842 XXXI International Mineral Processing Congress 2024 Proceedings/Washington, DC/Sep 29–Oct 3
Dynamic operational parameters, including mill RPM,
feed rate, recirculation rate, and feed characteristics, etc are
considered as represented in Figure 3. Employing govern-
ing equations, the precise angular position and coordinates
of the mill’s shoulder and toe are determined during opera-
tion. The analysis focuses on calculating the net energy loss
as media travel from the shoulder to the toe. At the toe,
media imparts impact force on iron ore, leading to coarse
breakage. Through energy calculations and the hardness fac-
tor of media, the energy transferred to iron ore particles for
their initial breakage is quantified while catracting motion.
Residual energy is then assessed, impacting the remaining
media as well as to adjacent wall/liners.
Calculations involving residual energy and the rota-
tional motion lead to the application of another governing
equation, determining the reduction in media weight. This
method systematically evaluates the loss of media due to
contracting forces in the ball mill. Continuing the inves-
tigation, cascading motion is examined. Net principle and
transitional wear kinetics criteria of first order kinetics,
allow for the calculation of cascading mass loss of media.
This further refines the understanding of media behaviour
and contributes to a comprehensive analysis of the ball
mill’s dynamic processes.
Simulation
In the simulation strategies for predicting ball mill media
wear, the initial stage involves real-time computation of
positional and angular coordinates of media during ball
mill operations. The governing equation for said co-ordi-
nates are given in the following.
Angular position of media at shoulder and Toe: In
the dynamics of a rotating ball mill, the angles of media
release
r
i from the shoulder position and impact
i
i at the
toe position assume critical importance. This is particularly
significant as the media concurrently undergo rotational
motion with the mill. These angles, pivotal in understand-
ing the intricate mechanics, offer insights into the efficiency
and wear dynamics of the grinding process. Following gov-
erning equation 1 and 2 reflect the angle of media release
from shoulder position and impacting angle at toe position
respectively.
%Vcr
100 ArcCosa
r
2 i =k (1)
sin *
cosi
V g t
V
ArcTane
i
r
r
k
0
0 i i =-o (2)
Direction Co-ordinate for media at shoulder and Toe:
To further refine the analysis, logics employ directional
coordinates in the X and Y directions. This facilitates the
Figure 3. Variables for wear estimation module for Ball Mill
Dynamic operational parameters, including mill RPM,
feed rate, recirculation rate, and feed characteristics, etc are
considered as represented in Figure 3. Employing govern-
ing equations, the precise angular position and coordinates
of the mill’s shoulder and toe are determined during opera-
tion. The analysis focuses on calculating the net energy loss
as media travel from the shoulder to the toe. At the toe,
media imparts impact force on iron ore, leading to coarse
breakage. Through energy calculations and the hardness fac-
tor of media, the energy transferred to iron ore particles for
their initial breakage is quantified while catracting motion.
Residual energy is then assessed, impacting the remaining
media as well as to adjacent wall/liners.
Calculations involving residual energy and the rota-
tional motion lead to the application of another governing
equation, determining the reduction in media weight. This
method systematically evaluates the loss of media due to
contracting forces in the ball mill. Continuing the inves-
tigation, cascading motion is examined. Net principle and
transitional wear kinetics criteria of first order kinetics,
allow for the calculation of cascading mass loss of media.
This further refines the understanding of media behaviour
and contributes to a comprehensive analysis of the ball
mill’s dynamic processes.
Simulation
In the simulation strategies for predicting ball mill media
wear, the initial stage involves real-time computation of
positional and angular coordinates of media during ball
mill operations. The governing equation for said co-ordi-
nates are given in the following.
Angular position of media at shoulder and Toe: In
the dynamics of a rotating ball mill, the angles of media
release
r
i from the shoulder position and impact
i
i at the
toe position assume critical importance. This is particularly
significant as the media concurrently undergo rotational
motion with the mill. These angles, pivotal in understand-
ing the intricate mechanics, offer insights into the efficiency
and wear dynamics of the grinding process. Following gov-
erning equation 1 and 2 reflect the angle of media release
from shoulder position and impacting angle at toe position
respectively.
%Vcr
100 ArcCosa
r
2 i =k (1)
sin *
cosi
V g t
V
ArcTane
i
r
r
k
0
0 i i =-o (2)
Direction Co-ordinate for media at shoulder and Toe:
To further refine the analysis, logics employ directional
coordinates in the X and Y directions. This facilitates the
Figure 3. Variables for wear estimation module for Ball Mill