Discussion of Papers Published Prior to 1951 - The Probability Theory of Wet Ball Milling and Its Application (1950) 187, p. 1267

F. C. Bond (Allis-Chalmers Mfg. Corp., Milwaukee) —This paper considers comminution as a first order process, with the reduction rate depending directly upon the amount of oversize material present. The data show that other factors should be taken into account, and it is possible that in time these may be evaluated as simultaneous or consecutive reactions: Development of the theory of comminution has been retarded for many years by the assumption that surface area measurements constitute the sine qua non of the work done in crushing and grinding, and it is encouraging to note the belated growth of other ideas. In the Abstract the term "net power" should be changed to "net energy." Throughout the paper the term "hp per ton" should be changed to "hp hrs per ton", or "hp hr t." The term "Probability Theory" in the title does not seem appropriate, since it is not clear how the probability theory is used in developing the ideas in the paper. There seems to be a contradiction between the large calculated advantages of closed circuit operation and the statement following that the closed circuit test results showed no significant change in grinding behavior, when compared with the batch grind curves. Tables I and II show that between 75 pct and 50 pct solids the energy input required decreases with increasing moisture content and may indicate the advisability of grinding at higher dilutions in certain cases. The calculation of the hp-hr per ton factor indicates an input in the laboratory mill of only 7.32 gross hp per ton of balls; this casts some doubt upon the accuracy of the factor used, since the power input in commercial mills at 80 pct critical speed is customarily much higher. The tests show that within fairly wide limits the amount of ore in the laboratory mill may be varied and a product of constant fineness obtained, provided that the grinding time is varied in the same proportion. This has often been assumed, and confirmation by actual testing is of value. The Cavg corrections for differences between the plant and laboratory size distributions do not seem very satisfactory, since in many cases the plant/laboratory ratio is farther from unity after correction than before. The following equation has been derived from the data in Table VI: Relative Energy (log new ball diam in in. + 0.410) Input = --------------—--------------- from which the relative energy inputs for balls of different sizes can be calculated and compared. The relative energy input is unity for balls of 2.715 in. diam. The equation indicates that the work accomplished by a ton of grinding balls per unit of energy input is roughly proportional to the square root of the total ball surface area; provided, of course, that the balls are sufficiently large to break the material. The data in support of this statement are admittedly meager, but are fairly consistent when plotted. The relative grindability values listed in Table VI for 200 mesh multiplied by 4/5 apparently correspond approximately to the A-C grindability at 200 mesh.' It would seem that for open circuit tests comparable accuracy could be obtained much more simply by the old method' of plotting the test grind, extending the mesh grinds to the left of zero time if necessary, and determining from the plot the equivalent time required to grind from the plant feed size to the plant product size, using the average of several mesh sizes. The en- ergy input value of one time interval could be determined by tests on materials of known grinding resistance, and this multiplied by the interval required should give the desired energy input value. The relative grindabilities would be the relative time intervals required for a specified feed and product size. When the plotted mesh size lines of a homogeneous material are extended to the left beyond zero time they meet at one point at zero pct passing. The horizontal distance of this point from zero time indicates the equivalent energy input required to prepare the mill feed. The author's results show that the closed circuit grinding tests give about the same K values as open circuit tests, from which he concludes that open circuit tests are satisfactory in many cases. The value of the closed circuit test is its ability accurately to predict energy requirements in closed circuit grinding for both homogeneous and heterogeneous materials. If the material is homogeneous, the open circuit test gives satisfactory results; but if the material contains appreciable fractions of hard and soft grinding ore, the open circuit tests will not be accurate because of the accumulation of hard grinding material in the circulating load. Since in most cases it is not possible to determine a priori whether the material contains hard and soft fractions, the closed circuit tests are preferable and more reliable. B. S. Crocker (Lake Shore Mines, Ontario)—Dr. Roberts probability theory of grinding is very similar to our log pct reduced vs. log tonnage method of plotting and evaluating grinding tests at Lake Shore. However, although we both seem to start at the same point we finish with different end results. Shortly after publishing our grinding paper (referred to by Dr. Roberts) in 1939, we did pursue the subject of the "constant pct reduction in the pct +28 micron material for each constant interval of time. We ran innumerable tonnage tests on the plant ball mills, rod mills, tube mills with 11/4 and 3/4 balls, and lastly pebble mills, with tonnage variations from 180 tons per day to 950 tons per day. We found that when we plotted the log of the tonnage against the log of the pct reduced of any reliable mesh, we had a straight line up until 90 pct of the mesh is reduced. We have also tested this in our 12-in. laboratory mill with the same results. We have used this method of evaluating grinds for the past 8 years and developed the recent four stage pebble plant on this basis. By pct reduced we mean the percentage of any given mesh that is reduced in one pass through a mill at a given tonnage (or time). For example, if the feed to a rod mill is 90 pct +35 mesh and the discharge at 500 tons per day is 54 pct +35, the pct reduced is 90 — 54/90 = 40 pct. If the feed had been 80 pct +35 the discharge would have been 48 pct +35 or pct re- duced 80-48/80 = 40 pct as long as the tonnage re- mained constant at 500 tons per day. Thus we can easily correct for normal variation of mill feeds. This log — log relationship derived from the tonnage tests of all our operating mills has proved of tremendous help in checking laboratory work and in designing alternate layouts or new plants. The difference between the log — log and the semi-log plot is only shown up when the extremes in tonnages are plotted. When the relationship between the pct reduced and the tonnage was first investigated, we used semilog