Media Charge_Optimal Ball Size - Ball Mill

7/27/2019 Media Charge_Optimal Ball Size - Ball Mill

1/4

About the Media Charge_Optimal Bal l SizeSpreadsheet ...

Scope :

The Media Charge_Optimal Ball Size spreadsheet was designed to estimate the ideal make-up ball size to any givengrinding application, on the basis of the empirical correlations independently proposed by Ettore Azzaroni and AllisChalmers. In the normal case that such ideal ball size is not commercially available, this spreadsheet also allows for thedesign 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 rechargedto any given grinding mill - in order to achieve maximum performance out of such mill - the following two (amongst othersindependent 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* = Ideal Make-up Ball Size, mmF80 = 80% Passing Size in the Fresh Feed Stream, microns

rs = Ore Density, ton/m3

W i = Bond's Work Index of the ore, kWh/ton (metric)N = Rotational Mill Speed, rpmNc = Rotational Mill Speed, as a percentage of the Mill Critical Speed.D = 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 attachedOptimal Ball Size worksheet. Gray background cells contain the results of the corresponding formulas there definedand 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 theuse of the attached worksheet self-explanatory.

Moly-Cop Tools / 166661717.xls.ms_office 8/23/2013 / 11:38 AM


2/4

Moly-Cop Tools / 166661717.xls.ms_office8/23/2013 / 11:38 AM


3/4

Moly-Cop Tools TM

Remarks :

Mill Dimensions and Operating Conditions :

Eff. Diameter, ft 21.50 Eff. Diameter, m 6.56

Eff. Length, ft 36.08 Eff. Length, m 11.01

% Critical Speed 75.75 Mill Speed, rpm 12.51

Ball Dens., ton/m3

(app) 4.65 Mill Volume, m3

371.69

Ball Filling, % (app) 38.00 Charge Weight, tons 656.22

Scrap Size, in 0.50

Ore Properties :

Ore Density Work Index Feed Size, F80

ton/m3 kWh/ton (metric) microns2.70 15.00 3175

RECOMMENDED OPTIMAL BALL SIZE :

AZZARONI's Formula :

Optimal Ball Size, in 2.16 String Area, m2/m

386.78

ALLIS CHALMERS' Formula :

Optimal Ball Size, in 1.46 String Area, m2/m

3125.85

OPTIMAL MAKE-UP BALL SIZE

Kemess Testing (Ball Mill)



4/4

Moly-Cop Tools TM

Remarks :

Mill Dimensions and Operating Conditions :

Eff. Diameter, ft 21.50 Eff. Diameter, m 6.56

Eff. Length, ft 36.08 Eff. Length, m 11.01

% Critical Speed 75.75 Mill Speed, rpm 12.51

Ball Dens., ton/m3

(app) 4.65 Mill Volume, m3

371.69

Ball Filling, % (app) 38.00 Charge Weight, tons 656.22

Scrap Size, in 0.50

Balanced Charge : Overall

String 1 String 2 Charge Area

Top Size, in 2.00 2.50 Current MixSpecific Area, m2/m3 93.38 75.11 86.78

Recharge Policy, % 68.75 31.25 Target Value

Mill Charge Content, % 63.90 36.10 86.78

Excess Area 0.00

Ball Size, in % Passing % Passing % Passing

2.5 100.00 100.00 100.00

2.0 100.00 40.87 78.65

1.5 31.37 12.82 24.67

1.0 5.88 2.40 4.63

0.5 0.00 0.00 0.00

0.5 0.00 0.00 0.000.5 0.00 0.00 0.00

0.5 0.00 0.00 0.00

Weight, tons 419.29 236.92 656.22

Volume, m3 (app) 90.25 51.00 141.24

Area, m2 8427 3830 12257

# Balls per ton 5666 3087 4735

BALL CHARGE COMPOSITION AT EQUILIBRIUM

Kemess Testing (Ball Mill)


Media Charge_Optimal Ball Size - Ball Mill

Documents

Transcript of Media Charge_Optimal Ball Size - Ball Mill