In comminution equipment classification, which of the following mill types all fall under the category of tumbling mills used for grinding by cascading/cataracting media motion?

Introduction / Context:
Tumbling mills are rotary cylinders partially filled with grinding media (balls, pebbles, or rods). As the shell rotates below critical speed, the charge cascades and cataracts, transmitting impact and attrition to break particles. Recognizing which mill designs are “tumbling” is basic to equipment selection.

Given Data / Assumptions:

• Mills considered: ball, pebble, rod, tube, and compartment mills.
• Operating principle: rotation of a horizontal cylinder with internal media.
• Product size range: from coarse grinding to fine finish grind depending on media and residence time.

Concept / Approach:
All listed mills share the same core mechanism: bulk media motion in a rotating drum. Ball and pebble mills use spherical media (steel or ceramic/flint). Rod mills use long steel rods to promote selective grinding and limit fines. Tube mills are long-length ball mills (L/D > 2). Compartment mills divide the tube into sections with different media sizes to improve grading and finish.

Step-by-Step Solution:
Identify common mechanism: rotating cylinder + loose media = tumbling.Map each listed type to this mechanism.Conclude that all listed variants are tumbling mills.

Verification / Alternative check:
Design texts group rod, ball, pebble, tube, and compartment mills under tumbling mills, in contrast to stirred media or jet mills.

Why Other Options Are Wrong:
Each single subset ignores the rest; all belong to the class.

Common Pitfalls:
Confusing tube/compartment mills with separate principles; they are ball mills with geometric or internal layout variations.

Final Answer:
All of the above (a), (b) and (c)