Media Charge_Optimal Ball Size - Ball Mill

About the Media Charge_Optimal Ball Size Spreadsheet ...

Scope : The Media Charge_Optimal Ball Size spreadsheet was designed to estimate the ideal make-up ball size to any given grinding application, on the basis of the empirical correlations independently proposed by Ettore Azzaroni and Allis Chalmers. In the normal case that such ideal ball size is not commercially available, this spreadsheet also allows for the design of a mix recharge policy (maximum 2 different make-up sizes) with the same ideal ball charge area.

Theoretical Framework : In a first attempt to provide an answer as to what would be the ideal size (diameter) of balls to be continuously recharged to any given grinding mill - in order to achieve maximum performance out of such mill - the following two (amongst others) independent empirical correlations have been proposed in the literature : Ettore Azzaroni's Formula : (3rd ARMCO-Chile Symposium, Nov. 10-14, 1980) dB* = 4.5 F800.263 ( rs Wi )0.4 / (N D)0.25 Allis Chalmers' Formula : (Mineral Processing Plant Design, Chapter 12, SME of AIME, 1980) dB* = 1.354 (F80)0.5 [ rs Wi / (Nc D0.5) ]1/3 where : dB* F80 rs Wi N Nc D

= = = = = = =

Ideal Make-up Ball Size, mm 80% Passing Size in the Fresh Feed Stream, microns Ore Density, ton/m3 Bond's Work Index of the ore, kWh/ton (metric) Rotational Mill Speed, rpm Rotational Mill Speed, as a percentage of the Mill Critical Speed. Effective Mill Diameter, feet.

For further background references on this sort of calculations, see Moly-Cop Tools spreadsheet Media Charge_Strings. Data Input : All input data required must be defined in each corresponding unprotected white background cell of the here attached Optimal Ball Size worksheet. Gray background cells contain the results of the corresponding formulas there defined and are protected to avoid any accidental editing. New Moly-Cop Tools users are invited to explore the brief inserted comments in the most relevant cells, rendering the use of the attached worksheet self-explanatory.

Moly-Cop Tools / 166661717.xls.ms_office

8/23/2013 / 11:38 AM

Moly-Cop Tools / 166661717.xls.ms_office

8/23/2013 / 11:38 AM

Moly-Cop Tools

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OPTIMAL MAKE-UP BALL SIZE Remarks :

Kemess Testing (Ball Mill)

Mill Dimensions and Operating Conditions : Eff. Diameter, ft Eff. Length, ft % Critical Speed Ball Dens., ton/m3 (app) Ball Filling, % (app) Scrap Size, in

21.50 36.08 75.75 4.65 38.00 0.50

Eff. Diameter, m Eff. Length, m Mill Speed, rpm Mill Volume, m3 Charge Weight, tons

6.56 11.01 12.51 371.69 656.22

Work Index kWh/ton (metric) 15.00

Feed Size, F80 microns 3175

Ore Properties : Ore Density ton/m3 2.70 RECOMMENDED OPTIMAL BALL SIZE : AZZARONI's Formula : Optimal Ball Size, in

2.16

String Area, m2/m3

86.78

1.46

String Area, m2/m3

125.85

ALLIS CHALMERS' Formula : Optimal Ball Size, in

Moly-Cop Tools / 166661717.xls.ms_office

8/23/2013 / 11:38 AM

Moly-Cop Tools

TM

BALL CHARGE COMPOSITION AT EQUILIBRIUM Remarks :

Kemess Testing (Ball Mill)

Mill Dimensions and Operating Conditions : Eff. Diameter, ft Eff. Length, ft % Critical Speed Ball Dens., ton/m3 (app) Ball Filling, % (app) Scrap Size, in

21.50 36.08 75.75 4.65 38.00 0.50

Eff. Diameter, m Eff. Length, m Mill Speed, rpm Mill Volume, m3 Charge Weight, tons

Balanced Charge : Top Size, in Specific Area, m2/m3 Recharge Policy, % Mill Charge Content, %

Ball Size, in 2.5 2.0 1.5 1.0 0.5 0.5 0.5 0.5

Weight, tons Volume, m3 (app) Area, m2 # Balls per ton

Moly-Cop Tools / 166661717.xls.ms_office

String 1 2.00 93.38 68.75 63.90

String 2 2.50 75.11 31.25 36.10 Excess Area

6.56 11.01 12.51 371.69 656.22

Overall Charge Area Current Mix 86.78 Target Value 86.78 0.00

% Passing 100.00 100.00 31.37 5.88 0.00 0.00 0.00 0.00

% Passing 100.00 40.87 12.82 2.40 0.00 0.00 0.00 0.00

% Passing 100.00 78.65 24.67 4.63 0.00 0.00 0.00 0.00

419.29 90.25 8427 5666

236.92 51.00 3830 3087

656.22 141.24 12257 4735

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