The critical speed of a ball mill is the rotational speed at which the grinding media (balls) begin to centrifuge, causing no grinding action. It is expressed as a percentage of the mill’s theoretical critical speed, which depends on the mill’s internal diameter and the size of the grinding media.
Formula for Critical Speed (Nc):
The critical speed (in revolutions per minute, RPM) is calculated using the following formula:
\[
N_c = \frac{42.3}{\sqrt{D – d}}
\]
Where:
– \( N_c \) = Critical speed (RPM)
– \( D \) = Internal diameter of the mill (meters)
– \( d \) = Diameter of the grinding balls (meters)
Steps to Calculate Critical Speed in India:
1. Measure Mill Diameter (D):
– Measure the internal diameter of the ball mill in meters.
– Example: If \( D = 2 \, \text{m} \).
2. Determine Ball Diameter (d):
– Measure or assume the diameter of the grinding balls.
– Example: If \( d = 0.05 \, \text{m} \) (50 mm balls).
3. Apply Formula:
\[
N_c = \frac{42.3}{\sqrt{2 – 0.05}} = \frac{42.3}{\sqrt{1.95}} ≈ \frac{42.3}{1.396} ≈ 30.3 \, \text{RPM}
\]
4. Operating Speed:
– Typically, ball mills operate at 65% to 75% of critical speed.
– For optimal performance in India, common operating speeds are around 70% of Nc.
Example Calculation for a 2m Ball Mill in India:
– Given: \( D = 2 \, \text{m}, d = 0.05 \, \text{m} \)
– Critical Speed (\( N_c \.jpg)
≈ 30 RPM
– Operating Speed ≈ \( 0.7 × 30 ≈ 21 \, \text{RPM} \)
Factors Affecting Critical Speed in Indian Mills:
– Liner design (smooth or lifter liners affect motion).
– Mill filling ratio (percentage of mill volume filled with media).
– Material properties (hardness, density).
– Wet vs dry grinding conditions.
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