Parsimonious models of grinding and their applications

The hierarchical relationship between three broad kinds of grinding models for a spatially homogeneous, linear, time-invariant batch grinding system are first established. Limiting and asymptotic arguments for arriving at approximate but simpler models are employed in all three cases. These parsimonious models -provide alternate and, in some respects, more incisive and convenient tools for the analyses of grinding processes and simulation of comminution circuits. In the discrete-size, discrete- time class of models, a reduced mill matrix is derived, which is seemingly adequate for those grinding circuits whose identification otherwise is difficult because of limitations on the quantity of data and its quality. In discrete-size, continuous-time types of models, parameter lumping has been employed for obtaining a G-H solution which is quite accurate and exceptionally useful for graphical display of data, model verification, and parameter estimation and simulation. In continuous-size, continuous-time models, a similarity transformation is used for solving the integrodifferential equation of grinding. This solution provides a unified framework for a number of apparently diverse empirical grinding phenomena such as self-preserving behavior of ground particle size distributions and energy laws.