Rotordynamic instability problems in turbomachinery have become more important in recent years due to rotordynamic components with higher speeds and higher power densities. These features typically lead to increased instability risk in rotor dynamic components as fluids-structure interactions take place. In addition, critical damage of rotordynamic components can result from high level vibrations of supporting bearing system, where the reduced rotor speed can lead to system operating near the rotor critical speed. Therefore, increased accuracy in modeling of rotordynamic components is required to predict the potential instability issues in high performance rotordynamic design. The instability issue may potentially be eliminated in design stage by varying the characteristics of the unstable components. One such turbomachinery component is the annular pressure seal. The annular pressure seals are specifically designed to prevent the fluid leakage from high pressure stage to low pressure stage in turbomachinery. Typical annular pressure seals have two different flow regions, an annular jet-flow region between the rotor and stator, and cylindrical or circumferential indentions on the stator/rotor surface that serve as cavities where flow recirculation occurs. As the working fluid enters the cavities and recirculates, the kinetic energy is reduced, resulting in a reduction of leakage flow. The current challenge is to model with higher precision the interaction between the rotordynamic components and the working fluid. In this dissertation, this challenge was overcome by developing a hybrid Bulk Flow/CFD method to compute rotordynamic responses for the annular pressure seals. In addition, design of experiments studies were performed to relate the surface patterning with the resulting rotordynamic response for the annular pressure seals, in which several different geometry specifications were investigated. This study on annular pressure seal design generated regression models for rotordynamic coefficients that can be used as optimization guidelines. Research topics related to the annular pressure seals were presented in this dissertation as well. The reduced order model of both hole-pattern seals and labyrinth seals were investigated. The results showed that the flow field representing the flow dynamics in annular pressure seals can be expressed as a combination of first three proper orthogonal decomposition modes. In addition, supercritical state of carbon dioxide (sCO2) process fluid was examined as the working fluid in a preliminary study to better understand the effects on annular pressure seals. The results showed that the performance and stability in the annular pressure seals using sCO2 as process fluid can both be improved. / Doctor of Philosophy / This dissertation focused on understanding the correlations between surface patterning and rotordynamic responses in the annular pressure seals. The annular pressure seals are a specific type of rotordynamic component that was designed to prevent the fluid leakage from high pressure stage to low pressure stage in turbomachinery. As the working fluid enters the cavities and recirculates, the kinetic energy is reduced, resulting in a reduction of leakage flow through the annular pressure seals. Rotordynamic instability becomes an issue that may be related to the annular pressure seals in some cases. In recent years, rotordynamic components with higher rotor speeds and higher power densities are commonly used in industrial applications. These features could lead to increased instability risk in rotor-bearing systems as fluids-structure interactions take place. Therefore, high precision modeling of the rotodynamic components is required to predict the instability issues in high performance rotordynamic design. The instability issue may potentially be eliminated in design stage by varying the characteristics of the potentially unstable components. In this study, the surface patterning and rotordynamic responses were investigated for several different annular pressure seal models with a hybrid Bulk Flow/Computational Fluid Dynamics method. This dissertation provides for the first time regression models for rotordynamic coefficients that can be used as optimization guidelines. Research topics related to the annular pressure seals were presented in this dissertation as well. The reduced order model of both hole-pattern seals and labyrinth seals were investigated. The results showed that the flow field representing the flow dynamics in annular pressure seals can be expressed as a combination of first three proper orthogonal decomposition modes. In addition, supercritical state of carbon dioxide (sCO2) process fluid was examined to better understand the effects of working fluid on annular pressure seals. The results showed that the performance and stability in the annular pressure seals using sCO2 as process fluid can both be improved.

Subsynchronous vibrations such as those caused by rotor instability represent one of the most harrowing scenarios of rotor vibration. They are related to a great diversity of destabilizing forces and some of them are not well understood yet. Therefore, special attention must be paid to this type of vibration. Active Magnetic Bearings (AMBs) monitor the position of the shaft and change the dynamics of the system accordingly to keep the rotor in a desired position, offering the possibility of being used as dampers for vibration control. In the present work, a single-disk and a three-disk rotor were built to evaluate the effectiveness of an Active Magnetic Damper (AMD) in damping subsynchronous vibrations. An AMD was used to inject a signal simulating a subsynchronous vibration in the rotor, as another AMD was used to perform active control. Two locations of the AMD were considered for each rotor. For the single-disk rotor, experimental data was taken with the AMD located at three-quarters of the rotor-span and with the AMD located at midspan. For the three-disk rotor, experimental data was taken with the AMD located at a quarter-span and with the AMD at two-thirds of the rotor span. An undamped critical speed and a forced response analysis were performed on the rotors in order to predict the dynamic characteristics of the rotors with and without the AMD. It was demonstrated that an AMD is effective in damping subsynchronous vibrations. The addition of an AMD introduces damping and stiffness to the rotor-bearing system resulting in a change in the synchronous response and a consequent increase of the amplitude of vibrations at synchronous frequencies. This effect must be carefully considered when designing a system with an AMD. / Master of Science

Aero-engine assemblies are complex structures typically involving two or three nested rotors mounted within a flexible casing via squeeze-film damper (SFD) bearings. The deployment of SFDs into such structures is highly cost-effective but requires careful calculation since they can be highly nonlinear in their performance, particularly if they are unsupported (i.e. without a retainer spring). The direct study of whole-engine models with nonlinear bearings has been severely limited by the fact that current nonlinear computational techniques are not well-suited for complex large-order systems. The main contributions of this thesis are: • A procedure for unbalance response computation, suitable for generic whole-engine models with nonlinear bearings, which significantly extends the capability of current finite element packages. This comprises two novel nonlinear computational techniques: an implicit time domain integator referred to as the Impulsive Receptance Method (IRM) that enables rapid computation in the time domain; a whole-engine Receptance Harmonic Balance Method (RHBM) for rapid calculation of the periodic response in the frequency domain. Both methods use modal data calculated from a one-off analysis of the linear part of the engine at zero speed.• First-ever analyses on real twin-spool and three-spool engines. These studies illustrate the practical use of these solvers, provide an insight into the nonlinear dynamics of whole-engines and correlate with a limited amount of industrial experimental data. Both IRM and RHBM are directly formulated in terms of the relative response at the terminals of the nonlinear bearings. This makes them practically immune to the number of modes that need to be included, which runs into several hundreds for a typical engine. The two solvers are extensively tested on two/three-shaft engine models (with 5-6 SFDs) provided by a leading engine manufacturer using an SFD model that is used in industry. The tests show the IRM to be many times faster than an established robust conventional implicit integrator while achieving a similar level of accuracy. It is also shown to be more reliable than another popular implicit algorithm. The RHBM enables, for the first time, the frequency domain computation of the nonlinear response of whole-engine models. Its use is illustrated for both Single-Frequency Unbalance (SFU) excitation (unbalance confined to only one shaft) and Multi-Frequency Unbalance (MFU) excitation (unbalance located on two or more shafts, rotating at different speeds). Excellent correlation is demonstrated between RHBM and IRM.The parametric studies compare and contrast the frequency spectra for SFU and MFU cases. They also reveal the varying degree of lift at the unsupported SFDs. The sensitivity of the response to end-sealing and bearing housing alignment is also illustrated. It is demonstrated that the use of suitably preloaded vertically oriented “bump-springs” at the SFDs of heavy rotors produces a significant improvement in journal lift. It is also shown that the consideration of a slight amount of distributed damping in the structure significantly affects the predicted casing vibration levels, bringing them closer to measured levels, while having little effect on the SFD orbits.

Orientador: Gilberto Pechoto de Melo / Resumo: A identificação de trincas ainda é um desafio na área de monitoramento da integridade estrutural em eixos rotativos. Embora muitas técnicas e modelos tenham sido desenvolvidos, encontrar uma técnica eficiente que possa localizar uma única ou múltiplas trincas ao longo do eixo, ainda é um grande desafio. Nesse trabalho, um novo índice para localização de trincas em eixos rotativos é apresentado. A equação do movimento do rotor com trinca utiliza a notação em coordenadas complexas a fim de separar as contribuições dos modos de precessão direta e retrógrada. O índice SDI (shape and directivity index) é calculado para o rotor, cujo modelo matemático considera a variação instantânea da rigidez do elemento finito devido à abertura e o fechamento gradual da trinca, conhecido como efeito breathing. Através da manipulação do SDI no modelo de cores HSV (hue, saturation and value), desenvolve-se uma escala métrica, visualizada em um mapa de cores, que possibilita localizar a anisotropia causada pela trinca ao longo do eixo. Profundidade e posição da trinca, presença de múltiplas trincas, entre outros fatores que afetam a assinatura da trinca em outros métodos de identificação são analisados. Bons resultados demonstram a eficiência e robustez do novo índice para diversos casos de operação do rotor. Essa métrica de dano acrescenta uma contribuição para os métodos de localização de trincas em sistemas rotativos. / Abstract: Crack identification is still a challenge in the area of structural health monitoring dedicated to rotating shafts. Although many techniques and models have been developed, finding an efficient technique capable of locating a single or multiple cracks along the shaft is still a challenge. In this work, a new index for locating cracks in rotating shafts is proposed. The equation of motion of the cracked rotor uses notation in complex coordinates in order to separate the contributions of forward and backward precession modes. The SDI (shape and directivity index) is calculated for the cracked rotor, which mathematical model considers the instantaneous variation of the finite element stiffness due to the gradual opening and closing of the crack, known as the breathing effect. By manipulating the SDI in the HSV (hue, saturation and value) color model, a metric scale is developed to locate the anisotropy caused by cracks along the shaft, visualized on a color map. Depth and position of the crack, presence of multiple cracks, among other factors that affect the signature of the crack in other identification methods are analyzed. Good results demonstrate the efficiency and robustness of the new index for several rotor operation conditions. This damage metric contributes to crack localization methods in rotating systems. / Doutor

[pt] Dentro do campo dos controladores passivos, um dos dispositivos usados pelas suas propriedades de amortecimento são os Apoios Elásticos, que constituem uma solução econômica e efetiva na supressão ou atenuação das vibrações em sistemas dinâmicos com problemas de ressonância ou instabilidade, freqüentemente pela falta de amortecimento suficiente. Este trabalho envolve o estudo de um rotor horizontal com apoios elásticos (silicone), adaptado a partir de um rotor existente, o estudo de diversos efeitos sobre a sua operação, a medição de seu movimento, a identificação dos parâmetros do problema, a medição e validação a partir de resultados simulados em um modelo numérico. Os fenômenos incluídos no estudo são o efeito giroscópio (rotor descentrado com respeito do vão), desbalanceamento do rotor e empenamento do eixo. Neste trabalho os parâmetros do sistema foram determinados usando técnicas de identificação, análise modal e otimização não linear devido à anisotropia do sistema. / [en] Viscoelastic Passive Controllers are an important field of technological research due to the development of new materials and design techniques. Damping properties allow an easy retrofit of existing machines with excessive vibration problems, developing Elastomeric Bearing Supports. They are an economic and effective solution in the suppression or attenuation of vibrations in dynamic systems suffering from instability or resonance problems, which often lack of sufficient damping. This work involves the study of an horizontal rotor with elastomeric bearing supports, adapted of another one, the study of several effects on his operation, the measurement of his motion, the identification of the problems parameters, the measurement and validation from the simulated results in a numeric model. Phenomena included in the study are the gyroscopic effect (rotor out of the middle), rotor unbalance and shaft bow. In this work the systems parameters were determined using identification, modal analysis and nonlinear optimization techniques due to the anisotropy of the system.

[pt] O controle de empuxo vetorial (TVC) é usado para o controle de atitude de foguetes aeroespaciais. No caso de propulsão usando combustível líquido, tradicionalmente o bocal é conectado ao corpo do foguete através de uma junta cardânica. Dois atuadores hidráulicos são colocados ao redor do bocal para controlar sua orientação. Nesta tese, o TVC é tratado como uma plataforma robótica de base fixa. Ao invés de usar servo-válvulas comerciais para controlar os atuadores, uma nova válvula de controle é proposta. Primeiro uma plataforma cardânica é considerada com transdutores de posição angular medindo o deslocamento da cruzeta da junta. Em seguida, uma nova configuração da plataforma é proposta substituindo o cardan por uma junta homocinética. Neste caso, a realimentação da posição da plataforma é feito usando um estimador de atitude em tempo real. Este estimador é um filtro complementar baseado em matrizes de orientação que coleta dados de uma central inercial (IMU). A modelagem do sistema começa com a cinemática. Na sequência, a modelagem dinâmica utiliza a formulação de Newton-Euler para obter a equação de movimento. A modelagem do sistema hidráulico é apresentada com o modelo da nova válvula de controle e do atuador. Inicialmente, um controlador puramente proporcional é proposto. Durante a validação experimental é mostrado que devido as características do sistema de atuação, mesmo este simples controlador é preciso e confiável. Em seguida é demonstrado um método para avaliar outras estratégias de controle. A comparação entre a plataforma cardânica e homocinética mostra que, nas condições analisadas, ambas têm um comportamento dinâmico similar. Nas duas configurações da plataforma o sistema se mostrou preciso e confiável. / [en] Thrust Vector Control (TVC) is used for the attitude control of spacecrafts. In the case of liquid-propellant fuel, the nozzle is traditionally connected to the rocket frame through a gimbal. Two hydraulic actuators are placed around the nozzle to control its orientation. In this Thesis, TVC is treated as a fixed base robotic platform. Instead of using commercial servo-valves to control the actuators, a novel control valve is proposed. First a gimbaled platform is considered with two angular position transducers to measure the angular displacement of the joint crosshead. Then, a homokinetic platform configuration is proposed replacing the gimbal by a constant velocity joint. In this case, the platform position feedback is done using a real-time attitude estimator. The estimator is a complementary filter based on orientation matrices that collects data from an inertial measurement unit (IMU). The modeling of the system begins with kinematics. Then, the dynamic modeling uses the Newton-Euler formulation to obtain the equation of motion. The modeling of the electro-hydraulic system is presented with the model of the novel control valve and the linear actuator. Initially, a full proportional controller is proposed. During the experimental validation it is shown that due to the characteristics of the actuation system, even this simple controller is accurate and reliable. Thereafter, method is demonstrated to evaluate novel control strategies. The comparison between the gimbaled and homokinetic platform shows that, under the analyzed conditions, they have a similar dynamic behavior. In both platform configurations the system is accurate and reliable.

Gas bearings in oil-free micro-turbomachinery for process gas applications and for power generation (< 400 kW) must offer adequate load capacity and thermal stability, reliable rotordynamic performance at high speeds and temperatures, low power losses and minimal maintenance costs. The metal mesh foil bearing (MMFB) is a promising foil bearing technology offering inexpensive manufacturing cost, large inherent material energy dissipation mechanism, and custom-tailored stiffness and damping properties. This dissertation presents predictions and measurements of the dynamic forced performance of various high speed and high temperature MMFBs. MMFB forced performance depends mainly on its elastic support structure, consisting of arcuate metal mesh pads and a smooth top foil. The analysis models the top foil as a 2D finite element (FE) shell supported uniformly by a metal mesh under-layer. The solution of the structural FE model coupled with a gas film model, governed by the Reynolds equation, delivers the pressure distribution over the top foil and thus the load reaction. A perturbation analysis further renders the dynamic stiffness and damping coefficients for the bearing. The static and dynamic performance predictions are validated against limited published experimental data. A one-to-one comparison of the static and dynamic forced performance characteristics of a MMFB against a Generation I bump foil bearing (BFB) of similar size, with a slenderness ratio L/D=1.04, showcases the comparative performance of MMFB against a commercially available gas foil bearing design. The measurements of rotor lift-off speed and drag friction at start-up and airborne conditions are conducted for rotor speeds up to 70 krpm and under identical specific loads (W/LD =0.06 to 0.26 bar). The dynamic force coefficients of the bearings are estimated, in a ‘floating bearing’ type test rig, while floating atop a journal spinning to speeds as high as 50 krpm and with controlled static loads (22 N) applied in the vertical direction. The parameter identification is conducted in the frequency range of 200-400 Hz first, and then up to 600 Hz using higher load capacity shakers. A finite element rotordynamic program (XLTRC2) models a hollow rotor and two MMFBs supporting it and predict the synchronous rotor response for known imbalances. The predictions agree well with the ambient temperature rotor response measurements. Extensive rotor response measurements and rotor and bearing temperature measurements, with a coil heater warming up to 200 ºC and placed inside the hollow rotor, reveal the importance of adequate thermal management. The database of high speed high temperature performance measurements and the development of a predictive tool will aid in the design and deployment of MMFBs in commercial high-speed turbomachinery. The work presented in the dissertation is a cornerstone for future analytical developments and further testing of practical MMFBs.

To increase efficiency, shafts are made lighter and more flexible, and are designed to rotate faster to increase the system's power-to-weight ratio. The demand for higher efficiency in rotordynamic systems has led to increased susceptibility to transverse fatigue cracking of the shaft. Shaft cracks are often detected and repaired during scheduled periods of off-line maintenance. Off-line maintenance can be expensive and time consuming; on-line condition monitoring allows maintenance to be performed as-needed. However, inadequate (or a lack of) monitoring can allow rapidly propagating cracks to result in catastrophic shaft failure. It is therefore imperative to develop on-line condition monitoring techniques to detect a crack and diagnose its severity. A particularly useful method for transverse shaft crack detection/diagnosis is vibration monitoring. Detection, and especially diagnosis, of transverse fatigue cracks in rotordynamic systems has proven difficult. Whereas detection assesses only the presence of a crack, diagnosis estimates important crack parameters, such as crack depth and location. Diagnosis can provide the operator with quantitative information to assess further machinery operation. Furthermore, diagnosis provides initial conditions and predictive parameters on which to base prognostic calculations. There is a two-fold challenge for on-line diagnosis of transverse fatigue crack parameters. First, crack characterization involves specifying two important parameters: the crack's depth and location. Second, the nature of rotating machinery permits response measurement at only specific locations. Cracks are typically categorized as breathing or gaping; breathing cracks open and close with shaft rotation, while gaping cracks remain open. This work concerns the diagnosis of gaping crack parameters; the goal is to provide metrics to diagnose a crack's depth and location. To this end, a comprehensive approach is presented for modeling an overhung cracked shaft. Two linear gaping crack models are developed: a notch and a gaping fatigue crack. The notch model best approximates experimentally manufactured cracks, whereas the gaping fatigue crack model is likely more suited for real fatigue cracks. Crack diagnosis routines are established using free and forced response characteristics. Equations of motion are derived for both crack models, including excitation due to gravity and imbalance. Transfer matrix techniques are established to expediently obtain the steady-state system response. A novel transfer matrix technique, the Complex Transfer Matrix, is developed to distinguish forward and backward whirl components. The rotor's angular response is primarily employed in this work for crack detection and diagnosis. The overhung shaft induces an increased sensitivity to variations in crack depth and location. In addition, an available overhung rotordynamic experimental test rig allows for comparison of the current analytic results to previously obtained experimental results. Under the influence of gravity, the steady-state response of the cracked system includes a prominent 2X harmonic component, appearing at a frequency equal to twice the shaft speed. The magnitude of the 2X harmonic is strongly influenced by the shaft speed. A resonant response occurs when the shaft speed reaches half of a system natural frequency. This work demonstrates that the profile of the 2X harmonic versus shaft speed is a capable diagnostic tool. Identification of the 2X resonance frequency restricts the crack parameters to certain pairs of location and depth. Following this limiting process, the magnitude of the 2X harmonic is used to identify the crack's depth and location. Orbital shapes at the rotor are discussed, as are orbital modes of the shaft deflection. Quantitative results and qualitative observations are provided concerning the difficulty of crack detection and diagnosis.

Rotordynamics is an important area in mechanical engineering. Many machines contain rotating parts. It is well known that rotating components can develop large amplitude lateral vibrations near certain speeds called critical speeds. This large amplitude vibration is called rotor whirl. This thesis is about rotor whirl. Conventional treatments in rotordynamics use what are called gyroscopic terms and treat the rotor as a one-dimensional structure (Euler-Bernoulli or Timoshenko) with or without rigid masses added to them. Gyroscopic terms are macroscopic inertial terms that arise due to tilting of spinning cross-sections. This approach, while applicable to a large class of industrially important rotors, is not applicable to a general rotor geometry. In this thesis we develop a genuine continuum level three dimensional formulation for rotordynamics that can be used for many arbitrarily shaped rotors. The key insight that guides our formulation is that gyroscopic terms are macroscopic manifestations of the prestress induced due to spin of the rotor. Using this insight, we develop two modal projection techniques for calculating the critical speed of arbitrarily shaped rotors. These techniques along with our prestress based formulation are the primary contributions of the thesis. In addition, we also present two different nonlinear finite element based implementations of our formulation. One is a laborious load-stepping based calculation performed using ANSYS (a commercially available finite element package). The other uses our nonlinear finite element code. The latter two techniques are primarily developed to provide us with an accurate answer for comparison with the results obtained using the modal projection methods. Having developed our formulation and the subsequent modal projection approximations, we proceed to validation. First, we analytically study several examples whose solutions can be easily obtained using routine methods. Second, we consider the problem of a rotating cylinder under axial loads. We use a semi-analytical approach for this problem and offer some insights into the role played by the chosen kinematics for our virtual work calculations. The excellent match with known results obtained using Timoshenko theory validates the accuracy of our formulation. Third, we consider several rotors of arbitrary shape in numerical examples and show that our modal projection methods accurately estimate the critical speeds of these rotors. After validation, we consider efficiency. For axisymmetric rotor geometries, we implement our formulation using harmonic elements. This reduces the dimension of our problem from three to two and considerable savings in time are obtained. Finally, we apply our formulation to describe asynchronous whirl and internal viscous damping phenomena in rotors.

Orientador: Katia Lucchesi Cavalca / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecanica / Made available in DSpace on 2018-08-09T21:44:58Z (GMT). No. of bitstreams: 1 Okabe_EduardoPaiva_D.pdf: 3699501 bytes, checksum: 9a744709014d0fd925784d9408f38690 (MD5) Previous issue date: 2007 / Resumo: Neste trabalho são investigados os efeitos da estrutura de suporte e de mancais hidrodinâmicos no comportamento de uma máquina rotativa. A estrutura de suporte, também conhecida como fundação, foi analisada experimentalmente, e através da análise modal das funções resposta em freqüência (FRF) foram calculados seus parâmetros modais. Estes parâmetros foram refinados através de dois métodos de otimização, o primeiro foi baseado na busca áurea, e segundo no método de mínimos quadrados não-linear. O modelo modal da fundação foi integrado ao sistema rotor-mancais através do método das coordenadas mistas, para o cálculo da resposta ao desbalanceamento do sistema completo. A análise modal complexa do sistema rotor-mancais-fundação foi utilizada para determinar a função resposta em freqüência direcional (dFRF), na qual foram observados os efeitos dos parâmetros testados sobre os modos diretos e retrógrados do rotor. Duas abordagens diferentes foram adotadas para a modelagem dos mancais hidrodinâmicos: o método das diferenças finitas e uma solução analítica usando a teoria de mancal curto. O método das diferenças finitas foi empregado no cálculo dos coeficientes de amortecimento e rigidez de um mancal hidrodinâmico finito, e estes foram aplicados no cálculo da resposta ao desbalanceamento e dFRF do rotor. A solução analítica foi usada no cálculo da resposta harmônica do rotor para demonstrar o comportamento não-linear do mancal. Os resultados das simulações foram verificados experimentalmente em um banco de testes / Abstract: This work investigates the effects of the support structure and the hydrodynamic bearings on the dynamic behaviour of rotating machinery. The support structure, also known as foundation, was analysed experimentally and its modal parameters determined through the modal analysis of its frequency response functions (FRF). These parameters were refined through two optimization methods, the first one based on the Golden Search, and the other one on the Nonlinear Least Squares method. The modal model of the foundation was integrated to the rotorbearings system through the Mixed Coordinates method for the calculation of the unbalance response of the complete system. The complex modal analysis of the rotor-bearings-foundation system was applied to calculate the directional frequency response function (dFRF), and determine the effects of the tested parameters on the forward and backward modes. Two different aproaches were adopted to model hydrodynamic bearings: the finite difference method and an analytical solution using the short bearing theory. The finite difference method was employed to calculate the stiffness and damping coefficients of a finite journal bearing, and they were applied in the calculation of unbalance response and dFRF of the rotor. The analytical solution was used to calculate the harmonic response of the rotor and demontrate the bearing nonlinear behaviour. The results of the simulations were verified through experimental tests in laboratory / Doutorado / Mecanica dos Sólidos e Projeto Mecanico / Doutor em Engenharia Mecânica