Ball Mill Performance & Efficiency Formulas

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Ball Mill Performance & Efficiency Formulas

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Ball Mill Performance & Efficiency
S. Description Symbol Formula Example
No.
1 Arm of gravity a 0.666 * ( 1 – 4 * R2 )1.5 h 0.583
TAN-1 [ 0.5 / R * (1 – 4*R2)0.5] – [ 2*R * (1 – 4*R2)0.5 ] Deff 4.18
h Centre Distance (from mill centre to media top layer), mts R 0.139
Deff Mill effective diameter, mts a 0.578
R h/Deff, ratio of centre distance to mill effective diameter Target
2 Torque factor matrix u
2 Power consumption, net Pn 0.514 * F * u * n * Deff * a F 175
kW F Grinding media weight, tons u 0.73
u Torque factor n 16
n Mill speed, rpm Deff 4.18
Deff Mill effective diameter, mts a 0.578
a Arm of gravity, – Pn 2538
Target
3 Power consumption, gross Pg Pn * 100 * 100 Pn 2450
kW Em * Eg Em 95
Em Motor efficiency, % Eg 95
Eg Gearbox/girth gear efficiency, % Pg 2715
Target
4 New production rate NPB Formula-1 OPB 118
(Mill output Vs. Blaine) tph OPB OB 4000
Exp ( ( NB – OB ) * 0.49 / 1000 ) NB 5000
OPB Old production rate, tph NPB 72
OB Old blaine, cm2/gm Target
NB New blaine, cm2/gm
Formula-2 OPB 118
OPB * ( OB / NB )1.3 OB 4000
OPB Old production rate, tph NB 5000
OB Old blaine, cm2/gm NPB 88
NB New blaine, cm2/gm Target
5 New production rate NPR OPR * ( 2 – log ( OR ) ) OPR 150
(Mill output Vs. Residue) tph ( 2 – log ( NR ) ) OR 11.5
OPR Old production rate, tph NR 9.5
OR Old residue, % NPR 138
NR New residue, % Target
6 Gypsum set point GSP 21500 * ( Scem – Sclk ) Scem 2.1
(at weigh feeder) tph Pu * ( 100 – Fgyp ) Pu 90
Scem Target SO3 content in cement, % Sclk 0.3
Pu Gypsum purity, % Fgyp 4.8
Sclk SO3 content in clinker, % GSP 4.52
Fgyp Free moisture in gypsum, % Target
7 Maximum ball size MBS 36 * F0.5 * { ( SG * Wi ) / ( %C * Deff0.5 ) }0.333 F 15
mm F Feed size (sieve size in mm which retains 20% material), mm SG 3
SG Specific weight of feed material, gm/cm3 Wi 15
Wi Bond’s work index, kWh/t %C 75
%C Mill speed as %critical, % Deff 5.1
Deff Mill effective diameter, mts MBS 90
Target
8 %Filling %F 112.5 – ( 125 * h / Deff ) h 2.5
% h Free height, mts Deff 4.155
Deff Mill effective diameter, mts %F 37.3
Target
9 Circulation factor C Formula-1 FF 150
F + G CR 170
F C 2.13
F Fresh feed rate, tph Target 2-3
G Coarse return, tph
Formula-2 Rg 54.92
Rg – Rf Rf 3.52
Rg – Rm Rm 34.16
Rg Residue of coarse return, % C 2.48
Rf Residue of fines, % Target 2-3
Rm Residue of separator feed, %
10 Circulation load CL ( C – 1 ) * 100 C 2.48
% C Circulation factor, – CL 148
Target
11 Separator efficiency SE Formula-1 Ro 100
% [log(Ro/Rf) – C * log[{Ro+(C-1)*Rg} / {Rf+(C-1)*Rg}]]*100 Rf 3.52
log(Ro/Rf) – C * log[{Ro+(C-1)*100} / {Rf+(C-1)*100}] C 2.48
Ro Residue of fresh feed, % Rg 54.92
Rf Residue of fines, % SE 68.8
C Circulation factor, – Target 70-80
Rg Residue of coarse return, %
Formula-2 (Fines Efficiency) Rf 3.52
( 100 – Rf ) * 100 Rm 34.16
( 100 – Rm ) * C C 2.48
Rf Residue of fines, % SEf 59.1
Rm Residue of separator feed, % Target 70-80
C Circulation factor, –
Formula-3 (Coarse Efficiency) Rg 54.92
Rg * ( C – 1 ) * 100 C 2.48
C * Rm Rm 34.16
Rg Residue of coarse return, % SEc 95.9
C Circulation factor, – Target 70-80
Rm Residue of separator feed, %
12 Critical speed nc 42.3 / Deff0.5 Deff 4.15
rpm Deff Mill effective diameter, mts Pn 20.8
Target
1 New production rate NPR Formula-1 OPB 118
(Mill output Vs. Blaine) tph OPB OB 4000
Exp ( ( NB – OB ) * 0.49 / 1000 ) NB 5000
OPB Old production rate, tph NPR 72
OB Old blaine, cm2/gm
NB New blaine, cm2/gm
Formula-2 OPB 118
OPB * ( OB / NB )1.3 OB 4000
OPB Old production rate, tph NB 5000
OB Old blaine, cm2/gm NPR 88
NB New blaine, cm2/gm
2 New Specific power cons. Formula
(sp. power Vs. Blaine) NPR E1 E (S1 / S)n
kWh/TC
E1 New specific power E 32.5
E Old specific power S1 5000
S1 New Blaine S 4000
S Old Blaine n 1.3
n Mill exponent for close ckt  = 1.3 E1 43.44
1 New production rate NPR Formula OPB 118
(Mill output Vs. Blaine) tph OPB * ( OB / NB )1.3 OB 4000
OPB Old production rate, tph NB 5000
OB Old blaine, cm2/gm NPR 88
NB New blaine, cm2/gm
2 New Specific power cons. Formula
(sp. power Vs. Blaine) NPR E1 E (S1 / S)n
kWh/TC
E1 New specific power E 32.5
E Old specific power S1 5000
S1 New Blaine S 4000
S Old Blaine n 1.3
n Mill exponent for close ckt  = 1.3 E1 43.44

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