*Article* **Fit-for-Purpose VSI Modelling Framework for Process Simulation**

**Simon Grunditz \*, Gauti Asbjörnsson, Erik Hulthén and Magnus Evertsson**

Department of Industrial and Materials Science, Chalmers University of Technology, SE-41296 Göteborg, Sweden; gauti@chalmers.se (G.A.); erik.hulthen@chalmers.se (E.H.); magnus.evertsson@chalmers.se (M.E.) **\*** Correspondence: simon.grunditz@chalmers.se

**Abstract:** The worldwide shortage of natural sand has created a need for improved methods to create a replacement product. The use of vertical shaft impact (VSI) crushers is one possible solution, since VSI crushers can create particles with a good aspect ratio and smooth surfaces for use in different applications such as in construction. To evaluate the impact a VSI crusher has on the process performance, a more fit-for-purpose model is needed for process simulations. This paper aims to present a modelling framework to improve particle breakage prediction in VSI crushers. The model is based on the theory of energy-based breakage behavior. Particle collision energy data are extracted from discrete element method (DEM) simulations with particle velocities, i.e., rotor speed, as the input. A selection–breakage approach is then used to create the particle size distribution (PSD). For each site, the model is trained with two datasets for the PSDs at different VSI rotor tip speeds. This allows the model to predict the product output for different rotor tip speeds beyond the experimental configurations. A dataset from 24 different sites in Sweden is used for training and validating the model to showcase the robustness of the model. The model presented in this paper has a low barrier for implementation suitable for trying different speeds at existing sites and can be used as a replacement to a manual testing approach.

**Keywords:** VSI; DEM; sand; breakage; modelling
