# Grinding & Classification Circuits

Grinding & Classification Circuits 2017-04-04T06:57:16+00:00
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## Mill Critical Speed Formula Derivation (2 replies)

randzzzzzzzzzz
12 months ago
randzzzzzzzzzz 12 months ago

How did you derived the formula for the critical speed of the ball mill?

David
12 months ago
David 12 months ago

Hello Randolf,

Critical speed is the speed at which the outer layer of balls would centrifuge if they did not slip.

I will refer you to:

For some hardcore theories on the fundamentals and mathemathics of critical speed please see Chapter 2 on page 35 of https://www.scribd.com/document/288842773/Ball-Tube-and-Rod-Mills-Rose-and-Sullivan-Publication-year-1958

I think the video below and the Patent in the PDF I attach here relate well to each other.

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(unknown)
12 months ago
(unknown) 12 months ago
1 like by David

When the ball mill rotates at the critical speed the theoretical trajectory of the charge is such that it would fall outside the shell as centrifuging occur at this stage and the medium is carried around in a fixed position against the shell. The formula to calculate critical speed is given below.

Nc = 42.305

/sqt(D-d)

Nc = critical speed of the mill.

D = mill diameter specified in meters

d = diameter of the ball.

In practice Ball Mills are driven at a speed of 50-90% of the critical speed, the factor being influenced by economic consideration. Mill capacity can be increased by increasing speed but there is very little increase in efficiency (i.e kWht-1) when the mill is operated above about 40-50% of the critical speed

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