# Real time Optimization Using Smart Sensors

SAG mills present a dual nature. One of simplicity, and a second of extreme complexity. They appear simple, just a big rotating drum. Big rocks go in one end, they come out smaller on the other. But this simplicity belies a much more complex truth. What happens inside them is unbelievably complex. The interactions between individual particles, grinding media, the liners and the fluid flows make for an extremely difficult to solve set of equations to describe the motion, and breakage of the particles. DEM modeling has shown us a very good picture of what happens inside and has proved to be a major step forward in design of mill liners, discharge grates etc., and to establish good starting points for mill control.

During operation however, the major variables that determine SAG mill performance are unmeasured and changing. SAG mills perform size-reduction through two major modalities, impact and attrition. For the purpose of this discussion let us think of impact as a parent particle breaking into multiple smaller child particles where the size of the child particles is dramatically smaller than the parent. These impacts are largely orthogonal. Let us think of attrition as a parent particle having just a small piece broken or removed, leaving it roughly the same size as before, but with a very small child particle removed. These interactions are largely very tangential. At any given moment, both types of size reduction are present in the mill. Breakage is happening as particles cataract down from their highest point, and break as they impact the toe of the charge, the liner, or are impacted from above by a grinding ball. Attrition happens large in the center of the charge volume at a region where there is an interface of high shear. Particles on one side of the interface are being lifted, while on the other they are cascading down the charge body, with high frequency small shear interactions.

This post largely focuses on impact breakage. It is our experience that the impact breakage of coarse hard rocks is very commonly the rate limiter for concentrator production. It is also very sensitive to operating conditions in the mill.

The energy for breakage is provided through the mill rotation to repeatedly lift and drop rocks. We will look closely at the trajectory of the dropped rocks, and we propose that understanding, and subsequently measuring trajectory is the key to maximizing impact breakage, and thus for a large subset of operational conditions maximizing SAG mill throughput, and concentrator throughput.

The kinetic energy of a falling object increases linearly with distance fallen. The breakage of characteristics of rocks do not follow a simple linear function, there is a complex relationship with minimum values required for breakage, which can explain why mills must “grind out” when they have become overloaded. There is a point at which impact breakage drops off so significantly, the mill’s performance is only restored by stopping new feed altogether until the volume load is reduced enough. Volume load is very important, as it represents the bottom end of the potential trajectory. The higher the volume load of the mill, the less distance the falling rocks can fall. The top end of the trajectory is determined by the combination of mill speed and liner profile.

The most energy for impact breakage is achieved by the longest vertical distance fallen. One might try to simplify this to believe that the most energy is achieved by the highest lift then, but this is incorrect. The mill liners in addition to lifting, also apply a translational force sideways. The trajectory is not vertical, but parabolic. More mill speed does indeed induce more lift, but it also induces more translational force. The rocks are not falling on to a flat surface, but a curved one. If they translate too far towards the opposite side of the mill they will not fall as far, as they will impact the shell of the mill too high. Thus, maximizing impact energy is not simply maximizing mill speed. **To further complicate matters, the horizontal velocity introduced by the liners changes with time as liners wear. **This means that for a given RPM, the horizontal component will decrease significantly over time meaning that we can’t simply create an empirical 2-d table that correlates load and RPM to mill performance because these combinations will be change with liner wear. Therefore we must optimize the combination of mill speed and volume load for current combination of liner profile, size distribution and specific gravity (bulk density) of the feed material. Mill Speed and specific gravity are readily available, and size distribution can be inferred using Ore Cameras. This leaves us needing mill load and liner profile. Mill load has traditionally been inferred from bearing pressure, despite having many shortcomings. Liners are often a blind spot. To address these gaps in data, we developed a sensor many years ago that will accurately measure these.

## Mill Scanner

In order to improve the real time optimization of the SAG mill, we sought to more directly measure charge trajectory rather than rely solely on proxy measurements. As a sensor, the mill scanner is simply a programable radio and 3 axis accelerometer. It attaches to the shell of the mill, and constantly samples and transmits the accelerometer values. It’s industrial design, energy harvester and software to interpret the transmitted data make it special. It has no batteries, powers itself whenever the mill is turning, and has no need for an external indexing for location, and self-locates correctly in either direction, over the full range of operational speeds of the mill.

**With this sensor we now know how full the mill is (volumetric fill measurement), and where the charge is impacting (throw)**. Once we know these things, we can adjust the load and RPM so that the trajectory of the ore optimizes breakage.

Liner profile is of extreme importance, as it directly transfers rotational energy of the mill into potential then kinetic energy of the lifted and dropped particles. The interaction of the particles on the face of the lifters determines their trajectory for any given mill speed. This interaction has been explored in depth in academia and by liner manufacturers. For the purposes of operating the mill, we must take what we are given and optimize under all conditions. The liner profile changes slowly over time as the liners wear. This has many effects and will be discussed further below. The trajectory changes, the mass of the mill changes, and the volume of the mill changes as the liners wear. None of these properties can be measured during mill operation, so they must be inferred from other measurements. The following time series shows the measured throw angle of the mill over several months starting with a liner change and normalized for mill speed.

## How To Turn Instrumentation into Throughput

By using the Millscanner sensor to collect data over the period of a liner life, we can correlate mill performance to ore types and liner profiles. Once this correlation has been modeled, these models can be used in realtime with the Millscanner sensor to suggest optimal load and RPM configurations to increase throughput. The idea is that we can adjust feed rate and RPM to maintain the ideal volumetric fill level and Throw so maximize breakage in realtime. We do this using machine learning algorithms over large sets of data to create realtime models, but a low resolution example can be created in excel for the sake of this post. First we can take the data spanning over a liner change, and isolate it by load ranges. For this example, I will use two crude bearing pressure ranges, low and average, and then separate the Throw into three categories (low, medium, high). We can then see how throughput changes with through for low and medium loads. Below is the result of performing this data sorting for the average load range. You can see that as throw increases so does throughput, but it begins to drop off sharply after 30 degrees.

Next, we can observe how throw will affect throughput for a low load condition:

**In this case, you can see that a high throw actually hurts throughput, as predicted previously. **This is a perfect example of how **slowing** the RPM will actually *increase* throughput! Furthermore, we can see that a medium throw and lower load actually yeilds the highest possible average feed rate (1770t/hr).

While this is a crude example, our machine learning system does a similar analysis but with a significantly higher resolution. Below is an example of this system in use. This particular example is the result of us outputting load and RPM targets (as governed by the measured throw) to an existing expert system. The expert system then adjusts feed rate to reach the desired load.

As you can see, by limiting RPM and selecting load targets using a Millscanner sensor, you can see significant increases in throughput over an existing expert system! This is an amazing example of a combination of automation, instrumentation, and large scale data analysis / machine learning models to see real world benefits. Please feel free to reach out to me with any questions.

Eric