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Analyze grinding efficiency by using particle Energy Spectra

Comminution is a term used for size reduction due to the application of energy. It is known as an energy-intensive process, representing a major percentage of mineral beneficiation costs. In an ore beneficiation plant, for example, comminution can be responsible for up to 70% of production costs, either due to power consumption or equipment parts degradation due to wear.

Quite often Autogenous (AG), Semi-Autogenous Grinding (SAG) and Ball Mills are present in mining and mineral processing plants. The grinding process of these tumbling mills is produced by a range of mechanisms including high-speed impact, abrasion, chipping and nipping of small particles between large ones due to the rotation of the mill upon its horizontal axis.

Although mills have great energy consumption, only a small part of this energy is converted into actual particle fragmentation. As an example, Cleary (2000) points out that the power consumption for a 5×7 m ball mill can reach 3.5 MW and only 1 to 5% of this power is directed to size reduction!

So why are tumbling mills so very inefficient?

It is mainly due to the fact that not all impacts lead to breakage. Impacts of low energy will not cause breakage, while excessive intensity impacts apply only part of the energy used to the breakage process. The rest is lost.

Given the above, it is not surprising that regardless of the industry, everyone seeks greater efficiency with these kinds of equipment, and many look to reduce costs caused by power consumption and liner changes, as well as increasing mill throughputs while keeping within the desired product size range.

Therefore, it is crucial to understand how power is consumed during comminution processes in order to improve grinding efficiency. One way this can be accomplished in Rocky DEM is by using a tool called Particle Energy Spectra.

Particle Energy Spectra: Why Use It?

Unlike breakage simulations, which require additional computational costs to calculate and visualize each individual broken fragment, Particle Energy Spectra uses energy statistics of particle collisions to predict breakage and attrition rates in a graphical format. This provides answers to breakage questions faster by avoiding the computationally intensive visualization step of the particles actually breaking.

A typical example of this energy statistics representation is the cumulative energy spectrum. Energy spectra represent statistics for specific energy applied to particles per unit of time. By looking at energy levels applied to particles you can predict breakage rates for continuous processes such as grinding mills (Figure 2).

Figure 1: Example plot showing Particle Energy Spectra for a rotating mill

In the plot above, the Y-axis gives the Cumulative Power (energy per unit time) resulting from all collisions with specific energies above the respective specific energy value. It accounts for all collisions with specific energy equal to or higher than the specific energy.

Why it is plotted this way? Notice that the blue dashed line defines the minimum specific energy for a certain particle break, which is known by the user.

All collisions with specific energy higher than this value may lead to breakage. All the remaining collisions would not lead to breakage. Therefore, the power available for this breakage is given by the corresponding Y-value.

Particle Energy Spectra: How to Use It

If you choose to collect particle energy spectra during your simulation, Rocky will calculate new energy curves for each particle group generated by each size of the particle size distribution, and separated by Normal and Shear Specific Power. These curves are grouped under specific energy on the Curves tab (Figure 3).

Figure 2: Curves tab for Particles showing new section for specific energy curves

Using these curves, you can then create a Cross Plot, similar to the example below (Figure 4).

Figure 3: Cross plot of showing energy spectra values

Besides saving you computational time when compared to typical breakage calculations, the Particle Energy Spectra tool can be used to help you decide easily between two different mill geometries, choose the optimal rotational velocity, or even compare the breakage efficiency for different ball sizes.

Particle Energy Spectra: How to Calculate Throughput

So what if it is not enough to simply compare two or more designs, but you need to calculate the throughput instead?

Doing so is just an additional math step. For each size group used, you get a different power value for a given specific energy value. That power value is fed into an equation that determines the probability that a particle from that group breaks.

With this probability in hand, the T10 curve for each particle size is obtained, which multiplied by the mass of that particle group tells you how much of each size group is created.

Tally up the size group of interest (typically the size that can fit through a mesh grate) and that gives you the tonnage. Divide the Power by the rate of throughput to get the efficiency (kW-h/T).

And with that, Particle Energy Spectra helps gives you the throughput value you needed without having to deal with large and time-intensive breakage simulations. How great is that!

Particle Energy Spectra: Combining Analyses

Lastly, the Particle Energy Spectra analysis ability can be combined with Rocky’s surface wear modification model. That means that you can not only evaluate breakage efficiency BUT ALSO effectively see how liner shape changes due to wear caused by particles. All in a single simulation. Nice, right?

Video 1. Rocky simulation video of a Mill slice showing surface wear modification

CLEARY, P. 2000. Charge behavior and power consumption in ball mills: sensitivity to mill operating conditions, liner geometry and charge composition. International Journal of Mineral Processing, 63, 79-114.

By Lucilla Almeida and Katie Aldrich


Rocky is a powerful, 3D discrete element modeling (DEM) program that quickly and accurately simulates particle behavior within a conveyor chute, mill, or other materials handling system. Rocky analyzes media flow patterns and energy absorption rates, particle breakage, and energy spectra analysis. The software optimizes life expectancy of conveyor belts and components, minimizes material spillage in a design, and reduces the need for dust control and suppression, among numerous other applications. This software is a revolutionary way to handle a problem through computer simulation.

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