# Gravitational Relief with Spiral Gutters, Formed by the Screw Movement of the Sinusoid

Conference paper
Part of the Lecture Notes in Mechanical Engineering book series (LNME)

## Abstract

The differential equations of the particle movement along a rough screw surface formed by the screw motion of a sinusoid under the action of the force of its weight are composed in the article. The sinusoid is located on a vertical plane and is an axial cross-section of the helical surface. The equations are solved by numerical methods and trajectories of a particle movement along a helical surface are constructed. Graphs of changing particle velocity and its distance from the surface axis were also received. The conditions of the stabilization of the particle movement are found. It is shown that in the general case, as a result of acceleration, the particle moves away from the surface axis and stops in one of its gutters. The changing of constant coefficients can control the depths and density of the gutters. In the particular case at zero depth of the gutter, a sinusoid becomes a straight line and the particle moves along the surface of the screw conoid.

## Keywords

Axial cross-sectional curve Friction coefficient Particle Movement trajectory Differential equations

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© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2020

## Authors and Affiliations

1. 1.National University of Life and Environmental Sciences of UkraineKievUkraine
2. 2.Sumy National Agrarian UniversitySumyUkraine
3. 3.Separated Subdivision of National University of Life and Environmental Sciences of Ukraine “Nizhyn Agrotechnical Institute”NizhynUkraine
4. 4.Sumy Regional Institute of Postgraduate Pedagogical EducationSumyUkraine
5. 5.Sumy State Pedagogical University named after A.S. MakarenkoSumyUkraine