Calculating the power consumption of a closed-circuit ball mill involves several factors, including the mill’s operating parameters, the properties of the material being ground, and the efficiency of the grinding process. Here’s a step-by-step guide to estimating the power consumption:
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1. Basic Formula for Power Consumption
The power consumption of a ball mill can be estimated using the following formula:
\[
P = \frac{Q \cdot E}{\eta}
\]
Where:
– \( P \) = Power consumption (kW)
– \( Q \) = Mill throughput (tonnes/hour)
– \( E \) = Specific energy consumption (kWh/tonne)
– \( \eta \) = Overall 
iciency of the mill and drive system (dimensionless, typically 0.85–0.95)
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2. Specific Energy Consumption (\( E \))
The specific energy consumption depends on factors such as:
– Feed size (\( F_{80} \))
– Product size (\( P_{80} \))
– Grindability of the material (Bond Work Index, \( W_i \))
The Bond equation is commonly used to estimate \( E \):
\[
E = W_i \cdot \left( \frac{10}{\sqrt{P_{80}}} – \frac{10}{\sqrt{F_{80}}} \right)
\]
Where:
– \( W_i \) = Bond Work Index (kWh/tonne)
– \( F_{80} \) = 80% passing size of feed (µm)
– \( P_{80} \) = 80% passing size of product (µm)
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3. Mill Throughput (\( Q \))
Mill throughput depends on:
– Mill dimensions (diameter and length)
– Mill speed (% critical speed)
– Charge volume (% of mill volume filled with grinding media)
– Material properties
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4. Efficiency (\( \eta \))
The overall efficiency accounts for losses in the drive system and other mechanical inefficiencies. Typical values range from 0.85 to 0.95.
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5. Example Calculation
Assume:
– Bond Work Index (\( W_i \)) = 12 kWh/tonne
– Feed size (\( F_{80} \)) = 2000 µm
– Product size (\( P_{80} \)) = 200 µm
– Mill throughput (\( Q \)) = 100 tonnes/hour
– Efficiency (\( \eta \)) = 0.90
Step 1: Calculate Specific Energy Consumption (\( E \))