For Cascading motion of grinding media, please keep RPM lower than Critical RPM. It can be found out from Centrifugal Force acting on any particular diameter. It works for Wet Grinding and mixing in dry grinding. Please let us know if you want size reduction or mixing?

Size reduction. Preferably grind into fine powder. Thank you so much

Dear Hong

Because you want the grinding balls to experience a free-fall motion, i.e. cataracting motion, I would recommend you consider a rotational speed between 65 and 85 % of the critical speed of the mill.

Note that the critical speed of the mill is calculated as follows:

Critical speed (in rpm) = 42.3/sqrt(D - d) with D the diameter of the mill in meters and d the diameter of the largest grinding ball you will use for experiment (also expressed in meters)

Then again, a cataracting motion produces a coarser grind. If you want your grind to be finer, it is the cascading motion that is your best choice. In this case then, the rotational speed of your mill should be somewhere between 45 and 65 % of the critical speed.

Please let me know if the proposed solution has worked

Regards

Francois

You may find worthwhile to check:

W. Matz, "Le Principe de Similitude en Génie Chimique" (French translation, by R. Krempff, of: "Anwendung des Ähnlichkeitsgrundsatzes in der Verfahrenstechnik", Springer-Verlag, Berlin / Göttingen/ Heidelberg, 1954), Dunod, Paris, 1959, pp. 95-104.

Roger Guillot, "Le Problème du Broyage et son Évolution  ― L'Aptitude des Matérieux au Broyage", Collection de L'A.N.R.T., Éditons Eyrolles / Éditions Gauthier-Villars, Paris, 1960.

Frank Rumford, "Chemical Engineering Operations", 2nd ed., Constable & Co. Ltd., London, 1957, pp. 300-301.

Determine the critical speed of mill. Then operate the machine at 60% speed of critical speed.

Dear Hong

1. First determine the critical speed of the Mill (Nc)

2. Then operate the machine at speed=2/3 of the Critical speed of the mill

There are a lot of equations to calculate the critical rotation speed, but it is not accurate.

If you can see ball motion of your ball mill. Best way to determine the critical rotation speed is to see the actual video of ball motion. (cascading, cataracting and rolling).

In the equation, did not relate the effects of ball density and ball material etc.