Prediction of power consumption and product size in cone crushing

Minerals Engineering, Vol. 4, No. 12, pp. 1243-1256, 1991

0892-6875/91 $3.00+0.00 Pergamon Press plc

Printed in Great Britain

PREDICTION OF POWER CONSUMPTION AND PRODUCT SIZE IN CONE CRUSHING

R.A. BEARMAN§, R.W. BARLEYt and A. HITCHCOCK§ § Pegson Ltd., Coalville, Leicester LE6 3ES, England f Camborne School of Mines, Redruth, Cornwall, England (Received 1 February 1991; revision accepted 8 March 1991)

ABSTRACT An investigation of the parameters affecting the performance of laboratory scale cone crushers is presented. This work forms part of a rock characterisation initiative undertaken by Pegson Ltd. and the Camborne School of Mines. The effect of feed size, closed side setting and rock strength on the power consumption and product size is examined. Rock strength is characterised via a series o/tests used in mining and associated areas. Certain rock strength parameters have been found to correlate closely with power consumption and product size. These parameters are then combined with closed side setting to produce predictive equations. These equations are capable of predicting power consumption and eighty percent passing size of product for a range o/closed side settings. The predictive equations are presented as a series of three dimensional graphs. The graphs allow the design engineer to envisage the variation in power and product size with variation in operating parameters. In addition to predicting the eighty percent passing product size, a method of predicting the full product grading is presented. This method is based on the Rosin-Rammler-Bennett distribution. The prediction of power consumption and product size/grading is based on a geotechnical approach developed by Pegson Ltd. and applied to the design and selection of crushing circuits. Keywords Comminution, rock characterisation. INTRODUCTION The production of a method of predicting crusher performance in terms of power consumption and product size has been the goal of many workers in the field of comminution. Both Kick [1] and Rittinger [2] proposed basic laws of comminution based on simple ideas of size reduction. Later Bond [3] re-examined their work and proposed his third law of comminution. Bond proposed that power consumption is a function of feed size, product size and crushing resistance of rock, i.e: 1243

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W = f (Fs0, Ps0, Wi) where:W - power consumption (kWh/t), Fs0 - eighty percent passing size of feed (/~m), Ps0 - eighty percent passing size of product (/~m), Wi - Work Index (kWh/t). The basic, parameters proposed by Bond have proved reasonably valid, however their applicability to all forms of crushing must be questioned. In order to investigate power consumption and product size in cone crushing, a major cooperative research project was undertaken by Pegson Ltd., in conjunction with the Camborne School of Mines. The aim of this research project was to identify rock mechanics test procedures that could be used alongside Bond's parameters to better charaeterise the performance of the Pegson Autocone crushers. Also, the potential of using geotechnical evaluation of rock types in the design and selection of crushing circuits was to be brought to the attention of the quarrying industry. TEST PROCEDURE AND CORRELATION OF DATA Twelve rock types were obtained from operating quarries throughout the United Kingdom. This allowed a good cross-section of rock types to be examined. Table 1 gives a summary of the rock types obtained, although a detailed lithological description of most of the rock types is given by Bearman, Pine and Wills [4]. TABLE 1 Summary of rock types tested Mode of formation

Rock type

Igneous

Cliffe Hill diorite, Bolton Hill diorite, Penryn granite, Whitwick andesite

Sedimentary

Harrycroft limestone, Wredon limestone, Middleton limestone, Pennant sandstone, Montcliffe sandstone, Ingleton greywacke, Dairy quarry greywaeke, Nuneaton quartzite

The rock types seen above were crushed down in a laboratory scale jaw crusher and split into three size ranges to act as feed to the laboratory scale cone crusher. The feed ranges used were -16 + 5.6mm, -11.2 + 5.6mm and -10 + 5.6mm. The eighty percent passing feed size was obtained for each rock type and feed range. A laboratory scale, single phase Massco cone crusher (see Plate 1), was then fed with the differing size fractions. Enough feed was prepared to allow the cone crusher to reach the choke fed condition and to then run for approximately 180 seconds. During this time the power consumption was continually monitored using an EW 604 wattmeter recording via a Racal 14 channel recorder. The data obtained in this manner was subsequently filtered to remove mains noise and then logged on to a Grant Squirrel data logger. The interpretation of the data was then performed by down loading the data into the Statgraphics computer package, via Lotus 1-2-3. An example output is seen in Figure 1. The power consumption combined with the throughput allows the kilowatt hour per tonne consumption to be calculated.

Prediction of cone crusher performance

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Plate 1 Massco l a b o r a t o r y scale cone c r u s h e r I

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R . A . BEARMAN et al.

The product obtained from each of the crushing tests was then sized to allow the determination of the eighty percent passing size. From this suite of crushing tests, data relating to power consumption, feed size and product size was recorded. In addition to these parameters, the rock strength was then assessed using a wide variety of tests used in mining and associated industries (see Table 2). TABLE 2 Rock characterisation tests

Source of test

Test

Mining/geotechnics

uniaxial compressive strength, Brazilian tensile strength, Point Load Index, Schmidt hammer, Elastic modulus (static)

Quarrying

Aggregate Crushing Value (ACV),Aggregate Impact Value (AIV), 10% Fines,

Fracture mechanics

Fracture toughness, Spall Fracture Strength,

Geophysics

P and S wave velocities, Elastic modulus (dynamic), Bulk modulus, Modulus of rigidity.

In order to determine which of the tests shown above can be used for predictive purposes a regression analysis was applied. Table 3 lists the tests which correlate with power consumption in laboratory scale cone crushing. TABLE 3 Test parameters correlating with power consumption at the 99.9% level or higher

Brazilian tensile strength Fracture toughness ACV Point Load Index 10% Fines AIV Spall Fracture Strength Table 4 shows the test parameters which were found to correlate with the eighty percent passing size of product. TABLE 4 Test parameters correlating with PeO at the 95% level or higher.

Point Load Index Fracture toughness ACV DEVELOPMENT OF EQUATIONS FOR THE PREDICTION OF LABORATORY SCALE CONE CRUSHER PERFORMANCE An investigation of the effect of feed size and closed side setting on power consumption and product size was undertaken. The findings of this study indicate that the feed size does not have a significant effect on either the power consumption or product size over the normal operating range of the laboratory scale cone crusher. It was found that the closed side setting and the rock strength parameters (shown in Tables 3 and 4), are the controlling parameters when considering power draw and product size, i.e

Prediction o f cone crusher p e r f o r m a n c e

1247

the performance characteristics can be expressed as a function o f the closed side setting and one of the controlling strength parameters: Power consumption ffif(css, Kcb)

where:css - closed side setting (ram), Kcb - fracture toughness ( M N / m 1.5). When power consumption is plotted against fracture toughness for a variety of settings the graph seen in Figure 2 is produced.

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Power consumption versus fracture toughness for a variety of rock types.

Thus the general form of the equation is: Power ffi m Kcb + C where: m - slope c - intercept Kcb - fracture toughness ( M N / m 1.s) To obtain an equation applicable to all closed side settings within the normal operating range the slope and constant need to be expressed as a function of the closed side setting. This is achieved by plotting the slope/constant for each closed side setting against the individual closed side settings. This produces an equation of the form: Power = f(css) Kcb + f(css)

where css - closed side setting (ram), Kcb - fracture toughness ( M N / m 1-5) HE 4 : 1 2 - D

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Prediction of cone crusher performance

1249

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1250

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Prediction of cone crusher performance

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Prediction of cone crusher performance

1253

In Figures 3-9 and 10-12, the following labelling is used:

a) b) c)

-16 + 5.6mm feed, -11.2 + 5.6mm feed, -10 +5.6mm feed.

From the examination of these figures, the effect of feed size is seen to be negligible. DEVELOPMENT OF EQUATIONS TO PREDICT PRODUCT GRADING CURVES The prediction of the eighty percent passing size of product is of great use in the design and selection of crushing circuits. Knowledge of the entire product grading curve is also important. Existing methods of estimating product grading include the Gaudin-Schuhmann (GS), [5], and Rosin-Rammler-Bennett (RRB), [6]. Both these methods rely on certain descriptors within the equation being known. The GS equation is seen below: F(x) = (x/x') n where: F(x) x X' n

- cumulative size distribution, particle size (mm), - reference particle size (mm), characteristic exponent of the distribution. -

-

This equation tends to expand the data below 50% and contract the data above 50%, this effect is more pronounced at the extremes of the distribution. The alternative is the RRB method which expands the range below 25% and above 75%, whilst contracting the range 30-60%. The RRB equation is seen below: In In ( I / ( I - Y ) ) = n In X - n In Xo where: Y n

X Xo

- fraction of cumulative undersize, slope of the RRB graph at 63.21% cumulative undersize, - size fraction (ram), - size fraction at 63.21% cumulative undersize. -

In terms of crushing the RRB method is the most applicable as the range over which it is most accurate is that which applies to crushing. To apply the RRB equation the descriptors Xo and n must be predicted. It has been shown during this project that these descriptors can be predicted using fracture toughness and closed side setting. The mathematical procedure for obtaining these predictive equations is similar to that used earlier in the text to produce equations for power consumption and eighty percent passing size of product. Figures 13 (a) and (b) show the response surface plots representing the predictive equations for estimating the descriptors applying to full scale crushing using the Pegson 900 Autocone. GEOTECHNICAL EVALUATION FOR THE DESIGN AND SELECTION OF CRUSHING CIRCUITS The study undertaken has shown that the geotechnical assessment of a deposit prior to plant installation is essential. A study of the rock strength using a variety of rock mechanics tests gives a good indication of the power requirements, eighty percent passing size of product and the product grading.

R. A. BEARMAN et al.

1254 &.

PREDICTION OF RRB Xo INTERCEPT

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Pegson Ltd. realise the potential of the geotechnics approach and have integrated this approach into their plant design and selection procedure. Pegson Ltd. now provide a full geological and geotechnical assessment of the rock type to be crushed. The data obtained for this purpose includes fracture toughness, compressive strength, point load strength index, ACV, AIV and 10% fines. After experimental work covering jaw crushing and scale up factors, equations applicable to all models of Pegson jaw and cone crushers is now available. The knowledge of these strength parameters combined with the proposed operating conditions and machinery allow a detailed picture of crusher performance to be obtained. A picture which is further enhanced by the use of expert systems shells developed by Pegson Ltd., which aid the engineer in the selection of crushers and screens, [7]. Expert system applications of this type are being expanded to include circuit simulation and fault finding. CONCLUSIONS The co-operative research project between Pegson Ltd. and the Camborne School of Mines has revealed the following: .

Power consumption and eighty percent passing size of product can be predicted for laboratory scale cone crushers based on rock mechanics tests and closed side settings.

.

In laboratory scale cone crushing the feed size does not affect the power consumption or product size over the normal operating range.

.

Power consumption and product size equations produced using a laboratory scale cone crusher can be scaled up to predict the performance of Pegson 900 and 1200 Autocone crushers.

.

The Rosin-Rammler-Bennett grading estimation method can now be used as a tool to predict product grading in full scale cone crushing. The descriptors Xo and n being estimated using a combination of fracture toughness and closed side setting.

.

Use of geotechnical characterisation of rock strength can now provide information essential to the design and selection of crushing circuits. ACKNOWLEDGEMENTS

The authors would like to thank the Camborne School of Mines for the use of their laboratory and computing facilities. In addition the assitance of the experimental officers Mr A. Clark and Mr M. Wyglendacz is gratefully acknowledged.

REFERENCES

.

Kick F., Das gesetz der proportiolalen winderstande und seine anwendugen, Leipzig (1885).

2.

Rittinger von P.R., Lebruch der aufbereitungskunde, Berlin (1867).

3.

Bond F.C., Crushing and grinding calculations, Allis Chalmers publication 07R923513. (1961 ).

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R . A . BEARMAN et al.

Bearman R.A., Pine R.J. and Wills B.A., Use of fracture toughness testing in characterising the commminution potential of rock. IMM/MMIJ Sym. Today's Technology for the Mining and Metallurgical Industries. Kyoto, Japan, 161-180 (October 1989). Schuhmann R., Principles of comminution. Part 1 Size distribution and surface calculations. Trans. AIME, Pub. 1189 (1940). Bennett J.G., Broken Coal. J. Instit. Fuel, 10, 22-39 (1936). Bearman R.A., Barley R.W. & Hitchcock A., The development of a comminution index for rock and the use of an expert system to assist the engineer in predicting crushing requirements. Minerals Eng., 3, No 1/2, 117-127, (1990).