Characterization of the Centrifugal Mill by Lumped Kinetic Math Model and Discrete Element Model T. Inoue and K. Okaya Department of Earth System Engineering, University of Tokyo

Centrifugal Mill Eccentricity: Acceleration Coefficient:

Force balance in centrifugal mill (Bradley et al.)

Theoretical Model (Bradley et al.)

Upper limit of phase angle (theoretical)

Mill Solver - A 2-D DEM Model -1

Mill Solver - A 2-D DEM Model -2

Mill Solver - A 2-D DEM Model -3

Effect of mill diameter (D) on mill power, determined by DEM simulation.

Effect of ball density on mill power, determined by DEM simulation

Effect of centrifugal coefficient (z) on mill power and energy consist,determined by DEM simulation -1

Effect of centrifugal coefficient (z) on mill power and energy consist,determined by DEM simulation -2

Effect of eccentricity (G/D) on mill power, determined by DEM simulation

Effect of ball filling (J) on power draft, determined by DEM simulation

Effect of eccentricity (G/D) on energy dissipation pattern Energy Consist

Effect of friction coefficient and restitution coefficient on power draft -1

Effect of friction coefficient and restitution coefficient on power draft -2

Effect of Restitution Coefficient on Power Dissipation

Weighted density distribution of energy spectrum

Theoretical (Bradley et al.) : DEM simulation (Inoue-Okaya) :

Specification of prototype X-Mill TypeDouble cylinder self- balancing centrifugal mill Mill OperationBatch or continuos Dimension of 150 mm dia. Mill cylinders300 mm length Eccentricity (G/D)0.2 Grinding media17 kg (for steel balls) Equipment size762 (W) * 935 (H) * 1190 (L) mm Motor7.5 kW

X-Mill

X-Mill (prototype)

X-Mill (prototype) in motion

Batch grinding (quartz)

Continuous grinding (quartz)

Autogenous grinding (limestone)

Figure 2. Phase angle of the centrifugal mill estimated from math model.

Figure 3. Net power draft of the centrifugal mill estimated from math model

Figure 4. Phase angle of the centrifugal mill estimated from math and simulator models.

Figure5. Net power draft of the centrifugal mill estimated from math and simulator models.

Conclusion §Theoretical model can present approximate but clear view of the equipment property in the form of a simple equation §DEM simulation can present a more realistic vision of the equipment and its performance §DEM simulation can present the property of the possible mill design under less restriction and less expenses §DEM simulation gives a microscopic view of the comminution events together with their integral effects in realistic figures