SPEED OF ROTATION
The speed of rotation of a tube mill is such that the pebbles are thrown over the center in a cascade and must not be so fast that the whole mass of pebbles and pulp revolves with the shell of the mill. Fig. 15 shows the theoretical path of the pebbles. This diagram serves the purpose of impressing upon the reader the necessity of grinding by impact for the balls are shown falling over the center in a cascade. It is impossible to obtain this action entirely in a tube mill for there is a constant tendency for the pebbles to skid on the lining and for the pebbles to roll down the incline (of pebbles) before reaching the apex of their ascent. Owing to the fact that the internal diameter becomes greater as the lining wears and that linings of different materials are of different thicknesses, we find mills of the same external diameter revolving at different rates of speed while the peripheral velocity of the inside of the lining may be identical.
The formula most generally used for determining the rate of rotation of a tube mill is that given by Davidsen, namely: R.p.m. = 200 / Sqrt(d) where d is the internal diameter of the mill in inches. The factor 200 will pertain more particularly to mills lined with flint pebbles or silex blocks for it has been found that the character of the lining determines to a certain extent the speed of rotation. A smooth liner, whether of steel or iron, whether originally placed in the mill as a smooth liner or an El Oro liner with the ribs worn off, will require a speed somewhat over that required for a rough liner because there is more tendency for the charge of pebbles to slip and the peripheral speed must be greater to lift the pebbles to the apex of the mill. A rough liner with lifting bars which firmly hold the pebbles- on the liner without slipping will require a somewhat slower speed of rotation, so we may revise this formula for the classes of liners
That these figures can only be taken as guides is true for we know that every mill and every ore is a distinct problem and what may be satisfactory in one case may be unsuited for another but the figures are sufficiently near to ensure but little chance of failure from not having the speed of the mill at the right point.
The following table shows the rates of rotation for many mills in various parts of the world.
This list of mills shows that the Hardinge mills run at a higher peripheral speed than any of the cylindrical mills and this speed is far above that given by Davidsen's formula. It will be noticed that the 5-ft. cylindrical tube mill is the most common size for regrinding gold ores following stamps, and that at least two of them, the Dome and the Gold Roads, run at a higher peripheral speed than the 7-ft. mill of the Butte and Superior. The best speed for a 5-ft. mill appears to be 28 r.p.m., at all events that is my experience; those revolving at 24 r.p.m. or less do most of the work by the attrition of the sliding pebbles. For ores containing high percentages of heavy sulphides with the values in this heavy material this speed may be justified, but not when capacity is wanted. The pebbles in a 5-ft. mill running at 24 r.p.m. become flat, indicating that the wear is caused by sliding while the same mill running 28 r.p.m. cause the pebbles to be more or less rounded showing that the grinding has been done by impact.
The amount of ore ground in a tube mill (to 200 mesh) depends largely upon its speed of rotation; for example, a 5 by 22- ft. mill revolving at 18 r.p.m. had a capacity of 28 tons a day, while the same mill revolving at 26 r.p.m. ground 48 tons and at from 27 to 28 r.p.m. about 55 tons. There was no means of measuring the amount of power required at the various speeds, or it might have been possible to balance tonnage against power cost but there is no doubt that in this particular instance the increased speed amply repaid in grinding efficiency for the extra power required. A 5 by 22-ft. mill at 28 r.p.m. will require about 55 hp. while the same mill revolving at 32 r.p.m. will require 85 hp. There must therefore be a greatly increased capacity to warrant this increased expenditure of power and, while figures for comparison are not available, judging from the actual mill tonnages in the mills where this speed is maintained the increased cost for power is not justified, unless, contrary to the usual rule, the power cost is an unimportant item of expense.
