills. Morgardshammar uses hydrostatic shoe bearings. They have many of the same advantages as roller bearings. They work with circulating oil under pressure.

The spherical roller bearing and the hydrostatic shoe bearing take a very limited axial space compared to a conventional sleeve bearing. This means that the lever of the bearing load is short. Furthermore, the bending moment on the head is small and as a result of this, the stress and deformation of the head are reduced. Ask Morgardshammar for special literature on trunnion bearings.

Ring gears are often supplied with spur gears. They are always split in 2 or 4 pieces in order to facilitate the assembly. Furthermore, they are symmetrical and can be turned round in order to make use of both tooth flanks. The material is cast steel or nodular iron. They are designed in accordance with AGMA.The ring gear may be mounted on either the feed or the discharge head. It is fitted with a welded plate guard.

The pinion and the counter shaft are integral forged and heat treated of high quality steel. For mill power exceeding about 2500 kW two pinions are used, one on each side of the mill (double-drive). The pinion is supported on two spherical roller bearings.

The trunnion bearings are lubricated by means of a small motor- driven grease lubricator. The gear ring is lubricated through a spray lubricating system, connected to the electric and pneumatic lines. The spray nozzles are mounted on a panel on the gear ring guard.

In order to protect the parts of the mill that come into contact with the material being ground, a replaceable lining of wear-resistant material is fitted. This may take the form of unalloyed or alloyed rolled or cast steel, heat treated if required, or rubber of the appropriate wear resistant quality. White cast iron, unalloyed or alloyed with nickel (Ni-hard), may also be used.

The shape of the mill lining is often of Lorain-type, consisting of plates held in place between lifter bars (or key bars) of suitable height bolted on to the shell. This system is used i.e. of all well-known manufacturers of rubber linings. Ball mills and autogenous mills with metal lining also can be provided with single or double waved plates without lifter bars.

In grate discharge mills the grate and the discharge lifters are a part of the lining. The grate plates with tapered slots or holes are of metal or rubber design. The discharge lifters are fabricated steel with thick rubber coating. Rubber layer for metal linings and heavy corner pieces of rubber are included in a Morgardshammar delivery as well as attaching bolts, washers, seal rings, and self-locking nuts. A Morgardshammar overflow mill can be converted into a grate discharge mill only by changing some liner parts and without any change of the mill. Trunnion liners are rubber coated fabricated steel or cast steel. In grate discharge mills the center cone and the trunnion liner form one piece.

Scoop feeders in combination with drum feeders are used when retaining oversize from a spiral or rake classifier. As hydrocyclones are used in most closed grinding circuits the spout feeders are used most frequently.

Vibrating feeders or screw feeders are used when charging feed to dry grinding mills. Trommel screens are used to protect slurry pumps and other transport equipment from tramp iron. Screens can have perforated rubber sheets or wire mesh. The trommel screens are bolted to the discharge trunnion lining.

Inching units for slow rotation of the mills are also furnished. Rods to the rod mills are charged by means of manual or automatic rod charges. Erection cradles on hydraulic jacks are used when erecting medium or big size mills at site.

A symbol of dependable quality ore milling machinery manufacturing, industrial and mining equipment, ball mills and rod mills as well as supplies created for your specific needs. During this period thousands of operators have experienced continuous economical and unequalled service through their use.As anindustrial ball mill manufacturer and supplier, we havecontinuously accumulated knowledge on grinding applications. It has contributed greatly to the grinding process through the development and improvement of such equipment.

Just what is grinding? It is the reduction of lump solid materials to smaller particles by the application of shearing forces, pressure, attrition, impact and abrasion. The primary consideration, then, has been to develop some mechanical means for applying these forces. The modern grinding mill applies power to rotate the mill shell and thus transmits energy to some form of media which, in turn, fractures individual particles.

Through constant and extensive research, in the field of grinding as well as in the field of manufacturing. Constantly changing conditions provide a challenge for the future. Meeting this challenge keeps our company young and progressive. This progressive spirit, with the knowledge gained through the years, assures top quality equipment for the users of our mills.

You are urged to study the following pages which present a detailed picture of our facilities and discuss the technical aspects of grinding. You will find this data helpful when considering the selection of the grinding equipment.

It is quite understandable that wetakes pride in the quality of our mills.Complementing the human craftsmanship built into these mills, our plants are equipped with modern machines of advanced design which permit accurate manufacturing of each constituent part. Competent supervision encourages close inspection of each mill both as to quality and proper fabrication. Each mill produced is assured of meeting the high required standards. New and higher speed machines have replaced former pieces of equipment to provide up-to-date procedures. The use of high speed cutting and drilling tools has stepped up production, thereby reducing costs and permitting us to add other refinements and pass these savings on to you, the consumer.

Each foundry heat is checked metallurgically prior to pouring. All first castings of any new design are carefully examined by the use of an X-ray machine to be certain of uniformity of structure. The X -ray is also used to check welding work, mill heads, and other castings.

Each Mills, regardless of size, is designed to meet the specific grinding conditions under which it will be used. The speed of the mill type of liner, discharge arrangement, size of feeder, size of bearings, mill diameter and length, and other factors are all considered to take care of the size of feed, tonnage, circulating sand load, selection of balls or rods, and the final size of grind.

All Mills are built with jigs and templates so that any part may be duplicated. A full set of detailed drawings is made for each mill and its parts. This record is kept up to date during the life of the mill. This assures accurate duplication for the replacement of wearing parts during the future years.

As a part of our service our staff includes experienced engineers, trained in the field of metallurgy with special emphasis on grinding work. This knowledge, as well as a background gained from intimate contact with various operating companies throughout the world, provides a sound basis for consultation on your grinding problems. We take pride in manufacturing rod mills and ball millsfor the metallurgical, rock products, cement, process, and chemical industries.

As an additional service we offer our testing laboratories to check your material for grindability. Since all grinding problems are different some basis must be established for recommending the size and type of grinding equipment required. Experience plays a great part in this phase however, to establish more direct relationships it is often essential to conduct individual grindability tests on the specific material involved. To do this we have established certain definite procedures of laboratory grinding work to correlate data obtained on any new specific material for comparison against certain standards. Such standards have been established from conducting similar work on material which is actually being ground in Mills throughout the world. The correlation between the results we obtain in our laboratory against these standards, coupled with the broad experience and our companys background, insures the proper selection and recommendation of the required grinding equipment.

When selecting a grinding mill there are many factors to be taken into consideration. First let us consider just what constitutes a grinding mill. Essentially it is a revolving, cylindrical shaded machine, the internal volume of which is approximately one-half filled with some form of grinding media such as steel balls, rods or non-ferrous pebbles.

Feed may be classified as hard, average or soft. It may be tough, brittle, spongy, or ductile. It may have a high specific gravity or a low specific gravity. The desired product from a mill may range in size from a 4 mesh down to 200 mesh, or into the fine micron sizes. For each of these properties a different mill would be indicated.

The Mill has been designed to carry out specific grinding work requirements with emphasis on economic factors. Consideration has been given to minimizing shut-down time and to provide long, dependable trouble-free operation. Wherever wear takes place renewable parts have been designed to provide maximum life. A Mill, given proper care, will last indefinitely.

Mills have been manufactured in a wide variety of sizes ranging from laboratory units to mills 12 in diameter, with any suitable length. Each of these mills, based on the principles of grinding, provides the most economical grinding apparatus.

For a number of years ball mill grinding was the only step in size reduction between crushing and subsequent treatment. Subsequently smaller rod mills have altered this situation, providing in some instances a more economical means of size reduction in the coarser fractions. The principal field of rod mill usage is the preparation of products in the 4-mesh to 35-mesh range. Under some conditions it may be recommended for grinding to about 48 mesh. Within these limits a rod mill is often superior to and more efficient than a ball mill. It is frequently used for such size reduction followed by ball milling to produce a finished fine grind. It makes a product uniform in size with only a minimum amount of tramp oversize.

The basic principle by which grinding is done is reduction by line contact between rods extending the full length of the mill. Such line contact results in selective grinding carried out on the largest particle sizes. As a result of this selective grinding work the inherent tendency is to make size reduction with the minimum production of extreme fines or slimes.

The small rod mill has been found advantageous for use as a fine crusher on damp or sticky materials. Under wet grinding conditions this feed characteristic has no drawback for rod milling whereas under crushing conditions those characteristics do cause difficulty. This asset is of particular importance in the manufacture of sand, brick, or lime where such material is ground and mixed with just sufficient water to dampen, but not to produce a pulp. The rod mill has been extensively used for the reduction of coke breeze in the 8-mesh to 20-mesh size range containing about 10% moisture to be used for sintering ores.

Grinding by use of nearly spherical shaped grinding media is termed ball milling. Strictly speaking, such media are made of steel or iron. When iron contamination is detrimental, porcelain or natural non-metallic materials are used and are referred to as pebbles. When ore particles are used as grinding media this is known as autogenous grinding.

Other shapes of media such as short cylinders, cubes, cones, or irregular shapes have been used for grinding work but today the nearly true spherical shape is predominant and has been found to provide the most economic form.

In contrast to rod milling the grinding action results from point contact rather than line contact. Such point contacts take place between the balls and the shell liners, and between the individual balls themselves. The material at those points of contact is ground to extremely fine sizes. The present day practice in ball milling is generally to reduce material to 35 mesh or finer. Grinding in a ball mill is not selective as it is in a rod mill and as a result more extreme fines and tramp oversize are produced.

Small Ball mills are generally recommended not only for single stage fine grinding but also have wide application in regrind work. The Small Ball millwith its low pulp level is especially adapted to single stage grinding as evidenced by hundreds of installations throughout the world. There are many applications in specialized industrial work for either continuous or batch grinding.

Wet grinding may be considered as the grinding of material in the presence of water or other liquids in sufficient quantity to produce a fluid pulp (generally 60% to 80% solids). Dry grinding on the other hand is carried out where moisture is restricted to a very limited amount (generally less than 5%). Most materials may be ground by use of either method in either ball mills or rod mills. Selection is determined by the condition of feed to the mill and the requirements of the ground product for subsequent treatment. When grinding dry some provision must be made to permit material to flow through the mill. Mills provide this necessary gradient from the point of feeding to point of discharge and thereby expedites flow.

The fineness to which material must be ground is determined by the individual material and the subsequent treatment of that ground material Where actual physical separation of constituent particles is to be realized grinding must be carried to the fineness where the individual components are separated. Some materials are liberated in coarse sizes whereas others are not liberated until extremely fine sizes are reached.

Occasionally a sufficient amount of valuable particles are liberated in coarser sizes to justify separate treatment at that grind. This treatment is usually followed by regrinding for further liberation. Where chemical treatment is involved, the reaction between a solid and a liquid, or a solid and a gas, will generally proceed more rapidly as the particle sizes are reduced. The point of most rapid and economical change would determine the fineness of grind required.

Laboratory examinations and grinding tests on specific materials should be conducted to determine not only the fineness of grind required, but also to indicate the size of commercial equipment to handle any specific problem.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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The batch ball mill is a kind of ball milling machine which discharges the material in one time according to the nature of the material. Different fromcontinuous ball mill, batch type ball mill grinds powder by times and adopts intermittent operation. The batch mill is mainly used for the mixing and grinding of materials, with uniform product fineness and saving power. The grinding time can be adjusted according to the fineness of the grinding material. The batch ball mills can be used for both dry andwet grinding. They are mostly used for fine grinding of feldspar, quartz, ore, clay and other raw materials.

In order to meet the grinding properties of different materials, differentball mill liner typescan be used on the batch type ball mill. Special lining can also reduce the possibility of mixing ferrous metals such as less steel, iron and manganese into raw materials.

The fineness of the grinding operation of the batch ball mill can reach 1000-16000 mesh, and the fineness can be controlled by the grinding time. The motor can be started with auto-decoupling and decompression to reduce the starting current. Its structure is divided into integral type and independent type.

The batch ball mill has the characteristics of less investment, energy saving and electricity saving, novel structure, simple operation, safe operation, stable and reliable performance, etc. It is suitable for mixing and grinding operations of ordinary and special materials. The user can select the appropriate type, liner and medium type according to the material specific gravity, hardness, yield and other factors. Of course, thebatch dry ball millor the batch wet ball mill can also be selected according to the nature of the processed material and its own situation. Please feel free tocontact usfor expert advice.

As a ball mills supplier with 22 years of experience in the grinding industry, we can provide customers with types of ball mill, vertical mill, rod mill and AG/SAG mill for grinding in a variety of industries and materials.

MQ series ball mills are mainly used in grinding operations in mining, cement, refractory, chemical and other industries. According to the discharging method, it is divided into MQG series dry type lattice ball mill, MQS series wet type lattice ball mill, MQY series wet overflow type ball mill, MQZ series peripheral discharge type ball mill; according to the type of liner, it is divided into A series (high manganese steel lining). Plate, magnetic lining) standard type and B series (rubber lining, high aluminum lining, silica lining, ceramic lining) energy-saving type; according to the transmission mode is divided into edge drive ball mill and center drive ball mill.

When Ball Mill is working, raw material enters the mill cylinder through the hollow shaft of the feed. The inside of the cylinder is filled with grinding media of various diameters (steel balls, steel segments, etc.); when the cylinder rotates around the horizontal axis at a certain speed, Under the action of centrifugal force and friction force, the medium and the raw material in the cylinder will drop or roll off the inner wall of the cylinder when the gravity of the cylinder reaches a certain height.

When material particle gravity is greater than centrifugal force, they will be crushed due to the impact force. At the same time, during the operation of the mill, the sliding movement of the grinding media to each other also produces a grinding effect on the raw materials. The rest material is discharged through a discharge hollow shaft. Due to the constant uniform feeding, the pressure causes the material in the cylinder to move from the feed end to the discharge end. During wet grinding, the material is carried away by the water flow; during dry grinding, the material is taken away by the airflow drawn out of the cylinder.

When Ball Mill is running, the raw material enters the mill cylinder through the hollow shaft of the feed. The inside of the cylinder is filled with grinding media of various diameters (steel balls, steel segments, etc.); when the cylinder rotates around the horizontal axis at a certain speed, Under the action of centrifugal force and friction force, raw material in the cylinder will drop or roll off the inner wall of the cylinder when the gravity of the cylinder reaches a certain height. When their own gravity is greater than the centrifugal force, they will be crushed due to the impact force. ore. At the same time, during the operation of the mill, the sliding movement of the grinding media to each other also produces a grinding effect on the raw materials. The ground material is discharged through a discharge hollow shaft. Due to the constant uniform feeding, pressure will causes the material in the cylinder to move from feed end to discharge end. During wet grinding, material is carried away by water flow; during dry grinding, raw material is taken away by the airflow drawn out of cylinder.

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