GRINDING MILLS Grinding is the last stage in the process of comminution ; in this stage the particles are reduced in size by a combination of impact and abrasion, either dry or in suspension in water. It is performed in rotating cylindrical steel vessels known as tumbling mills. These contain a charge of loose crushing bodies—the grinding
medium—which is free to move inside the mill, thus comminuting the ore particals. The grinding medium may be steel rods, or balls, hard rock, or, in some cases, the ore itself. In grinding process, particles between 5 and 250 mm are reduced in size to between 10 and 300 μ m. The motion of the charge in a tumbling mill The distinctive feather of tumbling mills is the use of loose crushing bodies, which are large, hard, and heavy in relation to the ore particles, but small in relation to the volume of the mill, and which occupy slightly less than half the volume of the mill. Due to the rotation and friction of the mill shell, the grinding medium is lifted along the rising side of the mill until a position of dynamic equilibrium is reached, when the bodies cascade and cataract down the free surface of the other bodies, about a dead zone where little movement occurs, down to the toe of the mill charge.(Fig.1)
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The speed at which a mill is run is important since it governs the nature of the product and the amount of wear on the shell liners. For instance, a practical knowledge of the trajectories followed by the steel balls in a mill determines the speed at which it must be run in order that the descending balls shall fall on to the toe of the charge, and not to the liner, which could lead to rapid liner wear. The driving force of the mill is transmitted via the liner to the charge. At relatively low speeds, or with smooth liners, the medium shaes tend to roll down to the toe of the mill and essentially abrasive comminution occurs. This cascading leads to finer grinding, with increased slimes production and increased liner wear. At higher speeds the medium shapes are projected clear of the charge to describe a series of parabolas before landing on about the toe of the
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charge. This cataracting leads to comminution by impact and a coarser end product with reduced linear wear. At the critical speed of the mill the theoretical trajectory of the medium is such that it would fall outside the shell. In practice centrifuging occurs and the medium is carried around in an essentially fixed position against the shell. In travelling around inside the mill the medium (and the large lumps of ore) follow a path which has two parts. The lifting section near to the shell liners is circular while the drop back to the toe of the mill charge is parabolic (Fig.2(a)).
Consider a ball, or rod, which is lifted up the shell of a mill of radius R metres, revoling at N rev min-1 . The rod abandons its circular path for a parabolic path at point P (Fig.2(b)), when the weight of the rod is just balanced by the centrifugal force, i.e. when
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m V2 ? m g cos? R
where m is the mass of the rod ball(kg), V is the linear velocity of the rod (m s-1), and g is the acceleration due to gravity (m s-1). Since
2?RN , 60 4? 2 N 2 R cos? ? ? 0.0011 2 R N 2 60 g V?
When the diameter of the rod, or ball is taken into account, the
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radius of the outermost path is (D-d)/2 where D is the mill diameter and d the rod, or ball diameter in metres. Thus
(D ? d ) cos ? ? 0.0011 N 2
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(equation 1)
The critical speed of the mill occurs when α = 0,i.e. the medium abandons its circular path at the highest vertical point. At this point, cosα =1, therefore
Nc ?
42.3 rev min?1 (D ? d )
(equation 2)
where Nc is the critical speed of the mill. Equation 2 assumes that there is no slip between the medium and the shell liner and, to allow for a margin of error, it has been commom practice to increase the value of the calculated critical speed by as much as 20﹪. It is questionable, however, whether with modern liners maintained in reasonable condition this increase in the value is necessary or desirable. Mills are driven in practice at speeds of 50-90﹪ of critical speed, the choice being influences by economic considerations. Increase in
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speed increases capacity, but there is little increase in efficiency (i.e. kWh t-1) above about 40-50﹪ of the critical speed. Very low speeds are used for high-capacity coarse grinding. Cataracting at high speeds converts the potential energy of the medium into kinetic energy o impact on the toe of the charge and does not produce as much very fine material as the abrasive grinding produced by cascading at lower speeds. It is essential, however, that the cataracting medium should fall well inside the mill charge and not directly onto the liner, thus excessively increasing steel consumption. Most of the grinding in the mill takes place at the toe of the charge, where not only is there direct impact of the cataracting medium on to the charge, but also the ore packed between the cascading medium shapes receive the shock transmitted. At the extreme toe of the load the descending liner continuously under-runs the churning mass, and moves some of it into the main mill charge. The medium and ore particles in contact with the liners are held with more firmness than the rest of the charge due to the extra weight bearing down on them. The larger the ore particle, rod, or ball the less likely it is to penetrate the interior of the charge and the more likely it is to be carried to the breakway point by the liners. The cataracting effect should thus be applied in terms of the shape of largest diameter.
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