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Crusher - Bond's Law | Power and Sizing

Input data

Inlet massic flow

Work index

Feed F80 - 80% passing size before crushing

Product P80 - 80% passing size after crushing

Output data

Required power

Description

Calculate grinding parameters using Bond's Law (Fred Bond, 1961), which establishes the relationship between specific energy consumed in material fragmentation and the granulometric characteristics of feed and product.

Failed to load imageCrusher

There are 5 calculation possibilities:

 

  • Calculate the required power
  • Calculate the mass flow
  • Calculate the work index
  • Calculate the diameter before crushing (F80)
  • Calculate the diameter after crushing (P80)

 

Bond's Law is expressed by the equation:

Pm=0.3162×Wi×(1P80−1F80)\frac{P}{m} = 0.3162 \times W_i \times \left(\frac{1}{\sqrt{P_{80}}} - \frac{1}{\sqrt{F_{80}}}\right)

Where:

  • P = Required power (kW)
  • m = Inlet mass flow (ton/h)
  • Wi = Work index of material (kWh/ton)
  • F80 = 80% passing size before crushing (μm)
  • P80 = 80% passing size after crushing (μm)

Input Data

Parameter
Default Units
Description
Inlet mass flow
ton/h
Material feed rate to the mill
Work index
kWh/ton
Specific energy required to reduce material from theoretically infinite size to 100 μm
Feed F80
mm
Opening size that allows passage of 80% of material before crushing
Product P80
mm
Opening size that allows passage of 80% of material after crushing
Required power
kW
Mechanical power needed for the grinding process

Output Data

Parameter
Default Units
Description
Required power
kW
Calculated mechanical power for the process
Inlet mass flow
ton/h
Calculated feed rate
Work index
kWh/ton
Calculated work index of material
Feed P80
mm
Calculated size before crushing
Product F80
mm
Calculated size after crushing

Work Index for Different Materials - Wet Grinding

Material
Wi (kWh/ton)
Bauxite
8.7
Raw cement
10.51
Clay
6.30
Coal
13.00
Granite
15.13
Wheat
4.35
Gravel
16.06
Iron ore (hematite)
12.84
Phosphate mineral
9.92
Quartz
13.57

Note: For dry grinding, multiply Wi by 1.33.

References

  • BOND, Fred, C. Crushing & Grinding Calculations - Part I. British Chemical Engineering, 1961.