Contents
Ball Mill Performance & Efficiency Formulas
| 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 | ||||||