With the help of the variation method based on the Euler-Lagrange equation have been determined the shapes of the guiding blades of centrifugal accelerating devices in which solids move between two specified points of the centrifugal field within minimal time limits. Detailed mathematical conversions have been done while solving the initial differential equation. Three forms of final brachistochrone equations have been received. The properties of this curve have been determined depending on the constant in the Euler-Lagrange condition. The conditions for real solutions and the integration constants have also been considered. Brachistochrone curves corresponding to three ranges of constant values requiring a minimum of initial integral while determining the minimum time for the body moving from one point of the centrifugal field to another have been constructed. The curves have been constructed both in absolute and relative coordinates. Simplified brachistochrone equations for the most abundant case in practice when the initial relative velocity of a moving particle can be neglected have been obtained. The parameter boundaries of the investigated curves under which their curvature can cause considerable frictional forces and even jamming of the material in the guiding blades have been determined. In this regard, the conclusion has been made that the blade shape should be as close to the rectilinear as possible for the acceleration of solid particles. The curvilinear blade profile can be justified in case of liquid or gaseous material acceleration.
A Curvilinear Blades Profile of Accelerating Devices
Lect.Notes Mechanical Engineering
Design, Simulation, Manufacturing: The Innovation Exchange ; 2023 ; High Tatras, Slovakia June 06, 2023 - June 09, 2023
23.05.2023
10 pages
Aufsatz/Kapitel (Buch)
Elektronische Ressource
Englisch
A Curvilinear Blades Profile of Accelerating Devices
TIBKAT | 2023
|Hydrodynamic characteristics of propeller blades in curvilinear motion
Online Contents | 2003
|Thin-walled pipe expansion by a punch with a curvilinear profile
British Library Online Contents | 2010
|