Effect of internal friction in the dynamic behavior of aerodynamic foil bearings

Iordanoff, Ivan; Said, Benyebka Bou; Mezianne, A.; Berthier, Yves

doi:10.1016/j.triboint.2007.09.010

Cited by 29 publications

(16 citation statements)

References 15 publications

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“…It should be noted that other analytical bump foil stiffness formulas including dry‐friction forces between the top foil and bumps, and the housing and bumps were proposed by Iordanoff for both free end and clamped (welded) end conditions …”

Section: Fundamental Equationsmentioning

confidence: 99%

Elasto‐aerodynamic lubrication analysis of a self‐acting air foil journal bearing

Bensouilah

Lahmar

Bou‐Saïd

2012

Lubrication Science

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Nowadays, air foil bearings find widespread use in very high speed, lightly loaded oil‐free rotating turbomachineries such as compressors and microgas turbines because they have theoretically no speed limitations and they are environmentally benign. In the design of such bearings, it is of cardinal importance to enhance their steady‐state and dynamic performance characteristics for the safety operation, especially against the external dynamic excitations. Most of elasto‐aerodynamic approaches under dynamic conditions proposed in the technical literature include only the static pressure induced deformation of foils. This paper presents a theoretical investigation on the effects of both static and dynamic deformations of the foils on the dynamic performance characteristics and stability of a self‐acting air foil journal bearing operating under small harmonic vibrations. For the dynamic deformations of foils to be taken into account, the perturbation method is used for determining the gas‐film stiffness and damping coefficients for given values of excitation frequency, compressibility number and compliance factor of the bump foil. The rotor‐dynamic coefficients serve as input data for the linear stability analysis of rotor‐bearing system. The nonlinear stationary Reynolds' equation is solved by means of the Galerkin's finite element formulation, whereas the finite differences method are used to solve the first‐order complex dynamic equations resulting from the perturbation of the transient compressible Reynolds' equation. As a first approximation, the corrugated subfoil is modelled as a simple elastic foundation, i.e. the stiffness of a bump is uniformly distributed throughout the bearing surface. It was found that the dynamic properties and stability of the compliant finite length journal bearing are significantly affected by the compliance of foils especially when the dynamic deformation of foils is considered in addition to the static one by applying the principle of superposition. Copyright © 2012 John Wiley & Sons, Ltd.

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Section: Fundamental Equationsmentioning

confidence: 99%

Elasto‐aerodynamic lubrication analysis of a self‐acting air foil journal bearing

Bensouilah

Lahmar

Bou‐Saïd

2012

Lubrication Science

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“…In Figure , on the right‐hand side, for the same boundary conditions, the shell behaviour changes with the type of loading unlike what has been shown so far with other models . In these papers, it has been shown that the type of loading does not influence the stiffness of the structure, which means that the interaction between the bumps has not been taken into account.…”

Section: Resultsmentioning

confidence: 77%

“…In the case of an airfoil bearing, hydrodynamic forces also depend on the flexible structure deformation. The solution methodology is based on the Verlet algorithm . The goal is to find the geometrical configuration of the rotor in the housing, which gives equilibrium position, i.e.…”

Section: Model Descriptionmentioning

confidence: 99%

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Aero‐elastic bearing effects on rotor dynamics: a numerical analysis

Barzem

Said

Rocchi

et al. 2013

Lubrication Science

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In recent decades, numerous models for airfoil bearings have been developed. However, these models are not sufficiently accurate for rotor response prediction in the presence of nonlinearities. It is essential to control the instabilities due to the nonlinear behaviour in order to quantify the energy dissipation in the bearings. By means of a variational approach, the flexible structure is modelled as a thin medium subject to a compressible fluid pressure, under isothermal conditions, in the laminar and turbulent regimes. The model is constructed using the finite element method for the structure response. Internal dry friction is taken into account with Coulomb's law and an updated Lagrangian method. The structure model is coupled with Reynolds equation to obtain the rotor displacement, using the equations of motion for the complete mechanical system. This work is performed to show the influence of the thin structure approach on the rotor behaviour and the field pressure. The link between deflection of the bumps and dry friction is established. The structure buckling is increased by both friction between the sheets and energy dissipation. A second objective is to identify the subsynchronous frequencies in order to establish the relevance of the new airfoil model for nonlinear and instability investigations. ! frame, Λ ¼ 6m dyn oR 2 =p a C 2 0 (compressibility number), R e (Couette Reynolds number) and m dyn (dynamic viscosity).The solution of equation (3) is obtained by means of finite differences, implicit method in time and Newton-Raphson method to solve the nonlinear algebraic system. Flexible structure: film thicknessThe flexible structure consists of a wavy foil called the bump foil and a smooth top foil. The flexible structure is usually modelled as an assembly of curved and straight beams ('beam model') or a spring 466 L. BARZEM ET AL.

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“…It should be noted that other analytical bump foil stiffness formulas including dry-friction forces between the top foil and bumps, and the housing and bumps were proposed by Iordanoff for both free end and clamped (welded) end conditions. [27][28][29]…”

Section: Fundamental Equationsmentioning

confidence: 99%

Elasto-Aerodynamic Lubrication Analysis of a Self-Acting Foil Air Journal Bearing

Bensouilah

Lahmar

̈d

2011

ASME/STLE 2011 Joint Tribology Conference

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Nowadays, air foil bearings find widespread use in very high speed, lightly loaded oil-free rotating turbomachineries such as compressors and microgas turbines because they have theoretically no speed limitations and they are environmentally benign. In the design of such bearings, it is of cardinal importance to enhance their steadystate and dynamic performance characteristics for the safety operation, especially against the external dynamic excitations. Most of elasto-aerodynamic approaches under dynamic conditions proposed in the technical literature include only the static pressure induced deformation of foils. This paper presents a theoretical investigation on the effects of both static and dynamic deformations of the foils on the dynamic performance characteristics and stability of a self-acting air foil journal bearing operating under small harmonic vibrations. For the dynamic deformations of foils to be taken into account, the perturbation method is used for determining the gas-film stiffness and damping coefficients for given values of excitation frequency, compressibility number and compliance factor of the bump foil. The rotor-dynamic coefficients serve as input data for the linear stability analysis of rotor-bearing system. The nonlinear stationary Reynolds' equation is solved by means of the Galerkin's finite element formulation, whereas the finite differences method are used to solve the first-order complex dynamic equations resulting from the perturbation of the transient compressible Reynolds' equation. As a first approximation, the corrugated subfoil is modelled as a simple elastic foundation, i.e. the stiffness of a bump is uniformly distributed throughout the bearing surface. It was found that the dynamic properties and stability of the compliant finite length journal bearing are significantly affected by the compliance of foils especially when the dynamic deformation of foils is considered in addition to the static one by applying the principle of superposition.This step is necessary to solve the first-order complex dynamic Equations (22) and (23). METHOD OF SOLUTION UNDER DYNAMIC CONDITIONSThe procedure for obtaining a numerical solution to the elasto-aerodynamic problem under dynamic conditions is outlined as follows:Set the initial value of the frequency ratio g (e.g. g = 1 corresponding to a synchronous excitation). Solve the linear partial differential Equations (22) and (23) over the finite difference grid with successive over-relaxation scheme to obtain the complex dynamic pressuresQ e andQ f (Figure 8). It should Figure 13. Example of the coded half fluid-film domain. (À) Ambient or subambient static pressure region. (+) Over-ambient static pressure region.Figure 12. 3D view of the steady-state pressure field calculated without the subambient pressures.

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Effect of internal friction in the dynamic behavior of aerodynamic foil bearings

Cited by 29 publications

References 15 publications

Elasto‐aerodynamic lubrication analysis of a self‐acting air foil journal bearing

Elasto‐aerodynamic lubrication analysis of a self‐acting air foil journal bearing

Aero‐elastic bearing effects on rotor dynamics: a numerical analysis

Elasto-Aerodynamic Lubrication Analysis of a Self-Acting Foil Air Journal Bearing

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