Operating speed for efficient ball milling: relative to the critical speed, which regime is recommended for effective grinding in industrial ball mills?

Introduction / Context:
Critical speed is the rotational speed at which centrifugal force holds the grinding media against the mill shell, preventing cataracting. Industrial mills are purposely run below this speed to maintain a cascading motion, which creates impact and abrasion necessary for size reduction.

Given Data / Assumptions:

• Standard lifter-equipped tumbling ball mills.
• Objective: stable cataracting/cascading without centrifuging.
• Common practice targets 65–80% of critical speed.

Concept / Approach:
Below critical speed, media rise and then fall, generating impact on the toe of the charge. At or above critical speed, media cling to the shell, drastically reducing effective breakage. Therefore, efficient operation is “less than” critical speed, typically tuned with media size and mill filling to reach target grind.

Step-by-Step Solution:
Define critical speed condition (centrifuging at the wall).Relate grinding action to cascading trajectories below critical.Select the sub-critical regime as the efficient range.

Verification / Alternative check:
Empirical correlations for mill power draw and breakage rates show peak performance around 70–78% of critical, consistent with decades of operating experience.

Why Other Options Are Wrong:
Equal to or more than critical: causes centrifuging and poor breakage.“Minimum possible small balls”: ball size selection depends on feed top size; exclusively small balls may underperform on coarse feed.

Common Pitfalls:
Ignoring lifter design and charge filling; both change the effective trajectory and optimal percent of critical speed.

Final Answer:
At a speed less than the critical speed