Computational Analysis of Foil Air Journal Bearings Using a Runtime-Efficient Segmented Foil Model

This paper presents a new structural bump foil model that can handle all operating conditions from start-up to full speed. The model is based on a nonlinear contact algorithm with friction and gaps. The top foil is modeled as a curved beam while bump foil uses a coupled truss model. The model considers the gaps between the bump foil and the bearing casing, between the bump foil and the top foil and between the rotor and the top foil. Thus, any numerical interference between the rotor and the top foil is avoided. A mixed lubrication model is used for the thin film pressures. Following this algorithm, contact pressures appear if the film thickness is less than three times the equivalent roughness of the rotor and of the top foil. Fluid pressures are calculated from numerical solutions of Reynolds equation while contact pressures, if present, are calculated with the model of Greenwood and Williamson. The model is validated by comparisons with the experimental results obtained for start-up operating conditions of a first-generation foil bearing of 38.1 mm diameter with static loads of 10–50 N. Theoretical predictions of the start-up torque and takeoff speed compare well with experimental results. It is also shown how manufacturing bump height errors can explain the differences between theoretical and experimental predictions. Further validations are presented for the same bearing operating at high speeds (30, 45, and 55 krpm) and heavy static loads (up to 200 N). The calculated minimum film thickness and attitude angle are compared with experimental data from the literature.

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“…dy s (15) Fluid and contact pressures are integrated over the rotor and the top foil surface. For the rotor, this yields…”

Section: The Foil Bearing Modelmentioning

confidence: 99%

“…The top foil was discarded in the first models because it was correctly anticipated that it had a negligible stiffness compared to the corrugated foil. However, it was subsequently taken into account with finite elements [9][10][11][12][13][14][15] and it was shown how sagging between bumps may occur.…”

Section: Introductionmentioning

confidence: 99%

A New Structural Bump Foil Model With Application From Start-Up to Full Operating Conditions

Arghir

Benchekroun

2019

Journal of Engineering for Gas Turbines and Power

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“…Depending on the rotor's angular velocity ω 0 , the PDE can be stated as [2] Figure 1 illustrates the bearing model with the fluid film thickness h = h(ϕ, z, t) = C − e(t) cos [ϕ − Γ(t)] − q(ϕ, z, t) involving the nominal lubrication gap clearance C = R − r, the journal eccentricity e(t), the attitude angle Γ(t), and the foil structure deformation field q(ϕ, z, t). With increasing accuracy, the foils are modeled using either a rigid shell, an elastic foundation [3], or elastically supported beams [4]. The bearing forces acting on the considered rigid rotor are obtained by pressure integration.…”

mentioning

confidence: 99%

Sensitivity of Computational Rotor Dynamics Towards the Empirically Estimated Lubrication Gap Clearance of Foil Air Journal Bearings

Leister

Baum

Seemann

2016

Proc Appl Math and Mech

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This contribution is concerned with the computational analysis of a rigid rotor supported by means of two self-acting foil air journal bearings. Even though the overall equation system is thereby typically written in a nondimensional form, prior knowledge about realistic value ranges of occurring dimensionless numbers is required in order to parameterize and interpret such simulations correctly. Unlike all other quantities, the nominal lubrication gap clearance between the rotating journal and the undeformed foil structure is reported to be only poorly known. Thus, even in the light of an advanced understanding of the bearing rotor system's fundamental behavior, the quantitative reproduction and prediction of experimental results by means of computational analysis need to be viewed critically. In this study, the sensitivity of numerical results towards the assumed nominal lubrication gap clearance will be investigated. To this end, the stability of the system is considered and the characteristics of occasionally observed equilibrium points and limit cycles are addressed. Motivation and ModelingOffering reduced wear and power loss compared to rolling-element bearings, self-acting foil air journal bearings are an upcoming technology in high-speed rotating machinery. The load-carrying capacity of such bearings is achieved via a thin film of ambient air forming an aerodynamic lubrication wedge. Some undesirable side-effects, e.g., the occurrence of self-excited vibrations, may be reduced by concepts featuring a compliant foil structure inside the lubrication gap [1]. In current research on this topic, reliable numerical tools are of major interest with regard to the complexity and costliness of experiments. When operating within the full fluid film lubrication regime, the pressure distribution p = p(ϕ, z, t) is governed by the REYNOLDS equation for compressible ideal gases. Depending on the rotor's angular velocity ω 0 , the PDE can be stated as [2] Figure 1 illustrates the bearing model with the fluid film thickness h = h(ϕ, z, t) = C − e(t) cos [ϕ − Γ(t)] − q(ϕ, z, t) involving the nominal lubrication gap clearance C = R − r, the journal eccentricity e(t), the attitude angle Γ(t), and the foil structure deformation field q(ϕ, z, t). With increasing accuracy, the foils are modeled using either a rigid shell, an elastic foundation [3], or elastically supported beams [4]. The bearing forces acting on the considered rigid rotor are obtained by pressure integration.

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Optimizing energy dissipation in gas foil bearings to eliminate bifurcations of limit cycles in unbalanced rotor systems

et al. 2022

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High-speed rotor systems mounted on gas foil bearings present bifurcations which change the quality of stability, and may compromise the operability of rotating systems, or increase noise level when amplitude of specific harmonics drastically increases. The paper identifies the dissipating work in the gas film to be the source of self-excited motions driving the rotor whirling close to bearing’s surface. The energy flow among the components of a rotor gas foil bearing system with unbalance is evaluated for various design sets of bump foil properties, rotor stiffness and unbalance magnitude. The paper presents a methodology to retain the dissipating work at positive values during the periodic limit cycle motions caused by unbalance. An optimization technique is embedded in the pseudo-arc length continuation of limit cycles, those evaluated (when exist) utilizing an orthogonal collocation method. The optimization scheme considers the bump foil stiffness and damping as the variables for which bifurcations do not appear in a certain speed range. It is found that secondary Hopf (Neimark–Sacker) bifurcations, which trigger large limit cycle motions, do not exist in the unbalanced rotors when bump foil properties follow the optimization pattern. Period-doubling (flip) bifurcations are possible to occur, without driving the rotor in high response amplitude. Different design sets of rotor stiffness and unbalance magnitude are investigated for the efficiency of the method to eliminate bifurcations. The quality of the optimization pattern allows optimization in real time, and gas foil bearing properties shift values during operation, eliminating bifurcations and allowing operation at higher speed margins. Compliant bump foil is found to enhance the stability of the system.

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Computational Analysis of Foil Air Journal Bearings Using a Runtime-Efficient Segmented Foil Model

Cited by 10 publications

References 5 publications

A New Structural Bump Foil Model With Application From Start-Up to Full Operating Conditions

A New Structural Bump Foil Model With Application From Start-Up to Full Operating Conditions

Sensitivity of Computational Rotor Dynamics Towards the Empirically Estimated Lubrication Gap Clearance of Foil Air Journal Bearings

Optimizing energy dissipation in gas foil bearings to eliminate bifurcations of limit cycles in unbalanced rotor systems

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