The primary purpose of this study is to determine stability boundaries (interaction curves) for a three degree of freedom, shallow arch model under multiple dynamic loads. The model consists of four rigid bars connected by frictionless pins, with rotational springs and dashpots at the three interior joints, and a translational spring at the right hand exterior joint. Three independent loads (P₁, P₂, P₃) are applied to the model, one at each of the three interior joints. The model's equations of motion, which are derived from Lagrange's equations of motion, are numerically integrated, using the Newmark-Beta method (β = 1/4), to determine the buckling loads. The buckling loads are those loads for which the buckling criterion, the end bars simultaneously below the horizontal, is satisfied. The interaction curves and buckling loads are determined for a parabolic arch with damping under step loads, a parabolic arch without damping under step loads, an eccentric arch without damping under step loads, a parabolic arch without damping under impulse loads, and an / Master of Science

This thesis describes the challenges involved in detecting sources of acoustic noise using an autonomous underwater vehicle (AUV) in real world environments. The initial part of this thesis describes the developments made for redesigning an acoustic sensing system that can be used to estimate the relative bearing between a source of acoustic noise and an AUV. With an estimate of the relative bearing, the AUV can maneuver toward the source of noise. The class of algorithms that are used to estimate bearing angle are known as beamforming algorithms. A comparison of the performance of a variety of beamforming algorithms is presented. When estimating the bearing to a source of noise from a small AUV, the noise of the AUV, especially its propulsor, pose significant challenges. Toward the goal of active cancellation of AUV self-noise, we propose placing an additional hydrophone inside the AUV in order to estimate the AUV self-noise that appears on the exterior hydrophones that are used for bearing estimation. / Master of Science / A real world application using an autonomous underwater vehicle (AUV) is presented in this thesis. The application deals with detecting and estimating the relative location (bearing angle) between sources of acoustic noise and the AUV. The thesis starts by describing design changes made to target data sensing system inside the AUV for collecting and estimating the bearing angle. The estimation of bearing angle is done with a class of algorithms called beamforming algorithms whose performance comparison is presented on real world data. Operating the AUV propulsor yields inaccurate bearing angle estimations and thus presents a huge challenge for bearing estimation. We propose measuring AUV self-noise using additional sensors to move towards the goal of cancelling AUV self-noise and recovering target signal for accurate bearing estimation.

The results obtained from the nonlinearly elastic, geometrically linear beam-column are almost identical to the results obtained by the method of Gurfinkel and Robinson [6] within the linear range of the stress-strain curve. When the displacements become large, the Gurfinkel and Robinson routine tends to give higher estimates of the strain state of the section being analysed as compared to the results via the finite element model. Changing the number of integration points seems to have a stronger effect on the results than refining the mesh. / Master of Science

The Morton Effect in the rotor - bearing systems may lead to an unstable operation. Up to the present, most of the established research efforts have been focused on the overhung rotor systems. In this dissertation, a systematic study on the Morton Effect induced instability in mid-span rotor systems is presented. First, the mechanism study is conducted. The simplified rotor models with isotropic linear bearing supports are adopted for the derivation of analytical expressions. The threshold speeds of instability in simple forms are obtained for the systems with the thermal imbalance acting concurrent with or perpendicular to the direction of the response displacement. For a perspective view of the system stability, a stability map for the damped rigid mid-span rotors with the thermal imbalance having arbitrary phase difference has been generated. It shows that the stable operating regions of the system are bounded by two curves of threshold of instability. The results show that the Morton Effect induced instability thresholds are actually affected by both the magnitude and relative phase of the thermal imbalance. The mechanism of the Morton Effect induced thermal instability of mid-span rotors supported by linear isotropic bearings can be explained through the fact that the Morton Effect introduces either negative stiffness or negative cross-coupled stiffness. Next, the steady-state response performance under the influence of the Morton Effect is discussed. The results show that the Morton Effect has a comprehensive impact on both the amplitude and phase lag of the steady-state unbalance response. It may shift both curves in a manner dependent on the relative magnitude and direction of the thermal imbalance. Then, the mid-span rotors supported by the hydrodynamic journal bearings are analyzed. The models to calculate the thermal bending of the shaft and the temperature distribution across the journal surface are established. The calculations of the temperature difference and its equivalent thermal imbalance are conducted and discussed with the comparison to the analytical results. It shows that the thermal imbalance may increase to the level of the mechanical imbalance and its influence on the system stability should be then included. The suggested thermal bending model also explains that the mid-span rotors are less liable to be influenced by the Morton Effect than are the overhung configurations, because of the restraining effect between the two supports. The simulation results of a symmetric mid-span rotor - hydrodynamic journal bearing system show that the inclusion of the Morton Effect may lead to an unstable operation of the system. Considering the existence of the oil film self-induced vibration due to the dynamic characteristics of fluid film bearings, the Morton Effect may make a further negative impact on the instabilities of the rotor system under some working conditions. Finally, the predictive solution method for the general mid-span rotors is discussed. The computer code, VT-MAP, is developed for the predictions of the Morton Effect induced instability of rotor systems in either mid-span and overhung configurations. / Ph. D.

A fabricação de ultraprecisão - com suas dimensões atingindo níveis submicrométricos - tem-se mostrado um campo de trabalho que exige combinação do que há de mais avançado nas áreas de materiais, metrologia e controle. Para alcançar tais níveis de precisão, é necessário que se garanta excelente desempenho de cada um dos componentes e/ou subsistemas das máquinas. Sendo o par tribológico mancal - eixo-árvore elemento vital para o desempenho de uma máquina ferramenta, e baseado em estudos recentes que mostram que mancais convencionais de rolamento estão rapidamente atingindo seu limite, o estudo dos mancais pressurizados externamente se impõe. Com a crescente demanda por rigidez e precisão de giro, tais mancais tem-se tornado solução convencional ao contrário de condição especial. Os mancais aerostáticos, em particular, apresentam alta precisão de giro, baixa geração de calor, ausência de desgaste, alto amortecimento e limpeza. Essas características os tornam bastante atrativos em ambientes de fabricação de ultraprecisão, especialmente na indústria óptica e eletrônica, como por exemplo, na fabricação de semicondutores. O presente trabalho objetiva a comparação entre os comportamentos de dois mancais aerostáticos, com restritor do tipo orifício e com material cerâmico poroso, em relação as capacidades de carga e rigidez. Os resultados indicam a superioridade do mancal com restritor poroso quanto a capacidade de carga e também em relação à rigidez. / Ultra-precision machining - whose dimensions can reach sub-micrometric levels - has been shown to be an area of work requiring a combination of the best of materials, metrology and control. To achieve such accuracy levels, it is necessary to guarantee excellent performance of every component and/or machine subsystems. Being the tribological associated pair bearing/spindle a vital element for the performance of a machine tool, and based on recent researches that show that rolling bearings are reaching their limit very quickly, there has been an increasing demand for aerostatic bearings. These present good characteristics of stiffness, radial and axial accuracy, low heating generation, wear resistance and cleanliness. These features make them quite attractive in ultra-precision manufacturing environments, specially in the optics and electronics industries, such as in the manufacturing of semiconductors. The present work compares the stiffness and load carrying capacity of orifice restrictor and porous ceramic aerostatic bearings. The results show the superiority of porous aerostatic bearings as to loading capacity as well stiffness.

Mancais magnéticos com controle uniaxial são mancais híbridos que combinam um mancal radial por imãs permanentes e um mancal axial eletromagnético com controle ativo. Estes mancais, a despeito das vantagens com relação a outras modalidades de mancais magnéticos, têm como principal deficiência a ausência de capacidade de amortecimento de vibrações radiais do rotor. De modo a eliminar tal deficiência, esta tese propõe um novo mancal magnético híbrido que conjuga um mancal com controle uniaxial a um mancal eletrodinâmico. Esta tese tem como objetivo investigar e demonstrar a eficácia desta solução. O objetivo final é apresentar um mancal magnético de elevado desempenho, de arquitetura simples e robusta, com possibilidades de aplicação em máquinas rotativas de alta velocidade. O mancal aqui proposto tem como base um mancal de controle uniaxial cuja arquitetura é definida de modo a apresentar elevada rigidez radial, elevada folga mecânica na porção rotativa, reduzida inércia no rotor, assim como simplicidade na construção e funcionamento. Para tanto, aqui se emprega mancais radiais com imãs disposto em camadas, operando em repulsão. Na direção axial, são usados atuadores eletromagnéticos compatíveis com a elevada rigidez gerada pelos mancais radiais. A estes mancais são associados mancais eletrodinâmicos homopolares de dois tipos, de fluxo magnético axial e de fluxo radial. Definido conceitualmente o novo mancal, protótipos foram desenvolvidos e foram realizados ensaios de validação do conceito do novo mancal, assim como de verificação do desempenho do protótipo. Com relação ao mancal proposto, foi verificada uma levitação estável do rotor e, obtida uma rigidez radial de 44 N/mm mediante uma folga de 2,5 mm. São valores que superam quaisquer resultados encontrados em literatura sobre mancais similares. Em seguida, demonstrou-se, ao menos até uma rotação de 35 Hz (2.100 rpm), a eficácia do mancal eletrodinâmicos de fluxo axial no amortecimento de movimentos assíncronos do rotor. / Single axis controlled magnetic bearings are hybrid bearings that combine a radial bearing based on permanent magnets and an electromagnetic bearing with active control. Such bearings, despite advantages with respect to other modalities of magnetic bearings, present an important problem of absence of vibration damping capability in the radial directions of the rotor. In order to solve this problem, this thesis proposes a new hybrid magnetic bearing that conjugates a single axis controlled bearing with an electrodynamic bearing. This thesis aims investigate and demonstrate the efficiency of the proposed solution. The final goal is to present a magnetic bearing with high capabilities, of simple architecture and robust, with possibilities for applications in high speed rotary machines. The presented bearing has, as the base, a single axis controlled bearing with an architecture suitable for achieving high radial stiffness, large gap in the rotary portion, low rotor inertia, as well as simplicity in its construction and operation. For this, the bearing employs radial bearings based on magnets arranged in layers operating in repulsion mode. In the axial direction, it uses electromagnetic actuators compatible with the high radial stiffness generated by radial bearings. These bearings are associated with electrodynamic homopolar bearings of two types: one of axial magnetic flux and other with radial flux. Once, the new bearing is defined conceptually, tests are conducted to validate the principle of the new bearing, as well, tests to evaluation of the efficiency of the prototype. With respect to the proposed bearing, a stable levitation of the rotor is obtained. Also, a radial stiffness of 44 N/mm is achieved with a gap of 2.5 mm. These values are higher than any results presented in literatures related to similar bearings. Finally, it is demonstrated that at rotations speeds of until 35 Hz (2,100 rpm), the electrodynamic of axial flux is efficient to attenuate asynchronous motions of the rotor.

Le roulement est l'un des composants les plus importants des machines tournantes. Néanmoins, dans des conditions normales d'utilisation, il est soumis à de la fatigue de roulement qui peut conduire à un défaut d'écaillage. Dans ce travail, nous présentons un suivi de la fatigue d'un roulement de butée grâce à un banc d'essais dédié. L'analyse vibratoire est une méthode qui permet de caractériser et de localiser les défauts dans les roulements. Des mesures successives de ces niveaux de vibrations donnent des indications quant à l'évolution de la sévérité des défauts. Le suivi de cette évolution est fait grâce à un indicateur statistique, la valeur RMS (Root Mean Square) qui peut être corrélée avec la taille d'un écaillage de roulement. L'approche suit le fonctionnement du roulement de butée jusqu'à la dégradation avec une acquisition on line des états vibratoires sous forme de signaux temporels. A l'aide du traitement de signal, on obtient les valeurs des amplitudes vibratoires qui caractérisent l'état vibratoire du roulement. Par conséquent, ces valeurs nous permettent de tracer les courbes de fatigue. Au cours de notre travail expérimental, cette opération est appliquée à un lot de butées à billes pour lesquelles nous avons obtenu des courbes semblables où la tendance de l'évolution suit un modèle mathématique à partir de la détection de l'apparition de la première écaille. Le résultat de ce travail contribuera à prédire la durée de vie résiduelle avant la panne. / The bearing is one of the most important components of rotating machines. Nevertheless, in normal conditions of use, it is subject to fatigue which creates a defect called a rolling fatigue spalling. In this work, we present a follow-up of the thrust bearing fatigue on a test bench. Vibration analysis is a method used to characterize the defect. In order to obtain the fatigue curve more adjusted, we have studied the vibration level according to statistical indicators: the Root Mean Square value (RMS value), which is one of the best indicators to show the evolution of the bearing degradation. The approach follows the working of the bearing until the degradation with an on line acquisition of vibration statements in form of time signals. With the signal treatment, we obtain the values of the vibration amplitudes which characterize the vibration state of the bearing. Consequently, these values allow us to plot the fatigue curves. During our experimental work, this operation is applied for a batch of thrust bearings for which we have obtained similar fatigue curves where the evolution trend follows a mathematical model from the detection of the onset of the first spall. The result of this work will contribute to predict the working residual time before failure.

This dissertation deals with three research topics; i) the catcher bearings life prediction method, ii) the Morton effect, and iii) the two dimensional modified Reynolds equation. Firstly, catcher bearings (CB) are an essential component for rotating machine with active magnetic bearings (AMBs) suspensions. The CB's role is to protect the magnetic bearing and other close clearance component in the event of an AMB failure. The contact load, the Hertzian stress, and the sub/surface shear stress between rotor, races, and balls are calculated, using a nonlinear ball bearing model with thermal growth, during the rotor drop event. Fatigue life of the CB in terms of the number of drop occurrences prior to failure is calculated by applying the Rainflow Counting Algorithm to the sub/surface shear stress-time history. Numerical simulations including high fidelity bearing models and a Timoshenko beam finite element rotor model show that CB life is dramatically reduced when high-speed backward whirl occurs. Secondly, the theoretical models and simulation results about the synchronous thermal instability phenomenon known as Morton Effect is presented in this dissertation. A transient analysis of the rotor supported by tilting pad journal bearing is performed to obtain asymmetric temperature distribution of the journal by solving variable viscosity Reynolds equation, energy equation, heat conduction equation, and equations of motion for rotor. The tilting pad bearing is fully nonlinear model. In addition, thermal mode approach and staggered integration scheme are utilized in order to reduce computation time. The simulation results indicate that the temperature of the journal varies sinusoidally along the circumferential direction and linearly across the diameter, and the vibration envelope increased and decreased, which considers as a limit cycle that is stable oscillation of the envelope of the amplitude of synchronous vibration. Thirdly, the Reynolds equation plays an important role to predict pressure distribution in the fluid film for the fluid film bearing analysis. One of the assumptions on the Reynolds equation is that the viscosity is independent of pressure. This assumption is still valid for most fluid film bearing applications, in which the maximum pressure is less than 1 GPa. In elastohydrodynamic lubrication (EHL) which the lubricant is subjected to extremely high pressure, however, the pressure independent viscosity assumption should be reconsidered. With considering pressure-dependent viscosity, the 2D modified Reynolds equation is derived in this study. The solutions of 2D modified Reynolds equation is compared with that of the classical Reynolds equation for the plain journal bearing and ball bearing cases. The pressure distribution obtained from modified equation is slightly higher pressures than the classical Reynolds equations. / PDF file replaced 10-21-2012 at the request of the Thesis Office.

With a new range of water jet assemblies under development, CWF Hamilton & Co. Ltd. highlighted the need to establish a validated model for predicting critical speeds. A review of the relevant literature revealed a significant lack of information concerning the operating properties of a lightly loaded, water lubricated marine bearing. Therefore, an instrumented test rig based on a CWF Hamilton & Co. Ltd. ‘HJ364’ water jet assembly was established to evaluate critical speeds and validate the predictive models. A number of analytical and numerical models for predicting critical speeds were investigated. Geometric modifications were made to the test rig and the changes in critical speeds were observed. The ability of the predictive models to measure these observed critical speeds was examined. Driveline mass and driveline overhang were found to have the most significant effects on critical speeds. Modifications to the thrust bearing housing, the impeller mass, the tailpipe stiffness and the marine bearing resulted in no significant shift in critical speeds. However, a change to the geometry of the thrust bearing resulted in a significant shift. This indicated that the thrust bearing was not performing ideally in the test rig. All three models predicted changes in critical speeds relatively accurately. However, the estimates of the critical speeds themselves were somewhat conservative; approximately 10 to 15 percent lower than those measured. Linearisation of the thrust bearing geometry is recommended if greater accuracy is to be achieved. Of all the predictive methods, the Myklestad-Prohl transfer-matrix and the Isolated-Mainshaft finite-element were deemed to be the most flexible and suitable for CWF Hamilton & Co. Ltd.

Mancais magnéticos com controle uniaxial são mancais híbridos que combinam um mancal radial por imãs permanentes e um mancal axial eletromagnético com controle ativo. Estes mancais, a despeito das vantagens com relação a outras modalidades de mancais magnéticos, têm como principal deficiência a ausência de capacidade de amortecimento de vibrações radiais do rotor. De modo a eliminar tal deficiência, esta tese propõe um novo mancal magnético híbrido que conjuga um mancal com controle uniaxial a um mancal eletrodinâmico. Esta tese tem como objetivo investigar e demonstrar a eficácia desta solução. O objetivo final é apresentar um mancal magnético de elevado desempenho, de arquitetura simples e robusta, com possibilidades de aplicação em máquinas rotativas de alta velocidade. O mancal aqui proposto tem como base um mancal de controle uniaxial cuja arquitetura é definida de modo a apresentar elevada rigidez radial, elevada folga mecânica na porção rotativa, reduzida inércia no rotor, assim como simplicidade na construção e funcionamento. Para tanto, aqui se emprega mancais radiais com imãs disposto em camadas, operando em repulsão. Na direção axial, são usados atuadores eletromagnéticos compatíveis com a elevada rigidez gerada pelos mancais radiais. A estes mancais são associados mancais eletrodinâmicos homopolares de dois tipos, de fluxo magnético axial e de fluxo radial. Definido conceitualmente o novo mancal, protótipos foram desenvolvidos e foram realizados ensaios de validação do conceito do novo mancal, assim como de verificação do desempenho do protótipo. Com relação ao mancal proposto, foi verificada uma levitação estável do rotor e, obtida uma rigidez radial de 44 N/mm mediante uma folga de 2,5 mm. São valores que superam quaisquer resultados encontrados em literatura sobre mancais similares. Em seguida, demonstrou-se, ao menos até uma rotação de 35 Hz (2.100 rpm), a eficácia do mancal eletrodinâmicos de fluxo axial no amortecimento de movimentos assíncronos do rotor. / Single axis controlled magnetic bearings are hybrid bearings that combine a radial bearing based on permanent magnets and an electromagnetic bearing with active control. Such bearings, despite advantages with respect to other modalities of magnetic bearings, present an important problem of absence of vibration damping capability in the radial directions of the rotor. In order to solve this problem, this thesis proposes a new hybrid magnetic bearing that conjugates a single axis controlled bearing with an electrodynamic bearing. This thesis aims investigate and demonstrate the efficiency of the proposed solution. The final goal is to present a magnetic bearing with high capabilities, of simple architecture and robust, with possibilities for applications in high speed rotary machines. The presented bearing has, as the base, a single axis controlled bearing with an architecture suitable for achieving high radial stiffness, large gap in the rotary portion, low rotor inertia, as well as simplicity in its construction and operation. For this, the bearing employs radial bearings based on magnets arranged in layers operating in repulsion mode. In the axial direction, it uses electromagnetic actuators compatible with the high radial stiffness generated by radial bearings. These bearings are associated with electrodynamic homopolar bearings of two types: one of axial magnetic flux and other with radial flux. Once, the new bearing is defined conceptually, tests are conducted to validate the principle of the new bearing, as well, tests to evaluation of the efficiency of the prototype. With respect to the proposed bearing, a stable levitation of the rotor is obtained. Also, a radial stiffness of 44 N/mm is achieved with a gap of 2.5 mm. These values are higher than any results presented in literatures related to similar bearings. Finally, it is demonstrated that at rotations speeds of until 35 Hz (2,100 rpm), the electrodynamic of axial flux is efficient to attenuate asynchronous motions of the rotor.