## Abstract

A recent concept called the fragmentation-energy fan has been used to analyze drop weight testing (DWT) data and to obtain

both the mathematical form of the breakage index equation, i.e., t10 versus impact energy and the parameter values needed

for making an actual prediction with it. The fan is visualized by plotting the progeny size corresponding to a set of percent

passing values versus scaled drop energy in log–log scale and fitting straight, i.e., linear fan lines with a common focal point

to these data. The fan behavior lies inherent in the fact that the DWT sieving data closely follow the Swebrec distribution. A

mathematical expression for t10 in closed form follows directly from a functional inversion, and this expression differs from

the forms it has been given by the JKMRC. In most cases five fan lines suffice to provide a very accurate t10 equation. When

applied 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).

both the mathematical form of the breakage index equation, i.e., t10 versus impact energy and the parameter values needed

for making an actual prediction with it. The fan is visualized by plotting the progeny size corresponding to a set of percent

passing values versus scaled drop energy in log–log scale and fitting straight, i.e., linear fan lines with a common focal point

to these data. The fan behavior lies inherent in the fact that the DWT sieving data closely follow the Swebrec distribution. A

mathematical expression for t10 in closed form follows directly from a functional inversion, and this expression differs from

the forms it has been given by the JKMRC. In most cases five fan lines suffice to provide a very accurate t10 equation. When

applied 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).

Original language | English |
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Pages (from-to) | 3129–3156 |

Number of pages | 28 |

Journal | Rock mechanics and rock engineering |

Volume | October 2018 |

Issue number | 51/10 |

DOIs | |

Publication status | Published - Mar 2018 |

## Keywords

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