What is critical speed in rpm of ball mill 1290 mm id charged with 64mm balls

To calculate the critical speed of a ball mill, you can use the following formula:

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

where:

• ( N_c ) is the critical speed in revolutions per minute (rpm).
• ( D ) is the internal diameter of the mill in meters.

Given:

• The internal diameter (ID) of the ball mill is 1290 mm.
• The diameter of the balls is 64 mm (though this is not needed for the critical speed calculation).

First, convert the internal diameter from millimeters to meters:

\[ D = 1290 \, \text{mm} = 1.29 \, \text{m} \]

Now, plug this value into the formula:

\[ N_c = \frac{76.6}{\sqrt{1.29}} \]

Calculate the square root of 1.29:

\[ \sqrt{1.29} \approx 1.136 \]

Then, divide 76.6 by 1.136:

\[ N_c \approx \frac{76.6}{1.136} \approx 67.45 \, \text{rpm} \]

So, the critical speed of the ball mill with an internal diameter of 1290 mm is approximately 67.45 rpm.