3881
Using Functional Performance Analysis and Apparent
Cumulative Grinding Rates to Optimize the Processing
Performance of Ball Milling Circuits
Kyle Bartholomew, Omar Arafat, Robert McIvor
Metcom Technologies, Inc.
ABSTRACT: Functional Performance Analysis of Ball Milling provides a clear understanding and uniquely
defines the separate roles of Circuit Classification System Efficiency and Ball Mill Grinding Efficiency. Each
of these efficiencies can be increased by following specified procedures to adjust circuit design and operating
variables. Apparent Cumulative Grinding Rates (ACGR), including the Functional Performance Mill Grinding
Rate at the size of interest, characterize the mill grinding performance both simply and accurately. Examples
of the use of said procedures to improve the performance of industrial ball milling circuits are presented. They
provide a practical and effective alternative to classical circuit computer modelling and simulation.
DERIVATION OF THE FUNCTIONAL
PERFORMANCE EQUATION FOR WET
BALL OR PEBBLE MILLING CIRCUITS
It was while studying the contrast in performance between
ball mill circuits with high versus low circulating load ratios
that the idea of using the portion of the mill solids con-
tent that is “coarser” than the target grind size for down-
stream processing, and also representing the same portion
of the mill power being applied to “coarse” material, as
one measure of circuit efficiency was conceived. (McIvor,
1988 McIvor et al, 1990). Davis (1925) demonstrated in
the pilot plant the enormous effect that the mill circulating
load has on the circuit productivity (Figure 1).Two plant
cases revealed that this was a direct effect of the extremely
different size distributions passing through the mill with
low versus high circulating load (Figure 2). Given a target
circuit classifier product passing size, say a given sieve size,
or perhaps the eighty percent passing size (P80), a much
larger fraction of the solids coarser than those sizes was
present in the mill feed and discharge as a result of high
circulating load ratio.
Davis (1946) also collected and measured the size dis-
tribution of the contents of a continuous, wet ball mill,
showing that the size distribution of the contents could be
estimated by averaging the size distributions of the mill feed
and discharge. This completed the picture. The sizing of the
mill solids feed/discharge/contents would depend also on
factors besides the circulating load ratio, like the separa-
tion performance of the classifier. All such related effects
combine to provide the “Ball Mill Circuit Classification
System Efficiency (CSE),” equal to the fraction/percentage
of the mill solids coarser than the circuit product target size.
That this also represents the fraction/percentage of the mill
power being effectively applied to grind material coarser
than the circuit product size is clearly true, if not in an
absolute sense, then certainly in a relative one.
As an example, the ball mill circuit depicted in
Appendix A by Clark et al., 2023, targets a P80 of 75
microns, and the ball mill power is 9,315 kW. The ball mill
Using Functional Performance Analysis and Apparent
Cumulative Grinding Rates to Optimize the Processing
Performance of Ball Milling Circuits
Kyle Bartholomew, Omar Arafat, Robert McIvor
Metcom Technologies, Inc.
ABSTRACT: Functional Performance Analysis of Ball Milling provides a clear understanding and uniquely
defines the separate roles of Circuit Classification System Efficiency and Ball Mill Grinding Efficiency. Each
of these efficiencies can be increased by following specified procedures to adjust circuit design and operating
variables. Apparent Cumulative Grinding Rates (ACGR), including the Functional Performance Mill Grinding
Rate at the size of interest, characterize the mill grinding performance both simply and accurately. Examples
of the use of said procedures to improve the performance of industrial ball milling circuits are presented. They
provide a practical and effective alternative to classical circuit computer modelling and simulation.
DERIVATION OF THE FUNCTIONAL
PERFORMANCE EQUATION FOR WET
BALL OR PEBBLE MILLING CIRCUITS
It was while studying the contrast in performance between
ball mill circuits with high versus low circulating load ratios
that the idea of using the portion of the mill solids con-
tent that is “coarser” than the target grind size for down-
stream processing, and also representing the same portion
of the mill power being applied to “coarse” material, as
one measure of circuit efficiency was conceived. (McIvor,
1988 McIvor et al, 1990). Davis (1925) demonstrated in
the pilot plant the enormous effect that the mill circulating
load has on the circuit productivity (Figure 1).Two plant
cases revealed that this was a direct effect of the extremely
different size distributions passing through the mill with
low versus high circulating load (Figure 2). Given a target
circuit classifier product passing size, say a given sieve size,
or perhaps the eighty percent passing size (P80), a much
larger fraction of the solids coarser than those sizes was
present in the mill feed and discharge as a result of high
circulating load ratio.
Davis (1946) also collected and measured the size dis-
tribution of the contents of a continuous, wet ball mill,
showing that the size distribution of the contents could be
estimated by averaging the size distributions of the mill feed
and discharge. This completed the picture. The sizing of the
mill solids feed/discharge/contents would depend also on
factors besides the circulating load ratio, like the separa-
tion performance of the classifier. All such related effects
combine to provide the “Ball Mill Circuit Classification
System Efficiency (CSE),” equal to the fraction/percentage
of the mill solids coarser than the circuit product target size.
That this also represents the fraction/percentage of the mill
power being effectively applied to grind material coarser
than the circuit product size is clearly true, if not in an
absolute sense, then certainly in a relative one.
As an example, the ball mill circuit depicted in
Appendix A by Clark et al., 2023, targets a P80 of 75
microns, and the ball mill power is 9,315 kW. The ball mill