# Mill power draw models

## Contents

## Mill Power Draw Models

The mill power draw models are used to predict how much power will be consumed by a particular type of mill, mill geometry and set of mill operating conditions. This power is transferred to the ore and used to predict the throughput when combined with the specific energy consumption models. Models of this type do not predict the particle size distribution of a milled product — the more complicated population balance models are required for such modelling.

Several authors have offered different types of models, and all generally work for the particular class of equipment they were intended for. The classes of models, and the models in each class are:

*SAG mill models*- Austin SAG model (hybrid phenomenological and empirical model)
- Morrell C-model (phenomenological model with empirical fitting. Sub-divided into a
*simplified*model with 'typical' defaults and*full*model with all parameters editable) - Loveday/Barratt SAG model (uses an internal table of empirical "Power Numbers")

*Overflow ball mill models*- Nordberg model (largely empirical model)
- Morrell C-model (phenomenological model with empirical fitting. Sub-divided into a
*simplified*model with 'typical' defaults and*full*model with all parameters editable)

*Grate ball mill models*- Nordberg model (largely empirical model)
- Morrell C-model (phenomenological model with empirical fitting. Only the
*full*model is available)

*Other models*- Cone crusher (secondary, tertiary or pebble crusher)

### Comments on flow restrictions

All mill models deal strictly with the power that can be evolved from a particular mill geometry and operating condition. All models assume that there are no flow restrictions of any kind in the circuit and that only mill power will limit the throughput of a grinding circuit. In reality, grinding circuit throughput is frequently limited by the volumetric flow of a hydrocyclone feed pump or the pulp discharging capacity of a SAG mill.

These models give project designers clues as to "at what volumetric flow should I design my plant" by ignoring flow restrictions. A geometallurgy data set will demonstrate a range of circuit throughput that are possible with unlimited flow, which then allows the designer to consider "what proportion should I choose to accommodate?".

The designer should check some basic rules of thumb (such as those in the SME Mineral Processing Handbook) against their design, including the range of circulating load in the ball mill and the superficial velocity of pulp through a ball mill.

### Power at the mill shell

The mill power draw models used in SAGMILLING.COM all reference power as drawn at the mill shell. Most surveys report power values as they are measured in the plant distributed control system (DCS), which is usually relative to the motor input power. Refer to the Measurement of power article for description of how to convert DCS indicated power to mill power at the shell.

Note that modern wrap-around (gearless) mill drives do a software correction to report mill motor output power (which is the same as shell power). Therefore, new gearless mill drives do not require any correction when comparing DCS power measurements to model power draw predictions.

### Power predictions are only valid below motor rated speed

Most mills (outside of Australia) use synchronous motors. These motor have the following characteristics (in general)

- The maximum power indicated on the name-plate is the power on the output shaft of the motor (or mill shell for gearless).
- The maximum power indicated can only be evolved at the rated speed indicated on the name-plate.
- Below the rated speed, the motor's available power reduces linearly as a function of actual speed over rated speed.
- Above rated speed, the motor available is fixed and constant. Operating above rated speed means less torque is available at that constant power.
- None of the power models in SAGMILLING.COM considers the speed-related restrictions imposed by a motor; the models predict what power the mill charge geometry could draw
**assuming the motor can provide it.** - You must manually check the motor's tent diagram to confirm that the predicted power draw is actually within the motor's capability at the indicated speed.

### Liner and grate design

The design of mill liners and SAG mill discharge grates will have a large effect on how efficiently the mill operates and the circuit throughput. All models generally assume that a mill is fitted with "efficient" liners and that the grate design neither limits passage of pebbles (and pulp) nor permits re-circulation of pulp back into the mill.

Determining a correct liner and grate design is beyond the scope of the models hosted on SAGMILLING.COM, and there are specialized tools available to do such designs such as discrete element model (DEM) simulations and certain population balance models.