MATHEMATICAL MODELING OF INTERACTION OF SPHERICAL MILL BODIES WITH ELEMENTARY AREAS OF MILL DRUM SURFACE

Abstract

: The purpose of the work is a mathematical modelling of interaction of spherical mill bodies with elementary areas of a mill drum surface for creation of foundations of control facilities of technological aggregate overload. Methods of the ball mill theory for obtaining efficient characteristics of fineness of ball load, provision of their invariability in the operation, determination of peculiarities of stratification of mill bodies by fineness along the drum and in separate areas of approximately equal fineness, modelling methods for determination of fineness characteristics of ball load, analysis methods for establishment of motion conditions of balls along an inclined heel, methods of the ball mill theory, probability theory and mathematical statistics, when grounding impact frequency of balls of identical size with elementary area on the mill drum internal surface, are used. Academic novelty consists in foremost grounding of probability to implement identification tool of ball mill overload with ore by energetic efficiency of material destruction directly into the technological apparatus drum. Practical significance of the conducted investigations is high, since the obtained results allow to develop tools of ball mill ore overload of new type. Thus, technological aggregates can be fully operational without fear of emergency mode. It is shown that one can select the best ball load composition and maintain it in service for separate technological ore type and its definite fineness. Along the drum, balls are located in separate areas by fineness, the smallest ones are near the charging nose. The smallest balls of almost identical size are situated in separate areas of approximately equal fineness due to segregation near the lining. This creates an external layer that moves during rotation of the drum and accomplishes a three-phase trajectory. Five impacts of a ball of 50 mm in diameter with elementary area of 30 mm in diameter occur for four minutes. One impact occurs, provided that its diameter is decreased by 15 mm. It allows to develop innovative means for identifying ball mill ore overload.