IMPROVED DEM MODEL FOR PREDICTING CONE CRUSHERS

PERFORMANCE

V. Murariu

METSO USA

4820 Centennial Blvd.

Colorado Springs, Colorado 80919

vasile.murariu@metso.com

D. Jacobson

METSO USA

20965 Crossroads Circle

Waukesha, Wisconsin 53186

dusty.jacobson@metso.com

ABSTRACT

Cone crushers have been applied in mineral processing or comminution circuits for

over a century. In that period of time, the principles of machine selection and optimization

have evolved from purely empirical methods (capacity tables and product size curves based

on best practice) to include newer simulation based approaches. A specific simulation

technique combines the strength of theory with traditional population balance techniques.

Metsos crusher simulation employs DEM with a proprietary fast breakage technique using

the concept of incremental damage. This technology has been successfully used to predict

cone crusher performance and in designing of new crushing equipment. This paper provides

an overview of the Metso cone crusher simulation technology, and highlights the value of the

virtual machine for equipment design and optimization.

INTRODUCTION

Modeling and simulation of cone crushers in order to predict performance is of great

importance when predicting the performance for the design and optimization of crushing

plants. There are many models and simulation tools with a view to explain the processes;

laboratory scale studies from academia concentrating on understanding the physical

phenomena, and then expressing that by mathematical means. The industry-based studies are

structured more towards gathering data on the performance of the crushers in relation to

existing design and operating conditions.

One of the first models of crushers was published in 1953 and 1954 by Gauldie [1-2]

in which he presents a method for prediction of the throughput for a jaw and cone crusher. His

assumption is that a material volume slides down the crusher cavity until it is nipped between

the two crushing surfaces. The material is assumed to behave plastically and to be porous. At

the same time, the material is considered non-sticky and a friction force determined by a

friction coefficient is describing the sliding process between the crusher parts and ore

particles. The results of the model are the throughput and whether or not the crusher can be

choke-fed. One of the drawbacks of this model is that the free fall of the particles is not

included. The free fall phenomena might occur at high eccentric speeds and it will affect the

throughput of the crusher. The other drawback is that the model might not really preserve

continuity. The model assumption that the feed material has bulk properties of porous plastic

clay might lead to inaccurate results.

Bearman [3] has proposed a set of predictive equations in a form of three dimensional

graphs to predict the power consumption and product size of a laboratory scale crusher. The

effect of feed size, closed side setting (CSS) and rock strength on the power consumption and

product size has been examined. In addition to predicting the product size, a method of

predicting the full product grading is also presented. The method is based on the Rosin-

Rammler distribution and the authors concluded that this method could be used as a tool to

predict the product grading of a full scale cone crusher.

A method for prediction of cone crusher performance based on Gauldies flow model is presented by Evertsson [4]. His method can predict both product size distributions and total

capacity of a cone crusher. By combining these results a Crusher Performance Map (CPM) is

obtained. The CPM is a description of crusher performance over a wide range of variation in

the operational parameters. The analytical model presented in this paper can be used to

optimize a single crushing stage if the feed properties are known.

An improved flow model for the cone crushers is presented by Evertsson in this paper

[5]. The new flow model describes the movement of an aggregate of particles down a crusher

using equations of motion. A constitutive relation between size distribution and the

uncompressed bulk density of the material is presented. Along with compatibility conditions

from the crusher geometry, mass continuity is preserved. The flow model provides detailed

information about how different machine parameters affect the flow of the rock material

through the crusher chamber.

A model to predict crushers performance has been developed by Ruuskanen [6]. The model is predicting the product grading, product shape, crusher capacity, crusher power and

Manganese consumption using the feed and the crusher parameters as inputs. The essential

part of the model is to find, by using extensive experiments, the relationship between different

parameters and then to describe the crushing phenomenon in mathematical terms. The model

is implemented in Metsos Bruno simulation program, which enables the prediction of the overall crushing plant performance.

All the models of the cone crushers described above have their own limitations and

have been developed under certain assumptions which limit their capability of predicting the

crusher performance under a wide range of operational and geometrical parameters. This

paper will describe Metsos current 3D Discrete Element Method (DEM) modeling techniques developed to allow a comprehensive study of the effect of different crusher

variables on actual performance of the crusher.

DESCRIPTION OF THE DEM WITH FAST BREKAGE MODEL

The Discrete Element Method (DEM) is a numerical technique in which the equations

of motion of every particle in the system are integrated numerically at every time step. Thus,

the motion of every particle is known in great detail. DEM simulations are often used to

simulate the flow of unbreakable particles in material handling applications within reasonable

time frame.

The application of DEM to crusher simulation must overcome an additional challenge.

The particles passing through the crusher must be broken and the DEM requires additional

realistic and fast breakage models. These breakage models must consider the ore properties

and the loading information from the DEM simulations and calculate the resultant size

reduction. On the other hand, the breakage model must provide the resultant forces that the

rocks apply to the mantle and liner.

The Newtons Second Law of motion is numerically solved in DEM simulations for

each particle in the system. If mi is the mass of the particle moving with velocity vi under the

action of a collection of forces fij including gravitational forces, friction, particle-particle,

particle-fluid and particle-boundary interaction forces the Newtons Second Law can be

written as:

(1)

The DEM modeling of the particles in this paper is done by using 3D polyhedral

particles.

Early techniques to develop a breakage model used clamps constructed of sub-

particles glued together by contact forces that are able to withstand specific tensile stresses

before being broken. This approach can provide good results but the computational time for

such technique is significantly high. The new approach referred as Fast Breakage (FB)

described by Potapov [7] combines DEM with Population Balance Modeling (PBM) and has

largely overcome the limitation of the clamps breakage modeling. The inherent requirement

for a realistic and robust breakage model is the conservation of mass and volume. The FB

model developed by Metso is using polyhedral shaped particles. This paper presents the

validation of the FB model against MP1000 and MP1250 Metso tertiary crushers.

METHODOLOGY AND EXPERIMETS

The validation exercise was based on plant data obtained on two new MP1000 and

MP1250 tertiary cone crushers. The crushers used were crushers with new liners for which the

cavity profile was very well known. By using new liners the effect of wear is eliminated from

the experiments. The feed material was copper ore and Drop Weight Tests were carried out at

Metso Technology Department in Colorado Springs, USA in order to determine the breakage

characteristics of the ore.

Feed and product samples were taken from the plant and the size distribution was

measured. During experiments the operating data was collected from the ASPEN software.

The measured data was Power Draw and Throughput. The crusher Closed Side Setting (CSS)

was reset within the previous half day of the test, if not sooner. A speed sensor verified the

crusher speed. The two tests used for the validation were named Test J for the MP1000 new

liner crusher and Test A for the MP1250 new liner crusher. Historical data shows that the

crushers may not be at peak production when the liners are completely new, however testing

in this condition allowed for more accurate replication of the chamber profile at the time of

testing. The operating parameters for the two tests are presented in the Table 1 below.

Table 1 Operating parameters for the crusher tests

Test name Crusher Type CSS (mm) Speed (rpm)

Test J MP1000 16.25 890

Test A MP1250 19.05 805

The feed size distributions for the two tests are shown in Table 2.

Table 2 Measured Feed Size Distribution for the two tests

Test J Test A

Size (mm) %Cum %Cum

101.6 100 100

76.2 100 98.6

50.8 96.4 81.8

38.1 76.6 53.6

25.4 27.8 18.0

19.05 8.8 3.5

12.7 1.7 0.9

The measured data of the two tests are presented in the Table 3 below.

Table 3 The measured Throughput, Power and P80 for the two tests

Test name Throughput

(mtph)

Power Draw

(kW)

P80

(mm)

Test J 400 655 13.7

Test A 705 800 13.2

DEM SIMULATIONS RESULTS FOR MP1000 AND MP1250 CRUSHERS

The DEM simulations of the two crushers were carried out on Metso proprietary Fast

Breakage code. The two crushers geometries were created using the drawings of the two cavities as provided by Metso Waukesha.

The ore used in the test work was analyzed and its breakage properties were determined. The

DEM code is generating polyhedral shaped particles of a certain size based on the feed size

distribution presented in Table 2. The particles are dropped into the crusher hopper in layers

of randomly distributed particles. The main goal was to fill the cavity as soon as possible and

to reach the cavity level that was observed during testing. Once this cavity level is reached the

simulation is run until the steady condition is reached. At steady conditions the throughput

and the power draw has reached a steady average value over the time. Figure 1 shows two

snapshots taken during simulation of the two crushers. On the images the instantaneous power

draw and throughput at the time when the snapshot was taken are also shown. The power

draw shown and calculated during the simulation represents the net power and doesnt count for drive losses in the crusher. Therefore, the measured power represents the total gross power

while the simulated one represents the net power. There is a difference of 10% to 20%

between the net power and the gross power. The images also show that the full cavity level

conditions have been reached for both simulations.

TestJ Snapshot

TestA snapshot

Figure 1 Snapshots of the two DEM simulations

The comparison between the simulation data and the experimental plant data is presented on

the plots below. In Figure 2 the throughput comparison for the two crushers versus measured

data is shown. The horizontal lines represent the measured value while the variable data

shows the simulated values. It can be easily notice that the simulation data reaches a steady

state after about 3 seconds of running time and the averaged simulated values match well with

the measured values.

Figure 2 Comparison between the measured throughput and the simulated one for the two crushers

Figure 3 shows the comparison for the power draw. As it has been mentioned before the

simulation can predict only the net power while the plant data is measuring the total electrical

power. Therefore, the simulated data shows a lower power draw than the measured one. The

difference between the simulated power draw and the total power draw measured at the plant

represents the losses and a 20% of the total power could be considered often as a good

approximation for it.

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tph

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Test J Test A

Figure 3 Comparison between the simulated values for the net power draw and the total measured power

The comparison between the measured and the predicted product size distributions of the two

crushers is plotted below.

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Feed-TestJ

Product - Test J -Experiment

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Figure 4 Comparison between the simulated size distribution and the experimental one for both tests

CONCLUSIONS

This paper has presented the results of two DEM simulations with Fast Breakage Code for

two tertiary crushers MP1000 and MP1250 set up to match site test conditions. The results

were compared with experimental plant data on the respective crushers. The experimental

work was carried out on crushers with relatively new wear liners in order to eliminate the

effect of abnormal chamber profile on the comparison exercise.

The estimated results are very close to the experimental data proving that Metso DEM Fast

Breakage code is a very powerful tool which could be successfully used to optimize the

design of the cone crushers liner profile or the crushers itself for better performance.

The model will aid in the selection of crusher design and parameters for any given criteria or

application, as well as the use in product development. The current DEM model is a micro

model and is sensitive to all aspects of a crusher design and operation while the previous

models were tailored for certain plants or experimental setups. The data provided by the

model can be also highly localized and thus opens the possibility of developing wear models

that will be sensitive to ore and crusher parameters.

The current DEM Fast Breakage code is implemented in Metsos PROSim plant simulating software and it can be used to predict crusher plant overall performance.

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Product - TestA -Experiment

Product - TestA -Simulation

REFERENCES

1. K. Gauldie, Performance of Jaw Crushers, Engineering, October 9, 1953, 456-458, October 16, 1953, 485-486.

2. K. Gauldie, The Output of Gyratory Crushers, Engineering, April 30, 1954, 557-559.

3. R.A. Bearman, R.W. Barley and A. Hitchcock, Prediction of Power Consumption

and Product Size in Cone Crushing, Minerals Engineering, Vol. 4, No.12, 1991,

1243-1256.

4. C.M. Evertsson, Output Prediction of Cone Crushers, Minerals Engineering, Vol.

11, No. 3, 1998, 215-231.

5. C.M. Evertsson, Modelling of Flow in Cone Crushers, Minerals Engineering, Vol.

12, No. 12, 1999, 1479-1499.

6. J. Ruuskanen, Influence of Rock Properties on Compressive Crusher Performance,

PhD Thesis, Tampere University of Technology, Tampere 2006.

7. A.V. Potapov, J.H. Herbst, M. Song and W.T. Pate, A DEM-PBM Fast Breakage

Model for Simulation of Solid Fracture of Comminution Processes, Proceedings of

the MEI Discrete Element Method (DEM) 2007 Conference