Hydrodynamic Analysis of Compliant Foil Bearings With Compressible Air Flow

Peng, Z-C.; Khonsari, M. M.

doi:10.1115/1.1739242

Cited by 107 publications

(69 citation statements)

References 11 publications

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“…For foil configurations where the top foil is stiffer than the bump foil, the top foil deflection can be regarded as constant along the axial direction of the bearing [26]. In these cases, the deflection h c ðp m Þ can be used where the pressure p m is taken as the arithmetic mean pressure along the axial direction for a given angle h. This situation is illustrated in Fig.…”

Section: Mesh and Boundary Conditionsmentioning

confidence: 99%

Efficient solution of the non-linear Reynolds equation for compressible fluid using the finite element method

Larsen

Santos

2014

J Braz. Soc. Mech. Sci. Eng.

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Section: Mesh and Boundary Conditionsmentioning

confidence: 99%

Efficient solution of the non-linear Reynolds equation for compressible fluid using the finite element method

Larsen

Santos

2014

J Braz. Soc. Mech. Sci. Eng.

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“…The foil structure used in this paper assumes that the variation of the deflection of the foil in the axial direction is negligible [14]: (7) where: , is the nondimensional form of , the stiffness per unit area of the foil structure (N/m 3 ) and is the average of the non-dimensional gauge pressure ( ) over the (or )-direction for a given : (8) As in [6,7], the damping in the foil structure is quantified by a hysteretic loss factor . However, is only defined for harmonic vibration [15] and its equivalent viscous damping coefficient in the time domain is , rad/s being the frequency of the vibration.…”

Section: Nomenclaturementioning

confidence: 99%

Nonlinear Dynamic Analysis of a Turbocharger on Foil-Air Bearings With Focus on Stability and Self-Excited Vibration

Bonello

Pham

2014

Volume 7B: Structures and Dynamics

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This paper presents a generic technique for the transient nonlinear dynamic analysis (TNDA) and the static equilibrium stability analysis (SESA) of a turbomachine running on foil air bearings (FABs). This technique is novel in two aspects: (i) the turbomachine structural model is generic, based on uncoupled modes (rotor is flexible, non-symmetric and includes gyroscopic effects; dynamics of support structure can be accommodated); (ii) the finite-difference (FD) state equations of the air films are preserved and solved simultaneously with the state equations of the foil structures and the state equations of the turbomachine modal model, using a readily available implicit integrator (for TNDA) and a predictor-corrector approach (for SESA). An efficient analysis is possible through the extraction of the state Jacobian matrix using symbolic computing. The analysis is applied to the finite-element model of a small commercial automotive turbocharger that currently runs on floating ring bearings (FRBs) and is slightly adapted here for FABs. The results of SESA are shown to be consistent with TNDA. The case study shows that, for certain bearing parameters, it is possible to obtain a wide speed range of stable static equilibrium operation with FABs, in contrast to the present installation with FRBs. INTRODUCTIONThe dynamics of FAB turbomachinery are governed by the interaction between the turbomachine, air films and foil structures. Due to the computational burden involved, the solution process has been subject to simplifications to three aspects of the problem:  The compressible Reynolds equation (RE) governing the air film pressure distribution;  The structural model of the turbomachine;  The foil structure model. This paper addresses the current simplifications to the first two aspects.

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“…Unlike all other quantities, the nominal lubrication gap clearance C is reported to be only poorly known. For one and the same first generation test bearing, different empirical estimations in the available literature [5,6] propose C = 20 × 10 −6 m or C = 50 × 10 −6 m. The arising uncertainty concerns in particular the nondimensional bearing number Λ ∝ ω 0 /C 2 , the nondimensional rotor mass M ∝ mC 5 , the nondimensional gravitational acceleration G ∝ g/C 5 , and the nondimensional time scale τ ∝ tC 2 . Typically, equilibrium points of foil air journal bearing rotor systems tend to become unstable for higher rotational speeds.…”

Section: Analysis Results and Conclusionmentioning

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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Hydrodynamic Analysis of Compliant Foil Bearings With Compressible Air Flow

Cited by 107 publications

References 11 publications

Efficient solution of the non-linear Reynolds equation for compressible fluid using the finite element method

Efficient solution of the non-linear Reynolds equation for compressible fluid using the finite element method

Nonlinear Dynamic Analysis of a Turbocharger on Foil-Air Bearings With Focus on Stability and Self-Excited Vibration

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

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