## calculate and select ball mill ball size for optimum grinding

In Grinding, selecting (calculate)the correct or optimum ball sizethat allows for the best and optimum/ideal or target grind size to be achieved by your ball mill is an important thing for a Mineral Processing Engineer AKA Metallurgist to do. Often, the ball used in ball mills is oversize just in case. Well, this safety factor can cost you much in recovery and/or mill liner wear and tear.

## calculate top ball size of grinding media - equation & method

Although it was developed nearly 50 years ago, Bonds 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. Bonds 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 theparticles in the feed and in the product of the material being comminuted. This is known as Bonds 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).

Early in the twentieth century, ball mill manufacturers and other research laboratories developed proprietary batch-grinding tests to measure the resistance of metallic mineral ores, industrial mineral ores, cement raw materials, cement clinkers, and related materials being ground to fine sizes in rod and ball mills. These tests, called grindability tests, were needed to help determine the energy required to grind these materials from a coarse-sized feed to the desired product size. During the first half of the century, none of these test methods could be used to directly determine the energy needed for grinding at plant size capacity. If grinding tests for direct determination of the energy required were needed, pilot-plant tests in small-diameter continuous operating ball mills were run. Pilot-plant grinding data always had to be adjusted for scale-up factors to larger-diameter mills.

## bond formula for the grinding balls size calculation

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 mills performance, the raw materials particle size in the mills 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, m; 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.

At result B = 25mm or less necessary to use the correction factor 1.3, i.e. the grinding balls average diameter should be 32.5 mm in the feed mixture. We draw your attention, a larger grinding balls need to use for future loads. As practice shows, the difference between the grinding balls average diameter in mill and loaded grinding balls diameter is 10-15 mm. In our example, the grinding balls diameter needed to load into the mill must be equal to 40-50 mm.

Lets sum up. The grinding balls diameter determined by the Bond formula has a recommendatory character and serves as a starting point for calculating the necessary proportion grinding media feeding a new mill. More precisely adjust the ball load in the mill can only by industrial test performing. During the industrial tests necessary to accurately monitor the grinding quality, mill productivity and other technological parameters adopted at the enterprise.

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