Complex circuit of milling-classify systems are used in different branches of industry, because the required particle size distribution of product can seldom be reached in a single-stage grinding on the same device. The multistage processes of comminution and classification make possible suitable selection of parameters process for variables graining of fed material, mainly through sectioning of devices or change of their size and the types. Grinding material usually contains size fractions, which meet the requirements relating finished product. Then profitable is preliminary distributing material on a few size fractions, so to deal out with them demanded fraction of product, whereas remaining to direct alone or together with fed material to the same or different device. If the number of mills and classifiers in a circuit is large enough, building the model of particle size distribution transformation becomes rather complicated even for the circuit of a given structure. The situation becomes much more complicated, if we want to compare characteristics of all possible circuits, that can be constructed from these mills and classifiers, because the number of possible circuits increases greatly with the increase of number of devices being in the milling-classify system. The method creating matrix model for transformation of particle size distribution in a circuit of arbitrary structure of milling-classify system is presented in the article. The proposed model contains the mass population balance of particle equation, in which are block matrices: the matrix of circuit M, the matrix of inputs F and the matrix of feed F0. The matrix M contains blocks with the transition matrix P, the classification matrix C, the identity matrix I and the zero matrix 0 or elements describing the transformation of particle size distribution in the circuit. The matrix F is the block column matrix, which elements describing all particle size distributions at inputs to the circuit elements. The matrix F0 is the block column matrix, which elements describing particle size distributions in all feeds to the circuit. In paper was discussed this model in details, showed algorithm and three examples formatrix construction for the closed circuit ofmilling-classify systems. In conclusion was affirmed, that presented model makes possible to forecasting particle size distribution of grinding product, which leaving chosen the unit of system. The matrix model can be applied to improving modeling of mineral processing in the different grinding devices.

The industrial grinding devices, which work in the high-energetic fluidized bed conditions make it possible to obtain guaranteed particle size distribution of product and decrease of consumption energy. The matrix model for transformation of particle size distribution in the fluidized bed opposed jet mill is presented in the part IV of article. The proposed model contains the mass population balance of particle equation, in which are block matrices: the matrix of circuit M, the matrix of inputs F and the matrix of feed F0. The matrix M contains blocks with the transition matrix P, the classification matrix C, the identity matrix I and the zero matrix 0. The matrix was marked using with discrete forms of the selection and breakage functions, mean while the matrices of classification - using the equation, describing classification of grains in the grinding chamber of mill. In paper was discussed this model in details (part 2.1). The correctness of received form of the selection and breakage functions was confirmed. The method determination of the transition matrix for fluidized-jet grinding of grains (part 2.2) and the classification matrix for gravitational and centrifugal zones of grains (part 2.3) are presented. The verification of model obtained on basis results with experimental investigations, which were performed on a laboratory fluidized bed opposed jet mill. The experiment contained grinding of selected narrow size fractions of limestone in turbulent fluidized layer conditions, what in part I and part II of article (Zbroński, Górecka-Zbrońska 2007a, b) are presented. The parameters of parametric identification were: factor of proportionality - contained in the equation on the discrete form of selection function and sizes of limiting grains - contained in equation on the diagonal elements of classification matrix for stage of gravitational and centrifugal (part 3). The classic Fisher-Snedecor test was applied for estimation of prediction particle size distribution of grinding product (part 4). The significant divergences between numerical and experimental results of particle size distribution weren't affirmed. The experimental verification, parametric identification and statistical estimation of the proposed model showed that this model make it possible to forecasting particle size distribution of grinding product.