Learning Resources / Crushing / Methodology

Crushing Methodology

Overview of the Whitten Breakage Model and Bond's Law used in the simulation.

Whitten Crusher Model

The simulation uses a standard matrix model for comminution. The process is defined by two key functions: Classification (Probability of breakage) and Breakage Distribution (Resulting size distribution).

Classification (Selection)

Probability $C(d)$ that a particle of size $d$ will be broken.

C(d) = 1 - \frac{1}{1 + (d / CSS)^m}

$CSS$ : Closed Side Setting.
$m$ : Sharpness of classification (Curve steepness).

Breakage (T10)

Reflects the intensity of breakage events.

The

t_{10}

parameter represents the percentage of material passing 1/10th of the original particle size after breakage.

A higher

t_{10}

means more fines are produced (softer rock or higher energy).

Power Consumption

To estimate the energy requirement, we calculate the $P_{80}$ and $F_{80}$ from the simulated size distributions and apply Bond's Third Theory.

W = 10 \cdot W_i \cdot \left( \frac{1}{\sqrt{P_{80}}} - \frac{1}{\sqrt{F_{80}}} \right)

Values used:

P_{80}, F_{80}

\mu m

W

in kWh/t.

Model Assumptions

Feed Distribution: Generated synthetically using a Rosin-Rammler distribution derived from user $F_{80}$ .
Perfect Mixing: The model assumes the crusher behaves as a perfect mixer for classification.
Single Stage: Simulation represents a single pass through the crusher (open circuit).