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Grinding media size calculation methods (4 replies)

Maya Rothman
2 months ago
Maya Rothman 2 months ago


in calculating the top size of grinding media for a ball mill, there are 2 methods/formulas (Fred C. Bond) and AZZARONI's. Am looking at a ball mill F80 1248um and 8m diameter, 78% Cs, BWi 14.3 and SG 3

Azzaroni's ball calc is almost 2X the Bond. What do I trust, which do I use?

Thanks. Maya

Alex Doll
2 months ago
Alex Doll 2 months ago
4 likes by mlticzon, shanford and Maya Rothman and 1 more...

Both Azzaroni and Bond are empirical models fit to a particular set of data that was available to the respective authors.  There is no single "correct" answer: your particular application may be more similar to one of these equations, or it could be completely different.  This is the problem with empirical models, they are only valid when your application is similar to the database the model was calibrated against.

Azzaroni seems to have come up with his calibration based on data from mills in the Andes, meaning it is most likely calibrated to copper porphyries.  Bond had a very diverse set of ore types to calibrate his equation against ranging from asbestos to zinc and everything in between.  If your application is a copper porphyry (ore density around 2.7 kg/L), then use Azzaroni.  If not, then you can use Bond, or even choose something in between the two, say 35 mm.  There is no single "correct" answer here, and you should experiment with different ball sizes in your own mill if you want to know what is optimum for YOUR ore.

Maya Rothman
2 months ago
Maya Rothman 2 months ago

Thank you very much Alex. Great have the difference between Bond and Azzaroni finally explained.

2 months ago
keithdangelo 2 months ago

Alex and Maya.  Good Day to you


What are the Bond and Azzaroni formulas _

Greg Henderson
4 weeks ago
Greg Henderson 4 weeks ago
1 like by David


Alex Doll is right in that these equations are based on empirical data and experimentation or benchmarking with mills processing similar ore is perhaps more practical.

Another consideration is related to the diameter of your mill at 8 m, which will experience a significant "inactive kidney" effect whereby due to the high population of balls in the charge there is a central kidney shaped core as the mill rotates that contributes little work to grinding.  The larger the diameter, the worse the effect.  This is why mill manufacturers specify lower operating ball charge volumes for larger mills, typically 30 to 32% volume for your mill diameter.

Also, for the duty you have indicated it looks like a secondary grinding application without pebble crushing as the F80 looks fairly fine at 1248 microns.  In this instance, 50 mm top size would suffice.  If there is a pebble crusher in operation and the rod mill work index is fairly high (>20 kWh/t) you might want to increase the makeup size to 65 mm, depending on the final product size you are looking for (life is full of compromises!). 

The Bond formula is better for primary ball mills, it typically gets the secondary ball mill ball size wrong, so the Azzaroni formula looks like it gives the right answer from an experience perspective.   However, given the inactive kidney issue, efficiency is generally improved by adding in some larger balls to your makeup, such as 75 to 80 mm.  You should see an improvement in the F80/P80 ratio across the ball mill and an overall reduction in circulating load.  The exact amount is difficult to specify, but if you have some balls of this size on hand you could trial putting in maybe 25% of makeup from this size, the rest being 50 mm.  There are published papers on this available through SME but they go back a while.

First of all though you should do some baseline surveys so that you can measure the effect of changing a variable otherwise it will be difficult to know if there is an improvement or not.


Hope this helps.  

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