Morrell C-model

This model was developed as part of the PhD thesis of Stephen Morrell at the University of Queensland and is the model used in the JK SimMet software for determining mill power draw. It is described as the "C-model" and should not be confused with the more empirical "D-model" that has a form similar to the Loveday equation.

The simplest explanation of the model is that it is a friction balance between concentric layers within a moving mill charge which is used to calculate the torque experienced by the mill due to the charge geometry. The model contains several sub-equations that govern the charge geometry and is too complicated to explain here. People seeking more information should buy the book Mineral Comminution Circuits, Their Operation and Optimisation from JK Tech: http://www.jktech.com.au/mineral-comminution-circuits .

Model Inputs

The same underlying model is used for SAG and ball milling, with minor differences for the way the charge density is calculated and whether the mill is a grate discharge (most of the SAG mills) or overflow discharge (typically a ball mill).

Within the classification, there are also two versions of the Morrell C-model, the "simplified" model where only the major inputs are requested from the user and the "full" model where all possible inputs are available.

• mill diameter
• mill effective grinding length
• ball load
• ball density (only full model, 7.8 t/m³ used for simplified)
• pulp percent solids
• mill speed
• sphere packing geometric factor J_void
• cone end angle (only full model, simplified: 30° for SAG and 15° used for ball mill)
• trunnion diameter (only full model, fraction of mill diameter used for simplified)
• k-factor, conversion of "net power to gross power" (1.26)

Model Outputs

Power measured at the motor input of an induction motor driving a gearbox on a geared mill. This motor input is immediately converted to mill shell power for use in equations by multiplying the model result by 0.97 mechanical efficiency factor and by 0.96 typical induction motor efficiency factor.