Ball Mill Grinding
International Journal of Mineral Processing, 4 (1977) 7--32
© Elsevier Scientific Publishing Company, Amsterdam -- Printed in The Netherlands
T H E BACK-CALCULATION OF SPECIFIC RA T E S OF B R E A K A G E AND NON-NORMALIZED B R E A K A G E D I ST R I BU T IO N P A R A M E T E R S FROM BATCH G R I N D I N G DATA
R.R. KLIMPEL and L.G. AUSTIN
Mathematics Division, Physical Research Laboratory, The Dow Chemical Company, Midland, Mich. 48640 (U.S.A.) Department of Material Sciences, The Pennsylvania State University, University Park, Pa. 16802 (U.S.A.)
(Received December 2, 1974; revision accepted July 29, 1976)
ABSTRACT
Klimpel, R.R. and Austin, L.G., 1977. The back-calculation of specific rates of breakage and non-normalized breakage distribution parameters from batch grinding data. Int. J. Miner. Process., 4:7--32. This paper describes a mathematical approach for calculating parameters relating specific rates of breakage and breakage products distribution from batch grinding a known feed for several grinding times. Knowledge of such parameters leads to improved equipment design criteria and consistent operating correlations. The approach involves the use of nonlinear optimization with appropriate statistical tests and gives parameter estimates close to those gained from direct experimental measurements. Some results and experiences using the technique are summarized.
INTRODUCTION Mill and mill circuit simulation by solution of grinding equations (Mika and Fuerstenau, 1971; Austin, 1971--72; Luckie and Austin, 1972), offers the prospect o f more accurate circuit design, operation and control. As recently discussed (Austin, 1973; Austin et al., 1976), however, the appropriate data is only slowly becoming available. The analysis o f grinding tests in terms of specific rates o f breakage, S, and breakage distribution functions, B, is tedious experimentally, although the information obtained is far m ore comprehensive than th a t from empirical
© Elsevier Scientific Publishing Company, Amsterdam -- Printed in The Netherlands
T H E BACK-CALCULATION OF SPECIFIC RA T E S OF B R E A K A G E AND NON-NORMALIZED B R E A K A G E D I ST R I BU T IO N P A R A M E T E R S FROM BATCH G R I N D I N G DATA
R.R. KLIMPEL and L.G. AUSTIN
Mathematics Division, Physical Research Laboratory, The Dow Chemical Company, Midland, Mich. 48640 (U.S.A.) Department of Material Sciences, The Pennsylvania State University, University Park, Pa. 16802 (U.S.A.)
(Received December 2, 1974; revision accepted July 29, 1976)
ABSTRACT
Klimpel, R.R. and Austin, L.G., 1977. The back-calculation of specific rates of breakage and non-normalized breakage distribution parameters from batch grinding data. Int. J. Miner. Process., 4:7--32. This paper describes a mathematical approach for calculating parameters relating specific rates of breakage and breakage products distribution from batch grinding a known feed for several grinding times. Knowledge of such parameters leads to improved equipment design criteria and consistent operating correlations. The approach involves the use of nonlinear optimization with appropriate statistical tests and gives parameter estimates close to those gained from direct experimental measurements. Some results and experiences using the technique are summarized.
INTRODUCTION Mill and mill circuit simulation by solution of grinding equations (Mika and Fuerstenau, 1971; Austin, 1971--72; Luckie and Austin, 1972), offers the prospect o f more accurate circuit design, operation and control. As recently discussed (Austin, 1973; Austin et al., 1976), however, the appropriate data is only slowly becoming available. The analysis o f grinding tests in terms of specific rates o f breakage, S, and breakage distribution functions, B, is tedious experimentally, although the information obtained is far m ore comprehensive than th a t from empirical
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