Calculation of models of some helical surfaces encountered in the theory of a spiral separator

Abstract

When studying the steady motion of a heavy material particle along a helical line on a rough helical surface with the Z axis of the cylindrical coordinate system directed vertically upward, M. I. Akimov noted helical surfaces corresponding to the values of the function (see article), the movement of a heavy point along helical lines, in the presence of friction, has special properties. On the first of these surfaces, the movement in question (with appropriate friction coefficients) along all helical lines is possible only at the same constant speed. On the second surface (with appropriate friction coefficients) along all helical lines it is possible only with the same constant vertical component of speed. Such a surface can find application in those designs of a spiral separator when the unloading of dissimilar separated particles of the mixture must occur simultaneously. On the third surface, with the same coefficient of friction k, the steady motion of heavy particles can occur along any helical line. This work contains the calculations necessary to construct the three helical surfaces under consideration for the purpose of experimentally studying the steady-state movements of heavy particles occurring on them.