Calculation of the guidedvane pump flexible ring shape
Authors: Leonov A.O.  
Published in issue: #7(84)/2023  
DOI: 10.18698/2541800920237917  
Category: Mechanics  Chapter: Mechanics of Deformable Solid Body 

Keywords: guidedvane pump, stator, flexible ring, rod mechanics, elastic line shape, Hooke’s law, differential equations, numerical integration 

Published: 24.07.2023 
A method was developed to determine the shape of a ring that ensures flow termination by the pump at the given forces value for a new design of the guidedvane pump with the flexible ring (pump stator) stretched by two forces. In the absence of force loading, the pump operates with the oval ring original shape. When the required load is applied, the pump stops working, because the ring shape becomes a perfect circle. Thus, the pump is controlled by applying a load to the ring. Algebraic and differential equations of the flexible rods mechanics were used to calculate the ring shape. Ring displacements exceed dimensions of its cross section. Thus, the problem is geometrically nonlinear, but deformations in this case remain insignificant, and physical relationships remain linear (Hooke’s law). Rotation angle dependence on the circumferential coordinate was plotted in the analytical form. Then, the ring shape was restored by numerical integration of the differential equations system.
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