What should be the RPM of a ball mill with a 45-inch diameter?

To determine the optimal RPM for a ball mill, you typically use the critical speed formula, which is:

\[ \text{Critical Speed (Nc)} = \frac{76.6}{\sqrt{D}} \]

where (D) is the diameter of the mill in feet.

For a ball mill with a 45-inch diameter:

1. Convert the diameter to feet: (45 \text{ inches} = 3.75 \text{ feet}).
2. Plug this into the formula to find the critical speed:

\[ \text{Nc} = \frac{76.6}{\sqrt{3.75}} \approx 39.54 \, \text{RPM} \]

The operating speed is typically between 65% and 75% of the critical speed: \[ \text{Optimal RPM} = 0.65 \times 39.54 = 25.70 \, \text{RPM} \] \[ \text{Optimal RPM} = 0.75 \times 39.54 = 29.66 \, \text{RPM} \]

Therefore, the optimal RPM should be between approximately 25.70 and 29.66 RPM.