# Predicting particle breakage with contact-based Energy Spectra

Quite often DEM users are interested in **predicting particle breakage**, either to promote it (for example, spending less energy in comminution processes) or to avoid it (such as preventing tablet break in coating processes).

Although it is possible to simulate particle breakage in Rocky, you can drastically decrease the computational cost by using another Rocky tool: **Energy Spectra**.

This useful tool collects different kinds of **collision statistics** and can help predict breakage and attrition rates for continuous processes. The types of energy statistics Rocky collects can be categorized into two groups:

**Particle-based statistics:**Energy is gathered per**particle type**, resulting from**all**the collisions the particle has been involved in a given timestep, regardless of the entity the particle has collided with. You can find here more details about the**Particle-based Energy Spectra**and how to use it i.

**Collision-based statistics:**Energy is collected per**collision type**; i.e., every particle-to-particle or particle-to-boundary impact will have its resulting collision energy stored. Therefore, each**pair**— composed of either two Particle Groups or one Particle Group and one Geometry — will present a unique**Energy Spectra**curve, separated into Normal and Tangential components.

**Contact-based Energy Spectra: How to Use It**

If **Contacts Energy Spectra **is enabled, Rocky calculates energy curves for each pair of particle-to-particle or particle-to-boundary contact types, separated by the Normal and Tangential contact types (Figure 1).

*Figure 1. Example of Collision Energy Spectra curves for a SAG mill analysis.*

These curves can be displayed in three different ways: **Power**, **Cumulative Power**, and **Collision rate**. You can choose the curve that best fits your needs and generate a Cross plot (as shown in Figure 2).

*Figure 2: Example cross plot showing both Cumulative Power (Normal) and Power (Normal) for collisions between rock particles and the liner in a SAG mill analysis.*

**Contact Energy Spectra: Why Use It?**

This feature is useful when you are interested in understanding how energy is distributed amongst collisions, i.e, comparing the **frequency** and **power** between different colliding pairs.

Let’s pick one common application to illustrate how useful this tool is: **SAG mills**. Users might be interested in comparing the **rock-rock** and **rock-grinding media** collisions rate (which would lead to both rock **comminution** and **ball wear**) with the energy involved in **ball-ball** collisions (which can lead to **ball wear**), **rock-liner** collisions (which can lead to **liner wear**) and **media-liner** collisions (which contributes to **ball and liner wear**). This is exactly what the **Contact Energy Spectra** tool provides us!

**Contact Energy Spectra: How to analyze it?**

A **SAG mill** simulation (Figure 3) was run in order to illustrate how to use the **Contact Energy Spectra** curves. A 1.9 m slice of a standard 11 m diameter **SAG mill** was used (typically applied for hard rock mineral processing). The rotational velocity of the mill is 9 RPM, around 67% of the critical speed. The overall fill level of the charge is 20% of the mill volume, while the steel ball loading (grinding media) is around 20% of the charge (by volume). The rock size distribution varies from 100-200 mm whereas the ball size is fixed in 0.2 m.

*Figure 3. SAG mill slice showing steel balls and rock particles.*

Figure 4. Cumulative power distribution of normal collisions for various particle-to-particle and particle-to-geometry contact pairs in a SAG mill analysis.

Figure 4 shows the **cumulative normal power distribution** for various particle-to-particle and particle-to-geometry contacting pairs. Assuming restitution coefficients of 0.3 for all interactions (so that 91% of the energy that goes into the collision is dissipated), it can be seen that around 60.3% of the (0.91*7.4) MW = 6.734 MW power draw is dissipated in rock-liner collisions (leading to both rock comminution and mill wear), 30.4% in rock-rock collisions (leading to rock comminution) and 7.5% in rock–ball collisions (leading to both rock comminution and ball wear). Only 0.95% of the energy is lost in ball-ball collisions, which lead to unwanted ball wear, while 0.77% of the energy is lost in ball-liner collisions, contributing to ball and liner wear.

But these are overall values. Let’s take a closer look at these interactions by analyzing simultaneously the collision rate and power plots for each contacting pair.

Figure 5 shows the **power distribution** in a non-cumulative way, while **the frequency distribution **of the collisions for various contacting pairs in a SAG mill analysis is shown in Figure 6.

*Figure 5. Power distribution of normal collisions for various particle-to-particle and particle-to-geometry contact pairs in a SAG mill analysis.*

*Figure 6. Frequency distribution of normal collisions for various particle-to-particle and particle-to-geometry contact pairs in a SAG mill analysis.*

Regarding the rock-rock interactions, Figure 5 shows that strongest dissipation rate occurs around 2J, with around 250 kW involved in these collisions. Figure 5 also shows that the most energetic collisions have energy around 100 J (and are due to the largest rock particles falling from the top and hitting the cataracting stream), whereas Figure 6 shows that the frequency of such high-energy impacts is small.

The rock-rock collisions that occur more frequently have very low energy (around 0.1 J, shown in Figure 6). Actually, even though a relevant number of collisions with this energy or even lower energies occurs, the energy dissipated by these low-energy collisions is minimal, as shown in Figure 5.

Regarding the rock-liner interactions, although Figure 6 shows that collisions rate are similar for a wide range of collision energies, Figure 5 shows that most of the dissipation occurs around 40J due to rock particles falling from the top of the stream and hitting directly the liner at the bottom. Although these collisions can lead to rock breakage, they will also lead to liner wear and should be avoided.

Similarly, the ball-liner energy dissipation is concentrated around 40J due to unwanted collisions of steel balls hitting directly the liner when falling from the cascading stream. These can lead to both balls and liner wear and should be minimized.

With this information on their hands, engineers can use **DEM simulations** to explore **design modifications** (for instance, modifying the liner geometry) and **operating parameters** (such as assessing the impact of the mill velocity, feed and ball size distributions and mill filling ratio) in order to shift energy dissipation from **non-useful/harmful** categories (such as liner collisions) to desired collisions (rock–rock and rock–media collisions), henceforth improving grinding rates.

**Particle and Contact Energy Spectra: Workshop**

Can’t wait to get your hands dirty and test both Particle and Contact Energy Spectra tools? Check it out in this **workshop** from our Customer Portal. The purpose of this workshop is to show how to perform an **Energy Spectra Analysis** on the simulation of a Semi-Autogenous Grinding Mill (SAG Mill) and also analyze surface **wear modification**. Step-by-step instructions are included with some best-practice rules and tips

**Mill design: Webinar**

Interested in using **DEM **for designing mills? In** this webinar**, Jason Aldrich from Conveyor Dynamics, Inc. (CDI) will explain how the Rocky DEM enables CDI to evaluate and optimize their designs faster and with higher accuracy. Specific Rocky features key to understanding mill liner designs will be demonstrated, including Eulerian statistics, particle trajectories, energy spectra, liner surface wear modification, and power consumption.