Orientador: Edson Antonio Capello Sousa / Banca: Kátia Luchese Cavalca Dedini / Banca: Jose Manoel Balthazar / Resumo: Neste trabalho, analisaram-se as freqüencias natuais (axiais, torsionais e de flexão) e as respostas em frequencia de um rotor vertical com um disco rígido na extremidade através da análise modal clássica e complexa. A equação que governa o movimento foi obtida através da formulação Lagrangeana. O modelo considerou os efeitos à flexão, torção e deformação axial do eixo, além dos efeitos giroscópicos e gravitacionais. o método dos elementos finitos foi utilizado para discretização da estrutura em elementos cilíndricos vazados com 12 graus de liberdade. As matrizes de massa, rigidez e giroscópia foram explicitadas de forma consistente. A análise modal tradicional, normalmente aplicada a estrutura estacionárias, não considera uma importante característica das máquinas rotativas que são os modos de precessão direta e retrógrada. Inicialmente, através da análise modal clássica, foram obtidas as frequencias naturais axionais e torsionais no eixo estacionário, já que estas não sofrem influência dos efeitos giroscópicos. Posteriormente a investigação foi executada através da análise modal complexa. Este tipo de ferramenta, que se baseia na utilização de coordenadas direcionais para descrever o comportamento dinâmico do eixo rotativo, permite a decomposição dos modos do sistema em dois submodos, sendo um direto e outro retrógrado. Dessa forma, consegue-se visualizar de maneira clara a órbita e a direção do movimento precessional em torno da linha não deformada do eixo rotativo. Um programa de elementos finitos foi desenvolvido utilizando o software MATLAB e simulações numéricas foram efetuadas de forma a validar o modelo construído. Foram obtidas as frequencias naturais e a resposta forçada em frequencia direcional (dFRF), com o uso da análise modal complexa, para um rotor vertical simples e também para uma coluna de perfuração típica utilizada na construção de poços de petróleo / Abstract: In this study, natural frequencies were analyzed (axial, torsional and flexural) and frequency response of a vertical rotor with a hard disk at the edge through the classical modal and complex analysis. The equation that rules the movement was obtained through the Lagragian formulation. The model considered the effects of bending, torsion and axial deformation of the shaft, besides the gravitational and gyroscopic effects. The finite element method was used to discretize the structure into hollow cylindrical elements with 12 degrees of freedom. Mass, stiffness and gyroscopic matrices were explained consistently. The classical modal analysis, usually applied to stationary structures, does not consider an important characteristic of rotating machinery which are the method of forward and backward whirl. Initially, through the traditional modal analysis, axial and torsional natural frequencies were obtained in a static shaft, since they do not suffer the influence of gyroscopic effects. Later research was performed by complex modal analysis. This type of tool, based on the use of complex coordinates to describe the dynamic behavior of rotating shaft, allows the decomposition of the system in two submodes, backward and forward. Thus, it is possible to clearly visualize that the orbit and direction of the precessional motion around the line of the precessional motion around the line of the rotating shaft is not deformed. A finite element program was developed using MATLAB, and numerical simulations were performed to validate this model. Natural frequencies and directional frequency forced response (dFRF) were obtained using the complex modal analysis for a simple vertical rotor and also for a typical drill string used in the construction of oil wells / Mestre

Helicopter flight dynamic, rotor aerodynamic and dynamic analyses activities have been a great dispute since the first helicopters, at both design and test stages. Predicting rotor aerodynamic and dynamic characteristics, helicopter dynamic behavior and trimmed flight conditions is a huge challenge to engineers as it involves the tradeoff between accuracy, fidelity, complexity and computational cost. Flight dynamic activities such as / predicting trim conditions, helicopter dynamic behavior and simulation of a flight condition or maneuver mostly require analysis tools with low computational cost and complexity. However this decreases accuracy and fidelity of the model. On the other hand, analyses at design stages, such as / blade geometric and structural design mostly requires accurate and higher fidelity aerodynamic load predictions over the rotor disk. Contrarily this brings high computational cost and complexity. Therefore separate analysis tools for each objective or one complete tool that can be used for all purposes are essential. Throughout this study a helicopter mathematical including trim model with a selective and modular structure is developed as a generic analysis tool. The selective structure enables the mathematical model to be used in both flight dynamic and comprehensive analysis while the modular structure plays a role as an infrastructure for further developments. The mathematical model developed is validated with flight test data of several helicopters. Besides, commercial helicopter comprehensive analysis tools are used to validate the mathematical model analyses. Results showed good agreement with the compared data.

In this work, the time varying stresses in a Howden axial flow fan are obtained by finite element analyses. Dynamic substructuring is used to obtain accurate values of the stresses in the threads of the blade shaft, the component which connects the blade with the hub. Three different global models are used to compare the influence of neglecting the fan shaft and the stiffness influence of the centrifugal force. The relative displacements, which are obtained from the global models, have been used as boundary condition in the detailed models. The detailed models are used to obtain the Von Mises stresses in the root of the threads of the blade shaft. Finally the results of the three global models are compared with experimental measured data provided by Howden. The experimental data results in the highest Von Mises stresses. The model with the fan shaft and the stiffness influence of the centrifugal force gives values for the Von Mises stresses which are approximately twenty percent lower. The model without the fan shaft results in the lowest stresses which are approximately forty percent lower than the stresses obtained using the measured data.

Made available in DSpace on 2014-06-11T19:27:14Z (GMT). No. of bitstreams: 0 Previous issue date: 2004-09-30Bitstream added on 2014-06-13T18:31:09Z : No. of bitstreams: 1 caldiron_l_me_ilha_prot.pdf: 995296 bytes, checksum: dc02ada2316a49ff3c8fd3dca71338ba (MD5) / Neste trabalho são otimizadas rotinas computacionais de um método de estimação de rigidez de mancais de máquinas através de um processo de ajuste de modelo, utilizando a análise de sensibilidade. Este método consiste em utilizar a análise de sensibilidade dos autovalores com relação à variação da rigidez dos mancais de um rotor. A eficácia e a robustez do método são analisadas através de simulações teóricas, bem como através de dados experimentais obtidos de um rotor de rotação variável e rigidezes dos mancais ajustáveis. O modelo matemático de ajuste do sistema é desenvolvido pelo método dos elementos finitos e o método de ajuste converge empregando-se um processo iterativo. Este método de ajuste baseia-se na minimização da diferença entre autovalores experimentais e autovalores obtidos com o modelo matemático de ajuste a partir de valores de rigidez dos mancais previamente adotados. A análise é feita com o rotor em diversas velocidades de rotação para verificar a influência do efeito giroscópio, e em diversas condições de valores da rigidez dos mancais para analisar o método quando aplicado em rotores flexíveis e em rotores rígidos. O desempenho do método é analisado com resultados teóricos e experimentais. / In this work, computational routines of estimation method of stiffness bearing of machine via a model updating process are optimized, using the sensitivity analysis. This method consists of using the eigenvalue sensitivity analysis, relating to the stiffness bearing variation of a rotor. The efficacy and the robustness of the method are analyzed through the theoretical simulations, as well as, based on the experimental data obtained of a test rotor with variable rotating speeds and adjustable bearing stiffness values. The mathematical model system is developed by the finite element method and the method of adjustment should converge employing an iterative process. The method of adjustment is based on the minimization of the difference between experimental eigenvalues and eigenvalues obtained via mathematical model from previously adopted stiffness bearing values. The analysis is made by using the rotor in different rotating speeds in order to check the influence of the gyroscopic effect, and in several conditions of the stiffness bearing values to analyze the method when applied on flexible and rigid rotors. The performance of the method is analyzed through theoretical and experimental results.

Submitted by Ramon Moreira Peres null (ramon.mpe@gmail.com) on 2016-11-16T12:51:39Z No. of bitstreams: 1 Dissertação de Mestrado - Ramon Moreira Peres.pdf: 2352271 bytes, checksum: f6a0129949b15510489022df29120c6d (MD5) / Approved for entry into archive by Felipe Augusto Arakaki (arakaki@reitoria.unesp.br) on 2016-11-23T11:44:03Z (GMT) No. of bitstreams: 1 peres_rm_me_guara.pdf: 2352271 bytes, checksum: f6a0129949b15510489022df29120c6d (MD5) / Made available in DSpace on 2016-11-23T11:44:03Z (GMT). No. of bitstreams: 1 peres_rm_me_guara.pdf: 2352271 bytes, checksum: f6a0129949b15510489022df29120c6d (MD5) Previous issue date: 2016-09-16 / Outra / O presente trabalho estuda a dinâmica de rotores e em particular a de um rotor modelo de Jeffcott. Para tanto, foi utilizada uma bancada experimental que consiste de um rotor montado sobre um eixo apoiado por mancais de rolamento fixo a uma base metálica, sendo o acionamento da bancada experimental feito por meio de um motor elétrico trifásico de 2 cv com uma rotação máxima de 3.475 rpm, onde foram realizados testes para determinação da primeira frequência natural estacionária (teste de impacto), tesde de partida e de parada. Dois eixos de materiais diferentes foram utilizados, sendo um de aço SAE 1020 e outro de material compósito. Foram determinadas através de análise estrutural pelo método dos elementos finitos as rigidezes dos mancais, com esses valores obteve-se analiticamente a primeira frequência natural do sistema. Ainda utilizando o método dos elementos finitos foram obtidas as frequências naturais, os modos de vibrar e o diagrama de Campbell através de análise modal. Os resultados experimentais obtidos foram discutidos e comparados com os resultados analíticos e com os resultados obtidos pela aplicação do método dos elementos finitos. Percebe-se que com essa comparação a aplicação do software na fase inicial de projeto mostra-se de extrema importância, visto que as frequências naturais podem ser previstas já na etapa inicial. / This work studied the dynamics of rotors and in particular a Jeffcott rotor. An experimental bench consisting of a rotor mounted on a shaft supported by a fixed bearing housings to a metal base. The drive of the testing bench is made a three-phase electric motor of 2cv power, having a maximum rotation of 3.475rpm, which were performed the tests to identify the first natural frequency (impact test), run up and coast down using two different material of shaft, one made by steel SAE 1020 and a composite shaft. It was determined through structural analyses by the finite element method and the rigidities of the bearings was obtained. With this values the first natural frequency for the system was obtained analytically. Still using finite element method was obtainedthe natural frequencies. The vibration modes and the Campbell diagram, using modal analysis. The experimental results were discussed and compared the analytical results and the results by applyingthe finite element method, with this comparion the software application in the initial phase project proved extremely important given that the natural frequencies can be provided in the initial stage. / PRH-ANP/MCTI: 48610.009725/2013

Com o intuito de otimizar o projeto de unidades hidrogeradoras e, por conseguinte, aumentar a sua disponibilidade, uma previsão mais precisa do seu comportamento dinâmico é de fundamental importância. Assim, o presente trabalho se propôs a modelar uma unidade hidrogeradora de forma mais completa, considerando os efeitos do empuxo magnético, mancais, perturbações hidráulicas, desbalanceamento e selos labirintos de turbina Francis. A partir do modelo construído, foram realizadas análises modais, temporais e espectrais. Os resultados numéricos são comparados com os dados experimentais de uma unidade hidrogeradora de grande porte. Tanto sinais de tendência temporal, como órbitas, e espectros de frequência dos fenômenos envolvidos são analisados e comparados. Dessa forma, pretende-se obter o modelo menos complexo possível, mas que seja capaz de representar de forma aceitável a dinâmica da unidade hidrogeradora sujeita a diferentes condições de operação. A maior dificuldade encontrada foi na representação das excitações externas ao sistema, principalmente quando a máquina está operando em regime parcial. Constatou-se uma importante influência do selo labirinto na simulação do comportamento dinâmica da turbina Francis operando em carga parcial. Ao final, os aspectos do modelo que podem ser aprimorados são discutidos. / In order to optimize the design of hydro-generating units and therefore increase their availability, a more accurate forecast of their dynamic behavior is of fundamental importance. Thus, the present work has proposed to model a more complete hydrogenerator unit, considering the effects of magnetic pull, guide bearings, hydraulic perturbations, unbalance and Francis turbine labyrinths. From the this model, modal, temporal and spectral analyzes were performed. The numerical results are compared with experimental data of a large hydrogenerator unit. Temporal trend signals, orbits and frequency spectrum of the phenomena involved are analyzed and compared. In this way, it is intended to obtain the less complex model possible, but that is able to represent in an acceptable way the dynamics of the hydrogenerator unit under different operation conditions. The greatest difficulty found was in the representation of external excitations to the system, mainly under partial load. It was observed an important influence of the labyrinth seal in the simulation of the dynamic behavior of the Francis turbine operating in partial load. Finally, aspects of the model that can to be improved are discussed.

Este trabalho propõe uma solução inovadora para o amortecimento de vibrações laterais indesejadas em máquinas rotativas através da conversão de energia cinética em energia elétrica por meio de um dispositivo eletromagnético passivo de colheita de energia, com o mínimo de geração de torque reativo. Para atingir estes objetivos, foram descritas e avaliadas as três principais técnicas de coleta de energia vibratória (piezelétrica, eletrostática e eletromagnética) juntamente com análises qualitativas das equações de eletromagnetismo e pelo Método dos Elementos Finitos. Um protótipo que consiste em um conjunto de ímãs permanentes anexos ao rotor e um conjunto de bobinas no estator demonstrou experimentalmente uma diminuição da amplitude de vibração em até 6,8%, na região de velocidades críticas, com geração não significativa de torque. Estes resultados foram obtidos experimentalmente mantendo-se os enrolamentos independentes entre si. / In this work, it is proposed a novel damping solution for undesired lateral vibrations in rotating machines by converting kinetic energy into electrical energy through a passive electromagnetic energy harvesting device, with minimal generation of reactive torque. In order to achieve these goals, it is described and evaluated the three main vibration energy harvesting techniques (piezoelectric, electrostatic and electromagnetic) along with qualitative analysis of electromagnetic equations and nite element analysis (FEA). Furthermore, a prototype consisting of a set of permanent magnets attached to the rotor and a set of coils attached to the stator showed a decrease in the amplitude of vibration up to 6,8% in the range of critical velocities, with non-signicant torque generation. Such results were obtained experimentally with independent-circuit coils.

The dynamic response of turbine flowmeters in low pressure gas flows (i. e. where the rotational inertia of the fluid is negligible) is well understood and methods for correcting meter signals for a lack of response are available. For liquid flows there has been a limited amount of experimental work on the response of meters to step changes but no reports have been found of the response of meters to sinusoidally pulsating flows. "Small" turbine meters are expected to behave differently from "large" meters for a number of reasons: a smaller meter would generally have: (1) a larger percentage of tip clearance leakage flow; (2) less fluid momentum between the meter blading; and, (3) less fluid friction forces on the effective surface area. In this research, arbitrarily, meters up to size 25 mm were defined as small; and within this study, meters of size 6 mm to 25 mm were investigated. The aim of the research was to investigate and to understand the response of small turbine meters to pulsating liquid flows and to provide methods for correction. Three approaches were used: (1) application of an existing theoretical model of turbine meter behaviour; (2) an experimental investigation of meter performance in pulsating flows; and (3) simulation of flow behaviour through one selected meter using CFD and extending the simulation to predict the rotor dynamics and, hence, the response of this meter to specified cases of pulsating flow. A theoretical model developed by Dijstelbergen (1966) assumes frictionless behaviour and that flow is perfectly guided by meter blading through the rotor and that fluid within the rotor envelope rotates as a "solid body". Results from this theoretical model applied for pulsating flows showed that there was likely to be positive error in predicted mean flow rate (over-registration) and negative error for predicted values of the amplitude of the pulsations (amplitude attenuation). This behaviour is due to the fundamental asymmetry between flows with increasing and decreasing angle of attack relative to the meter blades, throughout a pulsation cycle. This qualitative behaviour was confirmed by experimental work with meters up to size 25mm working with pulsation frequencies up to 300 Hz. For low frequency pulsations (below 10 Hz), the over-registration errors were within the limits of specified meter accuracy. At higher frequencies and larger pulsation amplitudes, the largest over-registration observed was 5.5 % and amplitude attenuation could be as large as 90 %. The dependence of these errors on both the flow pulsation amplitude and frequency were investigated. The theoretical model was also used as a basis for generating correction procedures, to be applied to both the mean flow and the pulsation amplitude measurements. The results from the CFD simulation showed qualitative good agreement with the experimental data. The same kind of meter error trends were observed and it was shown to provide a better correlation with the experimental trends than the theoretical model derived from Dijstelbergen. From the CFD simulation, the causes of over-registration and amplitude attenuation in turbine flowmetering were understood through the investigation of rotor dynamics coupled with fluid behaviour around meter blading within the pulsation cycle. The CFD results were used to evaluate fluid angular momentum flux and to review the validity of the assumption that fluid within the rotor "envelope" rotated as a solid body. For the case investigated, whilst the assumption that flow is perfectly guided is not inappropriate, the volume of fluid assumed to rotate as a "solid body" was found to be significantly less than the rotor envelope volume.

The concept of added hydrodynamic properties such as added mass is of importance in modern hydropower development, mainly for rotor dynamic calculations. Added mass could result in reduced natural frequencies and altered mode compared to existing simulation models. It is of importance to quantify added mass but also added damping to make the simulation models more accurate. Experiments are conducted on a model Kaplan turbine, D = 0,5 m, and a steel cube, S = 0,2 m, for linear vibrations in still water confined in a cylindrical tank. The experiments are conducted in air and water for evaluation of added forces. The vibrations are generated with an electrodynamic vibration exciter with a frequency range of approximately 1-10 Hz with amplitudes 0,5-3 mm. The experiments were repeated to check test rig reliability. Each individual working point [frequency, amplitude] were in total tested 40 times in 15 s intervals. The added mass was found to be function of acceleration for the model Kaplan with an increase in added mass from 10 % at 4 m/s2 to 35 % at 0,5 m/s2. The damping forces was at best measured at ±30 %, making added damping calculations unreliable. The cube experiments resulted in small differences between water and air. Cube results must be interpreted with caution due to test rig uncertainties.

The current development in the field of electric machinery is focusing on high-speed electric machines. This opens also other fields related to high-speed machines. One of them are magnetic bearing systems. Tradition approach of using ball bearing brings a few problems in design dealing with friction at high speeds. Together with magnetic bearings, development is their control. Faster chips opened a new way of thinking of control and helped to evolve robust control loops. The biggest advantage of magnetic bearing is non-friction run and almost no maintenance. Compare to traditional ball bearing, a magnetic bearing system needs more space and in some applications could happen that the shaft will be twice as long. This problem can be solved designing complex system with motor and integrated magnetic bearing what leads to downsizing. In this master thesis, the design of magnetic bearing for 12kw, 45000rpm is discussed. It focuses on practical design and correlations between parameter selection. The analytical approach is used to sketch the design and optimization is done afterwards. Problem with an analytical design is that it doesn't cover all parasitic phenomenae and thus numerical modelling snd optimization are demanded. Also, the critical speed analyze is included in this thesis. The results of the work will be used for manufacturing prototype as an extension to the existing high-speed machine.