Calibration and Validation of a Cone Crusher Model with Industrial Data

This paper reports the calibration and validation of a cone crusher model using industrial data. Usually, there are three calibration parameters in the condensed breakage function; by contrast, in this work, every entry of the lower triangular breakage function matrix is considered a calibration parameter. The calibration problem is cast as an optimization problem based on the least squares method. The results show that the calibrated model is able to fit the validation datasets closely, as seen from the low values of the objective function. Another significant advantage of the proposed approach is that the model can be calibrated on data that are usually available from industrial operation; no additional laboratory tests are required. Calibration and validation tests on datasets collected from two different mines show that the calibrated model is a strong candidate for use in various dynamic simulation applications, such as control system design, equipment sizing, operator training, and optimization of crushing circuits.

Investigation of Error Distribution in the Back-Calculation of Breakage Function Model Parameters via Nonlinear Programming

Despite its effectiveness in determining breakage function parameters (BFPs) for quantifying breakage characteristics in mineral grinding processes, the back-calculation method has limitations owing to the uncertainty regarding the distribution of the error function. In this work, using Korean uranium and molybdenum ores, we show that the limitation can be overcome by searching over a wide range of initial values based on the conjugate gradient method. We also visualized the distribution of the sum of squares of the error in the two-dimensional parameter space. The results showed that the error function was strictly convex, and the main problem in the back-calculation of the breakage functions was the flat surface of the objective function rather than the occurrence of local minima. Based on our results, we inferred that the flat surface problem could be significantly mitigated by searching over a wide range of initial values. Back-calculation using a wide range of initial values yields BFPs similar to those obtained from single-sized-feed breakage tests (SSFBTs) up to four-dimensional parameter spaces. Therefore, by searching over a wide range of initial values, the feasibility of the back-calculation approach can be significantly improved with a minimum number of SSFBTs.

Grinding Kinetics Study of Tungsten Ore

The European Commission (EC) maintains the consideration of tungsten as a critical raw material for the European industry, being the comminution stage of tungsten-bearing minerals an essential step in the tungsten concentration process. Comminution operations involve approximately 3–4% of worldwide energy consumption; therefore, grinding optimization should be a priority. In this study, the grinding behavior of tungsten ore from Barruecopardo Mine (Salamanca, Spain) is analyzed. A protocol based on Austin’s methodology and PBM is developed in order to study the influence of operational and geometallurgical variables on grinding kinetics. In addition to the kinetic parameters, the breakage probability (Si) and breakage function (Bij) is determined. The selection function was formulated for the Barruecopardo Mine with respect to the mill speed.