1086 XXXI International Mineral Processing Congress 2024 Proceedings/Washington, DC/Sep 29–Oct 3
factor, K. The geometric measurements of the roller gap, s,
and the roller diameter, D, are needed for the calculation.
First, the pressure gradient in the slip zone is calculated as
shown in equation (3):
cos
dx
dvM,st
D
s
1
2
4 2
2
4 2
4^i
,st M
e
e
e
0
0
0 v i i
r {
i i
r {
ihtan {i
=
-cosi
-+
-
-cot
-+
-
-
Jr
L
K
K
K
K-
Jr
L
K
K
K
K+
a
a
N
P
O
O
O
NW
PX
OW
OW
OW
kO
kOW
R1
T
S
S S+
S
R
T
S
S
S
S
VS
XS
WS
WS WScot
WS
V
W
W
W
W
W
(3)
where:
σM,st =Stress within the roller gap
φe =Effective angle of internal flow according to
Jenike
θ0 =Feed angle
The start of the no slip zone is defined by the feed angle, θ0.
It can be obtained by measuring the effective angle of the
internal flow, φe, and the wall friction angle, φw, according
to Jenike and can be calculated using formula (4):
sin
sin
arcsinc 2
1
e
w
0 i {w {
{
=+c mm (4)
where φw is Wall friction angle according to Jenike.
With the addition of the profile depth on the roller
surface (Mähler 1999), the pressure distribution in the no
slip zone can be obtained using equation (5):
cos
cos
s D^1
s D_1
,M st, M,st,iNip
T
T Nip
K
v v i
i
=++-
++-
i
_s
^s
iicosiNip
hhcosi
=G (5)
where:
σM,st,θNip =Stress at the nip angle
sT =Average profile depth on roller surface
θNip =Nip angle (transition between no slip and slip
zone)
K =Compressibility factor
With compressibility, K, Johanson introduced a new
parameter, which is material specific and describes the com-
paction behavior of a material as the relationship between
change in pressure and the resulting change in bulk den-
sity. K is given by formula (6) and a schematic diagram of
this relationship is displayed in Figure 6 (Heinz 1999). This
data can be obtained by using a piston and die hydraulic
press.
p
p0
flake
bulk
K
t
t
=c m (6)
where:
p
0 =Reference pressure
p =Compacting pressure
Finally, the nip angle, θNip, must be calculated. At this
angle, the pressure gradient and the absolute stress of both
the no slip zone and the slip zone must be equal. The biggest
principal stress at this angle can be described by formula
(7). This value is used as a starting variable for the integra-
tion of the pressure gradient to achieve the final pressure
distribution. With this distribution, approximations of the
compacting force, resulting torque or power consumption
of the roller press are possible (Mähler 1999).
si n1
,st,i e M 1,G
Nip
v {v =+^h (7)
where σ1,G is the biggest principal stress at the nip angle
The input parameters from the formulas established by
Schönert and Johanson change during the operation of the
machine as the compression status within the reactor vol-
ume of roller presses is non-consistent. In general, the prin-
cipal duty of the roller press is to transfer the energy from
the drive train onto the material in the most consistent
and effective manner. Therefore, utilizing the established
Figure 6. Schematic depiction of the pressure-density-
relationship according to Johanson
factor, K. The geometric measurements of the roller gap, s,
and the roller diameter, D, are needed for the calculation.
First, the pressure gradient in the slip zone is calculated as
shown in equation (3):
cos
dx
dvM,st
D
s
1
2
4 2
2
4 2
4^i
,st M
e
e
e
0
0
0 v i i
r {
i i
r {
ihtan {i
=
-cosi
-+
-
-cot
-+
-
-
Jr
L
K
K
K
K-
Jr
L
K
K
K
K+
a
a
N
P
O
O
O
NW
PX
OW
OW
OW
kO
kOW
R1
T
S
S S+
S
R
T
S
S
S
S
VS
XS
WS
WS WScot
WS
V
W
W
W
W
W
(3)
where:
σM,st =Stress within the roller gap
φe =Effective angle of internal flow according to
Jenike
θ0 =Feed angle
The start of the no slip zone is defined by the feed angle, θ0.
It can be obtained by measuring the effective angle of the
internal flow, φe, and the wall friction angle, φw, according
to Jenike and can be calculated using formula (4):
sin
sin
arcsinc 2
1
e
w
0 i {w {
{
=+c mm (4)
where φw is Wall friction angle according to Jenike.
With the addition of the profile depth on the roller
surface (Mähler 1999), the pressure distribution in the no
slip zone can be obtained using equation (5):
cos
cos
s D^1
s D_1
,M st, M,st,iNip
T
T Nip
K
v v i
i
=++-
++-
i
_s
^s
iicosiNip
hhcosi
=G (5)
where:
σM,st,θNip =Stress at the nip angle
sT =Average profile depth on roller surface
θNip =Nip angle (transition between no slip and slip
zone)
K =Compressibility factor
With compressibility, K, Johanson introduced a new
parameter, which is material specific and describes the com-
paction behavior of a material as the relationship between
change in pressure and the resulting change in bulk den-
sity. K is given by formula (6) and a schematic diagram of
this relationship is displayed in Figure 6 (Heinz 1999). This
data can be obtained by using a piston and die hydraulic
press.
p
p0
flake
bulk
K
t
t
=c m (6)
where:
p
0 =Reference pressure
p =Compacting pressure
Finally, the nip angle, θNip, must be calculated. At this
angle, the pressure gradient and the absolute stress of both
the no slip zone and the slip zone must be equal. The biggest
principal stress at this angle can be described by formula
(7). This value is used as a starting variable for the integra-
tion of the pressure gradient to achieve the final pressure
distribution. With this distribution, approximations of the
compacting force, resulting torque or power consumption
of the roller press are possible (Mähler 1999).
si n1
,st,i e M 1,G
Nip
v {v =+^h (7)
where σ1,G is the biggest principal stress at the nip angle
The input parameters from the formulas established by
Schönert and Johanson change during the operation of the
machine as the compression status within the reactor vol-
ume of roller presses is non-consistent. In general, the prin-
cipal duty of the roller press is to transfer the energy from
the drive train onto the material in the most consistent
and effective manner. Therefore, utilizing the established
Figure 6. Schematic depiction of the pressure-density-
relationship according to Johanson