Fundação de Amparo a Pesquisa do Estado de Minas Gerais / Dynamic analyses of a flexible rotor supported by fluid film radial bearings on elastomeric suspension are performed using the Finite Element Method. The response to the unbalance and the stability behavior are obtained for different types of damping devices configuration and viscoelastic materials. The stiffness and damping coefficients of the hydrodynamic bearings are evaluated through the Short Bearing Theory. The properties of the elastomers, as a function of the frequency at a given temperature, are obtained from tests conducted in the Laboratory of Mechanical Systems of the School of Mechanical Engineering in the Federal University of Uberlândia. Dissipative elastomeric devices have strong influence on the dynamic behavior of the rotor. It is observed that with the suitable choice of the damper, the amplitude of the unbalance response may be reduced. The threshold speed of stability is increased with the use of elastomeric dampers for the most analyzed cases. / Análises dinâmicas de um rotor flexível apoiado por mancais radiais de filme fluido montados em uma suspensão elastomérica são realizadas utilizando o Método dos Elementos Finitos. A resposta ao desbalanceamento e o comportamento da estabilidade são obtidos para várias configurações de dispositivos amortecedores e para diferentes materiais viscoelásticos. Os coeficientes de rigidez e de amortecimento dos mancais hidrodinâmicos são obtidos através da Teoria de Mancais Curtos. As propriedades dos materiais viscoelásticos, determinadas em função da frequência a uma dada temperatura, são obtidas através de ensaios conduzidos no Laboratório de Sistemas Mecânicos da Faculadade de Engenharia Mecânica da Universidade Federal de Uberlândia. Os dispositivos dissipativos elastoméricos possuem forte influência no comportamento dinâmico do rotor. Observa-se que, com a escolha adequada da configuração do amortecedor, a amplitude da resposta ao desbalanceamento pode ser reduzida. A velocidade limite de estabilidade é aumentada com o emprego dos amortecedores elastoméricos para a maioria dos casos analisados. / Doutor em Engenharia Mecânica

A potentially powerful influence on the dynamic characteristics of a journal bearing is the thermal deformation of the bearing surface and the journal. Although a few reported research projects consider this effect, most of the journal bearing codes currently utilized in the turbomachinery industry ignore this influence. A study of the thermohydrodynamic behavior including thermoelastic deformation of a two axial groove journal bearing is presented in this thesis. The finite element method has been used to solve the governing differential equations. Quadrilateral nine noded isoparametric elements are used in the finite element model of both the fluid film and the bearing liner. The analytical predictions are compared with the steady load data obtained from two identical 101 mm dia, 57 nm long bearings, one fabricated from steel and the other from bronze. The comparisons are made for several loading values and for operational speeds of 1000 and 5000 RPM (16.66 Hz and 83.33 Hz). Analytical results are also presented for an operating speed of 10000 RPM (166.66 Hz). / Master of Science

Ce document présente les analyses expérimentales de deux types de composants aérodynamiques, lubrifiés en air : les butées à feuilles et les paliers à feuilles. Ces éléments constituent une nouvelle génération d'organes de guidages, et gagnent à être implémentés dans des machines tournantes dont les performances sont critiques. En effet, ils permettent d'atteindre des vitesses élevées, sans usure en régime établit, et diminuent la puissance dissipée en comparaison à des solutions fonctionnant avec de l'huile. Ce mémoire est une contribution à l'étude de chacun de ces éléments, dont les niveaux respectifs de maturité technologique ne sont pas similaires. Le palier à feuilles possède une littérature plus riche que la butée, dont aucune analyse expérimentale dynamique n'a été menée jusqu'à présent. Un banc d'essai, destiné à l'étude de butées à feuilles, sous des charges statiques et dynamiques, est conçu. Les caractéristiques de démarrage montrent une augmentation linéaire du couple de démarrage avec la charge statique, une augmentation linéaire du couple en fonctionnement aussi bien avec la charge statique qu'avec la vitesse de rotation, et enfin, une augmentation globale de la vitesse de décollage avec la charge statique. Les essais dynamiques montrent, pour la raideur dynamique, une augmentation non linéaire avec la fréquence d'excitation (entre 150 Hz et 750 Hz) ainsi qu'avec la charge statique appliquée. L'amortissement visqueux équivalent diminue avec la fréquence d'excitation, mais augmente avec la charge statique. Les essais montrent, à charge équivalente, une diminution de la raideur et de l'amortissement avec l'augmentation de la vitesse de rotation. Les facteurs d'amortissements structurels diminuent avec l'augmentation de la fréquence d'excitation, et augmentent avec la charge statique. Afin de se rapprocher d'une architecture de turbomachine, un banc d'essai existant est adapté à l'utilisation de paliers à feuilles. L'étude du comportement de deux rotors rigides (un léger et un lourd) est menée. Celle-ci s'effectue de deux façons : par l'analyse de spectrogrammes enregistrés suivant deux directions du plan de chaque palier, ou bien en étudiant la réponse synchrone à différents balourds. Une confrontation avec deux modèles théoriques est effectuée, en comparant soit la réponse synchrone au balourd dans chaque palier, soit les spectrogrammes. Les balourds sont comparés avec un modèle de rotor rigide linéaire (analyse en petites perturbations) à 4 degrés de libertés, dans lequel les coefficients dynamiques des paliers obtenus grâce au code Foil sont utilisés. les spectrogrammes montrent des vibrations sous-synchrones, qui sont reproduites dans ce mémoire au moyen d'un modèle simplifié de force dynamique. Les résultats expérimentaux actuels montrent les limites des modélisations des paliers à feuilles existantes. Afin d'améliorer la connaissance et la prédiction de ces composants, il est dorénavant nécessaire d'établir un nouveau modèle dynamique, non linéaire, permettant de prédire les réponses synchrones aux balourds ainsi que la richesse sous-synchrone de la signature dynamique d'un rotor supporté par ces paliers. / This document deals with the experimental analyses of two types of air lubricated aerodynamic components: foil journal bearings and foil thrust bearings. These components belong to a new generation of bearings, and are well worth integrating in turbomachinery, which performances are at stakes. Indeed they enable to reach very high speeds without any wear in continuous regime and they diminish energy loss compared to oil bearings. This memoir is a contribution to these two elements, which maturity levels are different.A test rig dedicated to the study of foil thrust bearings under both static and dynamic loads is designed. Start-up characteristics show a linear increase of start-up torque with static load, a linear increase of the fluid film torque with both static load and rotation speed, and an increase of lift-off speed with rotation speed. Dynamical tests show a non linear increase of the stiffness with both excitation frequency (between 150 Hz and 750 Hz) and static load. Equivalent viscous damping decreases with excitation frequency, but increase with static load. Loss factor decreases with excitation frequency and increase with static load.An existing test rig was modified to test foil journal bearings, in a close architecture compared to turbomachines. Two rigid rotors (one light and one heavy) supported by two foil journal bearings were studied. Study is made in two different ways: by the analysis of the displacements spectrograms in two perpendicular directions on each bearing, or the study of the synchronous response at different unbalance masses. A comparison between experimental results and two theoretical models is made. Unbalance responses are compared to a linear rigid rotor model with 4 degrees of freedom, in which the dynamic coefficients of the foil journal bearings are obtained thanks to the Foil algorithm. Spectrograms show sub-synchronous vibrations that are computed thanks to a simplified dynamic force model. Experimental results show the limits in the foil journal bearings theoretical models. In order to improve knowledge and prediction of these components, it is now compulsory to establish a new non-linear dynamical model, enabling to predict both the synchronous unbalance responses and the complexity of the sub-synchronous dynamical signature of a rotor maintained by two foil journal bearings.

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.