3722 XXXI International Mineral Processing Congress 2024 Proceedings/Washington, DC/Sep 29–Oct 3
Impact of Mill Rotating Speed and Fractional
Mill Filling
Figure 4 illustrates the combined influence of mill rotating
speed and fractional mill filling on the dynamic voidage of
balls for all proposed BSDs by Bond. The dynamic void-
age generally increases with higher mill rotating speeds but
decreases with increasing fractional mill filling, as depicted
in the figure. Notably, the maximum dynamic voidage is
observed at the maximum rotating speed and the mini-
mum fractional mill filling across all BSDs. This behavior
can be attributed to the impact of mill rotating speed and
fractional mill filling on the motion of the balls. As the
mill rotating speed increases, the layers of balls slide over
each other more rapidly, leading to increased displacement
between the layers and effectively causing them to “vibrate”
more. Conversely, when the fractional mill filling (ball load)
increases, the pressure between the ball layers rises, damp-
ing the displacement amplitude. Hence, the arrangement
of ball layers relative to each other significantly influences
the voidage of the balls.
For better understanding, Figure 5 illustrates four dis-
tinct non-random arrangements of mono-sized ball layers,
Table 4. Results of analysis of variance
BSDs Source Sum of Squares df Mean Square F-Value
p-Value
(prob F)
Adequate
Precision
BSD1 Model 32.92 5 6.58 852.41 0.0001 88.74
Jt 22.50 1 22.50 2913.51 0.0001
C
s 3.05 1 3.05 394.53 0.0001
J
t *C
s 0.3636 1 0.3636 47.07 0.0002
Jt 2 5.77 1 5.77 747.12 0.0001
BSD2 Model 38.91 5 7.78 865.87 0.0001 97.92
J
t 25.05 1 25.05 2787.05 0.0001
C
s 7.39 1 7.39 822.70 0.0001
Jt*Cs 0.6642 1 0.6642 73.90 0.0001
Jt 2 4.72 1 4.72 525.45 0.0001
BSD
3 Model 41.30 5 8.26 488.53 0.0001 74.23
J
t 26.66 1 26.66 1576.83 0.0001
Cs 8.22 1 8.22 486.31 0.0001
Jt*Cs 0.6440 1 0.6440 38.09 0.0005
J2
t 4.66 1 4.66 275.87 0.0001
BSD
4 Model 45.16 5 9.03 1015.75 0.0001 106.32
Jt 29.29 1 29.29 3294.46 0.0001
Cs 8.58 1 8.58 965.02 0.0001
J
t *C
s 0.6642 1 0.6642 74.71 0.0001
J2
t 5.57 1 5.57 626.45 0.0001
BSD5 Model 45.79 5 9.16 1277.05 0.0001 121.45
Jt 28.42 1 28.42 3963.62 0.0001
C
s 10.41 1 10.41 1451.26 0.0001
J
t *C
s 0.7709 1 0.7709 107.50 0.0001
Jt 2 5.38 1 5.38 750.57 0.0001
BSD6 Model 48.44 5 9.69 419.24 0.0001 71.74
J
t 27.52 1 27.52 1190.82 0.0001
C
s 14.65 1 14.65 634.08 0.0001
Jt*Cs 0.7578 1 0.7578 32.79 0.0007
Jt 2 4.56 1 4.56 197.15 0.0001
BSD
7 Model 55.44 5 11.09 574.04 0.0001 84.46
J
t 31.59 1 31.59 1635.50 0.0001
Cs 17.19 1 17.19 889.88 0.0001
Jt*Cs 1.01 1 1.01 52.29 0.0002
J2
t 4.69 1 4.69 242.98 0.0001
Impact of Mill Rotating Speed and Fractional
Mill Filling
Figure 4 illustrates the combined influence of mill rotating
speed and fractional mill filling on the dynamic voidage of
balls for all proposed BSDs by Bond. The dynamic void-
age generally increases with higher mill rotating speeds but
decreases with increasing fractional mill filling, as depicted
in the figure. Notably, the maximum dynamic voidage is
observed at the maximum rotating speed and the mini-
mum fractional mill filling across all BSDs. This behavior
can be attributed to the impact of mill rotating speed and
fractional mill filling on the motion of the balls. As the
mill rotating speed increases, the layers of balls slide over
each other more rapidly, leading to increased displacement
between the layers and effectively causing them to “vibrate”
more. Conversely, when the fractional mill filling (ball load)
increases, the pressure between the ball layers rises, damp-
ing the displacement amplitude. Hence, the arrangement
of ball layers relative to each other significantly influences
the voidage of the balls.
For better understanding, Figure 5 illustrates four dis-
tinct non-random arrangements of mono-sized ball layers,
Table 4. Results of analysis of variance
BSDs Source Sum of Squares df Mean Square F-Value
p-Value
(prob F)
Adequate
Precision
BSD1 Model 32.92 5 6.58 852.41 0.0001 88.74
Jt 22.50 1 22.50 2913.51 0.0001
C
s 3.05 1 3.05 394.53 0.0001
J
t *C
s 0.3636 1 0.3636 47.07 0.0002
Jt 2 5.77 1 5.77 747.12 0.0001
BSD2 Model 38.91 5 7.78 865.87 0.0001 97.92
J
t 25.05 1 25.05 2787.05 0.0001
C
s 7.39 1 7.39 822.70 0.0001
Jt*Cs 0.6642 1 0.6642 73.90 0.0001
Jt 2 4.72 1 4.72 525.45 0.0001
BSD
3 Model 41.30 5 8.26 488.53 0.0001 74.23
J
t 26.66 1 26.66 1576.83 0.0001
Cs 8.22 1 8.22 486.31 0.0001
Jt*Cs 0.6440 1 0.6440 38.09 0.0005
J2
t 4.66 1 4.66 275.87 0.0001
BSD
4 Model 45.16 5 9.03 1015.75 0.0001 106.32
Jt 29.29 1 29.29 3294.46 0.0001
Cs 8.58 1 8.58 965.02 0.0001
J
t *C
s 0.6642 1 0.6642 74.71 0.0001
J2
t 5.57 1 5.57 626.45 0.0001
BSD5 Model 45.79 5 9.16 1277.05 0.0001 121.45
Jt 28.42 1 28.42 3963.62 0.0001
C
s 10.41 1 10.41 1451.26 0.0001
J
t *C
s 0.7709 1 0.7709 107.50 0.0001
Jt 2 5.38 1 5.38 750.57 0.0001
BSD6 Model 48.44 5 9.69 419.24 0.0001 71.74
J
t 27.52 1 27.52 1190.82 0.0001
C
s 14.65 1 14.65 634.08 0.0001
Jt*Cs 0.7578 1 0.7578 32.79 0.0007
Jt 2 4.56 1 4.56 197.15 0.0001
BSD
7 Model 55.44 5 11.09 574.04 0.0001 84.46
J
t 31.59 1 31.59 1635.50 0.0001
Cs 17.19 1 17.19 889.88 0.0001
Jt*Cs 1.01 1 1.01 52.29 0.0002
J2
t 4.69 1 4.69 242.98 0.0001