# Understanding the Working Principle of a Ball Mill for Efficient Grinding

Understanding the Working Principle of a Ball Mill for Efficient Grinding

In grinding, selecting (calculate) the correct or optimum ball size that 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.

Here is your ball mill design/sizing procedure.

Calculation of top size grinding media (Fred C. Bond)

Calculation of top size grinding media AZZARONI’s Formula

If you calculate from Figure 5 assuming you want/target a P90 of 60 microns you get around 22 mm (<1 inch) as a ball size. This is quite the difference…

OPTIMAL BALL DIAMETER IN A MILL

Grinding_Operations_Design

Preferred size of balls for ball mills, does not correspond to the optimal ball charge –, which means there’s a problem in design.

This is because the grinding balls can be greater than 100 mm diameter. The biggest balls in the charge, and with the decreased maximum size of the ball’s wear-rate will correspondingly decrease. Also, if the media is too large, then the size of particles that need to be ground may be adversely affected because of improper falling motion.

The rotational speed of the milling jar should be 65% of the critical speed of the jar. The critical speed is the speed when a ball mill becomes a centrifuge and may be calculated for a specific jar and ball diameters as follows:

CS[rpm] = 2676 / √(D [mm]).

where D is the internal diameter in meters.

In practice, Ball Mills are driven at a speed of 50-90% of the critical speed, the factor being influenced by economic considerations. Mill capacity can be increased by increasing speed but there is very little increase in efficiency (i.e kWht^-1) when the mill is operated above about 40-50% of the critical speed.

Before we go any further, a few terms need to be defined:

The critical speed of a mill is defined as the lowest rpm necessary to centrifuge an infinitely small particle next to the shell lining within the mill. By equation:

Where CS is the theoretical critical speed of rotation, and is the mill speed, rpm;

Mill diameter is the nominal inside diameter of the mill, m.

Since we are working with humans, a small change in efficiency can make a big change in profitability.

Therefore, besides ensuring that particles being dealt with are smaller than the ball size, at the same time, use small balls? What is the effect of low ball% full on grinding efficiency? One answer if the mill diameter is greater than 3.81m. The detrimental effects being the ‘build-up’ of coarse free gold, on the grinding circuit. In this case, an extra heavy ball charge up to 50% might be required. This page is about a SABC/AG/Ball/rod mill circuits.

Under specific conditions, it will grind finely crushed ( -6mm) ore to 75 microns. This is a Dual Media mill (rod or ball). This continuous grinding mill is offered as a wet or dry mill.

As such, FLSmidth has supplied some of the world’s largest horisontal grinding mills with ball mills up to 28ft in diameter (22MW) and SAG mills up to 40ft in diameter (28 MW).

By rearranging the equation to DMilling, the tonnage of rougher feed produced each year (the total tonnage of mill feed, mill discharge and classification overflow) from the mill mass flow rate is obtained. An energybased model was used to simulate the measured data.

This enabled study of the effects of lifter configuration and mill speed on the net power draw of the mill and final grinding circuit efficiency.

While too low a speed loses efficiency. While the viscosity is less contractor.