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The DEM has also been applied to studies of impact-induced particle breakage. Potapov and Campbell (1994) found that ratio of the impact velocity to propagation velocity of the longitudinal (sound) waves in the material (Vo/C) was a useful parameter that described the rate at which the kinetic energy of the collision was transferred to the strain energy of the particle. When the value of Vo/C was high, the produced fragments tended to have an elongated shape. This was in agreement with experimental results. Thornton et al. (1996) reported about 2D DEM of agglomerates impacting the rigid walls. Depending on the impact velocity and adhesive strength between particles, three regimes were observed: shattering, semi-brittle fracture and elastic rebound. Mishra and Thornton (2001) have studied the impact breakage of particle agglomerates. They found a distinct fracture pattern for dense agglomerates above a threshold impact velocity. The produced fragment size distributions showed a clear bi-modal distribution. However, application of the DEM to the impact crushers was rare in the literature.
Over years the Julius Kruttschnitt Mineral Research Centre (JKMRC) has successfully modelled two types of impact crushers: the vertical shaft impact crusher (Napier-Munn et al., 1996) and the horizontal shaft swing hammer mill (Shi, 2002; Shi et al., 2003). In the present work the PFC3D (particle flow code) that models the movement and interaction of particles by DEM techniques was employed to model the two types of impact crusher. Modelling of fragmentation has also been attempted using a strain rate concept. The data collected from a Canica crusher treating quartzite and a BJD swing hammer mill treating coal were used to verify the DEM simulation results of specific energy and fragment size distribution.
Upon the DEM procedures being validated, a detailed simulation study was conducted to investigate the effects of the machine design and operational conditions on velocity and energy distributions of collision inside the milling chamber and on the particle breakage behaviour.
2. The PFC3D models of impact crushers
Impact crusher modelling has been performed using the PFC3D discrete element code. This code models the behaviour of particles, which may be enclosed within a finite volume by the non-deformable walls. The code keeps a record of inpidual particles and updates any contact with other particles or walls. Each calculation step includes application of the law of motion to a particle, a force–displacement law to each contact and constant updating of the wall position (Cundall and Strack, 1979). Details of the DEM calculation of contact force, shear stiffness and slip model are referred to other publication (Djordjevic, 2003).
Two types of impact crushers were modelled using the PFC3D code. The Canica Model 90 is an industrial-scale vertical shaft impact crusher with 5 impellers of 0.48 m in their tip rotating radius. The crusher is fed by a belt feeder. Rocks drop into the centre of the rotor, and are hit or accelerated by the impellers to impact on the surrounding anvils. The distance from the rotor centre to the surface of the anvil is 0.65 m. The Canica crusher was employed to treat quartzite. The rotational speeds of the crusher varied from 650 to 950 rpm in the experiment at an average throughput of 102 tph.
The BJD swing hammer mill is a pilot-scale horizontal shaft impact crusher. The hammer tip diameter is 0.38 m, mill width 0.20 m, with a nominal capacity of 3 tph when driven by a 5.6 kW motor. The rotor, rotating at a fixed speed of 3000 rpm, carries four rows of rectangular hammers with a width 0.03 m, two rows of three hammers and two rows of two hammers. The BJD hammer mill was employed to treat coal.
The Canica vertical shaft impact crusher is represented by a cylindrical chamber and five rotating impellers in the DEM simulations (Fig. 1). Feed comes from 1 m above in the form of free falling particles. The code is designed to perform modelling in 3D. Similarly, the model for the BJD horizontal shaft hammer mill is given in Fig. 2. For simplicity in the DEM calculation code, the double-shaft swing hammers were simplified as single-shaft rigid hammers.