GRINDING OF FIBROUS SEMI-FINISHED PRODUCTS AS A MECHANOCHEMICAL PROCESS. MATHEMATICAL MODELING

Abstract

It is known that the process of grinding fibrous semi-finished products proceeds in the form of four successive stages, accompanied by complex processes of fibrillation and hydration of fibers subjected to mechanical action. The development of these processes over time determines the dynamics of changes in cellulose fiber, which ultimately leads to the formation of the necessary paper-forming properties. The paper shows that the representation of the grinding of fibrous semi-finished products as a mechanochemical process makes it possible to formulate a mathematical model of the grinding dynamics based on the principles of formal kinetics. The latter makes it possible to single out the stages of the milling process in the form of a standard kinetic mechanism of successively occurring reactions. The corresponding model is presented as a system of ordinary differential equations with constant coefficients, the solution of which presents no fundamental difficulties. Since it is not the degree of destruction that is determined experimentally, but the degree of grinding, it is proposed to present the relationship between these values as a power series with a limitation in the form of a linear approximation. However, due to the large dimension, the parametric identification of the model has fundamental difficulties. The paper proposes a reduction method that allows overcoming the problem. The corresponding parameters are identified by comparing the model and the array of experimental data. The presented approach makes it possible to obtain an adequate closed mathematical description of the dynamics of grinding fibrous semi-finished products.