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Mathematical models for fine grinding of powders

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In this paper we consider a mathematical model of the grinding process based upon the use of the one-dimensional rheological equation connecting tensions, deformations, variable mass and specific surface. New differential equations which describe specific surface dependence upon time are suggested. Specific surface enters the rheological equation, certifying its connection with the kinetic curves. A new system of differential equations of the continuum mechanics has been created in which the variability of the mass (size) of the demolished particles is allowed for. The author proposes a new way for solving this non-linear system. The models suggested are true for all types of mincing machines. However, some recommendations for the vibration grinding process are specified. They include the choice of zones of frequency and amplitude changes, as well as the experimental verification of these recommendations by the example of fine grinding of metallic powders used in powder metallurgy. Some conclusions for vibromills construction are made on the basis of the theoretical research.

Affiliations: 1: Odesskaya State Marine Academy, 8 Didrichson str., Odessa 270029, Ukraine


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