5
force and moisture content positively impact potential
energy savings in HPGR device.
.14M
[.04 ][0.02]
W 11.3 0.16Fsp 0
0
i =--
(4)
Where: Fsp is expressed in [N/mm2], moisture, M in
[%],and Wi is expressed in [kWh/Mg].
Values of Bonds work indices were the lowest for the
highest values of pressure and for the moisture 4%. The
multiple regression method was used to search for a spe-
cific model, describing the Wi as a function of the press
parameters and material properties. In the first step the
liner multiple regression model with Fsp and M was built.
Then the M parameter in the second power (M2) was
tested, but it didn’t bring improvements in model quality.
The determination coefficient R2 equals 0.902. Final form
of model was presented below (equation 9). Errors of coef-
ficients were listed in square brackets below the equation.
All independent variables are statistically significant on the
confidence level (1 – a) =0.95. The constant value has no
significant interpretation connected to the practice.
The model shows that an increase in Fsp by 1 N/mm2
decreases Wi by 0.16 kWh/Mg, while increasing M by 1%
effectively decreases Wi by 0.14 kWh/Mg .It can be con-
cluded that for this type of material, the moisture content
has potentially less significant influence on decreasing of
Bond work index, than Fsp. Both used variables, how-
ever, have positive effect on decreasing the Wi index and
thus, potential energy savings in downstream crushing and
grinding stages of technological circuit. It should be fair to
say, however, that this model is convergent to operational
reality only to some extent (i.e., within a certain range of
Fsp and M). Further increasing of pressing force in HPGR
results in relatively lower and lower fineness and also lower
reductions in Wi. The situation is different for the mois-
ture, because its excessive content generally has a negative
technological impact. Too high water content in the feed
material affects both the throughput, as an effect of the
material slip on rolls, and insufficient comminution.
The other energy model (equation 5) – specific unit
energy consumption – also shows a significant relationship
but mostly with Fsp. R2 =0.970. The M has some impact
on energy consumption, but it is of much lower signifi-
cance, compared to the pressure. The model better describes
the real situation, compared to model (4), because only 3%
of the variability is not explained by variables incorporated
into the model function.
..09M
[.04 ][0.02]
Esp 0 24 0.58F 0
0
sp =++
(5)
Technological Models of HPGR Operation
An impact of the selected parameters on the HPGR
throughput and the yield of the finest particles in HPGR
product, was also investigated. Equation (6) shows the
model of press capacity.
..04M
[.01 ][0.005]
Q 3 87 0.13Fsp 0
0
=--
(6)
The model shows that both the Fsp and the material
moisture have a negative impact on the press capacity, and
the influence of Fsp is much greater than the M. The level
of description of the phenomenon by the model expressed
by R2 equals 96.5%.
The finest particle size fractions are essential in lime-
stone flour production. If the HPGR product contains a
significant yield of these fractions, they might be bypassed
or separated from the material prior to downstream grind-
ing, thus mills grind a lower amount of material and energy
costs are lower, too. For this purpose the yield of particle
size fraction below 0.1 mm (g-0.1) was also modeled (for-
mula (7)).
..64
[.38 ][[3.29] [0.11]
F F 30 85 1 17.03 0.54M
0
sp sp 100
2 c =--+-
-(7)
Together with increasing the Fsp value, the yield of
fines in HPGR product is increasing too, but the relation-
ship is close to hyperbolical or even parabolic, therefore
the Fsp in the second power was included in the model. It
increased the model quality, because R2 equals 0.963, while
for the model without Fsp2 it equaled 0.855.
Models for Comminution Ratios Sx
In this part of investigations a series of models for commi-
nution ratios Sx were determined. Finally, the models for
S20, S50 and S80 comminution were calculated. Results
were presented in Table 5.
Impact of Fsp on specific value Sx is positive in each
model, while M is negatively bound. The M value is insig-
nificant in models for S50 and S80, and Fsp is statistically
significant in all models. Results of modeling also show
that in the case of the pressure, its highest impact on com-
minution ratio can be observed in the model for S20 and
Table 5. Results of modeling for comminution ratios as
functions of F and M
Sx Model R2
20 –2.73 +3.58 Fsp – 0.6 M 0.953
50 0.10 +1.59 Fsp – 0.19 M 0.928
80 0.78 +0.75 Fsp – 0.09 M 0.871
force and moisture content positively impact potential
energy savings in HPGR device.
.14M
[.04 ][0.02]
W 11.3 0.16Fsp 0
0
i =--
(4)
Where: Fsp is expressed in [N/mm2], moisture, M in
[%],and Wi is expressed in [kWh/Mg].
Values of Bonds work indices were the lowest for the
highest values of pressure and for the moisture 4%. The
multiple regression method was used to search for a spe-
cific model, describing the Wi as a function of the press
parameters and material properties. In the first step the
liner multiple regression model with Fsp and M was built.
Then the M parameter in the second power (M2) was
tested, but it didn’t bring improvements in model quality.
The determination coefficient R2 equals 0.902. Final form
of model was presented below (equation 9). Errors of coef-
ficients were listed in square brackets below the equation.
All independent variables are statistically significant on the
confidence level (1 – a) =0.95. The constant value has no
significant interpretation connected to the practice.
The model shows that an increase in Fsp by 1 N/mm2
decreases Wi by 0.16 kWh/Mg, while increasing M by 1%
effectively decreases Wi by 0.14 kWh/Mg .It can be con-
cluded that for this type of material, the moisture content
has potentially less significant influence on decreasing of
Bond work index, than Fsp. Both used variables, how-
ever, have positive effect on decreasing the Wi index and
thus, potential energy savings in downstream crushing and
grinding stages of technological circuit. It should be fair to
say, however, that this model is convergent to operational
reality only to some extent (i.e., within a certain range of
Fsp and M). Further increasing of pressing force in HPGR
results in relatively lower and lower fineness and also lower
reductions in Wi. The situation is different for the mois-
ture, because its excessive content generally has a negative
technological impact. Too high water content in the feed
material affects both the throughput, as an effect of the
material slip on rolls, and insufficient comminution.
The other energy model (equation 5) – specific unit
energy consumption – also shows a significant relationship
but mostly with Fsp. R2 =0.970. The M has some impact
on energy consumption, but it is of much lower signifi-
cance, compared to the pressure. The model better describes
the real situation, compared to model (4), because only 3%
of the variability is not explained by variables incorporated
into the model function.
..09M
[.04 ][0.02]
Esp 0 24 0.58F 0
0
sp =++
(5)
Technological Models of HPGR Operation
An impact of the selected parameters on the HPGR
throughput and the yield of the finest particles in HPGR
product, was also investigated. Equation (6) shows the
model of press capacity.
..04M
[.01 ][0.005]
Q 3 87 0.13Fsp 0
0
=--
(6)
The model shows that both the Fsp and the material
moisture have a negative impact on the press capacity, and
the influence of Fsp is much greater than the M. The level
of description of the phenomenon by the model expressed
by R2 equals 96.5%.
The finest particle size fractions are essential in lime-
stone flour production. If the HPGR product contains a
significant yield of these fractions, they might be bypassed
or separated from the material prior to downstream grind-
ing, thus mills grind a lower amount of material and energy
costs are lower, too. For this purpose the yield of particle
size fraction below 0.1 mm (g-0.1) was also modeled (for-
mula (7)).
..64
[.38 ][[3.29] [0.11]
F F 30 85 1 17.03 0.54M
0
sp sp 100
2 c =--+-
-(7)
Together with increasing the Fsp value, the yield of
fines in HPGR product is increasing too, but the relation-
ship is close to hyperbolical or even parabolic, therefore
the Fsp in the second power was included in the model. It
increased the model quality, because R2 equals 0.963, while
for the model without Fsp2 it equaled 0.855.
Models for Comminution Ratios Sx
In this part of investigations a series of models for commi-
nution ratios Sx were determined. Finally, the models for
S20, S50 and S80 comminution were calculated. Results
were presented in Table 5.
Impact of Fsp on specific value Sx is positive in each
model, while M is negatively bound. The M value is insig-
nificant in models for S50 and S80, and Fsp is statistically
significant in all models. Results of modeling also show
that in the case of the pressure, its highest impact on com-
minution ratio can be observed in the model for S20 and
Table 5. Results of modeling for comminution ratios as
functions of F and M
Sx Model R2
20 –2.73 +3.58 Fsp – 0.6 M 0.953
50 0.10 +1.59 Fsp – 0.19 M 0.928
80 0.78 +0.75 Fsp – 0.09 M 0.871