POWER HUNGRYUNDERSTANDING CHARGE MOTION DYNAMICS

INCREASES SAG MILL EFFICIENCY

From cement, to copper and gold production- raw material size reduction is a requirement and grinding mills, the final stage in this process, are the most expensive component to operate. Improvements in SAG mill operation offers the greatest potential for cost savings.        These improvements have arrived in the form of computer simulations and will change the way mills are designed maintained and operated.

The 36 ft. diameter semi-autogenous grinding (SAG) mill pictured to the right smashes up to 55,000 tons of granite ore per day and doing so its twin 6000 horsepower electric motors consume almost 9 MW of power - equivalent to 10 percent of all the electricity used in Fairbanks.                                                     

     Photo courtesy of Fairbanks Goldmining, Inc. (Fort Knox Gold Mine)

Using discrete element method (DEM) mathematical  modeling techniques and Newtonian mechanics, university and private industry researchers have developed 3D software simulations which accurately depict the simultaneous motion of all particles raising and crashing inside the mill.

For nearly 100 years, mill designers have relied on empirical performance data and personal experience to determine mill design specifications. Now, for the first time, a tool is available to evaluate how making such changes as modifying the lifter face angle affects liner wear, power consumption and overall cost per ton of ground material. 

To appreciate the significance and physical validity of 3D mill charge simulationsit is necessary to understand basics workings of a SAG mill, the physics of grinding mill particle trajectory, DEM modeling and how the software evolution.

WHAT IS A SAG MILL?

SAG MILL PARTICLE PHYSICS

DEM MODELING

MILL SOFT - evolution of mill simulation software.

APPENDIX

SAG Mill - Semi-Autogenous Grinding Mill                                   http://images.google.com/imgres?imgurl=http://ffden-2.phys.uaf.edu/211_fall2002.web.dir/Keith_Palchikoff/SAG_parts.png&imgrefurl=http://ffden-2.phys.uaf.edu/211_fall2002.web.dir/Keith_Palchikoff/grinding_mill_2.html&usg=__V2VnVgXmWixoHunngVlo7-N0DKA=&h=1537&w=1626&sz=38&hl=en&start=2&um=1&tbnid=BpOVmjFMz4BsxM:&tbnh=142&tbnw=150&prev=/images%3Fq%3Dsag%2Bmill%26hl%3Den%26rls%3Dcom.microsoft:en-za:IE-SearchBox%26rlz%3D1I7IRFA%26sa%3DX%26um%3D1

                A SAG mill is characterized by its large diameter and short length. It rotates, tumbling its contents violently , causing a breaking action. The mill is lined with wear  resistant steel liners which are fitted with lifters to assist with raising the load. The liners are replaced as they wear and the lifting action has degraded. The load  - dry ore, steel balls and water  - occupies approximately 30% of the volume. The steel grinding balls represent 8% of this volume. Fresh ore is continually conveyed into the mill feed chute and is crushed until small enough to pass though the openings in the discharge grates. The feed rate is limited by the horsepower available to turn the mill and the and the maximum weight the hydrostatic trunnion bearings which support the turning mill shell can withstand.

The power to spin the mill comes from large electric motors coupled to mill shell through a clutch and gear

system. These electricity consumed by these motors is the largest cost and inefficiency. Most of the power is converted to heat in the charge (load) and a small percentage into ore breakage.

The feed end of the 13000 hp Fort Knox

SAG mill.                              The mill is driven by two GE horizontal synchronous variable speed motors, one of which is depicted on the bottom right.         

   

SAG mill feed is conveyed from the coarse ore stockpile. The ore passes through a gyratory crusher where it is reduced to 8 inch diameter before being dumped on the pile.

  A line drawing of the Fort Knox SAG mill liner configuration and spare liners awaiting installation.       

Five and one quarter inch steel grinding balls  - cannon balls - occupy 8% of the mill volume and are consumed in the grinding action at the rate of 600,000 pounds per month. 

The SAG mill and all other grinding equipment is remotely monitored and controlled via computer from a central control room. The control room operator watches four video terminals and a CCTV monitor to keep track of critical process variables impacting mill throughput.

SAG PARTICLE PHYSICSDrawing from Dominion Engineering Works Limited

Energy Concepts  1. Liner design and rotational speed determine manner in which energy is transferred to ore breakage.  2. Input energy is imparted to the grind load by motor causing rotation.  3. The power draw will vary with different liner designs and throughout the wear life and depends on the wear pattern.  4. The most efficient grinding occurs at maximum power draft - operating the mill at its design capacity. 5. Higher energy collisions - caused by greater trajectories are less efficient than those is the lower energy range. Higher energy collisions cause liner damming and increased grind ball consumption.

MechanicsBall and ore particles follow Newton's laws of motion.1. A mill speed approaching 80% of critical can optimize grinding action and reduce wear. A charge with a increased trajectory does less work and more damage as grinding balls are flung against the oppositeside of the shell instead of falling down on top of the central mass.2. Mill critical speed is reached when a particle centrifuges - hangs on to the shell and does not fall. 3. Particle trajectory is independent of mill diameter and therefore optimum % of critical speed is independent of diameter4. A desirable trajectory will not be maintained throughout the

liner wear cycle unless the the wear profile is predictable and can be compensated by varying the rotational speed. 5. The trajectory of each particle is based on its geometry, dimensions, and material properties of grinding balls, steel liners and ore type.

The KEY concept is liner design has most effect on charge motion  - particle trajectory - and optimizing this charge motion can increase mill efficiency - reducing wasteful, power

consuming  collisions.

                                                                                                                                                                  DEM software simulated SAG charge motion, Conveyor-Dynamics.com

Optimizing liner design requires a valid charge motion model. The new DEM software, an image shown here,describes the performance of independent mill styles and liners

configurations.

DISCRETE ELEMENT METHOD

What is DEM?   DEM is a mathematical modeling technique that applied to communition uses Newton's second law - kinematics - to calculate the position of each elements  - balls and ore particles of all sizes  - as they are affected by each other and in contact with liners, lifters and grates. The first DEM models for milling were 2D and viewed the charge motion as a cross sectional slice of the cylindrical mill. The models improved into 3 space which included the effects of the cone shaped mill ends on particle motion. Recent improvements, a visual example displayed to the right, have incorporated other modeling methods such as computational fluid dynamics and discrete grain breakage.

High Fidelity Simulation is the term now used to describe the combined modeling techniques.

DEM continued...

DEM is well suited for computer programming since the computations involve solving the position formula simultaneously for huge number of particles and one instance in time. These vector based motion equations use fixed parameters for particle shape, density, stiffness, friction. Linear and rotational velocities of each photo from Conveyor-Dynamics.com sphere are calculated via numerical integration of  Newton's second law. The displacement of each sphere is calculated by a second integration. The particles start at rest and then set in motion. The calculation is performed for an initial t, then t +1, t+2, t+n.

THE SOFTWARE - MILL SIMULATIONS                   

This collection of charge profiles was generated by MillSoft - the initial DEM based 2D and later 3D mill modeling software. These profiles demonstrate the effect of changing liner style on charge motion. Improved mill efficiency is possible when a liner design is selected which minimizes contact between the cascading grinding media and opposing cylinder wall. In this series of models, it appears the configuration shown below - Hi Lifters with increased slant angle- demonstrate the best charge profile. The circular lifters shown at the far left are fitted on a ball mill  - which unlike a SAG mill, works to grind particle by rubbing the media together - not crashing and smashing.

APPENDIX

Information Sources

1. Rajamani,R.K., Joshi,A.D.,Mishra,B.K., 2002, "Simulation of Industrial SAG mill charge motion in 3D space",2002 SME Annual Meeting  pages 1-9

2. McIvor, R.E., 1981, "The effects of Speed and Liner Configuration on Ball Mill Performance", 1981 SME Fall Meeting, pages 1-10

3. ME International, Inc., reprint of Fort Knox Liner Drawing

4. WWW.Conveyor-Dynamics.Com, information and picture of DEM modeling software

5. Herbst,John, and Nordell,Lawrence,"Optimization of the Design of SAG Mill Internals Using High Fidelity Simulation", SAG 2001 conference, Vancouver,B.C  pages 1-5

6. Mishra,B.K, Rajamani, R.K., Songfack, P., Venugopal,R. 1999,"Millsoft - simulation software for tumbling mill design and troubleshooting",Mining Engineering, Dec.1999, pages 41-47

7. "Mill Power", Process Engineering of Size Reduction, pages 231-236

8. Fairbanks Goldmining,Inc., Fort Knox Gold Mine, site visit and mill photographs