On the theory of a spiral separator (About the movement with friction of a heavy point along a helical surface)

Abstract

The theory of a spiral separator, as well as a similar theory of a screw descent, has been very little developed. Therefore, it should be noted that Prof. L. B. Levenson attempted to carry out a constructive calculation of the separator based on an analysis of the movement of the enriched material. The corresponding differential equations of motion were compiled by Prof. M. I. Akimov. Their integration in the first approximation is performed in this article. An essential role in the design of a spiral separator is played by the construction of projections onto the horizontal plane of the trajectories of moving particles (the so-called unloading diagram). The latter allows you to judge how suitable the designed separator is for the enrichment of a certain material. The author set as his task to give another method for constructing an unloading diagram, namely analytical, based on the integration of the differential equations of motion in the first approximation. This latter also makes it possible to highlight the feasibility of new forms of spiral separator proposed by prof. M. I. Akimov. The question of how large the error of the first approximation is our further task.