Oil-free microturbomachinery (MTM) are inevitably subjected to base or foundation excitations: multiple periodic load excitations from internal combustion (IC) engines in turbochargers, for example. Too large base excitations can produce severe damage, even failure, due to hard collision or rubbing contact between a rotor and its bearings. Therefore, it is paramount to evaluate the reliability of rotor-air bearing systems to withstanding base load excitations. In 2008, intermittent shock excitations, up to 30 g (pk-pk), were introduced to a test rig consisting of a rotor (0.825 kg) supported on two hybrid flexure pivot tilting pad gas bearings (FPTPBs). The experiments demonstrated the reliability of the gas bearings to withstanding external transient load excitations. Presently, a shaker delivers periodic load excitations to the base plate supporting the test rig. The whole system, weighing 48 kg, is supported on two soft coil springs and its lowest natural frequency is ~5 Hz. The rod connecting the shaker to the base plate is not affixed rigidly to the test rig base. The rod merely pushes on the base plate and hence the induced based motions are intermittent with multiple impacts and frequencies. As with most practical conditions, the base motion frequencies (5-12 Hz) are low respective to the operating speed of the rotor-bearing system. Rotor speed coast down tests evidence the rotor-bearing system natural frequency when the gas bearings are supplied with feed pressures increasing from 2.36 to 5.08 bar (ab). Shaker excitation induced rotor response, relative to the bearing housings, contains the main input frequency (5-12 Hz) and its super harmonics; and because of the intermittency of the base motions, it also excites the rotor-bearing system natural frequency, with smaller motion amplitudes than synchronous motion components. The excitation of the system natural frequency does not mean rotordynamic instability. With base induced motions, the rotor motion amplitude at the system natural frequency increases as the gas bearing feed pressure decreases, as the rotor speed increases, and as the shaker input excitation frequency increases (5-12 Hz). Hence, the test rotor-air bearing system is highly sensitive to base motions, intermittent in character, in particular when the gas bearings are supplied with a low feed pressure. Predicted rotor motion responses obtained from XLTRC2 and an analytical rigid rotor model, both including the (measured) periodic base motions, show good correlation with the measurements. The research results demonstrate further the applicability of gas bearings into oil-free high speed MTM.

Gas bearings enable successful applications in high speed oil-free microturbomachinery. This thesis presents analysis and experiments of the dynamic performance of a rotor supported on Rayleigh step gas bearings. Comprehensive experiments demonstrate that Rayleigh step hybrid gas bearings exhibit adequate stiffness and damping capability in a narrow range of shaft speeds, up to ~ 20 krpm. Rotor coastdown responses were performed for two test bearing sets with nominal radial clearance of 25.4 ?m and 38.1 ?m, respectively. A near-frictionless carbon (NFC) coating was applied on the rotor to reduce friction against its bearings at liftoff and touchdown. However, the rotor still experienced dry friction at low shaft speeds (below ~ 4,000 rpm). Experiments show that the supply pressure raises the rotor critical speed and decreases the system damping ratio. The geometry of the Rayleigh steps distributed on the rotor surface generates a time varying pressure field and results in a sizable 4X super synchronous component of bearing transmitted load. The external supply gas pressure affects slightly the onset speed of instability of the rotor-bearing system. The unstable whirl frequencies are nearly fixed at the system natural frequency (~ 120 Hz). Analysis with a finite element model predicts the stiffness and damping force coefficients for the bearing accounting for a purely hydrodynamic operation condition. Predictions show the synchronous stiffness and damping coefficients decrease with shaft speed. Predicted threshold speeds of instability are lower, ~ 50% or less than the measurement due to the analytical model limitations assuming a grooved stator. The predicted synchronous responses to imbalance correlate well with the measurements, however. The Rayleigh step gas bearing shows similar characteristics to the flexure pivot tilting pad bearing (FPTPB) tested in 2003. However, the test Rayleigh step gas bearings exhibit a much reduced stable operating speed range, below 20 krpm. The maximum speed achieved is much lower to that determined with an identical rotor supported on FPTPBs, i.e. rotor dynamically stable up to 100 krpm. The FPTPB is more reliable in high speed oil-free applications due to its excellent stability characteristics.

Indiana University-Purdue University Indianapolis (IUPUI) / This thesis concentrates on the study of hybrid gas journal bearings (bearings with externally pressurized mass addition). It differs from most work in that it goes back to “basics” to explore the hydrodynamic phenomena in the bearing gap. The thesis compares geometrically identical bearings with 2 configurations of external pressurization, porous liners where mass-addition compensation is varied by varying the liner’s permeability, and bushings with 2 rows of 6 feedholes where the mass-addition compensation is varied by the feedhole diameter. Experimentally, prototype bearings with mass-addition compensation that spans 2 orders of magnitude with differing clearances are built and their aerostatic properties and mass addition characteristics are thoroughly tested. The fundamental equations for compressible, laminar, Poiseuille flow are used to suggest how the mass flow “compensation” should be mathematically modeled. This is back-checked against the experimental mass flow measurements and is used to determine a mass-addition compensation parameter (called Kmeas) for each prototype bushing. In so doing, the methodology of modeling and measuring the mass addition in a hybrid gas bearing is re-examined and an innovative, practical, and simple method is found that makes it possible to make an “apples-to-apples” comparison between different configurations of external pressurization. This mass addition model is used in conjunction with the Reynolds equation to perform theory-based numerical analysis of virtual hybrid gas journal bearings (CFD experiments). The first CFD experiments performed use virtual bearings modeled to be identical to the experimental prototypes and replicate the experimental work. The results are compared and the CFD model is validated. The ontological significance of appropriate dimensionless similitude parameters is re-examined and a, previously lacking, complete set of similitude factors is found for hybrid bearings. A new practical method is developed to study in unprecedented detail the aerostatic component of the hybrid bearings. It is used to definitively compare the feedhole bearings to the porous liner bearings. The hydrostatic bearing efficiency (HBE) is defined and it is determined that the maximum achievable hydrostatic bearing efficiency (MAHBE) is determined solely by the bearing’s mass addition configuration. The MAHBE of the porous liner bearings is determined to be over 5 times that of the feedhole bearings. The method also presents a means to tune the Kmeas to the clearance to achieve the MAHBE as well as giving a complete mapping of the hitherto misunderstood complex shapes of aerostatic load versus radial deflection curves. This method also rediscovers the obscure phenomenon of static instability which is called in this thesis the “near surface effect” and appears to be the first work to present a practical method to predict the range of static instability and quantify its resultant stiffness fall-off. It determines that porous liner type bearings are not subject to the phenomenon which appears for feedhole type bearings when the clearance exceeds a critical value relative to its mass-addition compensation. The standing pressure waves of hydrostatic and hybrid bearings with the 2 configurations of external pressurization as well as a geometrically identical hydrodynamic bearing are studied in detail under the methodology of the “CFD microscope”. This method is used to characterize and identify the development, growth, and movement of the pressure wave extrema with increased hydrodynamic action (either increasing speed or increasing eccentricity). This method is also used to determine the “cause” of the “near surface effect”. A gedanken experiment is performed based on these results which indicates that a bearing with a “stronger aerostatic strength” component should be more stable than one with a low aerostatic strength component. Numerical instability “speed limits” are found that are also related to the hydrostatic strength of the bearing. The local conditions in the standing waves are characterized in terms of their local Mach number, Knudsen number, Reynolds number, and Taylor Number. It is concluded that low eccentricity bearing whirl can be attributed to the off load-line orientation of the bearing load force caused by the overlay of the hydrodynamic bearing standing wave onto the hydrostatic bearing wave of the hybrid bearing, whereas it is hypothesized that aperiodic and random self-excited vibration which occurs at high eccentricity, as reported in the literature, is probably due to shock waves, turbulence, near surface effect, and slip at local areas of the standing wave.

Depuis plusieurs années à nos jours, les paliers à gaz sont utilisés avec succès sur une large gamme de turbo-machines. Certains de ces systèmes sont utilisés dans des environnements de contrôle de l’environnement par gaz réfrigérant. Dans ce travail, nous présentons un modèle théorique et numérique qui tient compte de la transition du lubrifiant vapeur / liquide, la transition de l’écoulement laminaire / turbulent et les variations 3D de la viscosité et de la température dans le fluide et les solides pour les deux situations statiques et dynamiques. Ce modèle comporte : la résolution de l'équation de Reynolds généralisée pour les fluides compressibles à viscosité variable en 3D, la description des effets de la turbulence en utilisant l'approche phénoménologique de Elrod, en utilisant un champ de viscosité turbulente 3D, la résolution de l’équation d’état non linéaire du lubrifiant, capable de décrire la transition vapeur / liquide et une approche thermique local afin d'obtenir une estimation 3D de la température du fluide, grâce à l'équation d'énergie pour film mince. La prise en compte également des effets thermiques dans les solides. Dans cette étude, nous avons montré l'importance d'une description précise des paramètres du film fluide, dont les variations influencent largement le comportement du palier. Parmi les principales théories, il y a: lubrifiant compressible, avec un comportement non-linéaire près de la transition vapeur / liquide, la transition vapeur / liquide et le calcul des paramètres équivalents du mélange, un écoulement turbulent du fluide pour le palier GFB à grande vitesse en utilisant un modèle 3D de la viscosité turbulente, un comportement 3D pour la viscosité, en particulier les variations inter-films (dépendant de la température), et un comportement 3D pour la température, en particulier dans le sens transversal du film afin d'être compatible avec la viscosité, mais également dans la direction axiale afin de tenir en compte du gradient de température potentiel qui modifie considérablement le profil 3D de la température du palier. Ces deux comportements statiques et dynamiques du palier compliant GFB sont analysés. / For years now, gas bearings are successfully used over a large panel of turbo-machineries. Some of these systems are bound to be run in controlled environments such as refrigerating gas. In this work we present a theoretical and numerical model which takes into account the vapor/liquid lubricant transition, the laminar/turbulent flow transition and both temperature and viscosity 3D variations in the fluid and the solids for both static and dynamic situations. This model involves: the resolution of the generalized Reynolds equation for compressible fluids with 3D variable viscosity, the description of the turbulence effects by the phenomenological approach of Elrod, using a 3D eddy viscosity field, the resolution of a non-linear equation of state for the lubricant, able to describe the vapor/liquid transition and a local thermal approach to obtain a 3D estimation of the fluid temperature, thanks to the thin-film energy equation. The thermal effects in solids are also taken into account. In this study, we showed the importance of an accurate description of the film parameters, which variations largely influence the bearing behaviour. Among the principal theories, there are: compressible lubricant, with an appropriate non-linear behaviour when close to the vapor/liquid transition, vapor/liquid transition and calculation of the mixture equivalent parameters, turbulent flow for high-speed GFBs with a 3D eddy viscosity mode, a 3D behaviour for viscosity, particularly the cross-film variations, (temperature dependent)and a 3D behaviour for temperature, particularly in cross-film direction in order to be consistent with viscosity, but also in the axial direction in order to account for potential temperature gradient which considerably modifies the bearing 3D temperature profile. Both static and dynamic behaviours of GFBs are analysed.

Air bearing radial turbo (also called centrifugal) compressors prevail in most mobile fuel cell air supply applications due to the small size and weight, the high efficiency and the oil- and maintenance free operation. An important aspect in mobile fuel cell applications is the vibration resistance of all system components, including the compressor, with vibration requirements up to 20 g in automotive applications. This paper gives the background of the air bearing vibration characteristics, depicting the dependencies of vibration resistance on inlet conditions and operating points. The critical operating conditions concerning vibration resistance are identified, and it is outlined how vibration requirements can be included in the design process of an air bearing turbo compressor. A visualization of vibration resistance in the commonly used compressor map is presented, allowing the fuel cell system integrator to take qualified decisions for the mechanical integration of the compressor concerning vibrations.

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