Impact of Ball Mills Diameter VS Length Compared Efficiency

Impact of Ball Mills Diameter VS Length Compared Efficiency

Operators may rightly ask how much reliance should be placed on laboratory ball milling when they are using mills so much larger. This question was foremost in the earliest work at Rolla; in fact, in the beginning more attention was given to plant tests than to laboratory tests. The operators had calculated their results in terms of useful grinding and stopped their calculations at 65-mesh because they did not wish to grind finer. Their power was in terms of gross horsepower.

At the various concentrators included in the examination the ores were markedly similar and the particle size of the feeds was about the same. Eventually, the companies gave each mill a rating in capacity in terms of surface tons per hour and in efficiency in terms of surface tons per horsepower-hour. When a mill, regardless of its size, was found to have a low efficiency it was given special attention. The examination generally showed that it was making too much of the minus 65-mesh size in its discharge. If an increase in new feed was not desirable to correct the malperformance, the speed of the mill was reduced to conserve power. This reduction in speed increased the circulating load and increased the selective grinding. In one instance a group of mills was allowed to continue to run at top speed and extra feed was obtained by laying off a superfluous mill. Tests were made concurrently in the laboratory with duplicate feeds, pulp consistency, and presumably duplicate ball loads. The indications were that the laboratory mill was a little superior to the plant mills. However, several indeterminable factors beclouded the tests, to-wit, the size of ball, the exact amounts, and their condition as to shape.

After the laboratory investigation had gone farther and it seemed that the subject was understood well enough for correct interpretations, the query was resumed. Table 25 contains some of the results. The first half of the table shows a comparison of two laboratory mills that are dissimilar in diameter and length. They were run at the same speed. The results are almost identical. The tests, being of the batch type, were timed so that the amount of work on a unit weight was the same in each mill. The conclusion was reached that a long laboratory mill of small diameter performed the same as a shorter mill with a larger diameter. Parenthetically, this pair of tests illustrates the principle that when two dissimilar mills are loaded and charged in proportion to their volumes the grind in the 24- by 24-inch mill (larger diameter) required only 6.75 minutes, whereas the 19- by 36-inch mill (smaller diameter) took 8.5 minutes. The explanation lies in the difference in the exponents applied to the diameters for volume and power, respectively—the exponent for volume is 2 and for power (capacity) it is 2.5.

The last half of table 25 shows a comparison of one of a group of 6- by 4-foot mills with a laboratory mill. In the concentrator the rate of feed was determined and the feed and discharge sampled. While sampling the feed, a goodly quantity was laid aside for laboratory tests. When the laboratory tests were made, a close parallelism of the grinding results was indicated; the two grinds were almost identical in type. However, some explanation is required.

mills of different diameters and lengths

In the first calculations, the net power assigned to the large mill was that of a companion mill taken about 2 years earlier and immediately after it had been dumped and reloaded with a fresh stock of balls. Finally, a power determination was made on the mill from which the samples had been taken, and it was found to be about 8 percent higher than expected. The nature of the ball load was suspected because it had not been renovated for many months. Many battered balls were present. It was this condition that prompted the test just shown in table 24, in which the battered balls were shown to take about 6 percent more power than new balls. Taking these things into consideration, it seems safe to expect laboratory mills to duplicate the work of mills of commercial size.

The comparison of the 6- by 4-foot (in reality, 68- by 50-inch) mill with the 19- by 36-inch mill gives an opportunity to investigate the accuracy of a simple formula for relative powers. Here the exponent 2.5 will be applied to the diameters, and since the lengths are so nearly the same the power will be taken also as a function of the length. The proportion used to solve for the net power required by the larger mill is


The value 63 horsepower, obtained by the proportion, lacks about 6 percent of checking the value, 67 horsepower, given in table 25. All of these power values are net. The failure to obtain a closer check might be due to a fault in the amount of ore charge selected in the laboratory run. How a small difference in ore charge affects the power may be illustrated by referring to the 80-percent speed with dolomite in table 13. There it will be seen that when the mill had a 125-pound charge the power was 1.75, and when the charge was 100 pounds the power was 1.85. Thus it is seen that the difference tween 100 and 125 pounds of ore in the mill makes a difference in power of about 6 percent, this being the disparity in the above calculation and illustrating that the use of formulas for forecasting power requires full appreciation of the influence of small changes in set and induced variables.

These tests led to the belief that if each one of a heterogeneous mixture of mills, large or small, is run under conditions analogous to the others, and if each applies a unit of work to a unit of ore, the effect (comminution) will be the same—that is, the same relation between cause and effect will maintain.