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Abstract In this paper we develop a performance model for impact crushers. The product size distribution is obtained as a function of the crusher’s rotor radius and angular velocity, the feed rate and the feed size distribution. The model is based on the standard matrix formulation that includes classification and breakage matrices. It can be applied to both hammer and vertical-axis impact crushers with the help of the corresponding estimations for the impact energy per unit mass.27735
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The model predictions are compared with experimental data for limestone treated in a pilot-plant hammer crusher. The variations of the product size distribution resulting from changes in the rotor velocity and the feed rate are investigated.
Keywords: Crushing, Modelling, Simulation.
1. Introduction
Nowadays, impact crushers are widely used for comminution operations because of their high size-reduction ratio, easy modification of the product and a relatively simple design. On the other hand, the prediction of the behaviour of mineral processing plants through modelling and simulations is the more and more employed as a reliable, time- and cost-saving approach for development, analysis and optimisation of crushing circuits. In this context, the availability of relevant mathematical models for impact crushers is important for a successful simulation of such plants.
Despite its importance, however, the modelling of the comminution behaviour of impact crushers received little attention in the literature. There have been some recent attempts to develop performance models for this type of crushers, for example by Csoke and Racz (1998) and Attou et al. (1999), but nevertheless, a significant amount of work remains to be done. In addition, the available commercial codes for simulation of ore processing plants still lack specific models for impact crushers, which obviously reduces their field of application.
In this work we develop a performance model that can be applied to all types of impact crushers. Our goal is to predict the product size distribution, provided that the crusher’s rotor velocity and radius as well as the feed rate and size distribution are known before hand. The specific ore properties and the crusher’s design are taken into account through a reasonable number of adjustable parameters.
Here, the standard model for cone and jaw crushers developed by Whiten and White (1979) is taken as a starting point. Because of the specificity of the impact breakage, this model cannot be used for impact crushers in its original form. While the general scheme of the breakage process in cone and jaw crushers (see Fig. 1) is still applicable in our case, the classification and the breakage functions that describe the fragmentation process from statistical point of view should be reconsidered.
The fragmentation process in cone and jaw crushers is relatively slow and is based on the application of a compression stress on a part of the particles’ surface. Alternatively, the impact breakage takes place at a much shorter time scale and implies a dynamic crack propagation that leads to a much faster failure of the particles. According to Austin (1984), the impact generates compressive and tensile shock waves travelling throughout the particle. The presence of a significant, rapidly growing tensile stress helps the particles to break from within. In addition, the particle breakage theory proposed by Oka and Majima (1970) states that larger particles should break more easily because they contain larger micro-cracks compared with the smaller ones.
In order to account for the dynamic character of the impact breakage, we replace the standard classification function for crushers with a cumulative Weibull distribution depending on the impact energy. Thus, important parameters for the performance of impact crushers such as the rotor radius and velocity as well as the feed rate are naturally incorporated in our model on the basis of simple particle dynamics considerations.