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Abstract
The breakage index equation (BIE), or t10 model from drop weight testing (DWT) data for rocks and ores is used in the design of crushers and mills. Such models are becoming increasingly difficult to visualize as the number of variables increases. The so-called double fan BIE, combined with the Swebrec distribution’s accurate description of the sieving curves, is applied to the modelling of drop-weight test fragmentation. The key parameters are geometric properties visible in the fan plot; slopes of straight lines and their point of convergence. The ability of the double fan BIE to reproduce DWT data had been previously established for 8 rocks with 480 DWT data sets. Here the fidelity of the double fan BIE is further evaluated for 18 new materials, based on 281 data sets. The fidelity of the double fan BIE with three fan lines is on par with the fidelity of the current state-of-the-art models for the new materials. Besides the breakage index equation, the new double fan BIE’s t10 equation produces, without additional parameters or fitted constants, the general breakage surface equation tn for an arbitrary n value as a bonus. The specific sieving curve for any combination of particle size and impact energy is also contained in the same formula. The result is an accurate, compact and transparent model.
Highlights
The mathematical form of the cumulative fragment size distribution (CDF) or mass passing function P( x ) with x being the fragment size, has been the focus of much attention and debate ever since Rosin and Rammler [1] introduced their well-known exponential function (RR) to describe the sieving curves of crushed coal
These0 parameters follow from the fan fitused by the others since it lets the scaled energy Ecs retain the same units as the impact ting though, but the fidelity is not as good as that of the JK new breakage index equation (BIE) [22]
The data set size weighted mean b-value is 2.27 and the mean value for Banini’s data (2.27) is the same as that for the new data (2.27), if the outlier data for Genç’s et al [24] gypsum and one quartz value are removed
Summary
The mathematical form of the cumulative fragment size distribution (CDF) or mass passing function P( x ) with x being the fragment size, has been the focus of much attention and debate ever since Rosin and Rammler [1] introduced their well-known exponential function (RR) to describe the sieving curves of crushed coal. 0 = E ( D/D )λ , Using normalized size data and scaled energy data, x 0P = x p /D and Ecs cs where D0 is an arbitrary reference size and λ a scaling exponent and fitting parameter, Ouchterlony and Sanchidrián [21] in a preliminary analysis with the linear fan derived the following equation for t10 for Banini’s [19] Mt Coot-tha hornfels data. Note that all five parameters in Equation (3) are directly related to linear t10 ( Ecs the geometry of the fragmentation energy fan in Figure 2 and to the Swebrec function in Equation (1), which determines the mathematical form of Equation (3).
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