In order to avoid ambiguity, a number of terms used in this paper to describe tumbling mills and their operation are defined hereunder.

Mill Speed is commonly given either as the number (AO of revolutions per minute, or as a percentage of the critical speed (%NC), or as the product of the square root of the mill radius in meters or inches-multiplied by the speed in r.p.m. (i.e. N^R). Here the speed is expressed in r.p.m., or as a percentage of the critical speed.

Critical Speed (r.p.m.) is commonly considered as the hypothetical mill speed at which infinitesimal particles touching a cylindrical shell of radius (R) will centrifuge, or the hypothetical speed at which finite particles (spheres of radius r) will centrifuge. If the angular velocity of a mill is w radians per sec. then the first expression is obtained from:

g/w2 = R; and the second from

g/w2 = R — r, where g is the acceleration due to gravity.

Here, the first expression only is used. Hence Nc/R or Ne/R—r equals 54-2 when R is in feet, equals 29-9 when R is in meters and equals 187-7 when R is in inches.

Size Analysis.—A size analysis represents the percentages by weight of material smaller than given particle sizes or between successive particle sizes. Size distribution implies that the size analysis has been expressed in terms of relative sizes such as fractions of the largest size or of some arbitrary size or of some mean size.

Surface Area.—This term, as well as specific surface (cm.2/gm. or better, cm.2/cm.3) implies a “direct measure” has been used, whereas surface units imply the “measure” of area has been deduced from a sieve or other size analysis.

Charge refers to the grinding media and burden together, whereas burden refers to the material being ground.

Degree of Filling denotes the fraction of the grinding chamber* filled by the charge (i.e. grinding media and burden) : it is frequently treated as equal to (bulk volume of grinding media) -=- (mill volume).

Breakage Process.—Any process in which some or all particles of an assembly of particles break, is termed a breakage process.

The mills described in this section appear to have been used fairly extensively: the descriptions are incorporated in a classification that the author has found useful. The classification, as with almost any of the wide variety available, has distinct limitations and is used largely as means of condensing a large and varied list to a smaller number of categories. It is based primarily on some constructional characteristics of tumbling mills and is broadly as Cylindrical mills: “short” mills, “long” mills, rod mills; Conical mills; Mills of unusual design.

Except for the uncommon vibratory mills, a tumbling motion is imparted to the charge by rotation of the grinding mill barrel. Mineral processing engineers will give detailed descriptions and illustrations of the various types of tumbling mill can be found in textbooks, given in the references, and in an extensive bibliography.

The diameter of “short” cylindrical mills is taken to equal very approximately the mill length, whereas for “long” mills the length is several times the mill diameter.

Short Cylindrical Mills.—Short mills may be classified by the methods used to feed and discharge the material being ground (a distinction between steel balls, pebbles or other grinding media is not attempted in this description). The sketches of Fig. 1 illustrate some forms of short mill. An internal lining is used to protect the mill shell from damage. If contamination of the product must be avoided, special materials may be used for the liners and grinding media, for example the linings of batch ball mills used in the manufacture of paints, enamels, etc. The production rate of batch ball mills is relatively small and often is equivalent to that of laboratory sample preparation. It is significant that much research has been done with batch ball mills and that often these studies have not simulated the larger continuously-fed mills of industry.

Peripheral discharge mills pass the burden on to screens surrounding the grinding chamber. Under-size material (i.e. the output) is discharged through the screen into a collection chamber whilst oversize particles are recirculated back to the grinding chamber. Special grinding plates between the tumbling charge and the screens serve two purposes: they prevent damage to the screens and assist the grinding processes, especially in mills with a central driving shaft.

Many short mills have a grate type of discharge; the grate retains useful grinding media whilst ground burden and worn media discharge through the slots of the grate into a collection chamber. Sometimes material leaves this collection chamber through a hollow trunnion. Another form of mill discharges ground material by overflowing through a hollow trunnion. Both these types of mills require external classifiers for closed circuit grinding.

Pulverized fuel is prepared by dry grinding methods and usually the unit must also dry the coal. The drying is generally effected by hot air and this same air flow transports the coal to the pulverized fuel burners in the unit system or to a separator in the bin and feeder system. Some coal pulverizers are sketched in Fig. 1. Peripheral discharge mills have also been used to pulverize coal.

Long Cylindrical Mills.—Long mills are used mainly for open circuit grinding and are particularly popular in the cement industry. The simplest form is a single compartment tube mill (Fig. 2) ; however, compound mills are more common and generally effect better grinding. Compound mills have several compartments, each containing different sizes of grinding media; they can accept a coarser feed than the tube mill and larger sized mills are built. The vertical diaphragms forming the partitions between compartments must be designed for long life and yet permit the easy passage of burden across them; the shape, number and total area of the slots in the diaphragms are important factors.

The diaphragms of compound mills are vertical, whereas in compartment mills, longitudinal partitions running the entire length of the mill are used. The “Concentra” mill is one example.

Rod Mills.—Rod mills (Fig. 3) are an important form of cylindrical mill; generally these are long mills, but short forms are manufactured. Rod mills do not efficiently produce a very fine output; but are very effective in the stages preparatory to a final fine grind.

Conical Mills.—Conical mills (Fig. 3) originated in an attempt to overcome a limitation common to most tumbling mills; large grinding media often migrate to the discharge end leading to a poor quality grind. However, ball migration can occur in conical mills; sometimes it arises from overloading the mill. Conical mills have been used for wet and dry grinding and as air-swept pulverizers.

Unusual Mill Designs. — Vibratory ball mills agitate a charge by means of oscillating springs. The frequency of the imposed oscillations is of critical importance and has been the subject of patents. The mills are reported to be used in Germany, but only very small numbers appear to have been tried elsewhere.

The Aerofall and Hadsel mills are grinding machines which crush and grind by using the burden as its own grinding media; however, in tests, a small quantity of grinding media has been used. Relatively little has been published on these mills’ performance or construction.

General Features.—Many types of mill liners are in use; they serve to protect the mill shell by an expendable item and to transmit the forces necessary to induce the charge of a mill to tumble. The latter facet of the effects of liners on mill performance is important and it is unfortunate that experience is practically the only guide when choosing the design for liners.

The most common grinding media are spherical, or nearly so, e.g. forged steel balls and flint pebbles. Various special shapes have been tried and some such Cylpebs have found continued favour at some plants; however, the disadvantages of special shapes are generally thought to outweigh advantages. In ore dressing, the cost of replacing worn media is appreciable, but in coal pulverizing it is a small item alongside other factors such as fan erosion in mills under suction.

The speeds at which ball mills operate range from 50 to 90 per cent of the critical speed with the lower speeds being more favoured in recent years, whereas rod mill speeds, although normally 50 to 60 per cent of the critical, have been increased to about 80 per cent recently. The nature of the agitation partly depends on the operating mill speed, but it also depends on the degree of filling, the density and shape of the grinding media and the liner conformation. The degree of filling varies from about 25 per cent in the case of some pulverizers up to about 50 per cent of the mill volume.