The main purposes of this tutorial are to:

The scenario considered is that of a semi-autogenous grinding (SAG) mill, which is a rotating machine that contains steel balls and ore.

You will learn how to:

And you will use these features:

This tutorial assumes that you are already familiar with the Rocky user interface (UI) and with the project workflow.

The geometry in this tutorial is composed of:

In the tutorial directory the .stl file can be found.

To start the tutorial, you have to create a new project:

The Study entity covers the first step of the simulation setup. The purpose is to define any useful information for the project.

For the Physics step, we will be lowering the softening factor to reduce simulation time, and will also set a rolling resistance model.

For the Modules step, we will be turning on the collection of some additional data.

But before we take these steps, it is necessary to understand more about Modules:

It is also important to understand that some Module settings will override similar default settings in the Rocky UI.

There are several Modules provided by default in Rocky. (Listed on next slides.)

You may also have access to other custom Modules that are not included with Rocky by default.

When working with Modules, it is important to realize that:

The following sixteen Modules are available by default in Rocky:

To enable the modules for this tutorial, do the following:

For this tutorial, we are primarily interested in the power- and energy-related data that will be collected by these Modules.

To save processing power and space, we can limit our collections to only the kinds of data we need.

Let's start by defining what data we want for Boundary Collision Statistics:

Continue with the remaining two statistics modules:

In Rocky, you can use a Breakage Model to simulate the breakage behavior of your particles. For our SAG Mill case, this would be useful information to analyze.

However, breakage models can increase both the computational cost and the processing length of your simulation.

With this in mind, Rocky offers a less costly and faster way to analyze breakage called Energy Spectra, which has the following features:

Collecting these kinds of energy statistics can help with the prediction of breakage and attrition rates for continuous processes such as grinding mills.

In Rocky, energy spectra is defined via two separate modules.

For each module, you can set the following:

After defining the parameter on the module itself, there are module-specific parameters enabled on the particle group and/or geometries involved in the simulation.

These additional parameters define the entity as participating in the energy spectra collection or not.

Let's continue to set up our modules by defining Contacts Energy Spectra:

Repeat similar steps for the Particles Energy Spectra module:

Both of the Energy Spectra modules and the Inter-group Collisions Statistics module enable additional parameters in other parts of the UI.

For each item listed below, you can determine whether it will participate in the type of collection specified:

For the Geometries step, we will import the geometry file in .stl format:

After the geometry is imported, you can view the results in a 3D View window:

You may notice that we have imported only the internal surface of the 3D geometry.

This method is a best practice for mill slice simulations where you are also calculating surface wear modification.

Doing so helps you avoid any potential wear issues that can occur to triangles (shown in green) that are parallel and coincident to the plane used by the periodic domain.

For the Motion Frames step, we will create two separate Rotation motions within the same Frame, and will then apply this Motion Frame to the mill slice geometry.

The two separate motions represent the following actions:

When the motion Type of Rotation is selected, the following options are available:

To add a new Motion Frame, do the following:

To define the first motion frame:

Now let's create a second motion within the same Frame:

Once the Motion Frame has been created, it must be assigned to the geometry.

For this tutorial, since the geometry has a motion with displacement assigned, the movement can be previewed using the Motion Preview window.

The Time toolbar can be used to play the preview. The yellow color of the slider indicates that the simulation has not yet been processed.

For this tutorial, we will activate the Shear Work Proportionality (Archard's Law) wear model on the Mill slice.

To enable this model, do all of the following:

When analyzing wear, it is very important to set the geometry parameters correctly, especially the Triangle Size option.

The number of triangles defines how refined the mesh will be when computing wear (and other geometry results).

Tips for proper meshing:

For this tutorial, we will decrease the triangle size in Rocky to create a more refined mesh.

To change this value, do the following:

Since the original geometry will be modified by the wear model, we will create a reference geometry for comparison purposes.

For the Materials step, we will create two new Materials:

The Default Boundary Material will be used for the mill slice geometry.

The other two default Materials (Default Particles and Default Belt) will not be used in this tutorial.

To create the new Materials, complete the following instructions:

Now let's set the interaction properties for the materials:

For the Particles step, we will create two new sphere-shaped particle groups with some added rolling resistance. These will represent the ore and grinding media.

To create the Rock particle group, do the following:

For the Steel Particles, do the following:

For the Inlets and Outlets step, we will create a Volumetric Inlet, which enables us to fill a spherical region with closely packed particles into the simulation all at one time.

When compared with the traditional Particle Inlet method, using Volumetric Inlet has the primary benefit of ensuring that the particle bed will already be formed in the mill at the start of the simulation.

When defining a Volumetric Inlet, it is important to understand the following components:

For this tutorial, we'll create a Volumetric Inlet constrained only by the mill geometry.

From the Region sub-tab, do the following:

A Contact in Rocky refers to a specific location on a geometry or particle that has experienced a collision with another particle during the simulation.

Always during processing, Rocky calculates and makes use of Contacts data. But to save file space, you can choose whether or not to keep it.

For this tutorial, we will enable the collection of the Contacts data so that we can post-process it later.

For the Domain Settings step, we will define a Cartesian Periodic Domain to recycle particles that leave one side of the mill slice back into the simulation from the opposite side.

For this case, we need Rocky to put any particles that leave the mill slice back into the mill slice.

To do this, we will define a Cartesian Periodic Domain at the extreme ends of the mill slice geometry.

By doing so, any particles that leave one side of the mill slice are introduced back into the simulation from the other side (as shown).

To define this domain, do to the following:

From the Solver | Time tab, do the following:

Once you click Start, the Simulation Summary window will be displayed.

Once initialization is complete, this screen will close automatically and Rocky will process your simulation.

Click the Refresh button (or use the Auto Refresh checkbox) to see the results in a 3D View window during processing.

Particle states can be viewed in real time as the simulation progresses.

The speed of the simulation depends on various factors such as:

This completes Part A of this tutorial.

For further information on any topic presented, we suggest searching the User Manual, which provides in-depth descriptions of the tools and parameters.

To access this manual, from the main Toolbar click Help, point to Manuals, and then click User Manual.

Rocky was used to set up and process a SAG Mill slice simulation that models wear and collects energy spectra data.

During this tutorial, it was possible to:

What's Next? If you completed this tutorial successfully, then you are ready to move on to Part B and post-process this project.

The main purposes of this tutorial are to use the results from the mill slice simulation we created in Part A to learn how to:

You will learn how to:

And you will use these features:

This tutorial assumes that you are already familiar with the Rocky user interface (UI) and with the project workflow.

After processing is complete, the geometry surface will appear to be worn away due to shear contact with the particles.

Comparing the profiles of the worn geometry with the reference geometry you duplicated in Part A (as shown) can help you better identify what changed.

Besides comparing the profiles, another way to analyze the effects of wear is by quantifying the radial displacement of the geometry nodes.

For example, to identify the regions in which the surface wear was most severe, do the following:

You can also analyze the Radial Displacement on a cut plane of the liner profile.

You can view the results in a 3D View window (as shown).

One final way you can analyze your worn geometry is by exporting it out of Rocky and viewing it in CAD or other 3D graphics program.

You can now open your saved .stl file in a CAD program, such as Ansys Discovery.

To analyze the path of the particles, follow these steps:

The Timestep you choose now appears in the Starting Timestep field (as shown).

Number of Timesteps: Defines how many future timesteps for which you want to track the particles. The higher the value, the longer the trajectory will be.

Particle Stride: Defines how the particles will be sampled. One out of n particles will be tracked, where n is the size of the sample. The higher the value, the lower will be the number of trajectories. If 1 is set, all the particles will be tracked.

Now to visualize the trajectories, we'll show them in a 3D View:

The default view that appears is not ideal for viewing trajectories for the following reasons:

Fix these issues with the view by doing the following:

By using the Eulerian Statistics User Process, discrete Properties can be converted into continuous values by averaging the values over discretized regions.

Eulerian Statistics can only be created for a Cube or a Cylinder User Process.

For this tutorial, a Cylinder will be created for this analysis.

This will discretize the Cylinder into 36 circular sectors, each one divided in 20 bins in the radial direction. A single bin is defined in the axial direction, as shown on the following slide.

Once the Eulerian Statistics is created, you can modify which Properties are shown through the Colorings tab.

To better visualize the data, you can adjust the limits of the color scale.

To see a continuous display of the plotted Properties, you can also enable Shown on Node? option.

On the Properties tab for Eulerian Statistics, several new properties are available to plot on the Eulerian bins, including:

This completes Part B of this tutorial.

For further information on any topic presented, we suggest searching the User Manual, which provides in-depth descriptions of the tools and parameters.

To access this manual, from the main Toolbar click Help, point to Manuals, and then click User Manual.

Rocky was used to post-process a simulation of a rotating SAG Mill slice.

During this tutorial, it was possible to:

What's Next? If you completed this tutorial successfully, then you are ready to move on to next tutorial.

The purpose of this tutorial is to evaluate the energy balance of the rotating SAG Mill slice simulation we performed earlier in Part A.

You will learn how to analyze the following Curves:

And you will use these features:

This tutorial assumes that you are already familiar with the Rocky user interface (UI) and with the project workflow.

Size reduction is a very energy-intensive process, representing a major percentage of mineral beneficiation costs.

Although mills have great energy consumption, only a small part of this energy is converted into actual particle fragmentation.

Because of this, it is crucial to understand how power is consumed during comminution processes in order to improve grinding efficiency and reduce costs.

One way this can be accomplished in Rocky is by using a tool called Energy Spectra.

Unlike breakage simulations, which require additional computational costs to calculate and visualize each individual broken fragment, 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.

In Energy Spectra plots, the collision data collected during a simulation is classified based on the energy levels of the individual collisions and then displayed accordingly.

Three types of collision energy can be evaluated using Energy Spectra plots:

Depending upon the source of the energy values considered, two types of Energy Spectra plots are available in Rocky:

To demonstrate how to evaluate breakage rate using an Energy Spectra curve, consider Cumulative Specific Power : Impact as it relates to the energy used in the instantaneous breakage models:

The blue dashed line defines the minimum specific energy for a certain particle to break.

All collisions with specific impact energy higher than this value may lead to breakage. The remaining collisions do not lead to breakage.

The power consumed that actually promotes particle fragmentation is given by the corresponding Y-value.

After the simulation is complete, information about Energy Spectra will be available on the Curves tab for the Particles entity.

The new Energy Spectra Curves will be displayed under two separate groups:

Both Energy and Specific Energy are separated into Impact, Shear, and Dissipation energies.

For Energy (Contacts energy spectra), each pair composed of either Particles & Particles or Particles & Geometries will present a separate Energy Spectra.

Energy Curves are displayed in three ways:

Cumulative sums and averages making use of Cumulative Power, Power, and Rate are computed from the Energy Spectra Start time (which is defined on the Solver | Energy Spectra tab) to the current timestep.

For Specific Energy (Particle energy spectra), each Particle set and Particle Size group will present a separate Energy Spectra.

Specific Energy curves are displayed only as Cumulative Specific Power, which displays the sum of all specific power coming from a collision with energy greater than a specified energy level.

Cumulative Power is computed from the Energy Spectra Start time (which is defined on the Solver | Energy Spectra tab) to the current timestep.

To plot the curves, follow these steps:

To edit the scale, do the following:

The resulting plot is shown on the next slide.

Repeat this same procedure to show Energy : Impact values:

In Rocky, it is possible to analyze how the energy is distributed in the system.

In this tutorial, the energy supplied by the mill is transferred to the particles. Part of this energy is dissipated and another part is transformed into mechanical energy. The equation below shows the Energy Balance of this system:

(4–1)

In terms of Power:

(4–2)

Where:

In Rocky, the power supplied by the mill and the mechanical energy variation of the particles are directly obtained.

The dissipated energy can be obtained directly or by using power curves depending upon how we want to analyze it.

In this way, we have two equations that can be used to calculate the Energy Balance:

(4–3)

(4–4)

For this tutorial, we will use Output Variables to compute the terms of these equations.

The value can be obtained from the Mill geometry by using the Power Curve.

The power supplied by the mill during the last timestep is shown in the Output tab.

The value can be obtained from any of the following Particles data:

For this tutorial, we will use the Energy Delta to compute the Mechanical Energy variation contribution to the energy balance.

The Energy Delta is the variation of the Mechanical Energy in a given timestep.

Since the term that involves the variation of Mechanical Energy is divided by , we can create a Custom Curve of Energy Delta divided by the Output Frequency (which is ).

To calculate the mechanical energy balance, follow these steps:

The power transferred to Mechanical Energy during the last output is shown in the Output tab.

Alternate Method:

can be obtained from the following Particles Properties or Curves:

For this tutorial, we will estimate in two different ways:

First, to calculate using Energy : Dissipation (between pairs of groups), do the following:

The Dissipated Power during the last timestep is shown on the Output tab.

Now, we recall the Energy Balance equation we stated before:

(4–5)

If we compare the values in a spreadsheet, we see that the Energy Balance is satisfied with a difference of ≈ 0.5%.

Next we will calculate using the Cumulative Power : Dissipation from Energy Spectra.

As implied earlier, the Energy Spectra curves are temporal averages.

To compare the dissipated power of the two different methods, instead of using Specific Time as the Operation on Curve in the Dissipated Power (pairs of groups) Output variable, we will be using Average from 7 s (Energy Spectra Start) to 25 s (Simulation Duration).

Since the Cumulative Power : Dissipation are cumulative curves, we just have to sum the maximum value of each pair of groups to obtain the Dissipated Power.

Follow the steps below to compare the dissipated power obtained by the Energy Spectra and the Inter-group Collision Statistics calculation methods.

If we compare the values in a spreadsheet, we see that the difference between the two Dissipated Power calculations is ≈ 1%.

Tips for further exploration:

This completes Part C of this tutorial.

For further information on any topic presented, we suggest searching the User Manual, which provides in-depth descriptions of the tools and parameters.

To access this manual, from the main Toolbar click Help, point to Manuals, and then click User Manual.

Rocky was used to evaluate the energy balance of a rotating SAG Mill slice simulation.

During this tutorial, it was possible to:

What's Next? If you completed this tutorial successfully, then you are ready to move on to next tutorial.