Calculation of the guided-vane pump flexible ring shape

Authors: Leonov A.O.
Published in issue: #7(84)/2023
DOI: 10.18698/2541-8009-2023-7-917
Category: Mechanics | Chapter: Mechanics of Deformable Solid Body
Keywords: guided-vane 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 guided-vane 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.

References

[1] Zaychenko I.Z., Myshlevskiy L.M. Plastinchatye nasosy i gidromotory [Vane pumps and hydraulic motors]. Moscow, Mashinostroenie Publ., 1970, 229 p. (In Russ.).

[2] Vil’ner Ya.M., Kovalev Ya.T., Nekrasov B.B. et al. Spravochnoe posobie po gidravlike, gidromashinam i gidroprivodam [Reference manual for hydraulics, hydraulic machines and hydraulic drives]. Minsk, Vysheyshaya shkola Publ., 1985, 416 p. (In Russ.).

[3] Lopastnye nasosy (tsentrobezhnye i osevye). Terminologiya i bukvennye oboznacheniya [Vane pumps (centrifugal and axial). Terminology and letter designations]. Moscow, AN SSSR Publ., 1961, 31 p. (In Russ.).

[4] Gidroprivod. Ch. 2. Ob"emnyy gidroprivod. Terminologiya [Hydraulic drive. Part 2. Volumetric hydraulic drive. Terminology]. Moscow, Nauka Publ., 1964, 35 p. (In Russ.).

[5] Prokof’ev V.N. Rotornye nasosy. ESM [Rotary pumps. ESM]. Moscow, Mashgiz Publ., 1948, vol. XII, 716 p. (In Russ.).

[6] Feodos’ev V.I. Soprotivlenie materialov [Strength of materials]. Moscow, BMSTU Press, 2004, 592 p. (In Russ.).

[7] Nosenko V.A., Tyshkevich V.N., Orlov S.V. Determination of permissible values of the vertical component of the surface grinding force of bearing rings of low axial rigidity. Spravochnik. Inzhenernyy zhurnal, 2008, no. 4 (133), pp. 24–32. (In Russ.).

[8] Svetlitskiy V.A. Mekhanika sterzhney. V 2 ch. Ch. 1. Statika [Rod mechanics. At 2 p.m. Part 1. Statics]. Moscow, Vysshaya shkola Publ., 1987, 320 p. (In Russ.).

[9] D’yakonov V.P. Mathematica 5.1/5.2/6. Programmirovanie i matematicheskie vychisleniya [Mathematica 5.1/5.2/6. Programming and mathematical calculations]. Moscow, DMK-Press Publ., 2008, 574 p. (In Russ.).

[10] Baranov V.A., Gabrielyan G.E., Lisov V.M. Calculation of a ring in an elastic medium with one-way constraints. Metody i algoritmy rascheta sooruzheniy i konstruktsiy: sb. st. [Methods and algorithms for calculating structures and structures: a collection of articles]. Voronezh, Voronezhskiy gosudarstvennyy arkhitekturno-stroitel’nyy universitet Publ., 1990, pp. 55–59. (In Russ.).