This work is concerned with the development and the implementation of a foil air journal bearing model. For this purpose, the numerical procedure resolving the Reynolds equation for compressible fluids has to be coupled to a structural, compliant foil model. The presented beam-based approach is supposed to reproduce most of the experimentally known particularities in the mechanical behavior of the foil structure, while being at least as runtime-efficient as the commonly used simple elastic foundation model. The developed modeling approach will be validated by comparing simulation results to data found with a more complex reference model. In the analysis part, most notably, the top foil compliancy is shown to deteriorate the load-carrying capacity of air bearings. Moreover, the influence of the top foil compliancy on the dynamics of a rigid rotor supported by two foil air journal bearings will be discussed.
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.
Even though the dynamic performance of rotors supported by refrigerant-lubricated gas foil bearings (GFBs) is very sensitive to the amount of energy dissipated in the foil structure, almost none of the existing computational models really capture dry friction with typical stick-slip transitions. The presented work addresses this shortcoming by incorporating an elasto-plastic bristle friction law into the structural model, which is coupled in an interconnected solution approach to a Reynolds equation for non-ideal compressible gases and to a modified Jeffcott-Laval rotor model. Numerical results confirm that properly designed GFBs have the potential to benefit significantly from the foil structure acting as a passive vibration control device. Motivation and ModelingAs a benefit of the low-viscosity lubricant film separating the rotor journal from the supporting structure, gas foil bearings (GFBs) are characterized by almost wear-free operation with remarkably small power losses [1], which renders them a key technology in the development of energy-efficient and oil-free turbomachinery. On the other hand, the absence of any major source of damping combined with strongly nonlinear fluid forces makes the system prone to instability phenomena such as self-excited subsynchronous vibrations [2]. As a countermeasure, the compliant and slightly movable foil structure inside the lubrication gap ( Fig. 1) possesses the excitation-dependent ability of dissipating some of the excessive energy by deliberately introduced dry friction. While stiction between the foil structure and the bearing sleeve is the predominant state in stationary operation ( Fig. 2a) or with only small unbalances present (Fig. 2b), contact breakaway and subsequent dissipative sliding occur in response to heavy cyclic loading (Fig. 2c), thus calming rotor vibrations before their amplitudes become severe [3].Despite this seemingly simple mechanism, almost none of the computational GFB models found in literature are capable of really capturing the switching nature of stick-slip transitions in dry friction and hence suffer from substantial inaccuracies when assessing the dissipated energy. To address this shortcoming, the presented foil structure model (Fig. 3) extends a proposition by Feng et al. [4] by incorporating an elasto-plastic bristle friction law, which is capable of reproducing stiction without spurious drift [5]. With the particular aim of investigating GFBs lubricated by the working fluid of vapor-compression refrigeration turbomachinery, this structural model is coupled to a Reynolds equation for non-ideal compressible gases with small amounts of condensed liquid, which requires a transient formulation of [6], and to a modified Jeffcott-Laval rotor model. Fig. 1: Sketch of the rotor journal (orange) supported by a GFB with bump foil (green) and top foil (yellow) inside the lubrication gap filled with refrigerant (adapted from [7]). a) Stationary operation b) Moderate excitation c) Strong excitation Fig. 2: Basic principle of how frictional ener...
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