- To participate in the 911Metallurgist Forums, be sure to JOIN & LOGIN
- Use
**Add New Topic**to ask a New Question/Discussion about Grinding. - OR
**Select a Topic**that Interests you. - Use
**Add Reply**= to Reply/Participate in a Topic/Discussion (most frequent).

Using**Add Reply**allows you to Attach Images or PDF files and provide a more complete input. - Use
**Add Comment**= to comment on someone else’s Reply in an already active Topic/Discussion.

## Feed Size VS Ball Size (7 replies)

From my limited knowledge, yes there exist a relation between the feed size (F80) and the optimal ball size especially in a ball mill operation. Moly-cop tools for evaluation and optimisation of milling circuits can give/predict a very fair ball size to be used for a specific milling circuit taking into consideration the ore (density, bond work index) and operational parameters(mill speed, mill filling degree and effective diameter). Smaller balls are effective in milling smaller particles and they will lose their efficiency with increase in particle size and hence SAG balls are needed to grind big ore particles. SAG mill operation is a bit complicated because of possible fluctuations you might have in your feed size distribution or ore competency. Once calculated this can be optimised by using trajectory spreadsheet from moly-cop tools. I’m attending JK-met course soon and I will be able to compare the two software!

For ball mill, Bond (1958) was proposing an empirical formula giving the top size of balls (make-up balls) DM function of the feed size xG (80% passing size - µm), the ore true specific gravity sg, the ore Bond Work Index Wi (kWh/st), the fraction of critical speed fc and the inside mill diameter D (m):

DM = C (xG)^1/2 * (sg * Wi / 100 / fc)^1/3 / D^1/6

C = 1.114 for wet grinding and C = 1.139 for dry grinding.

xG is the mill feed d80, not the circuit feed.

For SAG mill, the xG value has to be determined by scalping of the full size distribution. The particles larger than the minimum pebble size (given by the pebble extraction grate opening) has to be excluded from the distribution to calculate the top ball size!

There is a relationship. The following equation is used by Moly-Cop, I believe:

d(optimal) = 6.06 * (F80)^(0.263) * (ps*Wi)^(0.4) / (ND)^(0.25)

Where:

d(optimal) is the ideal ball size (mm)

F80 - 80% passing size of feed (micrometre)

ps - density of ore (tonne/m^3)

Wi - Bond's Work Index of the ore, kWh/tonne

N - Rotational mill speed, rpm

D - effective mill diameter (feet)

Granular particles can generally be grabbed (nipped) when the tapered angle between ball and rolling surface is less than 16 degrees. A ball diameter that grabs the particle must exceed the particle by 25 times to achieve this semi-self locking taper.

One can argue the f50 is a more realistic value since balls wear and the average ball size might be closer to half the maximum. Then the multiple would be closer to 13 times the maximum particle size fed to the ball mill. A f80 = 6 mm would need a ball size of 75 mm.

An empirical model from "Emerging Trends in Mineral Processing", 2005, is often used:

Here's location of a simple calculator - web-based - formula shown and data requirement shown:

http://is.gd/aHcRrd

This uses Bond's Formula for ball sizing as discussed in: Bond, F.C., Grinding ball size selection, Mining Eng., May 1958, Trans. AIME, 592-595.

This certainly identifies critical factors for consideration. The Moly-cop tools are worth obtaining - for analysis and understanding of milling circuits.

In cement industry, therefore in dry or wet circuits, I've been using the Bond empiric formulation mentioned above here, plus, with better results the following one, from Allis Chamber:

B = 25.4 (F/K)^0.5 * ((Sg * Wi) / (100 *Cs*(3.281 *D)^0.5))^0.34 result is B maximum ball size(mm),

Data input are D mill inside diameter(m),

F feed size of 80% passing(um),

K constant for 335 dry circuits or 330 wet ones,

Wi bond char material work index

Sg specific gravity (t/m2)

Cs fraction of an integer of critical speed(0.0 -1.0, usually 0.76)

Used for quite a time with great results, considering a coefficient of error if 10%, therefore over sizing, useful to overcome material with high wear rate.

Good to watch for potential build-up of oversize particles when initially running your circuit. There's nothing quite like starting to throw lots of oversize material into flotation.

Good to know the variability of Wi and other factors that might cause this.

Does anyone have a chart to know if there is any relation between the feed size and the size of the ball needed to grind the ore in SAG and Ball mills?