There is not a formula that predicts the optimum Ball size for a SAG mill. Usually operational people perform trial-error in order to improve performance.

What I can comment about the Ball size is that bigger the Ball more impact energy is release for impact., so Usually you obtain higher throughput using bigger balls, in other way. If your ore is more competent you need more energy for grinding.

My thoughts about this topic are more complex. I think the effect of ball size in grinding should include the effect over product size and not only over throughput. In a common SABC-B circuit you can obtain an improvement in t/h with increase ball size but with an increase in T80 too. This effect it’s critical in a Single Stage circuit like El Soldado for example. So understanding the complex role of ball size in grinding should include the effect over grinding efficiency and include the effect over comminution process downstream.

Discussions in relation to (top) ball size need to include ball hardness/ or hardness profile as well, particularly within the context of how a SAG mill is operated; i.e. SSAG, SABC, feed ore size and hardness (coarse feed, fine feed, etc). When you add the open/closed circuit type operation then the number of variables that need to be included in the analysis and selection of an appropriate top ball size becomes too many and the most practical way to select to (top) ball size selection can become a bit experimental. Also as important as the top ball size is the equilibrium ball charge size distribution. Particularly in mills with small grate openings operating at high ball charge / low charge scenario there will be significant quantities of sub optimal size media, which sit in the charge and can, contribute significantly to power draw, but not to throughput hence and the grinding efficiency.

I argue the opposite. Added small ball does increase power and throughput? Consider how grinding works. The peak comminution zone occurs when the force of the charge is maximized at the time when the ore circulation is reversed at the toe. I argue you need an increase in specific gravity of the charge, but, also must be cognizant of the ore filling. Too low a filling lower throughput. Too high a ball charge leads to higher grind rate, but at a high cost of wear. If there is insufficient ore in the high ball content, then overall throughput will suffer.

Larger balls have a small effect on throughput and as stated above will increase P80 size.

I totally agree with you, even belonging to cement industry, we basically see the same with our raw mills, when exaggerating and using too big media. The cascading effect makes sense and it is the essence and first step of downgrading the overall size of material. Certain ball size will have proper trajectory (given mill rot speed and liners). It's for everybody's sake (high production and low costs) important that the maximum ball size strike location on the mill to be at the correct toe/shoulder trajectory estimations, but still on toe, therefore over the ball charge, not on liners (easy if we think a ball mill section, on a polar graph). The risk of oversized ball charge is exactly to overpass this limit trajectory and have balls of max size hitting the liners instead of other balls (at toe location) where actually our precious raw material is sitting, waiting to be ground. Insufficient ore in the high ball content the overall throughput will suffer, as said. As correctly said as well increase in specific gravity of charge make sense up to a certain limit of %, think how many balls can have such trajectory, it is not a desired event: other ball size will have other trajectory (too fine balls will instead increase the dead zone volume of media). There are important studies made on this, and also vibration automation system which can visually predict the best speed of mill, size of balls and filling degree of SAG mills with good accuracy.

What you said it's right, and it has been said on the paper. This work is focussed on Copper Industry as i mentioned on my speech at IMPC 2014 and as it has been said on the paper.

You're arguments are logical, and you can solve it just reading the breakage curve for your process (SAG / Ball Mill) the answer is there.

I do not agree with statements that smaller media (may) (almost always) result in increase in grinding rate. In my earlier comment my specific reference was to the small grinding media that are irregularly shaped (almost coin like in shape and size) not shiny well rounded smaller top size (new) media addition. We all know all grinding media wears down to smaller size but a shape that is different than the staring shape. At what point (size and shape) do the grinding media lose its effectiveness?

Also increasing the proportion of grinding media without regard to the total grinding volume available in a mill may start affecting the grinding / throughput rate. You can add to the discussion the effect of ball trajectory where they should land in the charge, liner wear, lifter height ball size relationship, lifter spacing, etc.

Can I kindly ask you what is the feed size of your material and the expected product size d80? What is the grind ability factor you are looking at in tests for achieving such product fineness? What is your size of mill and average power consumption?

In addition, the throughput is depending on the ore to ball ration and fill % in addition to speed, when the ball trajectory is maximized to hit just short of the toes. The shape does have a small influence on throughput. The lifter shape, dimension, and pitch control the trajectory. The goal is to maximize the mill speed and life for a given lifter geometry that also fits within the liner handler capacity. All of the above have been validated with mill laser scan wear data and PI data via Discrete Element Method (DEM). Power, wear, collision and shear energy are closely matched to physical evidence. We can then program changes in speed to changes in liner wear both on belly lifters, end cone design, grate design plus pan cavity.

Great comments! Recently I’d been focusing on balls (It’s not kind of balls that you are thinking about 🙂 ). Well in SAG mills because of high impact energies, specific hardness is needed. What I mean is that volumetric harness should be soft core hardness. As you know these kinds of steel balls are resistant to impact but at a certain radius (worn balls) the spherical shape of balls will be change to irregular shapes which can affect grinding efficiency badly. So the ball size distribution inside SAG mill will be incomplete. For compensating this issue, extra ball size can be added with top size.