XXXI International Mineral Processing Congress 2024 Proceedings/Washington, DC/Sep 29–Oct 3 847
ANNEXURE
r
i Releasing Angle
i
i Impacting Angle
Vcr Critical Speed of Mill (m/s)
V0 Actual Speed of mill (m/s)
t Time of flight (s)
R Radius of Ball Mill
H Effective Height from filling level
dj Diameter of media of different size (m)
n, N No. of media of different size
Est Total energy of grinding media at
Shoulder (J)
PE
st Potential energy of grinding media at
Shoulder (J)
KE
st
Kinetic energy of grinding media at
Shoulder (J)
E
,T t+Dt
Total energy of grinding media at Toe (J)
&KE PE
,T t+Dt
Potential and Kinetic energy of grinding
media at Toe (J)
b
t ,t Density of media (kg/m3)
n
v
No. of media in transition and contact
v
m
Media velocity (m/sec)
v
s Spin Velocity of media (m/sec)
v
z
Relative velocity of media
k Radius of gyration (2nd moment of
inertia)
~Angular Velocity (rad/sec)
a Hardness factor
e
x co-efficient of tangential restitution
m
c Mass change rate due to Catracting (kg)
m
a Mass change rate due to Cascading (kg)
m
t Loss of mass of media (kg)
k
c
Collision Coefficient
h RK step size
k1, k2, k3, k4 RK intermediate values
REFERENCES:
[1] J. Menacho, Mathematical Model of Ball Wear in
Grinding Mills- Zero Order Wear, Powder Technology,
47 (1986) 87–96.
[2] J. Menacho, Mathematical Model of Ball Wear in
Grinding Mills- General Solution, Powder Technology,
52 (1987) 267–277.
[3] Geoming HU et al., Optimization of grinding per-
formance in tumbling ball mill, JSME International
Journal, Series C, Vol. 44, No. 1, 2001.
[4] Mishra, B.K and Rajamani, R.K, Simulation of
Charge Motion in Ball Mills-Part 2, International
Journal of Mineral Processing, vol. 40. No. 4 (1994),
pp. 187–197.
[5] K R Raju, Wear of grinding Media and order of wear
laws in tumbling Ball mill, International Journal of
Engineering and Material Sciences, vol. 1 (August
1994), pp. 217–220.
Graph 5. Operational condition—motor rpm
ANNEXURE
r
i Releasing Angle
i
i Impacting Angle
Vcr Critical Speed of Mill (m/s)
V0 Actual Speed of mill (m/s)
t Time of flight (s)
R Radius of Ball Mill
H Effective Height from filling level
dj Diameter of media of different size (m)
n, N No. of media of different size
Est Total energy of grinding media at
Shoulder (J)
PE
st Potential energy of grinding media at
Shoulder (J)
KE
st
Kinetic energy of grinding media at
Shoulder (J)
E
,T t+Dt
Total energy of grinding media at Toe (J)
&KE PE
,T t+Dt
Potential and Kinetic energy of grinding
media at Toe (J)
b
t ,t Density of media (kg/m3)
n
v
No. of media in transition and contact
v
m
Media velocity (m/sec)
v
s Spin Velocity of media (m/sec)
v
z
Relative velocity of media
k Radius of gyration (2nd moment of
inertia)
~Angular Velocity (rad/sec)
a Hardness factor
e
x co-efficient of tangential restitution
m
c Mass change rate due to Catracting (kg)
m
a Mass change rate due to Cascading (kg)
m
t Loss of mass of media (kg)
k
c
Collision Coefficient
h RK step size
k1, k2, k3, k4 RK intermediate values
REFERENCES:
[1] J. Menacho, Mathematical Model of Ball Wear in
Grinding Mills- Zero Order Wear, Powder Technology,
47 (1986) 87–96.
[2] J. Menacho, Mathematical Model of Ball Wear in
Grinding Mills- General Solution, Powder Technology,
52 (1987) 267–277.
[3] Geoming HU et al., Optimization of grinding per-
formance in tumbling ball mill, JSME International
Journal, Series C, Vol. 44, No. 1, 2001.
[4] Mishra, B.K and Rajamani, R.K, Simulation of
Charge Motion in Ball Mills-Part 2, International
Journal of Mineral Processing, vol. 40. No. 4 (1994),
pp. 187–197.
[5] K R Raju, Wear of grinding Media and order of wear
laws in tumbling Ball mill, International Journal of
Engineering and Material Sciences, vol. 1 (August
1994), pp. 217–220.
Graph 5. Operational condition—motor rpm