Conveyance of a particle by a vertical screw, which is limited by a coaxial fixed cylinder - S.F. Pylypaka; V.M. Nesvidomin; M.B. Klendii; I.L. Rogovskii; T.A. Kresan; V.I. Trokhaniak (Қарағанды университетінің хабаршысы. Математика сериясы, 2019)
Diﬀerential equations of relative particle motion along the periphery of a vertical screw have been deduced which rotates about its axis and is limited by a coaxial fixed cylinder. The equations have been solved by applying numerical methods and the trajectories of relative particle helical motion, that is to say, movement along the edge of a screw, which is common for a screw surface and for a limiting cylinder, have been built. The force of particle friction on the screw surface and on the surface of a cylindrical cover has been taken into consideration. The cases, when a helix angle, that is to say, the angle of screw edge inclination, is less than the angle of particle friction on the surface of a screw, when it is equal to a friction angle and when it is higher than a friction angle, have been considered. In addition, a specific case, when a screw is fixed and a particle moves downwards by gravity, which takes place in spiral chutes, has been analyzed. Kinematic characteristics - time curves have been presented.