The higher production efficiency of large‑diameter mills is not merely because they are “larger and hold more material.” There are profound comminution mechanics and flow dynamics reasons behind this. The core reasons can be summarised in the following five aspects:

1. Greater Impact Crushing Energy (Stronger Crushing Force)

The operating speed of a mill is generally set at 65%–85% of the critical speed (the rotation rate is roughly fixed). At this speed, the height to which the grinding media are lifted is directly proportional to the effective diameter D of the mill.

• Formula: The maximum drop height H of the grinding media is almost linearly related to the diameter D.
• Actual effect: The larger the diameter, the higher the grinding media are lifted, and the greater their terminal velocity upon impact. The single‑impact crushing energy (E=mgh) is far greater than that of a small mill. For hard, coarse particles, a large‑diameter mill can break them “in one blow,” whereas a small mill must rely on repeated grinding, which is naturally less efficient.

2. Larger Proportion of the Effective “Contraction Layer” Working Zone (Core Principle)

This is the core theoretical basis for the higher efficiency of large mills (the layer‑contraction theory).

• During mill operation, the grinding media do not rotate as a solid mass. Instead, they form a “waterfall‑like” layering: the outermost layer moves with the shell (the lifting layer), the innermost layer moves centripetally (the falling layer), and the middle layer (contraction layer) generates intense compression, friction, and impact among the media – this is the actual working zone that performs the grinding.
• Key point: The thickness of this effective contraction layer is essentially a constant and does not increase linearly with mill diameter.
• Conclusion: In a small‑diameter mill, this effective layer accounts for a relatively small proportion of the total media charge. In a large‑diameter mill, the proportion of the inner ineffective slipping zone decreases, and the volume percentage of the effective working zone increases significantly, leading to much higher energy utilisation.

3. Relatively Reduced “Edge Effect” Losses

• The layer of grinding media closest to the shell liners (the outer layer) is forced to rotate with the shell, with relatively little relative motion, so its grinding action is weak – it is a “low‑efficiency zone” or “dead zone.”
• The thickness of this low‑efficiency zone is influenced by liner structure and friction coefficient, and is largely independent of diameter.
• In a small mill, the low‑efficiency zone occupies a large proportion of the cross‑section. In a large mill, that proportion is significantly smaller, which means less useless power consumption and a higher proportion of effective power.

4. Optimised Material Throughput Capacity and Bed Distribution

• Smoother discharge: The discharge area at the end cover increases with the square of the diameter, so the material throughput capacity multiplies. The mill is less prone to “saturated grinding,” and the material flow velocity can be controlled more flexibly.
• Classification effect: In large mills with appropriate length‑to‑diameter ratios, the material distribution across the cross‑section is more uniform. Fine particles can be discharged more quickly, reducing “over‑grinding” (i.e., qualified fines that are not promptly discharged continue to occupy grinding space and consume energy). This increases the finished product output per unit time.

5. Lower Specific Power Consumption (kWh/t)

From a macro economic perspective:

• Small mills (e.g., Φ1.83 m) have a large ratio of shell surface area to volume, so heat dissipation losses are greater. Also, the ratio of the mill’s own dead weight (media + liners) to material output is relatively high.
• Large mills (e.g., ≥Φ4.2 m) benefit from economies of scale. Their specific energy consumption (kWh/t) is significantly lower than that of small mills. Although they hold more grinding media, the output per tonne of media is much higher.

A quick comparison table:

Practical note: Although large mills are more efficient, bigger is not always better. When the diameter exceeds a certain limit (e.g., ≥Φ5.0 m), the increase in output per unit power tends to enter a “saturation zone” due to aggravated centrifugal forces and inter‑layer slippage. This is why the main diameters of large cement mills currently on the market are mostly concentrated in the range of Φ4.2 m to Φ5.0 m.