3720 XXXI International Mineral Processing Congress 2024 Proceedings/Washington, DC/Sep 29–Oct 3
dependent parameter is influenced by multiple inde-
pendent parameters concurrently. Various types of RSM
designs, including factorial design, central composite design
(CCD), D-optimal design, and Box-Behnken design, have
been widely employed for this purpose. Specifically, we
employed the three-level factorial design, known for its
efficiency among other response surface designs, to plan
experiments and model the grinding media voidage. This
design involved two independent parameters: fractional
mill filling and mill rotating speed. Each parameter was
set at three levels: upper and lower bounds and an average
value. Table 2 presents the coded and actual levels consid-
ered for the fractional mill filling and mill rotating speed.
The designed experiments, totaling 91 experiments (13 for
each BSD), are detailed in Table 3.
RESULTS AND DISCUSSION
Statistical analysis
A three-level factorial response surface design with two
independent variables, fractional filling, and mill rotating
speed, was employed to investigate the effects of these vari-
ables on the voidage of the grinding media. The resulting
values of grinding media voidage, as presented in Table 3,
were incorporated into the Design Expert software for anal-
ysis. The analysis of variance (ANOVA), a valuable statisti-
cal tool, was then utilized to examine the data and develop
a mathematical model for each BSD listed in Table 1.
Among the linear, cross-product contribution (2FI),
quadratic, and cubic models generated in the Design Expert
software’s response, the quadratic model was suggested to
estimate the dynamic voidage of all BSDs based on the sta-
tistical analysis of the response data. The general equation
for the quadratic model is as follows (Montgomery, 2005):
Y A BX CX DX X EX FX
1 2 1 2 1
2
2
2 =+++++(9)
where A is the intercept, B to F are the estimated
coefficients derived from the experimental values of
Y, and X1 and X2 are the independent variables.
ANOVA, employing the Fisher method, was utilized
to evaluate the significance of the generated models and the
Figure 3. A schematic of the material configuration inside a mill during operation
Table 2. Design level in the coded and actual level
Parameters Symbol Units
Coded and Actual Levels
–1 0 1
Fractional mill filling J %15 30 45
Fraction of mill critical speed Cs %40 65 90
dependent parameter is influenced by multiple inde-
pendent parameters concurrently. Various types of RSM
designs, including factorial design, central composite design
(CCD), D-optimal design, and Box-Behnken design, have
been widely employed for this purpose. Specifically, we
employed the three-level factorial design, known for its
efficiency among other response surface designs, to plan
experiments and model the grinding media voidage. This
design involved two independent parameters: fractional
mill filling and mill rotating speed. Each parameter was
set at three levels: upper and lower bounds and an average
value. Table 2 presents the coded and actual levels consid-
ered for the fractional mill filling and mill rotating speed.
The designed experiments, totaling 91 experiments (13 for
each BSD), are detailed in Table 3.
RESULTS AND DISCUSSION
Statistical analysis
A three-level factorial response surface design with two
independent variables, fractional filling, and mill rotating
speed, was employed to investigate the effects of these vari-
ables on the voidage of the grinding media. The resulting
values of grinding media voidage, as presented in Table 3,
were incorporated into the Design Expert software for anal-
ysis. The analysis of variance (ANOVA), a valuable statisti-
cal tool, was then utilized to examine the data and develop
a mathematical model for each BSD listed in Table 1.
Among the linear, cross-product contribution (2FI),
quadratic, and cubic models generated in the Design Expert
software’s response, the quadratic model was suggested to
estimate the dynamic voidage of all BSDs based on the sta-
tistical analysis of the response data. The general equation
for the quadratic model is as follows (Montgomery, 2005):
Y A BX CX DX X EX FX
1 2 1 2 1
2
2
2 =+++++(9)
where A is the intercept, B to F are the estimated
coefficients derived from the experimental values of
Y, and X1 and X2 are the independent variables.
ANOVA, employing the Fisher method, was utilized
to evaluate the significance of the generated models and the
Figure 3. A schematic of the material configuration inside a mill during operation
Table 2. Design level in the coded and actual level
Parameters Symbol Units
Coded and Actual Levels
–1 0 1
Fractional mill filling J %15 30 45
Fraction of mill critical speed Cs %40 65 90