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Thesis (M.S. in Aeronautical Engineering) Naval Postgraduate School, June 1997. / Thesis advisor, Raymond P. Shreeve. AD-A333 428. Includes bibliographical references (p. 49-50). Also available online.

Thesis (M.S.) -- University of Tennessee, Knoxville, 2006. / Title from title screen (viewed Nov. 13, 2007). Thesis advisor: Robert B. Richards. Vita. Includes bibliographical references (p. 40).

Au cœur des moyens de transport, de transformation d'énergie, et de biens d'équipements, les machines tournantes peuvent avoir des comportements dynamiques complexes dus à de multiples sources de non linéarités liées aux paliers hydrodynamiques, à la présence de fissures, aux touches rotor-stator, ... Des phénomènes comme les décalages fréquentiels et donc de vitesses critiques, les cycles d'hystérésis avec sauts d'amplitudes, le changement brutal du contenu fréquentiel des réponses, sont des expressions de ces comportements. Résoudre les équations du mouvement induites par des modélisations avec des éléments finis de type poutre ou volumique, pour calculer les réponses à des sollicitations diverses (comme le balourd ou le poids propre), est réalisable avec des méthodes d'intégration pas à pas dans le temps mais au prix de temps de calcul prohibitifs. Cela devient particulièrement préjudiciable au stade du pré-dimensionnement où il est nécessaire de réaliser rapidement des études paramétriques. Aussi une alternative intéressante est de mettre en {\oe}uvre une méthode numérique, à la fois générale et efficace pour analyser la réponse non linéaire des rotors en régime stationnaire. La démarche proposée combine, dans un premier temps, la méthode de la balance harmonique (HBM) et la technique de bascule Temps-Fréquence (AFT) afin d'obtenir rapidement dans le domaine fréquentiel les réponses périodiques des rotors à grand nombre de degrés de liberté apportés par les éléments finis volumiques. Puis, l'association à la méthode de continuation par pseudo-longueur d'arc aboutit à établir continûment l'ensemble des solutions d'équilibre dynamique sur la plage de vitesse de rotation. Enfin la stabilité dynamique locale de la solution périodique est analysée grâce à des indicateurs de bifurcation basés sur l'évolution des exposants de Floquet. Ainsi sont détectées les bifurcations de branches de solutions périodiques de type point limite, point de branchement et notamment Neimark-Sacker. Leur localisation est déterminée précisément en résolvant un système augmenté constitué de l'équation du mouvement et d'une équation supplémentaire caractérisant le type de bifurcation considéré. En déclarant un paramètre du système (coefficient de frottement, jeu rotor/stator, amplitude de l'excitation,...) comme nouvelle variable, l'utilisation de la technique de continuation conjointement avec le système augmenté détermine directement le cheminement des bifurcations en fonction de ce paramètre sur la nappe des réponses non linéaires. Les suivis de bifurcations délimitent les zones de fonctionnement spécifiques, extraient efficacement l'essentiel du comportement dynamique et offrent ainsi une nouvelle approche pour dimensionner de façon efficace les systèmes notamment en rotation. Nombre des développements réalisés sont implantés dans le code de calcul Cast3M. / Generally speaking, the rotating systems utilized in the energy production have a small rotor-stator gap, are able to run during long periods, and are mounted on hydrodynamic bearings. Rotor-stator interactions in case of blade loss, crack propagation due to fatigue, and a variable stiffness due to the nonlinear restoring forces of the bearings can make the rotordynamics nonlinear and the responses complicated: significant amplitude and frequency shifts are introduced, sub- and super-harmonics appear, and hysteresis occurs. It is of great importance to understand, predict and control this complicated dynamics. Due to the large number of DOFs and the broad range of study frequency, the computation time for solving the equations of motion by a temporal integration method can be quite prohibitive. It becomes particularly disadvantageous at the design stage where a parametrical study need to be quickly performed. An alternative numerical method, which is general and effective at the same time, is proposed in order to analyse the nonlinear response of the rotors at steady state. Firstly, the periodic responses of nonlinear rotors are calculated in the frequency domain by combining harmonic balance method (HBM) and alternating frequency-time (AFT). With the help of continuation method, all dynamic equilibrium solutions of nonlinear systems are determined for the range of study frequency. Then, Floquet exponents which are the eigenvalues of Jacobian are sought for stability analysis of periodic solutions. Then the local stability of the periodic solution is analysed through the bifurcation indicators which are based on the evolution of Floquet exponents. The bifurcations of periodic solution branch, such as limit point, branch point, and Neimark-Sacker bifurcation, are thus detected. By declaring a system parameter (friction coefficient, rotor / stator gap, excitation amplitude, ...) as a new variable, applying once again the continuation method to the augmented system determines directly the bifurcation's evolution as a function of this parameter. Thus, parametric analysis of the nonlinear dynamic behaviour is achieved, the stability boundary or the regime change boundary is directly determined. Numerous developments are implemented in the calculation code Cast3M.

The presented diploma thesis deals with simulation of Laval rotor supported by nonlinear bearings. The first part of thesis deals with research, which is focused on description of Laval rotor and motion equations for case of rigid and flexible rotor, also on description and modeling of hydrodynamic and magnetic bearing, which is considered in thesis. The second part of thesis deals with simulation of rotor for different approaches to modeling hydrodynamic and magnetic bearings. Using simulations performer in time domain, the dynamic behavior of Laval rotor is evaluated and compared. Simulations are performer in MATLAB.

[pt] Este trabalho analisa a influência dos mancais hidrodinâmicos no comportamento rotodinâmico das turbomáquinas, no que diz respeito na resposta ao desbalanceamento, modos de vibrar e, principalmente, a instabilidade, que tende a manifestar-se em rotações elevadas ou baixas cargas. As propriedades de rigidez e amortecimento do mancal são determinadas a partir da solução analítica da Equação de Reynolds, usando a aproximação do mancal curto. Um procedimento é apresentado para modelagem dinâmica do sistema rotor-mancal. O modelo de elementos finitos inclui a influência da ação giroscópica. A análise rotodinâmica completa de um rotor concebido e projetado para apresentar o fenômeno da instabilidade é feita com auxílio do programa ROMAC da Universiry of Virginia. O programa calcula as propriedades do mancal a partir da solução numérica completa da Equação de Reynolds e o cálculo das velocidades críticas, dos modos e da análise de estabilidade é feito pelo Método dos Elementos Finitos. Finalmente, documenta-se o projeto do protótipo, o estudo realizado e os ensaios desenvolvidos. A partir das medições realizadas, valida-se a solução numérica. / [en] This work analyses the effect of fluid-film bearings on the dynam- ics of turbomachinery with respect to unbalance response, vibration mode shapes and, specially, instability that tends to occur, mainly, at high speeds or light loads. The bearing stffiness and damping bearing properties are calculated using the analytical solution of the Reynolds Equation, based in a short bearing approach. Following, a procedure is presented for the dynamic modelling of rotor-bearing systems based in the Finite Element Method, including the gyroscopic effect. The complete rotordynamic analysis of a rotor designed to undergo instability problem is performed by software ROMAC from University of Virginia. The software predicts the bearing properties by complete numerical solution of Reynolds Equation and critical speeds, mode shapes and stability analysis is performed using the Finite Element Method.Finally, it is presented the design of the rotor kit , accomplished studies and performed tests. The numerical solution is validated by measurements that were made.

A Escola Politécnica da Universidade de São Paulo (EPUSP) e o Instituto Dante Pazzanese de Cardiologia (IDPC) estão realizando um projeto conjunto visando o desenvolvimento de um implante Dispositivo de Assistência Ventricular (DAV). Esta dissertação é parte do desenvolvimento de um VAD implantável em que o rotor da bomba é suspenso por uma suspensão magnética com um grau de liberdade (1-DOF). A suspensão magnética aqui utilizada apresenta o controle ativo somente na direção axial do rotor. Este mancal magnético foi apresentado por Silva e Horikawa (2000) no qual o controle ativo é executado apenas na direção axial do rotor. Neste trabalho o mancal magnético será referenciado como MMA-EPUSP. O motor de corrente contínua sem escovas (BLDC) foi selecionado pelo mesmo motivo que o mancal magnético: o motor não pode ter nenhum contato com o rotor, minimizando os problemas de danos aos componentes do sangue. Entretanto, o acionamento do motor através de forças magnéticas pode interferir na suspensão magnética. Como a estabilidade da suspensão magnética é garantida pela rigidez axial, é razoável presumir que a interação magnética entre o mancal magnético e o motor elétrico pode interferir na suspensão magnética. Este estudo analisa experimentalmente o motor BLDC com rotor apoiado pelo MMA-EPUSP, para identificar o comportamento desse conjunto utilizando duas configurações distintas de motor com fluxo magnético: radial e axial. A análise inclui: (i) projeto, construção e teste de um motor BLDC axial e um radial; (ii) projeto, construção e teste do MMA- EPUSP e do rotor para ser acionado pelos motores BLDC; (iii) estimativa do comportamento dos motores BLDC utilizando análise MEF; e (iv) execução dos testes experimentais para identificar como cada opção de montagem do motor interage com o MMA-EPUSP. A análise MEF corrobora com a recomendação do motor BLDC de fluxo magnético radial como a melhor opção de motorização para o DAV com o MMA-EPUSP, já que este motor não induz nenhuma força magnética axial que precise ser compensada pela suspensão magnética. Entretanto, o projeto do DAV pode ser mais complexo devido à interferência mecânica entre a saída do sangue do DAV e o estator do motor. Já a força magnética axial induzida pelo motor BLDC de fluxo axial é suficientemente forte para desestabilizar o MMA-EPUSP, demandando uma alta corrente do controle de posição do rotor. Os dados indicam que o projeto do controlador atual não conseguirá garantir a estabilidade do mancal magnético com este tipo de motor a altas velocidades. Neste caso, estudos adicionais são recomendados para avaliar a estabilidade dinâmica do rotor com MMA-EPUSP com o rotor imerso em sangue, já que um ambiente líquido poderá absorver a energia das oscilações e minimizar as restrições associadas à instabilidade da suspensão magnética a velocidades inferiores a 5000 RPM. / The Escola Politécnica of São Paulo University (EPUSP) and the Institute Dante Pazzanese of Cardiology (IDPC) is conducting a joint project aiming the development of an implantable Ventricular Assist Device (VAD). This study is part of the development of an implantasuporte@poli.usp.brble VAD in which the pump rotor is suspended by single degree of freedom (1-DOF) magnetic suspension. The magnetic suspension here utilized presents active control only in the rotor axial direction. This magnetic bearing had been presented by Silva and Horikawa (2000) in which the active control is executed only in the axial direction of a rotor. In this work this Axial Magnetic Bearing is referred as AMB-EPUSP. The brushless direct current (BLDC) motor has been elected due to the same reason why a magnetic bearing: the motor should not contact the rotor, minimizing problems of damage to the blood components. However, the driving of the rotor by magnetic forces may interfere in the magnetic suspension. As the stability of this magnetic suspension has been established by the axial stiffness, it is reasonable to expect that the magnetic interaction between the magnetic bearing and the used electric motor may interfere in the magnetic suspension. This study analyzes experimentally the BLDC motor, which rotor is supported by the AMB- EPUSP, to identify the behavior of this set using two distinct magnetic flux motor configurations: axial and radial. The analysis includes: (i) design, construction and testing of the axial and the radial BLDC motors; (ii) design, construction and testing of AMB-EPUSP and the rotor to be driven be both BLDC motors; (iii) estimate the BLDC motors behavior using FEM analysis; and (iv) experimental tests execution to identify how each motor assemble option interact with the AMB- EPUSP. The FEM analysis corroborates on the recommendation of the radial magnetic flux BLDC motor option as the best choice to drive the VAD with AMB- EPUSP, since this motor does not generate any axial magnetic force to be compensated by the magnetic suspension. However, a more complex VAD design may be required due to the mechanical interference between the VAD outlet and the motors winding. The axial force generated by the axial magnetic flux BLDC motor option, induces a strong instability on the AMB-EPUSP, demanding high current to control the rotor position. The data indicates the current controller design will not be able to guarantee the magnetic bearing stability with this motor on higher velocities. On any case, additional study is recommend to evaluate the rotordynamic rotor dynamic instability of the AMB- EPUSP with the rotor surrounded by blood, since the liquid environment should absorb the oscillation energy and minimize the restriction due to the magnetic suspension instability on speed below 5000 RPM.

The world we are living in today is pushing the technology harder and harder. The products need to get better and today they also need to be friendlier to the environment. To get better products we need better analysis tools to optimize them and to get closer to the limit what the material can withstand. Siemens industrial Turbomachinery AB, at which thesis work is made, is constructing gas and steam turbines. Gas and steam turbines are important in producing power and electricity. Electricity is our most important invention we have and most of the people are just taking electricity for granted. One way to produce electricity is to use a gas turbine which is connected to a generator and by combing the turbine with a steam turbine the efficiency can be up to 60 %. That is not good enough and everybody want to get better efficiency for the turbines, meaning less fuel consumption and less impact on the environment. The purpose of this thesis work is to analyze a tool for rotor dynamics calculations. Rotor dynamics is important in designing a gas turbine rotor because bad dynamics can easily lead to disaster. Ansys Classic version 11 is the analyze program that is going to be evaluated for the rotor dynamic applications. Nowadays rotor dynamics is done with beam elements i.e. 1D models, but in this thesis work the beam elementsare going to be changed to solid elements. With solid elements a 3D model can be built and thanks to that more complex calculations and simulations can be made. For example, with a 3D model 3D effects can be shown and e.g. simulations with blade loss can be done. 3D effects are not any problem today but in the future the gas turbines have to get better and maybe also the rotational speed will increase. Ansys isn’t working perfectly yet, there are some problems. However Ansys have a good potential to be an additional tool for calculations of rotor dynamics, because more complex calculations and simulations can be done. More knowledge and time needs to form the rules to modeled a rotor and developing the analysis methods. Today the calculated lateral critical speeds are lower than the ones obtained from the in-house program Ardas version 2.9.3 which is used in Siemens Industrial Turbomachinery AB today. The difference between the programs are not so big for the four first lateral modes, only 3-8 %, but the next three lateral modes have a difference of 10-20 %. The torsion frequencies from Ansys are the same as the ones from Ardas, when the Solid186 elements are used to model the blades.

This dissertation describes the design, analysis and testing of an unconventional rotor featuring extremely flexible, retractable blades. These rotor blades are composed of a flexible matrix composite material; they are so flexible that they can be rolled up and stowed in the rotor hub. The motivation for this study is to equip the next generation of unmanned rotary-wing vehicles with morphing rotors that can change their diameter in flight, based on mission requirements. Due to their negligible structural stiffness, the static and dynamic behavior of these blades is dominated by centrifugal effects. Passive stabilization of the flexible blades is achieved by centrifugal stiffening in conjunction with an appropriate spanwise and chordwise mass distribution. In particular, such blades are susceptible to large deformations. For example, a combination of the trapeze effect and the tennis racquet effect induces a large negative twist that results in decreased efficiency. Additionally, the rotor blades are prone to aeroelastic instabilities due to their low rotating torsional frequency, and it is seen that without careful design the blades experience coupled pitch-flap limit cycle oscillations. The primary focus of this research is to develop analytical and experimental tools to predict and measure the deformations of an extremely flexible rotor blade with non-uniform mass distribution. A novel aeroelastic analysis tailored towards unconventional blades with negligible structural stiffness is developed. In contrast to conventional analyses developed for rigid rotor blades, the present analysis assumes very large elastic twist. The nonlinear coupled equations of motion for the flap bending, lead-lag bending and torsion of an elastic rotating blade are derived using Hamilton's principle. The virtual work associated with unsteady aerodynamic forces in hover is included in the analysis. An ordering scheme consistent with the relevant physical quantities is defined and terms up to second order are retained in the Hamiltonian. The equations of motion are solved using a nonlinear finite element analysis. The steady-state deformation of the rotor blade is obtained from the time invariant part of the solution. The rotating flap, lag and torsional frequencies are found by solving the eigenvalue problem associated with the homogeneous system of equations. Finally, stability boundaries are computed for various operating conditions and the influence of parameters such as rotational velocity and collective pitch angle is discussed. The analytical predictions are validated by experimental measurements of the blade deformation in hover. These measurements are obtained by a novel, non-contact optical technique called three-dimensional Digital Image Correlation (3D DIC). The use of this technique is demonstrated for the first time to obtain full-field deformation measurements of a rotating blade. In addition, stability boundaries are extracted from experimental observations and correlated with predictions. / text