Pharmaceutical Manufacturing Handbook: Production and

MILLING EQUIPMENT 1167
whereas smaller diameter balls facilitate the formation of fi ne product by reducing
void spaces between the balls.
The most important factors governing the performance of the mill and the
achievement of the desired particle size are as follows:
1. Amount of material required for subsequent testing (sample volume)
2. Speed of rotation of ball mill
A high volume of powder feed produces a cushioning effect whereas small
sample volumes cause a loss of effi ciency and abrasive wear of the mill parts. The
amount of material to be milled in a ball mill may be expressed as a material - to - void
ratio (ratio of the volume of material to that of the void in the ball charge). As the
amount of material is increased, the effi ciency of a ball mill is increased until the
void space in the bulk volume of ball charge is fi lled; then, the effi ciency of milling
is decreased by further addition of material.
Rotational speed is the most signifi cant factor controlling the particle size specifi
cation. The optimum speed of rotation is dependent on mill diameter. At low
angular velocities the balls move with the drum until the force due to gravity
exceeds the frictional force of the bed on the drum, and the balls then slide back
to the base of the drum. This sequence is repeated, producing very little relative
movement of balls so that size reduction is minimal. At high angular velocities the
balls are thrown out onto the mill wall by centrifugal force and no size reduction
occurs. At about two - thirds of the critical angular velocity where centrifuging occurs,
a cascading action is produced. Balls are lifted on the rising side of the drum until
their dynamic angle of repose is exceeded. At this point they fall or roll back to the
base of the drum in a cascade across the diameter of the mill. By this means, the
maximum size reduction occurs by impact of the particles with the balls and by
attrition.
The critical speed of a ball mill is the speed at which the balls just begin to centrifuge
with the mill. Thus, at the critical speed, the centrifugal force is equal to the
weight of the ball. At and above the critical speed, no signifi cant size reduction
occurs. The critical speed n c is given by the equation
n
c =
76 6
D
.
where D is the diameter of the mill.
A larger mill reaches its critical speed at a slower revolution rate than a smaller
mill. Ball mills are operated at from 60 to 85% of the critical speed. Over this range,
the output increases with the speed; however, the lower speeds are for fi ner grinding.
An empiric rule for the optimum speed of a ball mill is
n= 57 −40log
D
where n is the speed in revolutions per minute and D is the inside diameter of the
mill in feet.