Austin SAG model

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The SAG mill model by proposed by Leonard Austin (1990) was largely based on modifications of earlier tumbling mill models by Hogg & Fuerstenau and F. Bond. The model uses a kinetic-potential energy balance to describe the power draw of a mill charge. Many geometric components of the earlier models were fit to empirical relationships measured by Austin.

Model Form

The power draw model for a SAG mill cylinder of the following form:

P = K D^{2.5} L ( 1 - AJ_{total}) \left [ (1-\epsilon_{B}) \left( \frac{\rho_{solids}}{w_{C}} \right ) J_{total} + 0.6 J_{balls} \left( \rho_{balls} - \frac{\rho_{solids}}{w_C} \right)  \right ] \phi_{C} \left( 1 - \frac{0.1}{2^{9-10\phi_C}} \right)


  • P is the power evolved at the mill shell, kW
  • K and A are empirical fitting factors (use 10.6 and 1.03, respectively)
  • D is the mill effective diameter (inside the effective liner thickness), m
  • L is the mill effective grinding length (also referred to as the 'belly length), m
  • Jtotal is the mill total volumetric filling as a fraction (eg. 0.30 for 30%)
  • εB is the porosity of the rock and ball load (use 0.3)
  • wC is the charge %solids, fraction by weight (use 0.80 Doll, 2013)
  • Jballs is the mill volumetric filling of balls as a fraction (eg. 0.10 for 10%)
  • ρX is the density of component X, t/m3
  • φC is the mill speed as a fraction of critical (eg. 0.75 for 75% of critical)

Mill cone angles

The model supports flat-ended mills (cone angle of 0°) or a cone angle of 15°. Any other value entered for the cone angle will be treated as 15°.

To account for cone ends of mills, an allowance of 5% is used Doll, 2013 instead of the formula proposed by Austin.

Percent solids

The model is run with a fixed 80% solids by weight Doll, 2013. This is because the form of the equation proposed by Austin appears to have the %solids term in the wrong place (denominator of the expression rather than the numerator where other models put it). The calibration presented at IMPC 2016 suggests the fixed %solids term is reasonably valid over the range of 60% to 80% solids.

Model Inputs

the Austin model requests the following mill data:

  • mill nominal diameter inside shell
  • mill effective grinding length
  • ball load as vol percentage (eg. 10)
  • ball density
  • total charge load as vol percentage (eg. 30)
  • pulp percent solids
  • mill speed
  • liner effective thickness
  • cone end angle (only values 0-5 or >5 matter, minor angle changes have no effect)

Motor characteristics are also requested:

  • Motor rated power (output shaft)
  • Mechanical efficiency of downstream drive (pinions, gearboxes)
  • Motor efficiency and any other efficiency factors to the DCS measurement position in the network.
  • Motor rated speed, in units of mill RPM (not motor RPM, must multiply by gear ratios).
  • Quantity of pinions (and motors)