Orientador: Vicente Lopes Junior / Coorientador: Luiz de Paula do Nascimento / Banca: Gilberto Pechoto de Melo / Banca: kátia Luchese Cavalca Dedini / Resumo: Este trabalho trata do controle de vibrações em rotores utilizando mancais magnéticos ativos. Foram apresentadas simulações numéricas para o posicionamento ótimo de um atuador magnético utilizado para atenuar vibrações em rotor apoiado por mancais convencionais. O posicionamento ótimo do atuador foi implementado utilizando como função objetivo as normas H2 e H∞. Para modelar o rotor foi utilizado o método de elementos finitos (MEF) e a técnica de redução pseudo-modal para diminuir o esforço computacional durante o controle. As simulações mostraram que um bom posicionamento do atuador aliado ao controle LQR proporcionam grandes reduções dos níveis de vibração no rotor, quando comparado aos níveis de vibração do rotor original. Para a bancada de testes foram realizadas simulações adicionais, tendo em vista que o rotor experimental utiliza dois mancais magnéticos para levitar e controlar as vibrações. Foram apresentados os resultados de simulações de dois controladores LQR projetados com os dados da bancada de testes utilizada nos experimentos. O primeiro controlador considera modelo de rotor flexível modelado pelo método de elementos finitos e reduzido com a técnica de redução pseudo-modal. O segundo controlador foi modelado considerando o rotor como sendo um corpo rígido. Os resultados experimentais foram confrontados com os resultados de simulação e com os resultados obtidos do controlador do fabricante que forneceu a bancada / Abstract: This paper deals with vibration control of rotors using active magnetic bearings. Numerical simulations were presented for the optimal positioning of a magnetic actuator used to attenuate vibrations in rotor supported by conventional bearings. The optimal positioning of the actuator was implemented using as objective function the norm H2 e H∞. To model the rotor was used finite element method (FEM) and the pseudo-modal reduction technique to reduce computational effort during the control. The simulations showed that a good positioning actuator combined to the control LQR provide great reductions in the levels of vibration in the rotor, compared the vibration of the original rotor. For the test rig were realized adittional simulations, in view of the rotor experimental uses two magnetic bearings for levitating and control the vibrations. Were present the results of two simulations designed LQR controllers with data from the test rig used in the experiments. The first controller model considers flexible rotor modeled by finite element method and reduced with the pseudo-modal reduction technique. The second controller is modeled considering the rotor as a rigid body. The experimental results were compared with simulation results and the results obtained from the controller manufacturer who supplied the test rig / Mestre

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In this research, a laboratory platform which has 2 degrees of freedom (DOF), the Twin Rotor MIMO System (TRMS), is investigated. Although, the TRMS does not fly, it has a striking similarity with a helicopter, such as system nonlinearities and cross-coupled modes. Therefore, the TRMS can be perceived as an unconventional and complex "air vehicle" that poses formidable challenges in modelling, control design and analysis and implementation. These issues are the subject of this work. The linear models for 1 and 2 DOFs are obtained via system identification techniques. Such a black-box modelling approach yields input-output models with neither a priori defined model structure nor specific parameter settings reflecting any physical attributes. Further, a nonlinear model using Radial Basis Function networks is obtained. Such a high fidelity nonlinear model is often required for nonlinear system simulation studies and is commonly employed in the aerospace industry. Modelling exercises were conducted that included rigid as well as flexible modes of the system. The approach presented here is shown to be suitable for modelling complex new generation air vehicles. Modelling of the TRMS revealed the presence of resonant system modes which are responsible for inducing unwanted vibrations. In this research, open-loop, closed-loop and combined open and closed-loop control strategies are investigated to address this problem. Initially, open-loop control techniques based on "input shaping control" are employed. Digital filters are then developed to shape the command signals such that the resonance modes are not overly excited. The effectiveness of this concept is then demonstrated on the TRMS rig for both 1 and 2 DOF motion, with a significant reduction in vibration. The linear model for the 1 DOF (SISO) TRMS was found to have the non-minimum phase characteristics and have 4 states with only pitch angle output. This behaviour imposes certain limitations on the type of control topologies one can ado·pt. The LQG approach, which has an elegant structure with an embedded Kalman filter to estimate the unmeasured states, is adopted in this study. The identified linear model is employed in the design of a feedback LQG compensator for the TRMS with 1 DOF. This is shown to have good tracking capability but requires. high control effort and has inadequate authority over residual vibration of the system. These problems are resolved by further augmenting the system with a command path prefilter. The combined feedforward and feedback compensator satisfies the performance objectives and obeys the constraint on the actuator. Finally, 1 DOF controller is implemented on the laboratory platform.

As a high speed rotating device, a modern turbocharger rotor is commonly supported by floating ring bearings (FRBs), owing to their cost effectiveness for mass production and good damping performance. Thanks to the rapid growth of the power of the modern computer, rotordynamic analysis of turbocharger rotor-bearing systems becomes feasible, and it is closely related to the healthy operation and noise generation of turbochargers. The work in this thesis is concerned with the nonlinear rotordynamic modelling, simulation and analysis in the rotor-FRB system of turbochargers. The conventional linear eigenvalue analysis is shown first in a gradually deepening manner to provide a deeper insight into the results from nonlinear simulations and reported experimental results. It is subsequently found the onset of first two nonlinear jumps can be effectively predicted by the linearized FRB model, although the rotordynamic characteristics at higher rotor speeds can hardly be linearly predicted. The desired oil-film forces for nonlinear simulations are calculated from a newly proposed analytical method, which is extended from the Capone's journal bearing model. Stationary simulations under the perfectly balanced condition show two major subsynchronous components throughout the considered speed range, while the inclusion of in-phase unbalance places a considerable effect on the rotor response at relatively low speed and delays the occurrence of oil-film instability. However, at higher rotor speeds, the lower subsynchronous component can still establish the dominance. The engine induced vibrations are also considered, and it is seen the rotor response over the lower end of the speed range will be considerably affected, whereas, at higher rotor speeds, the engine induced vibrations can be suppressed by the dominant lower subsynchronous vibrations. Through carrying out many run-up and run-down simulations, the FRB outer clearance is found to be a critical parameter of the rotordynamic performance of the investigated TC rotor-FRB system, since distinct frequency maps are obtained with varying FRB outer clearances. The nonlinear effects of unbalance are also investigated, and it is observed the rotor response can be considerably affected by the amount and distribution of the imposed unbalance.

This thesis is concerned with enhancing analysis tools for evaluating the non-linear dynamics of rotor bearing systems and in particular those where non-linearity is likely to result in aperiodic or chaotic behaviour, such as rolling element bearing systems. The tool to be enhanced was the transfer matrix approach which has been extensively used in the past for analysing linear rotor bearing systems. However, its use for evaluating non-linear behaviour has been virtually non-existent. Hence, the major aim of the thesis is to extend transfer matrix capabilities to handle non-linear systems. To this end a harmonic balance transfer matrix technique capable of analysing non-linear systems with multiple pedestal supported bearings was first developed. However, this approach is restricted to periodic response. To enable the analysis of non-linear systems with non-periodic response and provide a stability check for the harmonic balance technique, a transient transfer matrix has also been developed. The softwares for both of these newly developed transfer matrix techniques have been successfully verified for various non-linear rotor bearing systems using an established system matrix based transient rotordynamics software as the yardstick. These developments have been published in refereed journals. To investigate systems with rolling element bearings, appropriate bearing modelling which incorporates angular contact and rolling element inertia needed to be developed and incorporated into transient analysis softwares. Theoretical results from this were compared to data obtained from an experimental test rig which was designed to represent the salient features of an F/A-18 aircraft mounted accessory drive. The rig allowed for variation of bearing preload, unbalance loading and bearing support stiffness and could be run up to 17,000rpm. Full details of the design and commissioning are presented. Results showed better agreement than linear analyses but significant differences were encountered. Errors were largely due to estimated bearing parameters, in particular bearing damping, which was found to be a sensitive variable, so that agreement between theory and experiment was mainly qualitative. Other sources of error were those associated with experimental measurement and limitations of the bearing modelling. Further improvement of the bearing model is needed if better quantitative agreement is to be obtained between the predictions and experiment.

Thesis (M.S. in Aeronautical Engineering)--Naval Postgraduate School, September 1990. / Thesis Advisor(s): Shreeve, Raymond P. Second Reader: Hobson, Garth V. "September 1990." Description based on title screen as viewed on December 18, 2009. DTIC Descriptor(s): Rotors, Turbofan Engines, Waves, Gases, Pressure, Ratios, Computer Programs, Cycles. DTIC Identifier(s): Wave Rotors, Rotors, Waves, Theses. Author(s) subject terms: Turbofan Engines, Turbofan engines with a Wave Rotor. Includes bibliographical references (p. 95-96). Also available in print.

Thesis (M.S. in Aeronautical Engineering)--Naval Postgraduate School, December 2003. / Thesis advisor(s): E. Roberts Wood, Raymond Shreeve. Includes bibliographical references (p. 145-146). Also available online.

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