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.