# Morrell C-model

Applies to both SAG and ball mills, with variants for grate-discharge and overflow mills.

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" Morrell C-model **where only the major inputs are requested from the user

- mill nominal diameter inside shell
- mill effective grinding length
- ball load
- ball density
- pulp percent solids
- mill speed
- liner effective thickness

**the "full" Morrell C-model** where all possible inputs are available.

- mill nominal diameter inside shell
- mill effective grinding length
- ball load
- ball density
- pulp percent solids
- mill speed
- liner effective thickness
- cone end angle
- trunnion diameter
- k-factor, empirical conversion of "net power to gross power" (1.26)

**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)

## Model Outputs

The published version of this model provides 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 circuit model equations by multiplying the model result by 0.97 mechanical efficiency factor and by 0.96 typical induction motor efficiency factor.

The displayed Morrell C-model result in sagmilling.com is always corrected to **mill shell power**.