Nearly every mining and metallurgical engineer will recall his early experience and method of producing step- or stage- reduction in preparing ore-samples for assay, in which he employed idea, step- or stage-reduction simply because it was a self-evident fact that it would be easier to break coarse ore with a hammer than it would be to roll it back and forth under the muller, and after having reduced it to a size easy for a rubbing or bucking division he then placed it under the muller on the bucking-board and further reduced it in proportion to the physical energy he wished to expend, which was generally the minimum to produce results. After this step in our experience we seem to have ceased to consider stage-reduction as mechanically essential, probably because it did not apply to individual exertion. Moreover, we did not retain the mass under the muller until it was all reduced to pass the 80-mesh assay-office screen, but practiced further step-reduction by screening out the fine in order that it should not interfere with subsequent work, replacing the coarse for further reduction on the bucking-board.

It was many years after the bucking-board stage of metallurgical practice that we were brought to a full realization that there was a more economical method in applying the crushing forces usually employed in metallurgical work by taking advantage of this individual experience and applying it to mechanical ends. We have made some advance to this end in bringing out the conical ball-and-pebble mill—a device which fairly well automatically adjusts power to the results obtained, mechanically repeating the bucking-board experience. In the action of the conical mill, theory is evolved from practice, rather than practice from theory, as is commonly the case.

The conical mill, or what is more commonly known as the Hardinge mill, is one of those inventions which, if not fathered by actual necessity, was at least induced by the desire to get better results from the energy expended in operating the older types of pebble-mills in my metallurgical work. The more common use of pebble-mills goes back some 10 or 12 years, while their first commercial introduction will date to about 1895 or 1896; at least, it was about that time that I first came across the cylindrical pebble-mill, and while I was not a theoretical convert upon sight, I soon became a practical or empirical convert upon trying out the device. In studying the action of the old style of cylindrical tube-mill, Fig. 1, I could not reconcile the fact that initial and final energies remained the same throughout the length of mill in spite of previous reduction of size of

particles. The first mills were comparatively short, from 4 to 8 ft. long, then suddenly they were standardized at about 20 ft., probably by the builders of machinery, and the additional fact that they were more commonly used in the grinding of cement, which must be finished in one operation. The final conclusion at which I arrived was that the later practice of using a long tube-mill was wrong. My next construction of a tube-mill reduced it to 8 ft., and still later to 6 ft. At the feed end of the mill a certain energy was applied, which I will designate as a 1 lb. pebble unit, which is necessary to crush a 0.25-in. unit of material. At the outlet end of the mill this same pound-pebble unit was still being employed even though the particle had been reduced to 1/8 to 1/16, to 1/32 in. and so on in the same proportion of mass division, so that the 0.25-in. mass had been successively divided until the original particle was represented by more than 500 particles of 1/32 in., upon which, or, at best, upon several of which, particles there was being used the same 1 lb. energy unit as was employed at the feed end of the mill. This would be equivalent to crushing 1-in. cubes of ore in a rock-crusher designed to reduce a mass containing several hundred 1-in. cubes. The latter would be ridiculed simply because the discrepancy is physically evident, but we go on with the still poorer practice of trying to reduce a 1/500 particle with the same medium used to reduce the original unit mass, simply because we cannot see or feel the energy difference. It is equivalent to the return constantly of the 1-in. cube to the giant crusher in the hope that it may, as it eventually will, ultimately meet with some obstructions and be by chance further reduced. But during all this time energy is being expended in friction of moving parts without material division. On the other hand, it is hardly to be hoped that we can reach beyond mechanical means to obtain a required result, as would be the case if we endeavored accurately to adjust the cause to the effect desired, but we certainly can do better than to continue to employ the pound-pebble unit of energy when a 1-oz. unit will produce better results. This I have endeavored to do in the conical mill, in the different diameters of which are segregated forces proportional to the work to be performed; using the largest pebbles, the greatest peripheral speed, and the greatest gravimetric force upon the coarsest particles, gradually reducing them in the diminishing diameters of the cone, thus gradually diminishing all the forces commensurate, or proportionately commensurate, to the work required in reduction, though retaining the same number of grinding mediums. In other words, lines of force in the Hardinge mill converge at a point where the greatest power is needed and energy recedes in proportion to the force required in reduction, as illustrated in Fig. 2. Kick’s law of power required for dividing particles of matter, although formulated by Kick 50 years ago, is still referred to in textbooks as defining the work performed in division and is as follows:

” The energy required for producing analogous changes of configuration of geometrically similar bodies of equal technological state varies as the volumes or weights of these bodies.”

Apparently the principle in the inanimate machine is nearing that of the animate, and is a survival of the fittest, for it is an inherent mechanical property of the machine which controls the conditions whereby the largest bodies seek and maintain positions of greatest force and exert their power upon the weaker, if the latter are in the path of the larger; and it appears to be a case of the survival of the largest; e.g., in the conical mill the largest pebbles or balls, the greatest superincumbent weights, and the greatest peripheral speeds all segregate towards the greatest diameter of the mill, likewise other sizes seek zones or positions in proportion to mass and weight acting in conjunction with gravity and central forces. The same rule holds

good in regard to the particles undergoing division, as illustrated in Fig. 2, in which it will be noted that the grinding mediums automatically adjust or classify themselves to the work to be performed, embodying a step- or stage-reduction within a single machine through a combination of percussion and attrition. Comparatively, a sledge-hammer is used upon a spike, a nail-hammer upon a nail, and a tack-hammer upon a tack, utilizing the mechanical forces more economically than would be the case in using a sledge-hammer without regard as to whether the blow was to be delivered upon the spike, nail or tack.

The illustration of the segregation of the large and small grinding bodies (Danish pebbles) shown in Fig. 3 is taken from a report of an independent engineer of international reputation in order to verify if possible my claims.

These general results are obtained in other systems of dividing or reducing by multiplying the number of machines; for instance, in rolls it is common practice to pass the successively

reduced material to rolls of different sizes, as illustrated in Fig. 4, although more often the poorer practice is resorted to of returning to the same roll the “ oversizes ” of its previous reduction, which must now depend for further division upon crushing (mashing) in a “ choked feed ”—an energy-wasting method.

The above remarks relative to the conical pebble-mill also apply to the conical ball-mill, which is similar in all respects to the pebble-mill except that instead of using flint lining and pebbles, steel lining and balls are used to do the crushing. The latter is now coming into use in the place of stamps as a more economical device. The stamp to-day is gradually receding from its former prestige owing to its being neither an economical fine or coarse crusher, as the term is now understood. A few years ago 30-mesh was considered fine crushing, but it is so no longer. If one should insist upon its use as a fine crusher and to obtain mechanically commensurate results for power expended, the stamp should be reduced in proportional size to the work required and the screen-aperture should also be likewise reduced. It has taken us a long time to recognize the fact that to economize energy, the units of force must correspond to the units of matter being acted upon, as explained in Kick’s law. In the breaking of a 2-in. cube of ore by a single drop of a 1,000-lb. stamp, we divide the mass into an approximate average size of 0.25-in. cubes, and perform reduction of 1 to 500. Assuming the energy has been well applied, the further reduction should be in the same ratio of energy to work, but instead of reducing the weight of the stamp to 1/500 of the original, the work continues with the initial 1,000 lb. of energy—a sledge-hammer is now doing tack-hammer work.

The step-reduction mentioned above is further illustrated by the reducing sizes of stamps, shown in shadow, against the Hardinge mill, as in Fig. 5, in which the weight and number of the balls are proportional to the reduced size of stamps.

We have many times been asked to explain the action within the conical mill and a cause for its reasonably uniform product. The answer would resolve itself into the explanation of the automatic segregation of forces in proportion to mass being acted upon by different degrees of rotative energy. In addition to these natural automatic laws, the conical mill is subject to still further regulation by changing the axis to various inclinations from the horizontal, which will cause the finer particles to travel towards the outlet much more rapidly and consequently be subject to lesser action of the grinding bodies, as their travel will be assisted by gravity rather than displacement by the heavier bodies and the attendant crushing. A practical illustration of this action can easily be obtained by placing two glass funnels base to base after partly filling them with gravel and fine dry sand, joining them with cement or adhesive tape, then evenly revolving with the axis horizontal; the experiment may also be tried having the axis at a slight inclination from the horizontal, as illustrated in Fig. 6. The result will be found to be curious and interesting mainly because unexpected.

A feature of considerable importance in the Hardinge mill is the fact that the grinding bodies, whether of steel balls, flint pebbles, or large pieces of the ore itself, are utilized to a finality; thus there is no rejection before actual final consumption, no scrap-heap of costly and partly-consumed material, for after the first charging of the mill with its grinding mediums, the subsequent and desirable difference in sizes of grinding mediums is produced by the wearing away of the larger sizes. No grinding body is thus discarded because it is too small.

Ball Mill Lining

The pebble-mills are lined with silex blocks throughout, or a combination of silex and ribbed steel or smooth plates, the plates being fitted with a special design of lifting-bar, which not only assists in lifting the mass of grinding bodies higher, affording greater impact in the central portion of the mill, but also prevents any slipping of the charge.

Speed of Ball Mills

Authorities vary widely as to the best speed for rotation of pebble-mills; in the case of the ordinary cylindrical mill (Fig. 1) the speed is rarely brought above 500 peripheral ft. per min., ranging between 400 and 500 ft. per min.; this speed, of course, is maintained throughout the total length (average) of 20 ft. In the case of the conical mill it can be more effectively operated at a peripheral speed of about 750 ft. per min. for the 8-ft. mill, but is maintained at this speed only for a length of about 20 in. instead of 20 ft. For the ordinary granular reduction, desired in concentration and other metallurgical processes, wherein a maximum of about 20-mesh and a minimum of slimes is the end desired, this speed of 750 peripheral ft. per min. (in the 8-ft. mill) is gradually reduced in proportion to the energy necessary for the further reduction of the previously divided particle. Thus in the one machine peripheral speeds—consequently the energies—vary from 200 to 750 ft. per min. in gradual stages or steps. It is a device wherein the same revolutions per minute produce a multiplicity of gradually changing peripheral speeds proportional to the diameter of the cone.

Compare a Hardinge Ball Mill to Chilean Pan Mill

The following figures in Table I. and Fig. 7 are the analysis of data furnished by a very large mining company which ran an 8-ft. Hardinge mill in direct competition with a 6-ft. Chilean mill.

The company was under the impression that the Chilean mill had the better of the argument, based upon gross tonnage fed, even though the power and water consumed (both costly items) were in favor of the Hardinge mill. Net tonnage was the economic feature, therefore also vastly in favor of the Hardinge mill.

In order to examine the results of this test properly, the cumulative percentage on each mesh was plotted for both machines, as shown on the lower half of Fig. 7. The line marked “ Line of Ideal Product ” is a uniformly graded product through 20-and all on 200-mesh, which will give a maximum extraction of copper from this ore, which was a disseminated sulphide.

As may be seen from the curves, the product from the Hardinge mill approaches this “ ideal ” line more closely than does that from the Chilean mill, and, is therefore, better suited for the economical extraction of its metal-content. The curves also show the Hardinge mill has finished 98.2 per cent, of its feed through 20-mesh, whereas the Chilean mill puts through this screen only 66.6 per cent, of the same feed. Of these quantities, the Hardinge mill has only put 21.89 per cent, through 200-mesh, as compared with 45.49 per cent, for the Chilean mill. In other words, the Hardinge mill gives 76.7 per cent, of its total feed as a product from which the maximum amount of copper can be extracted, while the Chilean mill gives only 36.3 per cent, between the same limits (through 20-mesh and on 200), as is shown in the upper half of diagram. Here the percentage on each mesh has been plotted, as shown, and from the figures on “Per Cent, of Total Copper” in Table I. the values at the right were calculated.

Considering the amount of copper contained in the two products, that from the Hardinge mill has 71.8 per cent, of its total copper-content in the material through 20- and on 200- mesh, as compared with 34.34 per cent, for the Chilean mill.

This result will materially affect the amount and cost of recovery.

As to the amount of water required, the Hardinge mill used only 19.25 gal. per minute per ton per hour put through 20-mesh, whereas the Chilean mill used 43.84 gal. In a locality where water is scarce, this is a very important item. Although no mention is made of horse-power in the data given us, nevertheless, judging from other installations of the same character, the Hardinge mill requires less than 70 per cent, of that needed to operate the Chilean mill.

To recapitulate, the above data may be presented as follows :

These figures show that although the Chilean mill received a feed of 17 per cent, more than the Hardinge mill, the latter finished 27 per cent, more through 20-mesh, and has 82.5 per cent, more than the Chilean mill between the desirable limits of 20- and 200-mesh. The Hardinge mill also has over twice as much copper within these limits of economical extraction, using less than half the amount of water per ton; and presumably requiring two-thirds the horse-power.

Performance Comparison: Conical Ball Mills VS Cylindrical Ball Mills

A certain prejudice appears to exist against the use of ball-mills, particularly the older types which have mainly been successful on dry crushing, and to which Philip Argall refers in his article as follows :

“Ball mills are successful in dry crushing, and of little account in wet work, because of the heavy abrasion of balls, plates and particularly screens.”

Those who are not familiar with ball-mills might do well to consider the difference between the Hardinge and the German type probably referred to by Mr. Argall. These two distinct types of ball-mills should hardly be classed together any more

than a gyratory should be classed with the jaw type of rock crusher, simply because they both come under the general head of crushers. Fig. 8 graphically illustrates the difference in the two types of ball-mills above mentioned, which we further compare as follows:

The German ball-mill has been in successful operation many years, particularly in Australia, though it has not found much use in America. The conical ball-mill as now constructed and used comes into direct competition with stamps owing to its extreme simplicity, and enters into a particularly simple flow-sheet, shown in Fig. 9, producing a crushed material of the grades shown in Table IV., furnished by the Porcupine Gold Mining Co., of Porcupine, Canada. For the particular installation mentioned the consumption of balls and lining is given as less than 1 lb. per ton of ore ground. The material fed to the ball-mill, some of which exceeds 2 in. in diameter, is taken directly from a rock-crusher.

Metallurgical requirements calling for granulation with a minimum of colloids or slimes are fulfilled along the lines of flow-sheet shown in Fig. 10. We append results of this style of installation furnished by the Beaver Consolidated Mines, Ltd., of Cobalt, Canada, shown in Table V.

As further illustrative of the wide range of the conical mill, Table VI. gives results of crushing in the same size (8 ft.) of mill upon different classes of material, from flint-conglomerate ores of the Lake copper-district to the softer porphyry copper-ores of Arizona. Naturally, vastly different tonnages are obtained according to hardness and other physical properties.

Several types of conical mills are manufactured in different sizes for the following purposes:

(a) Granular grinding for concentration with a minimum of slimes, taking a product or feed passing ¼- to 3/8-in. screen.
(b) Fine or slime crushing with a minimum of coarse, taking a feed of 0.25 in. or less.
(c) Ball-mills taking 2 in. and smaller cubes, replacing stamps, rolls and other coarse to fine crushers.

The horse-power required for these mills depends somewhat upon the charge of grinding bodies and the material undergoing disintegration, but is approximately :

The Hardinge mill has gone through the usual stages of competition and patent infringement which ordinarily follow the introduction of a successful device. The patents have been upheld by the U. S. Circuit Court and the U. S. Circuit Court of Appeals.