• To participate in the 911Metallurgist Forums, be sure to JOINLOGIN
  • Use Add New Topic to ask a New Question/Discussion about Grinding.
  • OR Select a Topic that Interests you.
  • Use Add Reply = to Reply/Participate in a Topic/Discussion (most frequent).
    Using Add Reply allows you to Attach Images or PDF files and provide a more complete input.
  • Use Add Comment = to comment on someone else’s Reply in an already active Topic/Discussion.

Mill Critical Speed Formula Derivation (2 replies)

randzzzzzzzzzz
4 weeks ago
randzzzzzzzzzz 4 weeks ago

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

David
4 weeks ago
David 4 weeks 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:

https://www.911metallurgist.com/blog/ball-mill-critical-speed
https://www.911metallurgist.com/blog/grinding-mills#grinding_mill_rpm_8211_rotating_speed
https://www.911metallurgist.com/blog/ball-mill-rod-mill
https://www.911metallurgist.com/blog/tumbling-mill-critical-speed
 
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.
 
 
sajid khan
3 weeks ago
sajid khan 3 weeks 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

Please join and login to participate and leave a comment.