3728 XXXI International Mineral Processing Congress 2024 Proceedings/Washington, DC/Sep 29–Oct 3
Table 7. A database of industrial ball mills (Morrell 1993)
Mills’ Discharge
Mechanism
and Size
Operating
Parameters
Actual
Gross
Power
(kW)
Predicted Gross Power (kW) MAPE
Original Models
Modified
Morrell C-Model
Modified H&F
Model Original Models
Modified
Morrell
C-Model
Modified H&F
Model
Discharge
Mechanism
D
(m)
L
(m) CS
Jt
(%)
ρo
(gr/cm3)
Morrell
C-Model
H&F
Model
By
Eq. 10
by
Eq. 18
By
Eq.10
by
Eq. 18
Morrell
C-Model
H&F
Model
By
Eq. 10
by
Eq. 18
By
Eq.10
by
Eq. 18
Overflow 2.3 4.2 0.82 36 7.98 299 280.77 261.32 300.65 291.80 275.15 272.15 6.10 12.60 0.55 2.41 7.98 8.98
Overflow 2.65 3.4 0.77 36 4.97 334 312.10 301.43 325.09 322.52 317.39 313.93 6.56 9.75 2.67 3.44 4.97 6.01
Overflow 2.52 3.66 0.67 35 8.04 265 249.65 231.23 259.84 258.36 243.71 241.75 5.79 12.74 1.95 2.51 8.04 8.77
Overflow 3.48 4.62 0.71 39 8.88 834 785.05 719.92 819.69 814.11 759.93 753.59 5.87 13.68 1.72 2.38 8.88 9.64
Overflow 3.54 4.88 0.76 42 11.31 1029 939.39 864.88 980.84 973.72 912.67 904.62 8.71 15.95 4.68 5.37 11.31 12.09
Overflow 4.12 5.49 0.75 45 6.69 1600 1528.82 1416.43 1595.35 1584.49 1492.92 1480.50 4.45 11.47 0.29 0.97 6.69 7.45
Overflow 4.38 7.45 0.75 30 0.81 2026 2030.93 1951.32 2106.09 2088.84 2042.34 2021.04 0.24 3.69 3.95 3.10 0.81 0.22
Overflow 5.29 7.32 0.7 40 10.65 3828 3500.24 3242.10 3650.086 3627.07 3420.28 3393.20 8.56 15.31 4.65 5.25 10.65 11.36
Overflow 4.8 6.1 0.69 40 11.92 2498 2250.10 2084.84 2348.22 2333.47 2200.23 2183.11 9.92 16.54 6.00 6.59 11.92 12.61
Overflow 3.05 4.27 0.7 40 12.55 580 533.62 781.46 573.14 570.14 507.22 503.30 8.00 16.99 1.18 1.70 12.55 13.22
Overflow 2.6 3.7 0.69 40 16.23 347 319.81 275.91 330.99 329.31 290.69 288.50 7.84 20.49 4.61 5.10 16.23 16.86
Overflow 3.05 4.27 0.73 45 10.42 600 584.89 510.73 606.59 603.22 537.49 533.43 2.52 14.88 1.10 0.54 10.42 11.10
Overflow 3.5 4.42 0.74 35 9.91 820 757.79 701.53 789.32 783.34 738.71 731.75 7.59 14.45 3.74 4.47 9.91 10.76
Overflow 3.04 3.05 0.82 45 10.18 475 386.04 405.32 400.53 397.81 426.63 422.75 18.73 14.67 15.68 16.25 10.18 11.00
Overflow 2.29 2.74 0.83 44 26.84 235 173.13 163.26 179.54 178.31 171.93 170.30 26.33 30.53 23.60 24.12 26.84 27.53
Grate 1.7 2.7 0.81 40 17.43 103 101.81 80.62 106.15 105.30 85.05 84.19 1.16 21.73 3.06 2.23 17.43 18.26
Overflow 3.55 4.87 0.72 40 11.28 970 893.65 815.36 915.89 926.47 860.58 853.37 7.87 15.94 5.58 4.49 11.28 12.02
Overflow 3.5 4.75 0.75 42 7.39 921 885.56 808.37 924.17 917.69 852.94 845.59 3.85 12.23 0.34 0.36 7.39 8.19
Overflow 0.85 1.52 0.71 40 25.63 10 8.63 7.05 8.97 8.92 7.44 7.38 13.70 29.53 10.30 10.80 25.63 26.23
Overflow 0.85 1.52 0.71 20 27.29 6.8 5.83 4.83 6.03 5.88 4.94 4.90 14.26 28.95 11.32 13.53 27.29 28.00
Overflow 4.75 6.26 0.77 28 0.91 2050 2057.91 1984.03 2127 2108.80 2068.72 2046.33 0.39 3.22 3.76 2.87 0.91 0.18
Overflow 3.85 5.9 0.77 30 7.42 1300 1217.46 1150.51 1257.83 1250.67 1203.60 1190.86 6.35 11.50 3.24 3.79 7.42 8.40
Grate 2.64 3.66 0.7 43 27.54 420 377.38 288.43 393.91 391.47 304.32 302.02 10.15 31.33 6.21 6.79 27.54 28.09
Overflow 4.12 7.04 0.7 38 4.14 1800 1742.01 1634.60 1820 1807.89 1725.44 1711.08 3.22 9.19 1.11 0.44 4.14 4.94
Overflow 3.48 6.33 0.75 34 9.34 1150 1030.48 991.11 1106 1095.50 1042.65 1032.47 10.39 13.82 3.83 4.74 9.34 10.22
Overflow 5.34 8.69 0.73 28 0.04 3669 3607 3517.01 3725 3696.40 3667.44 3631.67 1.69 4.14 1.53 0.75 0.04 1.02
Overflow 5.34 8.69 0.73 26 1.52 3549 3421 3364.91 3521.3 3494.30 3494.97 3460.42 3.61 5.19 0.78 1.54 1.52 2.50
Overflow 5.34 8.69 0.73 24 2.33 3385 3224 3197.57 3306 3281.70 3306.03 3272.99 4.76 5.54 2.33 3.05 2.33 3.31
Overflow 5.34 8.69 0.73 23 1.40 3251 3123 3108.18 3196.1 3171.57 3205.54 3173.36 3.94 4.39 1.69 2.44 1.40 2.39
Overflow 5.33 8.54 0.72 34 4.44 4100 3860.9 3722.35 4026 3995.70 3918.13 3882.19 5.83 9.21 1.80 2.54 4.44 5.31
Overflow 5.29 7.32 0.7 40 10.65 3828 3500.3 3242.10 3650 3627.07 3420.28 3393.20 8.56 15.31 4.65 5.25 10.65 11.36
Overflow 4.87 8.84 0.75 30 2.14 3225 3107.5 3014.83 3224.7 3197.80 3155.95 3123.72 3.64 6.52 0.01 0.84 2.14 3.14
Overflow 4.87 8.84 0.72 27 2.04 2900 2748.5 2727.11 2840 2817.30 2841 2813.25 5.22 5.96 2.07 2.85 2.04 2.99
Overflow 4.85 5.92 0.73 41 8.64 2550 2393.6 2207.78 2498.8 2481.70 2329.68 2310.14 6.13 13.42 2.01 2.68 8.64 9.41
Overflow 4.73 7.01 0.61 32 6.99 1840 1847.8 1872.04 1922.2 1911.60 1968.69 1954.97 0.42 1.74 4.47 3.89 6.99 6.25
Overflow 4.68 5.64 0.72 48 12.00 2300 2115.1 1925.51 2202.1 2189.08 2023.97 2009.72 8.04 16.28 4.26 4.82 12.00 12.62
Overflow 4.41 6.1 0.74 35 3.51 1900 1915 1743.97 1983.6 1970.60 1833.35 1816.62 0.79 8.21 4.40 3.72 3.51 4.39
Overflow 4.1 5.92 0.75 34 3.33 1525 1504.5 1402.16 1564 1552.10 1474.18 1459.96 1.34 8.06 2.56 1.78 3.33 4.27
Overflow 3.83 4.83 0.63 31 3.70 842 777.5 771.97 808.2 803.34 810.85 804.77 7.66 8.32 4.01 4.59 3.70 4.42
Overflow 2.6 4.57 0.75 34 9.25 400 370.8 345.04 385.8 388.60 363.02 359.47 7.30 13.74 3.55 2.85 9.25 10.13
The mean absolute percentage error (MAPE) 7.02 12.86 4.41 4.73 8.97 9.65
Table 7. A database of industrial ball mills (Morrell 1993)
Mills’ Discharge
Mechanism
and Size
Operating
Parameters
Actual
Gross
Power
(kW)
Predicted Gross Power (kW) MAPE
Original Models
Modified
Morrell C-Model
Modified H&F
Model Original Models
Modified
Morrell
C-Model
Modified H&F
Model
Discharge
Mechanism
D
(m)
L
(m) CS
Jt
(%)
ρo
(gr/cm3)
Morrell
C-Model
H&F
Model
By
Eq. 10
by
Eq. 18
By
Eq.10
by
Eq. 18
Morrell
C-Model
H&F
Model
By
Eq. 10
by
Eq. 18
By
Eq.10
by
Eq. 18
Overflow 2.3 4.2 0.82 36 7.98 299 280.77 261.32 300.65 291.80 275.15 272.15 6.10 12.60 0.55 2.41 7.98 8.98
Overflow 2.65 3.4 0.77 36 4.97 334 312.10 301.43 325.09 322.52 317.39 313.93 6.56 9.75 2.67 3.44 4.97 6.01
Overflow 2.52 3.66 0.67 35 8.04 265 249.65 231.23 259.84 258.36 243.71 241.75 5.79 12.74 1.95 2.51 8.04 8.77
Overflow 3.48 4.62 0.71 39 8.88 834 785.05 719.92 819.69 814.11 759.93 753.59 5.87 13.68 1.72 2.38 8.88 9.64
Overflow 3.54 4.88 0.76 42 11.31 1029 939.39 864.88 980.84 973.72 912.67 904.62 8.71 15.95 4.68 5.37 11.31 12.09
Overflow 4.12 5.49 0.75 45 6.69 1600 1528.82 1416.43 1595.35 1584.49 1492.92 1480.50 4.45 11.47 0.29 0.97 6.69 7.45
Overflow 4.38 7.45 0.75 30 0.81 2026 2030.93 1951.32 2106.09 2088.84 2042.34 2021.04 0.24 3.69 3.95 3.10 0.81 0.22
Overflow 5.29 7.32 0.7 40 10.65 3828 3500.24 3242.10 3650.086 3627.07 3420.28 3393.20 8.56 15.31 4.65 5.25 10.65 11.36
Overflow 4.8 6.1 0.69 40 11.92 2498 2250.10 2084.84 2348.22 2333.47 2200.23 2183.11 9.92 16.54 6.00 6.59 11.92 12.61
Overflow 3.05 4.27 0.7 40 12.55 580 533.62 781.46 573.14 570.14 507.22 503.30 8.00 16.99 1.18 1.70 12.55 13.22
Overflow 2.6 3.7 0.69 40 16.23 347 319.81 275.91 330.99 329.31 290.69 288.50 7.84 20.49 4.61 5.10 16.23 16.86
Overflow 3.05 4.27 0.73 45 10.42 600 584.89 510.73 606.59 603.22 537.49 533.43 2.52 14.88 1.10 0.54 10.42 11.10
Overflow 3.5 4.42 0.74 35 9.91 820 757.79 701.53 789.32 783.34 738.71 731.75 7.59 14.45 3.74 4.47 9.91 10.76
Overflow 3.04 3.05 0.82 45 10.18 475 386.04 405.32 400.53 397.81 426.63 422.75 18.73 14.67 15.68 16.25 10.18 11.00
Overflow 2.29 2.74 0.83 44 26.84 235 173.13 163.26 179.54 178.31 171.93 170.30 26.33 30.53 23.60 24.12 26.84 27.53
Grate 1.7 2.7 0.81 40 17.43 103 101.81 80.62 106.15 105.30 85.05 84.19 1.16 21.73 3.06 2.23 17.43 18.26
Overflow 3.55 4.87 0.72 40 11.28 970 893.65 815.36 915.89 926.47 860.58 853.37 7.87 15.94 5.58 4.49 11.28 12.02
Overflow 3.5 4.75 0.75 42 7.39 921 885.56 808.37 924.17 917.69 852.94 845.59 3.85 12.23 0.34 0.36 7.39 8.19
Overflow 0.85 1.52 0.71 40 25.63 10 8.63 7.05 8.97 8.92 7.44 7.38 13.70 29.53 10.30 10.80 25.63 26.23
Overflow 0.85 1.52 0.71 20 27.29 6.8 5.83 4.83 6.03 5.88 4.94 4.90 14.26 28.95 11.32 13.53 27.29 28.00
Overflow 4.75 6.26 0.77 28 0.91 2050 2057.91 1984.03 2127 2108.80 2068.72 2046.33 0.39 3.22 3.76 2.87 0.91 0.18
Overflow 3.85 5.9 0.77 30 7.42 1300 1217.46 1150.51 1257.83 1250.67 1203.60 1190.86 6.35 11.50 3.24 3.79 7.42 8.40
Grate 2.64 3.66 0.7 43 27.54 420 377.38 288.43 393.91 391.47 304.32 302.02 10.15 31.33 6.21 6.79 27.54 28.09
Overflow 4.12 7.04 0.7 38 4.14 1800 1742.01 1634.60 1820 1807.89 1725.44 1711.08 3.22 9.19 1.11 0.44 4.14 4.94
Overflow 3.48 6.33 0.75 34 9.34 1150 1030.48 991.11 1106 1095.50 1042.65 1032.47 10.39 13.82 3.83 4.74 9.34 10.22
Overflow 5.34 8.69 0.73 28 0.04 3669 3607 3517.01 3725 3696.40 3667.44 3631.67 1.69 4.14 1.53 0.75 0.04 1.02
Overflow 5.34 8.69 0.73 26 1.52 3549 3421 3364.91 3521.3 3494.30 3494.97 3460.42 3.61 5.19 0.78 1.54 1.52 2.50
Overflow 5.34 8.69 0.73 24 2.33 3385 3224 3197.57 3306 3281.70 3306.03 3272.99 4.76 5.54 2.33 3.05 2.33 3.31
Overflow 5.34 8.69 0.73 23 1.40 3251 3123 3108.18 3196.1 3171.57 3205.54 3173.36 3.94 4.39 1.69 2.44 1.40 2.39
Overflow 5.33 8.54 0.72 34 4.44 4100 3860.9 3722.35 4026 3995.70 3918.13 3882.19 5.83 9.21 1.80 2.54 4.44 5.31
Overflow 5.29 7.32 0.7 40 10.65 3828 3500.3 3242.10 3650 3627.07 3420.28 3393.20 8.56 15.31 4.65 5.25 10.65 11.36
Overflow 4.87 8.84 0.75 30 2.14 3225 3107.5 3014.83 3224.7 3197.80 3155.95 3123.72 3.64 6.52 0.01 0.84 2.14 3.14
Overflow 4.87 8.84 0.72 27 2.04 2900 2748.5 2727.11 2840 2817.30 2841 2813.25 5.22 5.96 2.07 2.85 2.04 2.99
Overflow 4.85 5.92 0.73 41 8.64 2550 2393.6 2207.78 2498.8 2481.70 2329.68 2310.14 6.13 13.42 2.01 2.68 8.64 9.41
Overflow 4.73 7.01 0.61 32 6.99 1840 1847.8 1872.04 1922.2 1911.60 1968.69 1954.97 0.42 1.74 4.47 3.89 6.99 6.25
Overflow 4.68 5.64 0.72 48 12.00 2300 2115.1 1925.51 2202.1 2189.08 2023.97 2009.72 8.04 16.28 4.26 4.82 12.00 12.62
Overflow 4.41 6.1 0.74 35 3.51 1900 1915 1743.97 1983.6 1970.60 1833.35 1816.62 0.79 8.21 4.40 3.72 3.51 4.39
Overflow 4.1 5.92 0.75 34 3.33 1525 1504.5 1402.16 1564 1552.10 1474.18 1459.96 1.34 8.06 2.56 1.78 3.33 4.27
Overflow 3.83 4.83 0.63 31 3.70 842 777.5 771.97 808.2 803.34 810.85 804.77 7.66 8.32 4.01 4.59 3.70 4.42
Overflow 2.6 4.57 0.75 34 9.25 400 370.8 345.04 385.8 388.60 363.02 359.47 7.30 13.74 3.55 2.85 9.25 10.13
The mean absolute percentage error (MAPE) 7.02 12.86 4.41 4.73 8.97 9.65