Grinding and Crushing Energy (Bond Work Index)
The energy and motor power behind a size reduction.
Example
You enter
- Bond work index Wi (kWh per short ton) 13
- Feed size F80 (microns; 25,400 per inch) 1000
- Product size P80 (microns) 75
- Feed rate (short tons per hour, blank for energy only) 100
You get
- Specific energy kwh st 10.9
- Power (kW) 1090
No published worked example is on file for this calculation. It is checked against a hand-worked derivation of its method and an independent reference test.
Details, formula, and sources
ScopeFrom the ore's Bond work index and the feed and product sizes at 80% passing: W = 10 Wi (1/sqrt(P80) - 1/sqrt(F80)) kWh per short ton, sizes in microns. A 13 kWh/st ore ground from 1,000 to 75 microns takes 10.9 kWh per short ton, so 100 tons an hour needs about 1,090 kW (1,460 hp) at the mill pinion. Fine grinding is where the energy goes. Rowland's efficiency factors are not applied. A screen; the mill vendor governs.
Formula or tableW = 10 Wi (1/sqrt(P80) - 1/sqrt(F80)) kWh per short ton (F80, P80 in microns); power_kW = W x feed rate (short tons per hour); hp = kW / 0.7457; with an available power, the finest product is P80 = [(kW/tph)/(10 Wi) + 1/sqrt(F80)]^-2.
Source and editionBond's third theory of comminution (F. C. Bond, 'The Third Theory of Comminution,' Trans. AIME 193, 1952; 'Crushing and Grinding Calculations,' Allis-Chalmers, 1961), by name.
Free accessA published empirical law; the work index (from a Bond lab test), the sizes, and the feed rate are the user's inputs.
What governsEstimate. AHJ and licensed professional govern.
API field nameswork_index_kwh_st, feed_f80_um, product_p80_um, feed_rate_stph, specific_energy_kwh_st, power_kw
- Bond's law W = 10 Wi (1/sqrt(P80) - 1/sqrt(F80)), sizes in microns at 80% passingBond (1952, 1961)
- Work index unit kWh per short ton; Wi is the energy from infinite size to 80% passing 100 micronsBond (1961)
- Efficiency factors Rowland EF1-EF8 not appliedscope of this tile