XXXI International Mineral Processing Congress 2024 Proceedings/Washington, DC/Sep 29–Oct 3 3687
tan P kD DJ J Se 3
.9
.7
gross b c
2
0
2 a =+-cL ^0.05ARh m_J it (3)
where:
Pgross =Gross power at motor, kW
K =Coefficient depending on discharge type
(grate =0.255 and overflow =0.222)
D =Internal mill diameter between liner plates
not the effective diameter, m
Lb =Internal belly length, m
J =Total load, fraction
α =Angle of conical ends, sexagesimal degree
c t =Charge density, t/m3
S =Speed, rpm
AR =Aspect ratio (D/Lb)
e =2.71828…
The charge density is calculated from:
%S %S
J
J J Jbh
100
100
s
c
c s
c
t
f fch
t
tbb
=
-+--
+Jf
+-
^1
f
^^1 h
p
(4)
where:
Jb =Ball load, fraction
b t =Ball density, t/m3
c f =Porosity of the charge, fraction
%S =Percent solids in the slurry
s t =Ore density, t/m3
The proposed equation (3) works for total loads less than
50% and speeds less than 100% of critical speed.
For the equation (4) and then replacing in the equa-
tion (3), εc and ρb have been taken as 0.40 and 7.8 t/m3
respectively, so the correct application of the equation (3) is
always considering εc as 0.40.
Then, applying the proposed model by the equation
(3), the Figure 4 shows its parity graph for the 191 indus-
trial data sets from Table 1.
RESULTS AND DISCUSSION
The Table 2 shows the mean and standard deviation of the
proposed model.
The power prediction has been expressed in term of
gross power, i.e., motor input power. If the reader is inter-
ested in power at the pinion like the Bond and Austin mod-
els, one must apply the corresponding efficiency factors of
losses for each type of motor and drive.
Figure 3. Observed vs predicted power draws (S. Morrell–IMPC 2003)