## Grinding Test Example

**Experimental Conditions**

Standardized experimental conditions may be stated thus:

Under the foregoing conditions experiments were designed to obtain data on (1) the relation of time of grind to mill output in g.p.m., and (2) the relation of mill output in g.p.m. to size of finished product. The relation of time of grind to mill output was studied by two procedures: (1) By a “batch continuous grind” technic and (2) by a “batch cycle grind” technic. The batch cycle grind technic is described in Part II of this Paper, Batch Closed-Circuit Grinding.

The technic of the batch continuous grind used in this study was as follows:

A short period of grind was selected, which far purposes of discussion can be assigned a value of x minutes. A number of individual 1,750-gram charges were weighed out. One of them was ground for x minutes, one for 2x minutes, one for 3x minutes, and so on up to 8x minutes.

The product of each grind was dried, thoroughly mixed, and sieve-sizes, using 48, 65, 100, 150, 200, 250 mesh Tyler sieves. A 100-gram sample was used and the sieving was done by hand.

The g.p.m. output of the mill for any x-minute time increment is readily calculated by simple arithmetic. If Wx is the weight of finished product resulting in the first x-minute grind, the g.p.m. output is Wx % x. If W2x is the weight of finished product produced in 2x minutes time, the mill output for the second x-minute increment is W2x – Wx/x g.p.m., and so on.

By this procedure the output of the mill is approximately determined for any x-minute increment of grind. For the experiments with quartz, x was assigned a value of three minutes.

It is obvious that the maximum percentage (by weight) of unfinished product (feed) is present in the mill when x is zero, and that although the mill load remains constant, the weight of unfinished feed starts diminishing at the initial turn of the mill. For this reason it was thought that in batch grinding, which may be assumed to compare in a limited way to open-circuit grinding, the efficiency of the mill possibly should be a maximum at the very initial revolution of the mill. This proved not necessarily to be the case, as may be seen by reference to the experimental data given.

The many missing links in the science of ball-mill grinding as revealed in mailing the study here presented and as brought out in the subsequent analysis of the experimental data, led to the studies by the author and H. E. Lee which are presented elsewhere under the title of Ball Mill Studies, Parts I, II, III, etc., and to Part II of this paper.

**Experimental Data and Discussion**

The condensed experimental data of this research and calculations based on these data are given in Table 1. The time of grind is given in vertical column 1. The sieve analysis of the product of each grind test is given, showing total grams, weight per cent, weight per cent cumulative, grams per minute, grams per minute cumulative, total surface, and total surface cumulative of each sieve size. There is also a horizontal column for each time, increment of grind, giving “grams per minute cumulative” for each three-minute grind increment throughout the entire 24-minute time, range—that is, the g.p.m. output for the 0 to 3 minute period, for the 3 to 6 minute period, for the 6 to 9 minute period, and so on for each period.

Figure 1 shows the “finished product-per cent of total mill charge” plotted vertically against “time of grind” horizontally for each of the finished sizes considered—namely, 65, 100, 150, 200, and 250 mesh. These lines may be termed “cumulative rate curves.”

**Batch Grinding using Morning Ore**

A set of tests similar to those previously described for quartz was made with Morning mine ore. The data are presented in Table 2. This ore is an aggregate largely of quartzite, siderite, sphalerite, and galena. These, data are shown graphically in Figure 4, in which “finished product, g.p.m.” is plotted vertically against “time of grind increment” horizontally. These curves indicate that at all sizes the highest rate of production of finished product is for the initial two-minute grind increment, except in the cases of the finished minus-48 mesh and minus-65 mesh products. In the absence of surface data, such as were calculated for quartz, it can not be known if the maximum finished product points for the minus-48 and minus-65 mesh sizes—which occur at the second two-minute grind increments—are due to increases in unfinished sand surface in the mill or to some other element.

The rate curves for Morning ore are unlike those for quartz in that the finished minus-150, minus-200, and minus-250 mesh product rate curves for

quartz reached a maximum after the grinding operation had continued through several time of grind increments. With Morning ore the rate curves fall off steadily from the start of the grind.

The significant fact to note from this set of experiments is that finished product is made most rapidly at the very beginning of the grind. This suggests that in the practical closed-circuit plant the circulating load should be large in order to keep a high percentage of unfinished sand in the mill.

For quartz grinding to, say, finished minus-100 mesh sand, a 100 per cent circulating load should give approximate maximum efficiency. For Morning ore the circulating load should be high for maximum efficiency. The charge should not remain in the mill longer than two minutes, or possibly one minute. For this (two min.) length of grind for, say, finished minus-100 mesh product, 20.6 per cent of the charge is reduced to finished size. Therefore, for high efficiency, a circulating load of not less than 500 per cent is required. This corresponds closely to practice now in vogue in the Morning Mill, Mullan, Idaho, where this material is being milled. In designing a plant to treat a new ore, a test of this kind should be of much value in selecting the type of “ball mill and classifier to be used. These experiments led to the “batch closed-circuit experiments, which are to be described in Part II of this paper.

**Relation of Mill Capacity and Fineness of Finished Product**

If the capacity of the mill used in these experiments be rated at one unit of finished minus-65 mesh product in a unit of time, its capacity to make finished product at any finer mesh may be calculated from Table I for quartz and from Table 2 for Morning ore. See Table 3.

These data show that the mill has four times as much capacity when grinding to finished minus-65 mesh as when grinding to finished minus-250 mesh. It has approximately three times as much capacity to produce finished minus-150 mesh Morning ore as finished minus-150 mesh quartz. These figures all are based on the output of the mill for the initial grind period—three minutes for quartz and two minutes for Morning ore.

In batch grinding, and to a much lesser extent in closed-circuit grinding, the weight (not surface) of unfinished feed in the mill drops off rapidly as the time of grind continues.

To learn if a greater mill output could be obtained than in any of the previous tests, an experiment was designed in which the period of grind was one minute. Quartz was used, and all other experimental conditions were the same as in previous experiments. At the end of each one-minute grind the charge was removed from the mill and the weight, in grams, of finished minus-100 mesh sand was determined. A quantity of new ore equal to the determined weight of finished product with the original charge was returned to the mill. The grind was conducted for another one-minute period. This process was repeated seven times, and each time enough new water was added to keep the water-ore ratio at 30:70 by weight. At seven new ore additions the mill became choked, and further additions could not be made.

The object in the plan of this experiment was to keep in the mill a nearly constant weight of unfinished feed, without removing the finished product. This procedure should, of course, result in high unfinished sand surface in the mill. The experimental data of this run are compiled in Table 4.

The output of finished minus-100 mesh sand produced the first minute is 175 grams; the output per minute for the first two minutes is 154 grams; for the first three minutes, 127 grams; for the first four minutes, 143 grams; for the first five minutes, 108 grams; for the first six minutes, 119 grams; and for the full seven minutes, 106 grams. On the basis of these figures the output is a maximum for the initial one-minute grind during, which only original feed is in the mill. Considered on the basis of output for each of the time increments, calculation shows that the output of the mill is greatest during the fourth minute grind increment, when 195 grams were produced. This result may be due to experimental error, and it is believed to be, for during the next minute (the fifth) increment the output is negative and for the sixth-minute increment the output is 166 grams. That the mill output was less for the third and fifth minute increments than for the fourth-minute increment is almost proof of experimental error, and the conclusion may safely be drawn that nothing is to be gained by overfeeding a ball mill, and that choking of the mill with finished product cuts down the mill efficiency.

**Summary and Conclusions**

- A “batch-grind technic is described which was designed for use in studying the rate of production of finished product in a “ball mill. This rate is given in grams per minute.
- The rate of production of finished product may or may not increase with time of grind over a limited time range. With quartz, the rate, when grinding to finished minus-65 and minus-100 mesh products, is greatest for the initial three-minute time of grind increment. For finished sizes finer than 100 mesh the maximum rate of production of finished product occurs at later time increments of grind.
- The rate of production of finished product, disregarding the element of friction “between balls and liners, seems to “be a function of the total surface of unfinished sand grains in the mill. As long as there is an increase of surface of unfinished sand in the mill, regardless of weight, there is an increase in rate of production of finished product. Rate of production drops off with decrease of surface of unfinished sand in the mill.
- The rate of production is an inverse function of fineness of finished product. The mill employed grinding quartz had four times as much capacity to produce finished minus-65 mesh product as it had to produce finished minus-250 mesh sand. For Morning ore the capacity of the mill was, roughly, twice as great when grinding finished minus-65 mesh product as when grinding finished minus-250 mesh product.
- The rate of production of finished minus-150, minus-200, and minus-250 mesh Morning ore is approximately three times the rate of production of the same finished sizes of quartz.