Mathematical modeling of a vertical shaft impact crusher using the Whiten model

Vertical Shaft Impact (VSI) crushers have been used as interesting alternatives to cone crushers, particularly in the production of aggregates for the construction industry, not only due to their good energy efficiency but also to their ability to generate more isometric and tougher particles, which is highly desirable in cement mortars and concrete applications. Several mathematical models for the VSI crusher have been proposed in the last two decades or so. The Whiten crusher model, originally developed for cone crushers, has served as the basis of several approaches to model VSI crushers. In the present work, the Andersen/Awachie/Whiten model has been used as the basis for modeling a VSI crusher operating in an industrial plant in Brazil, processing quarry rock to product manufactured sand. Nineteen industrial experiments, covering a range of feed rates, rotor speeds, feed distributor types and feed size distributions, have been carried out. The approach demonstrated to be capable of providing satisfactory estimates of the VSI performance, being able to predict the product size distribution and the specific energy consumption with confidence over a wide range of operating conditions. Since it uses a model that is already available in commercial plant simulators, it may be used, with additional expressions, in simulating any desired circuit. Model parameters such as K3 and T10 were found to be particularly influenced by key operational variables such as feed rate and rotor frequency. The significant effect of feed rate on the performance of the VSI crusher studied has been discussed on the basis of simulations of the material flow pattern inside its feed distributing system, simulated using the discrete element method. According to these simulations, it has been inferred that change in the behavior of VSI from lower to higher feed rates may be related to the transition from material being fed predominantly to the rotor, to the increasing contribution of the cascading effect.