sizing of tph ball mill

The sizing of a TPH (Tonnes Per Hour) ball mill depends on several factors, including the feed size, desired product size, ore characteristics, and operating conditions. Below is a step-by-step guide to estimate the required ball mill size for a given throughput.

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Key Factors for Ball Mill Sizing

1. Throughput (TPH) – Desired grinding capacity in tonnes per hour.
2. Feed Size (F80) – 80% passing size of the feed material (microns or mm).
3. Product Size (P80) – 80% passing size of the ground product (microns or mm).
4. Bond Work Index (Wi) – A measure of ore hardness (kWh/tonne).
5. Mill Diameter & Length – Determines grinding volume.
6. Mill Speed (% Critical Speed) – Typically 65-75% of critical speed.
7. Ball Charge & Liner Type – Affects grinding efficiency.
8. Circulating Load – Percentage of material returned to the mill.

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Step-by-Step Calculation

1. Calculate Required Power Using Bond’s Law

The power required for grinding can be estimated using Bond’s equation:

\[
W = 10 \times Wi \times \left( \frac{1}{\sqrt{P_{80}}} – \frac{1}{\sqrt{F_{80}}} \right)
\]

Where:

\( W \) = Specific energy consumption (kWh/tonne)
\( Wi \) = Bond Work Index (kWh/tonne)
\( P_{80} \) = Product size (µm)
\( F_{80} \) = Feed size (µm)

2. Total Power Required

Multiply specific energy by throughput:

\[
P_{total} = W \times TPH \quad (\text{kW})
\]

3. Mill Sizing Based on Power

Ball mills are rated by power rather than capacity, so select a mill that can deliver the required power.

A rough empirical formula for mill power is: sizing of tph ball mill

\[
P = C \times D^{2.5} \times L \times J \times \phi_c
\]

Where:

\( P \) = Mill power draw (kW)
\( C \) = Constant (~0.223 for wet overflow mills)
\( D \) = Mill diameter inside liners (m)
\( L \) = Mill length inside liners (m)
\( J \) = Fractional ball charge (~0.2–0.35)
\(\phi_c\) = % critical speed (~0.65–0.75)

4. Typical Ball Mill Dimensions

For a given power requirement, common ball mill dimensions follow industry standards:
| TPH Range | Typical Ball Mill Size |
|———–|———————–|
| 5–20 TPH | 1.8m × 3m–2m × 4m |
| 20–50 TPH | 2.4m × 4m–3m × 5m |
| 50–100 TPH| 3m × 6m–4m × 7m |
| >100 TPH | Larger mills (>4m dia.)|

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Example Calculation

Given:

Throughput: 50 TPH
Feed size (\(F_{80}\)): 2000 µm
Product size (\(P_{80}\)): 75 µm
Bond Work Index (\(Wi\)): 12 kWh/tonne

Step 1: Calculate specific energy (\(W\)):

\[
W = 10 \times 12 \times \left( \frac{1}{\sqrt{75}} – \frac{1}{\sqrt{2000}} \right)
\]
\[
W ≈ 10 × 12 × (0.115 – 0.022) ≈ 11.16 \, kWh/tonne
\]

Step 2: Total power required: sizing of tph ball mill

\[
P_{total} = 11.16 \, kWh/tonne × 50 \, TPH ≈ 558 \, kW
\]

Step 3: Select an appropriate mill (~600 kW). A typical choice could be:

Diameter: 3 m, Length: 5 m, ~600 kW motor.

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Additional Considerations

✔ Use manufacturer data for exact mill selection (Metso, FLSmidth, etc.).
✔ Consider closed-circuit grinding if finer product is needed (with hydrocyclones).
✔ Optimize ball charge and liner design for efficiency.

Would you like help with a specific ore type or circuit configuration?