The Bond Ball Mill Work Index (BBWi) is a measure of the resistance of a material to grinding in a ball mill. It is used to calculate the power required for grinding in industrial ball mills. The standard Bond test involves a locked-cycle dry grinding and sieving process to determine the work index.
Bond Ball Mill Work Index Calculation Formula
The Bond Ball Mill Work Index is calculated using the following formula:
\[
W_i = \frac{44.5}{P_1^{0.23} \times G_{bp}^{0.82} \times \left( \frac{10}{\sqrt{P_{80}}} – \frac{10}{\sqrt{F_{80}}} \right)}
\]
Where:
– \( W_i \) = Bond Ball Mill Work Index (kWh/ton)
– \( P_1 \) = Test sieve size (µm) (usually 106 µm for the standard Bond test)
– \( G_{bp} \) = Net grams of undersize per mill revolution (g/rev)
– \( P_{80} \) = 8
passing size of the product (µm)
– \( F_{80} \) = 80% passing size of the feed (µm)
Step-by-Step Calculation Procedure
1. Perform Grindability Test:
– Grind a known mass of material in a standard Bond ball mill (305 mm × 305 mm) under controlled conditions.
– Conduct multiple grinding cycles until equilibrium is reached (where the mass of undersize per cycle stabilizes).
2. Determine \( G_{bp} \) (Grindability):
\[
G_{bp} = \frac{\text{Mass of undersize per cycle (g)}}{\text{Number of revolutions in the cycle}}
\]
3. Measure \( P_{80} \) and \( F_{80} \):
– Perform sieve analysis on feed and product samples.
– Determine the 80% passing sizes (\( F_{80} \) for feed, \( P_{80} \) for product).
4. Plug Values into Bond’s Formula:
\[
W_i = \frac{44.5}{(106)^{0.23} \times G_{bp}^{0.82}} \times \left( \frac{10}{\sqrt{P_{80}}} – \frac{10}{\sqrt{F_{80}}} \right)
\]
Example Calculation
Given:
– Test sieve size (\(