Calculating the capacity of a ball mill involves several factors, including the mill’s dimensions, operating conditions, and material properties. Below are the key steps and formulas used to estimate ball mill capacity.
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1. Basic Ball Mill Capacity Formula
The general formula for ball mill capacity is:
\[
Q = V \times C \times \eta \times J \times \rho_b \times 60
\]
Where:
– \( Q \) = Mill capacity (tonnes/hour)
– \( V \) = Effective mill volume (m³)
– \( C \) = Specific grinding rate (kg/kWh)
– \( \eta \) = Fraction of critical speed (typically 0.65–0.75)
– \( J \) = Filling degree of grinding media (typically 0.2–0.4)
– \( \rho_b \) = Bulk density of grinding media (tonnes/m³, ~4.5 for steel balls)
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2. Effective Mill Volume Calculation
The effective mill volume (\( V \)) is calculated as:
\[
V = L \times D^2 \times k
\]
Where:
– \( L \) = Mill length (m)
– \( D \) = Mill diameter (m)
– \( k \) = Geometric factor (~0.785 for cylindrical mills)
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3. Specific Grinding Rate (\( C \))
The specific grinding rate depends on:
– Material hardness
– Feed and product size distributions
– Grindability index (Bond Work Index \( W_i \) can be used)
For Bond’s approach:
\[
C = 10 / W_i
\]
Where:
– \( W_i \) = Bond Work Index (kWh/tonne)
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4. Critical Speed & Operating Speed
The critical speed (\( N_c \)) is the rotational speed where centrifugal force equals gravitational force:
\[
N_c = 42.3 / \sqrt{D}
\]
The actual operating speed (\( N_{op} \)) is usually 65–75% of \( N_c \) (\( N_{op} = 0.65–0.75 \, N_c \)).
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5. Power Consumption & Capacity Relationship
Mill power draw (\( P_{mill} \) in kW) can be estimated using Bond’s equation:
\[
P_{mill} = W_i \, Q \, (10 / P_{80}^{0.5} –