miguel becerra

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How Standard is The Standard Bond Test?

Miguel Becerra

Peter Amelunxen



Grinding Technology, 1930



Minas Britania, Colombia Británica c. 1930’s

1200 tpd Cu/Au/Zn



Introduction

• The Bond test existed for many years before the

Bond equation

• The work index is an empirical unit of measure

• Differences in test equipment, procedures, and

calculation methods between the variouslaboratories have emerged over the many years



Variations in Mill Dimensions

• Lab 1 and 2: 12 inches diameter by 12 inches in

length

• Lab 3: 12.125 inches diameter by 12.125 inches in

length

• Lab 4: 12 inches in diameter by 11.875 inches inlength

• Lab 5: 12 inches in diameter by 11.5 inches long



Variations in Mill Dimensions

• This Figure shows drum interior after polishing the

surface to avoid the effect of imperfections in the

cylinder



Variations in Ball Charge

Nominal Size Real Size Quantity TotalWeight SuperficialArea

inch CmMax

(inch)

Min

(inch)

Max

(cm)

Min

(cm)N° gr inch

2

1,45 3,68 1,50 1,25 3,81 3,18 43 8800 284,84

1,17 2,97 1,25 1,12 3,18 2,84 67 7209 289,11

1,00 2,54 1,12 0,875 2,84 2,22 10 672 31,52

0,75 1,91 0,875 0,625 2,22 1,59 71 2012 125,88

0,61 1,55 0,625 0,500 1,59 1,27 94 1432 110,18

TOTAL 285 20125 841,55



Variations in Ball Charge (*)

(*) Reproducibility of Bond Work Index with Different Standard Balls Mills, Kaya E. , Fletcher P.C &

Thompson P., SME Annual Meeting, 2002



Variations in The Interpolation Procedure

• Lab 1 : Cubic Spline

• Lab 2: Quadratic Log

• Lab 3: Linear

• Lab 4: Swebrec

• Lab 5: Rosin Rammler

• Lab 6: Modified Rosin Rammler



Example: Variations in The Interpolation Procedure

• These differences can translate into approximately

2.3% difference in the work index

F80 P80 WI WI Calculation

(mm) (mm) kWh/st kWh/mt Method

2.323 2202 174 11.9 13.2 Cubic Spline

2.323 2243 175 11.9 13.2 Quadratic Log

2.323 2258 171 11.7 12.9 Linear

2.323 2225 171 11.8 13.0 Swebrec

2.323 2217 170 11.7 12.9 Rosin-Rammler

2.323 2197 169 11.7 12.9 Rosin-Rammler Modif

Gpr



Modified Bond Test

• The standard Bond test usually requires 6-7 kilos of

minus 6-mesh sample and requires approximately 6

hours, for a skilled technician

• The length of the test is a result of the original

procedures, designed to reproduce the continuousclosed circuit configuration of the ball mill circuits in

use during the 1930’s

• To simplify the laboratory procedures, and to make it

more practical, it was designed as a locked cycle testusing a dry charge, rather than as a wet, continuous,

closed loop test



Modified Bond Test

• The test is deemed an empirical test, as it does not

provide any scalable breakage or fracture kinetics

that can be inserted into an accepted plant-scale

phenomenological model

• For this reason, researchers have been proposingalternative Bond test procedures



Modified Bond Test : Empirical Method

y = 1.0012x

R² = 0.9219

02

46

810

1214

16

1820

222426

28

30

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30

S

t a n d a r d B o n d W

i ( k W h / m t )

Modified Bond Wi (kWh/mt)



Modified Bond Test : Phenomenological Model (1)

y = 0.9852x

R² = 0.6529

0

2

4

6

8

10

12

14

16

18

20

22

24

26

28

30

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30

W o r k I n d e x ( S t a

n d a r ) , k W h / s t

Work Index (Modified), kWh/st



Modified Bond Test : Phenomenological Model (2)

y = 0.9721x

R² = 0.9812

0

2

4

6

8

10

12

14

16

18

20

22

24

26

28

30

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30

W o r k I n d e x ( S t a n d a r ) , k W h / s t




Modified Bond Test : Semi - Empirical Model

y = 1.0059x

R² = 0.9203

0

2

4

6

8

10

12

14

16

18

20

22

24

26

28

30

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30

W o r k I n d e x ( S t a n

d a r ) , k W h / s t




Conclusions

• A survey of Bond mill dimensions was conducted, indicating

that Bond mills vary in diameter and length, sometimessignificantly so. Errors of up to 10% between Bond mills may

result from this variation

• Variations in the method used to interpolate the F80 and P80

values was found to contribute up to 2.3% error to the Bondwork index

• It was found that either the completely empirical approach,

or the semi-empirical method, yields Bond work index

precisions that are adequate for typical geo-metallurgical

programs

• Fully phenomenological models require further development

and will be the subject of future research



Conclusions

• The modified method allows for 7 tests per day

per mill (a team of two)

• Aminpro Chile has completed a study of 500

tests in almost 6 weeks

miguel becerra

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