## A study of comminution in a vertical stirred ball mill.

##### Abstract

A 20 litre experimental batch and continuous test rig and 5 litre batch
and 50 litre continuous test rigs for stirred ball milling were built at the University
of Natal and Mintek respectively. All the mills featured a grinding vessel with a
central shaft equipped with pins and a torque measurement system. A washed
chrome sand from the Bushveld Igneous Complex was used for the grinding
experiments. Particle size analysis of products was performed using standard
sieves and a Malvern Particle Sizer.
Batch tests were run in the 20 litre stirred ball mill to achieve efficient
grinding conditions. The effects of grinding conditions such as pulp density, media
size, media density and shaft rotation speed and mill design parameters such as
ball load, pin spacing and pin diameter on product size, power consumption and
media wear were studied. It has been shown that the median size of the product
can be calculated by the Charles' Energy-Size Equation.
The stirred ball mill has been found to be more energy efficient than the
tumbling ball mill. An energy reduction of 50% was possible for a product size of 6
microns when the stirred ball mill was employed instead of the tumbling ball mill.
The energy input per ton of grinding media in the stirred ball mill could be 10 times
higher than for the tumbling ball mill. Although during coarse grinds the media
wear was higher in the stirred ball mill than in the tumbling mill, it became less so
as grinding proceeded and for a product median size of 4.8 microns it was the
same.
Using a 5 litre batch mill, an experimental programme was designed to
study the comminution characteristics of the stirred mill. A factorial design was
prepared with the following parameters, which influence grinding in the stirred ball
mill: pulp density, pin tip velocity and ball density and size. The energy required for
grinding the chromite sand in the stirred ball mill was determined by the use of
Charles' Equation. The findings were in agreement with the results predicted by
this equation. It was shown that the Rosin-Rammler size distribution equation was
a suitable procedure for presenting and comparing grinding data obtained from the
stirred ball mill. The factors that had the greatest effect on grindability were, in
order of importance: ball size, pin tip velocity and ball density. Interactions
between grinding parameters were negligible. results implied that accurate
predictions can be made to determine the grinding conditions required to achieve
a desired product specification.
An attempt was made to study the grinding kinetics the chromite are
using the mass population·balance model. Grinding tests were performed with two
mono size fractions ·53+38 and -38+25 microns and natural feed ·100 microns
using various pin tip velocities, ball densities and within the normal stirred
ball milling operating range. relationship between the ball diameter and the
particle was explained by the "angle of nip" theory which applied for roller
crushers. It was shown that the particle giving the maximum breakage rate
was directly proportional to the ball diameter. Estimated grinding kinetic
parameters from monosize provided a good basis for predictions of
natural feed. However, the breakage rate obtained from monosize tests
appeared to be lower than those from the natural feed It was found that if the
selection and breakage functions were determined by monosize tests, it was
possible to modify selection function parameters by back-calculation which gave
the best fit to the natural feed size. A good correlation was obtained between the
experimental and product distributions using a population-balance
model. The links between the empirical model combining Charles' and
Rosin-Rammler equations and the first-order batch grinding equation were also
shown.
The stirred ball mills were operated in batch and continuous mode. The
median size of the products from the batch stirred ball mill experiments closely
matched those of the continuous grinding experiments under similar grinding
conditions. Using a salt solution as a tracer material, an attempt was made to
estimate the residence time distribution based on a simplified analysis of the
motion of the water in tile mill.
The current scale-up methods for the stirred ball mill are discussed. A
torque model was developed for given shaft geometry and ball relating the
power rements of the stirred ball mill to the following prime design and
operating parameters : mill diameter, mill height, pin tip velocity and effective
density of the mill load. The basic assumptions underlying the model were that the
mill content behaved as a fluidised bed, consequently a P effg h type model for the
pressure was applied throughout the grinding media bed the effective charge
velocity was proportional to the pin tip velocity. It was found that pin spacing, pin
diameter and ball diameter significantly affected the mill torque. A semi-empirical
torque model was derived to include these parameters. The relationships
formulated from these models were shown to be in excellent agreement with
experimental results.