Machinery & Energetics

The differential equations of particle movement on a rough surface which is formed by the helical motion of a sinusoid under the action of the force of own weight were obtained in the article. The sinusoid is the axial cross-section curve of the helical surface and is located in the vertical plane. The obtained equations were solved by numerical methods and the trajectories of the particle on the helical surface were constructed. In addition, graphs of the change in the particle velocity and its distance from the axis of the surface were found, as a result of which the conditions when stabilization of the particle movement is possible were found. It is shown that in the general case, as a result of acceleration, the particle moves away from the axis of the surface and stops in one of its gutters. The depth and density of the gutters are controlled by changing the constant coefficients parameters. Also, a partial case at zero depths of the gutter, when the sinusoid turns into a straight line and the particle moves on the surface of the helical conoid, were considered.

cross-sectional curve, sinusoid, coefficient of friction, particle, motion, equation