Toward a theory of the spiral separator ( On the motion with friction of a heavy point along a helical surface)
Abstract
The theory of the spiral separator, as well as the analogous theory of the helical chute, is 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 material being processed. The corresponding differential equations of motion were formulated by Prof. M. I. Akimov. Their integration in the first approximation is carried out in this article. A significant role in the design of the spiral separator is played by the construction of the projections onto the horizontal plane of the trajectories of moving particles (the so-called discharge diagram). The latter allows one to judge how suitable the designed separator is for the concentration of a particular material. The author set as his goal to provide another method for constructing the discharge diagram, specifically an analytical one, based on the integration of the differential equations of motion in the first approximation. This latter method also makes it possible to clarify the practicality of the new forms of the spiral separator proposed by Prof. M. I. Akimov. The question of how large the error of the first approximation is constitutes our further task.
None
References
- "On Some Problems of Dynamics Related to Mining and Mineral Processing," § 2, Zapiski Gornogo Instituta, vol. VIII, 1934. (in Russian)
- L.B. Levenson. Spiral separator: its theory, calculation and design, 1925, Leningrad, Inst. mech. obr. pol. isk. (in Russian)
- V. A. Steklov. Journal of Mathematics and Mathematical Analysis, Vol. 125, 1903, p. 214. Notes of the St. Petersburg Academy of Sciences, Vol. XV, Issue (1904), p. 20. N. M. Krylov. Minutes of the Meetings of the Academy of Sciences, Vol. 150, 1910, p. 316. News of Kiev University (1910), #10. Report of the Meeting, Vol. 144 (1907), pp. 615–1022.