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In this paper, we present a phenomenological model that predicts the size distribution of the product issued from impact crushing in function of the rotor strike radius and velocity, the material properties and size distribution of the feed as well as the feed rate. The model is based on the standard matrix representation including classification and breakage matrices. It can be applied to both horizontal- and vertical-shaft impact crushers by means of the corresponding estimations for the average impact energy per unit mass presented here.
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We propose a new classification function for impact crushers in the form of a Weibull cumulative distribution. The minimum size of the particles that undergo breakage is assumed to be a function of the impact energy and the feed rate.
The model predictions are compared with experimental data obtained for limestone treated in a pilot-plant hammer crusher.
The dependence of the product size distribution on the rotor velocity is investigated. The influence of the feed rate on the
product size is also simulated.22259
D 2004 Published by Elsevier B.V.
Keywords: impact crushing; standard matrix representation; Weibull cumulative distribution
1. Introduction
During the past few decades, impact crushers have
become widely used machines for comminution
operations because of their high size-reduction ratio,
easy modification of the product size distribution and
a good dcubicT shape of the product. On the other
hand, computer simulations are increasingly used in
the modern design of ore processing plants containing
crushers as a reliable, time- and cost-saving approach.
* Tel.: +32 69 88 42 66; fax: +32 69 88 42 59.
E-mail address: ctp@honet.be.
0301-优尔6/$ - see front matter D 2004 Published by Elsevier B.V.
doi:10.1016/j.minpro.2004.07.031
Despite their importance, however, impact crushers
received little attention in what concerns the model-
ling and simulation of their comminution behaviour.
For this reason, the commercial codes for ore
processing simulations still lack specific models for
this type of crushers. There have been some recent
attempts to develop phenomenological models for
impact crushers (e.g., by Czoke and Racz, 1998;
Attou, 1999), but nevertheless, significant amount of
work has yet to be done in this field.
Here we take the standard size distribution model
for cone and jaw crushers developed by Whiten and
White (1979) as a starting point. Because of the
specificity of the breakage process in impact crushers,
S. Nikolov / Int. J. Miner. Process. 74S (2004) S219–S225
this model cannot be used for these machines in its
original form. Impact breakage takes place at a much
shorter time scale compared to the fragmentation
process used in cone or jaw crushers. Hence, the
nature and magnitude of forces as well as the energy
transfer and dissipation related to impact breakage are
very different from the relatively slow breakage by
compression and shear used in other types of crushers.
In order to solve this problem, we replace the
classification breakage function used for cone and jaw
crushers with a new one based on a Weibull
probability distribution. Thus, important parameters
such as the rotor radius and velocity as well as the
feed rate are naturally incorporated in our model. We
also propose estimations for the average impact
energy per unit mass for both horizontal- and
vertical-shaft impact crushers.
The model structure is presented in Section 2,
results are shown and commented in Section 3.
Throughout the text, vectors ( f ) and matrices (C )
BP represents the redistribution of the broken particles
among the predefined size classes.
According to Fig. 1, the particles entering the