Investigation of particle breakage mechanisms in a batch ball mill using back-calculation

Simultaneous estimation of breakage rate and distribution function parameters has been carried out for two industrial ore samples and three types of cement clinker using dry batch ball mill data. Unique parameter estimates were obtained through a back-calculation approach using non-linear least squares fitting. The batch mill operating conditions were chosen to resemble industrial grinding situations. Investigation showed that breakage distribution and rate parameters did not conform to the commonly used functional forms. The analysis demonstrates that the breakage distribution function correlates to material property and particle size, and the breakage rate function also changes with material type and with mill content size distribution. The mechanisms of particle breakage in a ball mill inferred from the fitted breakage rate and distribution functions are also discussed in this paper.

[1]  K. R. Weller,et al.  Multicomponent models of grinding and classification for scale-up from continuous small or pilot scale circuits , 1988 .

[2]  Leonard G. Austin,et al.  Rate equations for non-linear breakage in mills due to material effects , 1982 .

[3]  W. J. Whiten.  The Use of Periodic Spline Functions for Regression and Smoothing , 1972, Aust. Comput. J..

[4]  Daniel Hodouin,et al.  The estimation of rate and breakage distribution parameters from batch grinding data for a complex pyritic ore using a back-calculation method , 1981 .

[5]  N. Draper,et al.  Applied Regression Analysis , 1966 .

[6]  V. K. Gupta,et al.  Empirical correlations for the effects of particulate mass and ball size on the selection parameters in the discretized batch grinding equation , 1974 .

[7]  L. G. Austin,et al.  Determination of Selection-for-Breakage Functions in the Batch Grinding Equation by Nonlinear Optimization , 1970 .

[8]  Timothy J. Napier-Munn,et al.  Application of comminution and classification modelling to grinding of cement clinker , 1988 .

[9]  Kam Leung,et al.  An energy based, ore specific model for autogenous and semi-autogenous grinding mills , 1988 .

[10]  D. Marquardt.  An Algorithm for Least-Squares Estimation of Nonlinear Parameters , 1963 .

[11]  D. Fuerstenau,et al.  Effect of fine particles on the kinetics and energetics of grinding coarse particles , 1991 .

[12]  E. G. Kelly,et al.  The breakage function; What is it really? , 1990 .

[13]  W. J. Whiten,et al.  Studies on Scale-Up of Ball Mills , 1984 .

[14]  Leonard G. Austin,et al.  The back-calculation of specific rates of breakage and non-normalized breakage distribution parameters from batch grinding data , 1977 .

[15]  A comparison of dry and wet grinding of a quartzite ground in a small batch ball mill , 1979 .

[16]  L. G. Austin,et al.  The kinetics and shape factors of ultrafine dry grinding in a laboratory tumbling ball mill , 1990 .

[17]  Douglas W. Fuerstenau,et al.  Scale-up procedure for continuous grinding mill design using population balance models , 1980 .