I wonder why a hybrid ball mill with so-called "Figure 8" motion requires a typical frequency of 14.6HZ，More details from "" Chen, L., Leslie, D., Coleman, M. G., Mack, J. Recyclable heterogeneous metal foil-catalyzed
cyclopropenation of alkynes and diazoacetates under solvent-free mechanochemical reaction
conditions. Chem. Sci. 2018, 9, 4650–4661.
Chen Ding The document can be obtained on RG as a free download and this direct link would be easier to post:
Article Recyclable Heterogeneous Metal Foil-Catalyzed Cyclopropenati...
I read through the text and I see 18 Hz quoted not 14.6 Hz. Please indicate where you see 14.6 Hz in the text. Mining engineers will know about the critical speed of a ball mill. I covered this at undergraduate level in extraction metallurgy. For example take a look at:
http://www.mine-engineer.com/mining/ballmill.htm#:~:text=A%20Ball%20Mill%20grinds%20material,the%20diameter%20of%20the%20mill
The balls in a ball mill need to flow in a figure-of-8 movement to maximize the energy converted to comminution/size reduction (most is converted to heat, light and sound. Indeed many ball mills are controlled by a sound device). Too fast and the balls centrifuge; too slow and they just slop around at the bottom of the mill). The best condition has them sliding up and down (also maximizes the wear on the balls) in a pseudo-figure-of-8 movement. This critical speed (onset of centrifuging) is based on the diameter of the mill and can be calculated with a simple formula as shown in the link above. Most ball mills will be operated at 65 - 75% of the critical speed.
Chen Ding
Here's some more information with links to YouTube videos:
https://www.911metallurgist.com/blog/ball-mill-critical-speed#:~:text=A%20Ball%20Mill%20Critical%20Speed,its%20position%20onto%20the%20shell
Alan F Rawle thank very much for your reply. About the informaton of "a hybrid ball mill with so-called "Figure 8" motion requires a typical frequency of 14.6HZ" come from one book named as "Mechanochemistry,A Practical Introduction from Soft to Hard Material"Edited by Evelina Colacino, Guido Ennas, Ivan Halasz,
Andrea Porcheddu and Alessandra Scano. More details are following:
Chen Ding The optimal rotation speed is usually between 4 to 20 revolutions per minute, depending upon the diameter of the mill. This can be estimated with the formula I gave above or (better still) found practically. 14.6 (or 18) Hz or any other number) will depend on the diameter of the mill and (to a minor extent) the diameter of the balls in it, the amount of balls added etc. 14.6 Hz will only apply to a single mill under defined conditions. It seems far too precise to me and the statement of academics rather than practical engineers.
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