TY - JOUR

T1 - The fragmentation‑energy fan concept and the Swebrec function in modeling drop weight testing

AU - Ouchterlony, Finn

AU - Sanchidrián, José Angel

PY - 2018/3

Y1 - 2018/3

N2 - A recent concept called the fragmentation-energy fan has been used to analyze drop weight testing (DWT) data and to obtainboth the mathematical form of the breakage index equation, i.e., t10 versus impact energy and the parameter values neededfor making an actual prediction with it. The fan is visualized by plotting the progeny size corresponding to a set of percentpassing values versus scaled drop energy in log–log scale and fitting straight, i.e., linear fan lines with a common focal pointto these data. The fan behavior lies inherent in the fact that the DWT sieving data closely follow the Swebrec distribution. Amathematical expression for t10 in closed form follows directly from a functional inversion, and this expression differs fromthe forms it has been given by the JKMRC. In most cases five fan lines suffice to provide a very accurate t10 equation. Whenapplied to a suite of eight rocks, ores mostly, the coefficient of determination R2 for the equation lies in the range 0.97–0.99 or almost as high as when JKMRC’s size-dependent breakage model is used. To obtain such a high fidelity a generalization of the original linear fan concept to so-called double fans with piecewise linear rays is developed. The fragmentation-energy fan approach is more compact and general in that tn for an arbitrary value of the reduction ratio n is obtained at the same time as t10 and with t n the complete closed-form solution for mass passing P(x,D, Ecs).

AB - A recent concept called the fragmentation-energy fan has been used to analyze drop weight testing (DWT) data and to obtainboth the mathematical form of the breakage index equation, i.e., t10 versus impact energy and the parameter values neededfor making an actual prediction with it. The fan is visualized by plotting the progeny size corresponding to a set of percentpassing values versus scaled drop energy in log–log scale and fitting straight, i.e., linear fan lines with a common focal pointto these data. The fan behavior lies inherent in the fact that the DWT sieving data closely follow the Swebrec distribution. Amathematical expression for t10 in closed form follows directly from a functional inversion, and this expression differs fromthe forms it has been given by the JKMRC. In most cases five fan lines suffice to provide a very accurate t10 equation. Whenapplied to a suite of eight rocks, ores mostly, the coefficient of determination R2 for the equation lies in the range 0.97–0.99 or almost as high as when JKMRC’s size-dependent breakage model is used. To obtain such a high fidelity a generalization of the original linear fan concept to so-called double fans with piecewise linear rays is developed. The fragmentation-energy fan approach is more compact and general in that tn for an arbitrary value of the reduction ratio n is obtained at the same time as t10 and with t n the complete closed-form solution for mass passing P(x,D, Ecs).

KW - Crushing · Milling · Drop weight testing · t10 · Breakage index equation · Swebrec function · Fragmentationenergy

U2 - 10.1007/s00603-018-1458-5

DO - 10.1007/s00603-018-1458-5

M3 - Article

VL - October 2018

SP - 3129

EP - 3156

JO - Rock mechanics and rock engineering

JF - Rock mechanics and rock engineering

SN - 0723-2632

IS - 51/10

ER -