# ball mill size and motor power requirements

To match a ball mill size and its motor size, some math is required. The power requirement calculated above is the motor power that must be applied at the mill drive in order to grind the tonnage of feed from one size distribution. The following shows how the size of mill required to draw this power is calculated. The represents a section of a mill in operation. The power input required to maintain this condition is theoretically:
hp = (W) (C) (Sin a) (2π) (N)
33.000
where     W = weight of charge
C = distance of center of gravity or charge from center of mill in feet
a = dynamic angle of repose of the charge
N = mill speed in rpm

The value of the angle a varies with the type of discharge, percent of critical speed, and grinding condition.
In order to use the preceding equation, it is necessary to have considerable data on existing installations. Therefore, this approach has been simplified as follows:
Five basics conditions determine the horsepower drawn by a mill:
1. Diameter   2. Length   3. % Loading   4. Speed   5. Mill type
These conditions have been built into factors which are given in Figure 6. The approximate horsepower of a mill can be calculated from the following equation:
HP = A x B x C x L
Where A = factor for diameter inside shell lining
B = factor which includes effect of % loading and mill type
C = factor for speed of mill
L = length in feet of grinding chamber measured between head liners at shell- to-head junction

Many grinding mill manufacturers specify diameter inside the liners whereas Rexnord mills are specified per inside shell diameter. (Subtract 6” to obtain dia. inside liners.) Likewise, a similar confusion surrounds the length of a mill. Therefore, when comparing the size of a mill between competitive manufacturers, one should be aware that mill manufacturers do not observe a size convention.