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Although it was developed nearly 50 years ago, Bond‘s method is still useful for calculating necessary mill sizes and power consumption for ball and rod mills. This paper discusses the basic development of the Bond method, the determination of the efficiency correction factors based on mill dimensions and feed characteristics, and the application of the results to designing grinding circuits
The development of the ball mill during the twentieth century has been described as the most significant development in the machinery for performing the grinding of ores (Lynch and Rowland 2006). A key part of the implementation of ball mills was the development of the ability to predict their performance in the plant based upon grindability data from standardized tests performed in small-diameter laboratory mills
In 1930, Allis-Chalmers hired Fred Bond to design and build a laboratory for testing ores and grains, for minerals processing and flour milling, and to conduct research for processes for the treatment of ores and grains. Bond’s first developments for grinding ores and rocks are now known as the Bond rod milling and ball milling grindability tests. The grindability results from these tests are still reported as “net grams produced per revolution of the test mill.” Bond carried out two studies using his grindability tests:
1. The first study was to determine if either of the two existing theories of comminution the Rittenger theory or the Kick theory were correct. Bond concluded that neither was correct. He developed a theory that the energy required for comminution was a function of the difference in the square root of the size of the particles in the feed and in the product of the material being comminuted. This is known as Bond’s third theory of comminution
2. The second study was used to develop a correlation between ball mill operating data and grindability test data. This was based on the Work Index concept. From this concept came two equations: (a) the equation to determine the Work Index from Bond grindability tests, and (b) the Bond equation, which uses the Work Index to determine the energy needed for grinding
When Bond introduced the Work Index concept (Bond 1952), he introduced a new method for determining the energy required for grinding ores and outlined a mathematical method for using the Work Index to design grinding circuits. Though it is an empirical procedure, even at this time, there is little prospect that the Work Index will be replaced as a tool for determining the energy required to grind a mineral or ore. Numerical examples of the use of the Work Index are given in this paper. The calculations are based upon measurements giving the amount of the size reduction by the difference in the size distributions of the feed (F) and the product (P)
The enterprises consumers grinding media have a question about right choise the grinding ball size (diameter) for the mill in order to achieve the required grinding quality. We noted earlier, this information can be obtained from several sources:
— Technical documentation. It attached to the milling equipment (mill). Each mill manufacturer recommends certain grinding media type for mill operation under certain conditions: the crushed material parameters, the mill’s performance, the raw materials particle size in the mill’s «feed», and the required grinding fineness (finished class content)
— Past experience of a ball mill. It is possible to calculate the grinding media average diameter formed in the mill operation, during grinding media unload from mill (the grinding balls bulk weight in fully unloaded mill)
— Other enterprises. It is possible to obtain the necessary data on a grinding media granulometric composition from other enterprises with a similar grinding process, including similar requirements to the grinding quality
There is a mathematical solution to this problem — the Bond formula. It uses to help determine the grinding media optimal size must be loaded into the ball mill for proper operation ensure. The calculation formula is below:
B — the grinding balls diameter, mm; A — the correction factor (for grinding balls A = 20,17; for cilpence A = 18,15); F — the feedstock grain size in 80% of the material, μm; K — the grinding correction coefficient (for wet grinding — 350; for dry grinding — 355); S — the grind material bulk mass, g/cc. It is a tabulated value. Wi — specific energy consumption, kW*h/ton; C — the mill drum rotational speed,% of the critical speed; D — the mill internal diameter, m
We can calculate the steel charge volume of a ball or rod mill and express it as the % of the volume within the liners that is filled with grinding media. While the mill is stopped, the charge volume can be gotten by measuring the diameter inside the liners and the distance from the top of the charge to the top of the mill. The % loading or change volume can then be read off the graph below or approximated from the equation and calculation:
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