4
purpose values of the Bond work indices Wi were calcu-
lated (Table 3).
The results show that both the pressure Fsp and the
moisture content M have an impact on Bond values Wi.
Together with increasing of Fsp, Wi values decrease less
than proportionally, what may indicate that comminution
of the feed material with too high operational pressure in
HPGR may not be energetically and economically effec-
tive. It should be noted, however, that this is a complex
issue because also other parameters have an impact on the
obtained effects (i.e., comminution resistance of material,
particle size composition, HPGR device operational regime
like speed of rolls, gap, recycle and others). In this case, it
can be seen that the moisture content has a positive effect
on decreasing of Bond Wi value, because together with
increasing of M, Wi decreases what may potentially bring
energetic savings. On the other hand, too high moisture
content may cause a material slip on the rolls what affects
the press productivity. This feature is very individual for
each type of material. For the material under testing it can
be seen that moisture 4% still reduces Wi indices.
Both Fsp and M have proportional impact for increas-
ing the energy consumption. Figure 5 indicate that we can
talk about proportional or even linear relationship between
the specific energy consumption and operational pressure
Fsp, as well as between specific energy consumption and
moisture content.
MATHEMATICAL MODELS OF HPGR
OPERATION
As it was mentioned in “Materials and Methods” section,
the following models of HPGR press device operation were
worked out: a model for Bond work index Wi, models for
energy consumption and press throughput, technological
models concerning breakage intensity, and finest particles
production. Two independent variables – pressure and feed
moisture – were used as independent values in each model.
It should be underlined that these both parameters have
different units: Fsp is expressed in [N/mm2] and moisture
M in [%].Therefore all presented analyses apply to the fol-
lowing interpretation: a single unit of change for Fsp is 1
N/mm2 and for M it is 1%.
Prior the modelling, the correlation between specific
variables was checked (Table 4.). The results show that Fsp
and M are not correlated.
Values in red font are statistically significant on the
confidence level of 95%. The Fsp variable is in a strong
and statistically significant correlation with most of the
other variables. It confirms and strengthens the findings of
individual models, that this parameter efficiently influences
comminution intensity, fines production, and potential
energy savings in downstream grinding operations The Fsp
is strongly and negatively correlated with throughput, what
confirms a general relationship observed in operational
practice. An even stronger and positive correlation (r =0.94)
can be also observed between Fsp and Esp, which confirms
the results of various experiments that can be found in the
literature. In the case of parameter M we can see that it is
significantly correlated only with the Bond work index.
Models Connected with Energy Consumption
Equation (4) presents the relationship between Wi, F and
M. It can be seen that for this type of material, both pressing
Table 3. Values of Bond Wi indices for individual HPGR
products
Fsp 0% 2% 4%
3.3 10.92 10.44 10.18
4.3 10.53 10.22 10.01
5.3 10.44 10.18 9.97
Table 4. Calculated correlation matrix
Fsp M
Fsp 1.00 0.00
M 0.00 1.00
Wi –0.46 –0.84
Esp 0.94 0.31
Q –0.83 –0.53
g
–100 0.88 –0.33
S20 0.93 –0.31
S50 0.94 –0.23
S80 0.93 –0.21
Figure 5. Impact of pressure on energy consumption in
HPGR crushing
purpose values of the Bond work indices Wi were calcu-
lated (Table 3).
The results show that both the pressure Fsp and the
moisture content M have an impact on Bond values Wi.
Together with increasing of Fsp, Wi values decrease less
than proportionally, what may indicate that comminution
of the feed material with too high operational pressure in
HPGR may not be energetically and economically effec-
tive. It should be noted, however, that this is a complex
issue because also other parameters have an impact on the
obtained effects (i.e., comminution resistance of material,
particle size composition, HPGR device operational regime
like speed of rolls, gap, recycle and others). In this case, it
can be seen that the moisture content has a positive effect
on decreasing of Bond Wi value, because together with
increasing of M, Wi decreases what may potentially bring
energetic savings. On the other hand, too high moisture
content may cause a material slip on the rolls what affects
the press productivity. This feature is very individual for
each type of material. For the material under testing it can
be seen that moisture 4% still reduces Wi indices.
Both Fsp and M have proportional impact for increas-
ing the energy consumption. Figure 5 indicate that we can
talk about proportional or even linear relationship between
the specific energy consumption and operational pressure
Fsp, as well as between specific energy consumption and
moisture content.
MATHEMATICAL MODELS OF HPGR
OPERATION
As it was mentioned in “Materials and Methods” section,
the following models of HPGR press device operation were
worked out: a model for Bond work index Wi, models for
energy consumption and press throughput, technological
models concerning breakage intensity, and finest particles
production. Two independent variables – pressure and feed
moisture – were used as independent values in each model.
It should be underlined that these both parameters have
different units: Fsp is expressed in [N/mm2] and moisture
M in [%].Therefore all presented analyses apply to the fol-
lowing interpretation: a single unit of change for Fsp is 1
N/mm2 and for M it is 1%.
Prior the modelling, the correlation between specific
variables was checked (Table 4.). The results show that Fsp
and M are not correlated.
Values in red font are statistically significant on the
confidence level of 95%. The Fsp variable is in a strong
and statistically significant correlation with most of the
other variables. It confirms and strengthens the findings of
individual models, that this parameter efficiently influences
comminution intensity, fines production, and potential
energy savings in downstream grinding operations The Fsp
is strongly and negatively correlated with throughput, what
confirms a general relationship observed in operational
practice. An even stronger and positive correlation (r =0.94)
can be also observed between Fsp and Esp, which confirms
the results of various experiments that can be found in the
literature. In the case of parameter M we can see that it is
significantly correlated only with the Bond work index.
Models Connected with Energy Consumption
Equation (4) presents the relationship between Wi, F and
M. It can be seen that for this type of material, both pressing
Table 3. Values of Bond Wi indices for individual HPGR
products
Fsp 0% 2% 4%
3.3 10.92 10.44 10.18
4.3 10.53 10.22 10.01
5.3 10.44 10.18 9.97
Table 4. Calculated correlation matrix
Fsp M
Fsp 1.00 0.00
M 0.00 1.00
Wi –0.46 –0.84
Esp 0.94 0.31
Q –0.83 –0.53
g
–100 0.88 –0.33
S20 0.93 –0.31
S50 0.94 –0.23
S80 0.93 –0.21
Figure 5. Impact of pressure on energy consumption in
HPGR crushing