<p>  </p> <p>High cycle fatigue, regarding turbine engines, is one of the main causes of rotating component failure. Specifically, the blades of the wheels in the fan, compressor, and turbine sub-assemblies. Traditionally strain gauges are employed as a means of measuring blade vibration during component or full engine development testing. For rotating machinery, strain gauges require the use of a slip ring or a telemetry package. This becomes increasingly complicated as the number of strain gauges increase, thus the need for a more non-intrusive measurement capability for discernment of blade stress responses. Non-Intrusive Stress Measurement Systems (NSMS) allow engineers to detect high cycle fatigue (HCF) issues prior to component failure. It is important for the turbine engine industry to monitor for high cycle fatigue issues to maintain a fleet readiness. When unexpected HCF causes component or system failure the potential consequences are grounded fleets, cancelled flights, monetary loss, and loss of life. Once these issues occur an investigation is initiated and could take a few weeks to several months or more to resolve. This time impacts the engine companies as well as the people dependent upon functional engines. HCF monitoring processes and techniques are crucial to preserving fleet maintenance. One of the ways to prevent premature HCF failure is by detecting cracks in the blades or the wheels of the rotor.</p> <p>It <a href="https://hammer.purdue.edu/account/home#_msocom_1" target="_blank">[NLK1]</a> is the subject of this thesis to determine whether the static deflection of the blade as it rotates will begin to grow independent of rotational changes experienced by the rotor for an internal crack in the wheel as opposed to the blade of a rotor. Should a crack in the wheel occur, the stiffness should decrease, which would manifest when testing the rotor’s natural frequencies as a decrease in the natural frequency compared to an un-cracked rotor. The experiment was conducted using analysis tools for predicting blade natural frequencies of the pre-cracked rotor as well as physical experiments to determine the natural frequencies of the post-cracked rotor. The spin facility set up, data acquisition, data reduction, experiment details and results are provided. Both strain gauges and NSMS techniques were used to measure the natural frequencies of the rotor, and detection of damage while mounted in the spin facility. This research effort concluded it is possible to detect a crack in the wheel of a rotor using the NSMS blade stack capability. It is necessary to have a baseline vibration survey to understand the pre-damaged static deflection of each blade. This research also concluded that a comparison of the pre-cracked and post-cracked natural frequencies manifested roughly a 5% decrease. With a crack in the wheel, the expected stiffness of the wheel would decrease, thus, causing a decrease in the natural frequency of the component. This is evident in the comparison of the pre-cracked ping test data and the post-crack bench test data. In summary, it is possible to detect an internal crack of a rotor and the natural frequencies of the blades can change with an internally cracked wheel. </p>

<p dir="ltr">The continuous advancements in material science and manufacturing engineering have revolutionized the material design and fabrication techniques therefore drastically accelerating the development of complex structured materials. These novel materials, such as micro/nano-structures, composites, porous media, and metamaterials, have found important applications in the most diverse fields including, but not limited to, micro/nano-electromechanical devices, aerospace structures, and even biological implants. Experimental and theoretical investigations have uncovered that as a result of structural and architectural complexity, many of the above-mentioned material classes exhibit non-negligible nonlocal effects (where the response of a point within the solid is affected by a collection of other distant points), that are distributed across dissimilar material scales.</p><p dir="ltr">The recognition that nonlocality can arise within various physical systems leads to a challenging scenario in solid mechanics, where the occurrence and interaction of nonlocal elastic effects need to be taken into account. Despite the rapidly growing popularity of nonlocal elasticity, existing modeling approaches primarily been concerned with the most simplified form of nonlocality (such as low-dimensional, isotropic, and homogeneous nonlocal problems), which are often inadequate to identify the nonlocal phenomena characterizing real-world problems. Further limitations of existing approaches also include the inability to achieve a mathematically well-posed theoretical and physically consistent framework for nonlocal elasticity, as well as the absence of numerical approaches to achieving efficient and accurate nonlocal simulations. </p><p dir="ltr">The above discussion identifies the significance of developing theoretical and numerical methodologies capable of capturing the effect of nonlocal elastic behavior. In order to address these technical limitations, this dissertation develops an advanced continuum mechanics-based approach to nonlocal elasticity by using fractional calculus - the calculus of integrals and derivatives of arbitrary real or even complex order. Owing to the differ-integral definition, fractional operators automatically possess unusual characteristics such as memory effects, nonlocality, and multiscale capabilities, that make fractional operators mathematically advantageous and also physically interpretable to develop advanced nonlocal elasticity theories. In an effort to leverage the unique nonlocal features and the mathematical properties of fractional operators, this dissertation develops a generalized theoretical framework for fractional-order nonlocal elasticity by implementing force-flux-based fractional-order nonlocal constitutive relations. In contrast to the class of existing nonlocal approaches, the proposed fractional-order approach exhibits significant modeling advantages in both mathematical and physical perspectives: on the one hand, the mathematical framework only involves nonlocal formulations in stress-strain constitutive relationships, hence allowing extensions (by incorporating advanced fractional operator definitions) to model more complex physical processes, such as, for example, anisotropic and heterogeneous nonlocal effects. On the other hand, the nonlocal effects characterized by force-flux fractional-order formulations can be physically interpreted as long-range elastic spring forces. These advantages grant the fractional-order nonlocal elasticity theory the ability not only to capture complex nonlocal effects, but more remarkably, to bridge gaps between mathematical formulations and nonlocal physics in real-world problems.</p><p>An efficient nonlocal multimesh finite element method is then developed to solve partial integro-differential governing equations in the fractional-order nonlocal elasticity to further enable nonlocal simulations as well as practical applications. The most remarkable consequence of this numerical method is the mesh-decoupling technique. By separating the numerical discretization and approximation between the weak-form integral and nonlocal integral, this approach surpasses the limitations of existing nonlocal algorithms and achieves both accurate and efficient finite element solutions. Several applications are conducted to verify the effectiveness of the proposed fractional-order nonlocal theory and the associated multimesh finite element method in simulating nonlocal problems. By considering problems with increasing complexity ranging from one-dimensional to three-dimensional problems, from isotropic to anisotropic problems, and from homogeneous to heterogeneous nonlocality, these applications have demonstrated the effectiveness and robustness of the theory and numerical approach, and further highlighted their potential to effectively model a wider range of nonlocal problems encountered in real-world applications.</p>

A method to adapt the Generalized Predictive Control parameters to improve broadband disturbance rejection was developed and tested. The effect of the parameters on disturbance rejection has previously been poorly understood and a trial and error method was used to achieve adequate results. This dissertation provides insight on the effect of the parameters, as well as an adaptive tuning method to adjust them. The study begins by showing the effect of the four GPC parameters, the control and prediction horizons, control weighting &lambda , and order, on the disturbance rejection and control effort of a vibrating plate. It is shown that the effect of increases in the control and prediction horizon becomes negligible after a certain point. This occurs at nearly the same point for a variety of &lambda 's and orders, and hence they can be eliminated from the tuning space. The control effort and closed-loop disturbance rejection are shown to be highly dependant on &lambda and order, thereby becoming the parameters that need to be tuned. The behavior is categorized into various groups and further investigated. The pole and zero locations of the closed-loop system are examined to reveal how GPC gains control and how it can fail for non-minimum phase plants. A set of fuzzy logic modules is developed to adapt &lambda with order fixed, and conversely to adapt order with &lambda fixed. The effectiveness of the method is demonstrated in both numerical simulations and laboratory experiments. / Ph. D.

<p dir="ltr">Shape memory alloys (SMAs) belong to the category of smart materials due to their unique shape memory properties induced by a thermomechanically-triggered phase transformation. This phase changing process is also associated with a pronounced energy dissipation capacity. In recent years, the shape-recovery and energy-dissipating capabilities of SMAs have been object of extensive studies with particular focus on the opportunities they offer for the design of smart composites. The restoring stress of constrained SMAs as well as the modulus change, following thermal loading, can be leveraged to improve the static and dynamic performance, such as the pre/post-bulking behavior, the aerodynamic stability, and the impact resistance of composite materials embedded with SMA wires or fibers. The nonlinear damping resulting from the nonlinear material behavior associated with the ferro-elastic and pseudo-elastic phases was explored in a few studies focusing on vibration suppression in composites. Nonetheless, existing research mainly focused on either SMA wire or fiber reinforced composites, while the understanding of the dynamics of hybrid composites integrating SMA layers still presents several unexplored areas. In part, this technological gap might be explained by the fact that the most common SMA alloy, the so-called Nitinol, is expensive and hence not amenable to be deployed in large scale applications. With the most recent advancements in low-cost SMAs (e.g. Fe-based and Cu-based alloys), new applications that make more extensive use of SMAs are becoming viable. It follows that the understanding of the dynamic response of composites integrating SMA laminae becomes an important topic in order to support the development of innovative hybrid composite structures.</p><p dir="ltr">This dissertation explores the design and the nonlinear dynamic response of hybrid composites integrating SMA laminae, with a particular emphasis on the damping performance under different operating conditions. The dynamic properties of SMA monolithic beams and hybrid composite beams integrated with SMA laminae are investigated via one-dimensional constitutive models. Monolithic SMA beams are investigated to understand the fundamental aspects of the damping capacity of the material as well as possible bifurcation phenomena occurring under different types of harmonic excitations and different levels of pre-strain. The study then focuses on hybrid composite beams, highlighting the effects of design parameters, such the thickness, position, and pre-strain level of SMA layers on the transient and forced dynamic characteristics.</p><p dir="ltr">To further explore the potential of embedding SMA laminae to tailor the damping capacity of the hybrid composite and optimize the distribution of SMA materials, hybrid composite plates (HCPs) assembled by stacking fiber composites and SMA layers (either monolithic or patterned) are explored. The damping capacity of the HCP is assessed under different operating conditions, with emphasis on the effect of pre-strain levels in the SMA layers. The optimization study focuses on understanding the distribution of SMA materials and the synergistic role of patterning and pre-straining individual SMA layers within the HCP. The damping capacity of the HCP is also estimated as a function of the SMA total transformed volume fraction in order to identify the types of patterns and the pre-strain profiles capable of improving the overall damping capacity of the HCP.</p><p dir="ltr">The investigation on the dynamics of SMA hybrid composites continues with the optimal design of sandwich composite beams with elastic face sheets and SMA cellular cores. A deep learning-based surrogate model is proposed to efficiently predict the nonlinear mechanical response of the SMA sandwich beams subject to transverse loading, hence enabling the optimization of the SMA cellular core. The multi-objective optimization of the energy-dissipating capacity and of the overall stiffness is then performed by taking advantage of evolutionary algorithms. Once the optimal geometric parameters of the SMA cellular cores are obtained, finite element simulations are conducted to numerically validate the optimal configurations of the sandwich beams.</p><p dir="ltr">Finally, the numerical models are validated via experimental measurements conducted on monolithic SMA beams. Tests include both tensile and vibration measurements in both the ferro-elastic and pseudo-elastic regimes. The stress-strain relations obtained from tensile tests are used to calibrate the constitutive model of SMAs. Subsequently, experimental vibration tests are performed on clamped-clamped SMA beams to assess the effect of pre-strain levels on the damping capacity of SMA beams via a dedicated experimental setup to apply and maintain the pre-strain levels. The theoretical, numerical, and experimental results provided in this dissertation can serve as important guidelines to design lightweight SMA smart composites with customizable dynamic behavior.</p>

Given the advantages of parallel manipulators and lightweight manipulators, a 3-PRR planar parallel manipulator with three lightweight intermediate links has been developed to provide an alternative high-speed pick-and-place positioning mechanism to serial architecture manipulators in electronic manufacturing, such as X-Y tables or gantry robots. Lightweight members are more likely to exhibit structural defection and vibrate due to the inertial forces from high speed motion, and external forces from actuators. Structural flexibility effects are much more pronounced at high operational speeds and accelerations. Therefore, this thesis presents the dynamics and vibration control of a 3-PRR parallel manipulator with three flexible links. Firstly, a procedure for the generation of dynamic equations for a 3-PRR parallel manipulator with three flexible intermediate links is presented based on the assumed mode method. The dynamic equations of the parallel manipulator with three flexible intermediate links are developed using pinned-pinned boundary conditions. Experimental modal tests are performed using an impact hammer and an accelerometer to identify the mode shapes, frequencies, and damping ratios of flexible intermediate links. The mode shapes and frequencies, obtained from experimental modal tests, match very well the assumed mode shapes and frequencies obtained based on pinned-pinned boundary conditions, and therefore the dynamic model developed is validated. Secondly, this thesis presents the investigation on dynamic stiffening and buckling of the flexible links of a 3-PRR parallel manipulator by including the effect of longitudinal forces on the modal characteristics. Natural frequencies of bending vibration of the intermediate links are derived as the functions of axial force and rigid-body motion of the manipulator. Dynamic stiffening and buckling of intermediate links is investigated and configuration-dependant frequencies are analyzed. Furthermore, using Lagrange multipliers, the fully coupled equations of motions of the flexible parallel manipulator are developed by incorporating the rigid body motions with elastic motions. The mutual dependence of elastic deformations and rigid body motions are investigated from the analysis of the derived equations of motion. Open-loop simulation without joint motion controls and closed-loop simulation with joint motion controls are performed to illustrate the effect of elastic motion on rigid body motions and the coupling effect amongst flexible links. These analyses and results provide valuable insight into the design and control of the parallel manipulator with flexible intermediate links. Thirdly, an active vibration control strategy is developed for a moving 3-PRR parallel manipulator with flexible links, each of which is equipped with multiple PZT control pairs. The active vibration controllers are designed using the modal strain rate feedback (MSRF). The amplification behavior of high modes is addressed, and the control gain selection strategy for high modes is developed through modifying the IMSC method. The filters are developed for the on-line estimation of modal coordinates and modal velocity. The second compensator is used to cut off the amplified noises and unmodeled dynamics due to the differentiation operation in the developed controller. The modal coupling behavior of intermediate links is examined with the modal analysis of vibrations measured by the PZT sensors. The error estimation of the moving platform is examined using the measurement of PZT sensors. Finally, an active vibration control experimental system is built to implement the active vibration control of a moving 3-PRR parallel manipulator with three flexible links. The smart structures are built through mounting three PZT control pairs to each intermediate flexible link. The active vibration control system is set up using National Instruments LabVIEW Real-Time Module. Active vibration control experiments are conducted for the manipulator moving with high-speed, and experimental results demonstrate that the vibration of each link is significantly reduced.

Given the advantages of parallel manipulators and lightweight manipulators, a 3-PRR planar parallel manipulator with three lightweight intermediate links has been developed to provide an alternative high-speed pick-and-place positioning mechanism to serial architecture manipulators in electronic manufacturing, such as X-Y tables or gantry robots. Lightweight members are more likely to exhibit structural defection and vibrate due to the inertial forces from high speed motion, and external forces from actuators. Structural flexibility effects are much more pronounced at high operational speeds and accelerations. Therefore, this thesis presents the dynamics and vibration control of a 3-PRR parallel manipulator with three flexible links. Firstly, a procedure for the generation of dynamic equations for a 3-PRR parallel manipulator with three flexible intermediate links is presented based on the assumed mode method. The dynamic equations of the parallel manipulator with three flexible intermediate links are developed using pinned-pinned boundary conditions. Experimental modal tests are performed using an impact hammer and an accelerometer to identify the mode shapes, frequencies, and damping ratios of flexible intermediate links. The mode shapes and frequencies, obtained from experimental modal tests, match very well the assumed mode shapes and frequencies obtained based on pinned-pinned boundary conditions, and therefore the dynamic model developed is validated. Secondly, this thesis presents the investigation on dynamic stiffening and buckling of the flexible links of a 3-PRR parallel manipulator by including the effect of longitudinal forces on the modal characteristics. Natural frequencies of bending vibration of the intermediate links are derived as the functions of axial force and rigid-body motion of the manipulator. Dynamic stiffening and buckling of intermediate links is investigated and configuration-dependant frequencies are analyzed. Furthermore, using Lagrange multipliers, the fully coupled equations of motions of the flexible parallel manipulator are developed by incorporating the rigid body motions with elastic motions. The mutual dependence of elastic deformations and rigid body motions are investigated from the analysis of the derived equations of motion. Open-loop simulation without joint motion controls and closed-loop simulation with joint motion controls are performed to illustrate the effect of elastic motion on rigid body motions and the coupling effect amongst flexible links. These analyses and results provide valuable insight into the design and control of the parallel manipulator with flexible intermediate links. Thirdly, an active vibration control strategy is developed for a moving 3-PRR parallel manipulator with flexible links, each of which is equipped with multiple PZT control pairs. The active vibration controllers are designed using the modal strain rate feedback (MSRF). The amplification behavior of high modes is addressed, and the control gain selection strategy for high modes is developed through modifying the IMSC method. The filters are developed for the on-line estimation of modal coordinates and modal velocity. The second compensator is used to cut off the amplified noises and unmodeled dynamics due to the differentiation operation in the developed controller. The modal coupling behavior of intermediate links is examined with the modal analysis of vibrations measured by the PZT sensors. The error estimation of the moving platform is examined using the measurement of PZT sensors. Finally, an active vibration control experimental system is built to implement the active vibration control of a moving 3-PRR parallel manipulator with three flexible links. The smart structures are built through mounting three PZT control pairs to each intermediate flexible link. The active vibration control system is set up using National Instruments LabVIEW Real-Time Module. Active vibration control experiments are conducted for the manipulator moving with high-speed, and experimental results demonstrate that the vibration of each link is significantly reduced.

[pt] Nesse trabalho, estuda-se o desempenho de um absorsor pendular no controle de vibrações de torres altas e esbeltas, ocasionadas por carregamentos dinâmicos, tais como, por exemplo, cargas ambientais. Em virtude da possibilidade de oscilações de grande amplitude, considera- se na modelagem do problema a não-linearidade do pêndulo. O principal objetivo é estudar o comportamento do sistema torre-pêndulo, submetido a um carregamento harmônico, no regime não-linear, abordando-se aspectos gerais ligados à estabilidade dinâmica. Apresenta-se, inicialmente, a formulação necessária para obter o funcional de energia do sistema coluna-pêndulo, tanto para o caso linear quanto para o caso não-linear, do qual derivam-se as equações diferenciais parciais de movimento. A partir das equações lineares, obtêm-se as freqüências naturais e modos de vibração para alguns casos relevantes de coluna. A seguir, com base na análise modal do sistema coluna-pêndulo, deriva-se um modelo de dois graus de liberdade capaz de descrever com precisão o comportamento do sistema na vizinhança da freqüência fundamental da coluna, do qual obtêm-se as equações de movimento e as equações de estado não- lineares. Uma análise paramétrica detalhada das oscilações não-lineares do sistema coluna-pêndulo demonstra que o absorsor pendular passivo pode reduzir ou amplificar a resposta da coluna. No estudo da influência da não-linearidade geométrica do pêndulo, verifica-se a importância dessa na resposta do sistema, evidenciando que a nãolinearidade não pode ser desprezada nessa classe de problema. Por fim, com base nos resultados, propõe-se um absorsor pendular híbrido. Os estudos revelam que este controle é mais eficiente que o passivo e que não requer grande gasto de energia. / [en] In the present work the performance of a pendulum absorber in the vibration control of tall and slender towers, caused by dynamic loads, such as, environmental loads, is studied in detail. Due to the possibility of large amplitude oscillations, the non-linearity of the pendulum is considered in the modeling of the problem. The main objective of this research is to study the behavior of the tower-pendulum system, submitted to a harmonic load, in the nonlinear regimen, with emphasis on general aspects related to its dynamic stability. It is presented, initially, the formulation necessary for the derivation of the system´s energy functional, both for the linear and the nonlinear cases, from which the partial differential equations of motion are derived and the vibration frequencies and related vibration modes are obtained. Then, based on the modal analysis of the column-pendulum system, a two degrees of freedom model, capable of describing with precision the behavior of the system in the neighborhood of the fundamental frequency of the column is derived, from which the equations of motion and the nonlinear state-space equations are obtained. A detailed parametric analysis of the nonlinear oscillations of the system is carried out. It shows that the pendulum may reduce or amplify the response of the column. The results show a marked influence of the geometric not-linearity of the pendulum on the response of the system, showing that its not-linearity cannot be neglected in this class of problems. Finally, based on the results, a hybrid control approach is proposed. These studies show that this control strategy is more efficient than the passive control alone and that it does not require a large amount of energy.

Esta dissertação apresenta uma análise numérica do controle de vibrações estruturais através de cerâmicas piezoelétricas em extensão e em cisalhamento conectadas a circuitos ativo-passivos compostos por resistência, indutância e fonte de tensão. Para tal, um modelo de elementos finitos de vigas sanduíche com três camadas elásticas e/ou piezoelétricas foi desenvolvido. Realizou-se também uma modelagem dos componentes do circuito elétrico e seu acoplamento à estrutura gerando assim uma equação de movimento acoplada para a estrutura com elementos piezoelétricos conectados aos circuitos elétricos. Uma análise harmônica das equações obtidas foi realizada para se obter uma avaliação preliminar dos efeitos causados pelos componentes elétricos do circuito na estrutura. Observou-se que os elementos passivos do circuito, resistência e indutância, tem não somente um efeito de absorvedor dinâmico de vibrações mas, também, promovem uma amplificação da autoridade de controle no caso de se atuar através da fonte de tensão. Usando a metodologia tradicional de projeto de absorvedores dinâmicos de vibrações, derivou-se expressões para os valores de resistência e indutância de modo a maximizar o desempenho passivo do sistema. Uma análise numérica do desempenho na redução das amplitudes de vibração em um viga engastada-livre com uma cerâmica piezoelétrica em extensão ou cisalhamento foi realizada mostrando bons resultados. Em seguida, uma análise da autoridade de controle para estas estruturas foi realizada visando a implementação de um controle híbrido ativo-passivo. A parcela ativa do controle foi obtida usando-se uma estratégia de controle por retroalimentação ótima do tipo linear quadratic regulator para calcular a tensão aplicada ao circuito. Uma comparação entre os resultados mostra que o controle híbrido ativo-passivo é sempre superior aos controles puramente ativos ou passivo para os dois casos estudados, com cerâmicas piezoelétricas em extensão e cisalhamento. / This work presents a numerical analysis of the structural vibration control using piezoelectric materials in extension and shear mode connected to active-passive electric circuits composed of the resistance, inductance and voltage source. For that, a finite element model for sandwich beams with three elastic or piezoelectric layers was developed. A modeling of the electric circuit dynamics and its coupling to the structure with piezoelectric elements was also done. A harmonic analysis of the resulting equations was performed to yield a preliminary evaluation of the effects caused by the electric circuit components on the structure. It was observed that the passive circuit components not only lead to a dynamic vibration absorber effect but also to an amplification of the control authority in case of actuation using the voltage source. Using the standard methodology for the design of dynamic vibration absorbers, expressions were derived for the resistance and inductance values that optimize the passive vibration control performance of the system. A numerical analysis of the passive vibration control was performed for cantilever beams with extension and shear piezoelectric ceramics showing satisfactory results. Then, an analysis of the control authority was carried out for the same structures aiming at an active-passive vibration control. The active control was achieved using a linear quadratic regulator optimal feedback strategy to evaluate the voltage applied to the circuit. A comparison between the obtained results show that hybrid active-passive control is always superior to the purely active or purely passive control for both cases studied, with extension and shear piezoelectric ceramics.

Este trabalho apresenta uma análise paramétrica da reposta dinâmica de colunas de perfuração de poços de petróleo com controle proporcional-integral de velocidade não colocalizado. A operação de perfuração de poços de petróleo e gás em águas profundas consiste na abertura de poços em solo rochoso através de uma broca cuja rotação é controlada por uma mesa rotativa na superfície. O torque imposto pela mesa é transmitido à broca por meio de uma coluna de perfuração. Particularmente no caso de perfuração em águas profundas, as colunas de perfuração podem ser muito extensas e, portanto, bastante flexíveis. As vibrações ocasionadas pela grande flexibilidade das colunas de perfuração são as principais responsáveis por falhas no processo de perfuração. Em particular, o fenômeno não-linear conhecido como stick-slip e relacionado às vibrações torcionais da coluna de perfuração, faz com que um sistema de controle projetado para manter a velocidade da mesa constante dê origem a grandes oscilações na velocidade da broca. Na prática, este fenômeno é amplificado pela inerente não-linearidade do contato entre broca e formação rochosa e pela forte não colocalização entre mesa rotativa e broca. Este trabalho tem por principal objetivo realizar uma análise paramétrica da dinâmica do processo de perfuração, usando um modelo de dois graus de liberdade para representar o conjunto mesa rotativa, coluna de perfuração e broca, para identificar condições nas quais uma lei de controle simples do tipo linear proporcional-integral pode fornecer um desempenho de perfuração estável e satisfatório. / This paper presents a parametric analysis of the dynamics of oilwell drillstrings with non-collocated proportional-integral velocity control. The drilling operation for oil and gas in deep waters consists of opening wells in rocky ground formation by a drill, whose angular speed is controlled by a rotary table at the surface. The torque applied by the table is transmitted to the drill-bit through the drillstring. Particularly in the deepwater drilling case, the drillstring can be very long and therefore very flexible. The vibrations caused by the great flexibility of drilling columns are mainly responsible for the failures in the drilling process. In particular, the nonlinear phenomenon known as stick-slip and related to the torsional vibration of the drillstring, makes that a control system designed to maintain a constant angular velocity at the table yield large variations at the drill-bit angular velocity. In practice, this phenomenon is amplified by the inherent nonlinearity of the contact between drill bit and rock formation and by the strong non-colocalization between rotary table and drill-bit. The main objective of this work is to perform a parametric analysis of the dynamics of the drilling process, using a two degrees of freedom model in order to represent the rotary table assembly, the drilling column and drill-bit, to identify conditions in which a simple control law, such as a linear proportional-integral velocity control, can provide a stable and satisfactory drilling performance.

Máquinas rotativas são sempre sujeitas à vibrações mecânicas, em menor ou maior grau, e para garantir um correto funcionamento destas máquinas, evitando falhas de operação, é necessário realizar o controle destas vibrações. Uma das frentes que vem se destacando nesta área é o controle ativo de vibrações. Neste tipo de abordagem as vibrações são controladas ativamente através de um sistema de atuação e de uma técnica de controle a ser empregada de forma satisfatória. Neste contexto, existem inúmeras abordagens da teoria de controle que podem ser aplicadas, e aqui é avaliada a aplicação da metodologia proposta por Udwadia e Kalaba para o controle de trajetória de sistemas não lineares, uma técnica de controle ainda não utilizada no controle ativo de vibrações em sistemas rotativos. Em um primeiro momento a avaliação do desempenho e potencial de aplicação desta metodologia é realizada em sistemas com quatro graus de liberdade através de comparação com controladores do tipo proporcional-integral-derivativo e regulador linear-quadrático. Os resultados obtidos pelo controlador avaliado são similares aos resultados obtidos pelo controlador proporcional-integral-derivativo com melhorias em termos de erro de posicionamento. A metodologia também é avaliada em um sistema rotativo com um maior número de graus de liberdade, no qual é possível compreender o comportamento do controlador em um sistema flexível. Por fim realiza-se um exemplo de aplicação da técnica em um sistema com um eixo rígido e mancal hidrodinâmico ativo de atuação eletromagnética. Os resultados de simulação obtidos mostram que a metodologia possui potencial de aplicação para sistemas que apresentam eixo rígido, no qual uma drástica redução na amplitude de vibração do sistema foi observada por toda faixa de operação avaliada, enquanto que a sua aplicação em sistemas com eixo flexível se tornou restrita aos dois primeiros modos de vibrar do sistema flexível utilizado, modelado através do método dos elementos finitos. / Rotating machinery are always subject to mechanical vibration to a lesser or greater degree, and to ensure proper operation of these machines, avoiding faulty operation, it is necessary to carry out the control of these vibrations. One of the fronts that stood out in this area is the active vibration control. In this type of approach, vibrations are actively managed through an actuation system and a control technique to be used satisfactorily. In this context, there are numerous approaches to control theory that can be applied, and here the application of the methodology proposed by Udwadia and Kalaba for trajectory control of nonlinear systems is evaluated, a control technique not yet used in active vibration control in rotating systems. At first the evaluation of the performance and potential application of this methodology is performed on systems with four degrees of freedom by comparison with controllers of the proportional-integral-derivative and linear-quadratic regulator type. The results of the evaluated controller are similar to results obtained by proportional-integral-derivative controller with improvements in positioning error. The methodology is also evaluated in a rotating system with a larger number of degrees of freedom, wherein we can understand the controllers behavior in a flexible system. Finally, an application example of the technique on a system with a rigid shaft and hydrodynamic bearing with electromagnetic actuators is presented. The obtained simulation results show that the method has application potential to systems having rigid shaft, in which a dramatic reduction in the amplitude of vibration of the system was observed at all the operating range evaluated, whereas their application in systems with flexible shaft became restricted to the first two vibration modes of the flexible system used, modeled by the finite element method.