About the Mill Power_SAG Mills Spreadsheet ...
Scope : The Mill Power_SAG Mills spreadsheet was designed to estimate the Net and Gross Power Demand (kW) of a semiautogenous grinding (SAG) mill, as a function of its known dimensions and basic operating conditions.
Theoretical Framework : The Net Power Demand of a SAG mill may be well estimated by the simple Hogg and Fuerstenau Model (“Power Relations for Tumbling Mills”, Trans. SME -AIME, -AIME, Vol. 252, pp. 418-432, 1972), here expanded from its original formulation to represent the independent contribution of each component of the mill charge (balls, rocks and slurry) to the total net power draw of the mill : Pnet =
Pgross = 0.238 D3.5 (L/D) Nc
ap
(J - 1.065 J2) sin
where : Pgross h D L Nc J a
= = = = = =
gross power draw of the mill (kW) = Pnet / h. electrical and power transmission efficiency, efficiency, °/1. effective mill diameter, ft. effective mill length, ft. tumbling speed; expressed as a fraction (°/1) of the critical centrifugation speed : Ncrit = 76.6/D0.5. apparent volumetric fractional mill filling, °/1 (including the balls, the rocks and the interstitial voids in between such balls and rocks). = charge lifting angle (defines the dynamic dynamic positioning of the center of gravity of the mill load (the ‘kidney’) with respect to the vertical direction. Typically in the range of 40° to 45° 45°.
and where rap denotes the apparent density of the charge (ton/m 3), which may be evaluated on the basis of the indicated charge components (balls, rocks and interstitial slurry) : ap
= { (1-f v)
b
Jb + (1-f v)
m
(J – Jb) +
p
Jp f v J } / J
In this formulation, the contribution to the net mill power by the balls in the charge becomes : Pb = [(1-f v)
b
Jb /
ap
J] · ( Pgross)
Similarly, the contribution to the net mill power by the rocks in the charge becomes : Pr = [ (1-f v)
m
(J - Jb) /
ap
J] · ( Pgross)
and finally, the contribution of the slurry in the charge becomes : Ps = [
p
Jp f v J /
ap
J] · ( Pgross)
Data Input : All data required by the m odel must be defined in each corresponding unprotected white background cell of the here attached Data File worksheet. Gray background cells contain the results of the corresponding formulas there defined and are protected to avoid any accidental editing.
Moly-Cop Tools TM SAG MILL POWER ESTIMATION Hogg & Fuerstenau Model Remarks
Example : 36'f x 17' SAG Mill.
Mill Power, kW 5142 3344 1491 9977 3.00 10286
Balls Rocks Slurry Net Total % Losses Gross Total
Mill Charge Weight, tons Ball O´size Interstitial Charge Rocks Slurry 215.79 140.33 62.55
Apparent Density ton/m3 3.222
Mill Dimensions and Operating Conditions Diameter Length Mill Speed Charge ft ft % Critical Filling,% 35.00 17.00 76.00 28.00 rpm 9.84
Balls Interstitial Filling,% Slurry Filling,% 10.00 60.00
% Solids in the Mill Ore Density, ton/m3 Slurry Density, ton/m3 Balls Density, ton/m3
Charge Volume, m3 129.94
Moly-Cop Tools / 138332517.xls.ms_office
78.00 2.80 2.01 7.75
Lift Angle, (°) 45.00
4/6/2013 / 1:45 PM
