October 2023
Volume 75    Issue 10

Reliability of nonlinear modeling in predicting the size distribution of grinding products under different operating conditions

Petrakis, Evangelos; Varouchakis, Emmanouil; Komnitsas, Konstantinos


In the modeling of grinding systems, population balance modeling (PBM) that considers a constant breakage rate has been widely used over the past years. However, in some cases, PBM exhibited some limitations, and time-dependent approaches have been developed. Recently, a nonlinear framework that considers the traditional linear theory of the PBM as a partial case has been introduced, thus allowing the estimation of product particle size distribution in relation to grinding time or the specific energy input to the mill.
   In the proposed model, the simplified form of the fundamental batch grinding equation was transformed into the well-known Rosin–Rammler (RR) distribution. The adaptability and reliability of the prediction model are, among others, dependent upon the operating conditions of the mill and the adjustment of the RR distribution to the experimental data. In this study, a series of grinding tests were performed using marble as test material, and the adaptability of the nonlinear model was investigated using three loads of single-size media: 40, 25.4 and 12.7 mm in size, respectively. The results indicate that the proposed model enables a more accurate analysis of grinding, compared to PBM, for different operating conditions.

Full-text paper:
Mining, Metallurgy & Exploration (2023) 40:1265–1278, https://doi.org/10.1007/s42461-023-00793-3


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