Orientador: Robson Pederiva / Dissertação (mestrado) - Universidade Estadual de Campinas. Faculdade de Engenharia Mecanica / Made available in DSpace on 2018-08-07T00:56:52Z (GMT). No. of bitstreams: 1 Silva_GilbertoMachadoda_M.pdf: 1128289 bytes, checksum: e5a6e2d7aeb16be17a0a3d45dd834193 (MD5) Previous issue date: 2006 / Resumo: Aplica-se neste trabalho a metodologia de diagnóstico de falhas em sistemas mecânicos rotativos sustentados por mancais magnéticos ativos em conjunto com um sistema de controle ativo de vibração, excitados por forças de desbalanço e ruído branco. Este diagnóstico baseia-se no emprego das equações de correlações, através da formulação matricial de Ljapunov, para sistemas lineares estacionários juntamente com redes neurais artificiais. Este procedimento utiliza apenas as variáveis de estado medidas, através da correlação das variáveis de saída. É gerado um conjunto de relações envolvendo os parâmetros físicos do sistema juntamente com as matrizes de correlações das variáveis medidas. As falhas no sistema são detectadas através do monitoramento da variação dos parâmetros físicos e da comparação das funções de correlação teóricas e estimadas. As redes neurais artificiais são usadas para mapear as correlações que envolvem estados que não são medidos. Dado ao grande número de equações de compatibilidade resultantes, é proposta uma metodologia para selecionar as equações relacionadas com as falhas propostas. Com o método de diagnóstico de falhas proposto é possível detectar e discernir as falhas tanto mecânicas quanto elétricas, bem como sua localização no sistema / Abstract: This work applies the methodology of fault diagnosis in rotating machinery supported by active magnetic bearings and active con1rol systems, excited by unbalance and white noise. This diagnostic applies the correlation matrices based on the Ljapunov matrix formulation and artificial neural network for linear stationary systems. The procedure uses only measured state variables, computing the correlation between the output variables. It is possible to derive specific relations involving the physical parameter of the system and the correlation matrices of the measured variables. Faults in the system can be detected by monitoring the variation of the physical parameter through a comparison of theoretical and estimated correlation functions. Artificial neural networks are used to map the correlations involving the variables, which are difficult to be measured. There is a large number of resultant compatibility equations and it is proposed a methodology to select the equations that establish relationships with the faults. The proposed fault diagnosis method can detect the fault present in the system and it is also possible to distinguish between mechanical and electrical fault as well as their location in the system / Mestrado / Mecanica dos Sólidos e Projeto Mecanico / Mestre em Engenharia Mecânica

O presente trabalho consiste no projeto de um modelo em elementos finitos de um absorvedor dinâmico rotativo utilizando-se um material viscoelástico como componente dissipador do sistema. O absorvedor é composto por um anel de material viscoelástico interposto entre dois anéis de aço, o qual é fixado na extremidade livre de um sistema rotativo representado por um eixo flexível, suportado por dois rolamentos, no qual estão fixos dois discos igualmente espaçados do centro entre os dois mancais. O modelo em elementos finitos do sistema rotativo é validado com os dados experimentais do modelo real e suas velocidades críticas são determinadas baseadas no diagrama de Campbell e na resposta ao desbalanço em um dos discos. O modelo inicial do absorvedor dinâmico rotativo é replicado de um modelo da literatura e as respostas a uma excitação na forma de impulso são comparadas. O modelo desenvolvido equipara-se ao da literatura para frequências até 600 Hz, intervalo que compreende as velocidades críticas a serem amortecidas. A otimização do absorvedor é realizada através de variações da geometria do mesmo e são traçadas curvas de influência de cada parâmetro sobre suas frequências naturais. Com base nestas curvas são realizadas análises de influência conjunta dos parâmetros geométricos sobre tais frequências. Pelos resultados obtidos verifica-se a possibilidade da obtenção de um modelo que atue sobre modos de flexão específicos do sistema rotativo, atenuando as amplitudes de vibração das velocidades críticas correspondentes a cada modo. Uma vez obtidos os modelos de absorvedores dinâmicos correspondentes aos dois primeiros modos de flexão do sistema rotativo, ambos são acoplados ao sistema e se observa grande redução dos picos de amplitude do primeiro modo de flexão, enquanto os picos do segundo modo sofrem baixa alteração. / The present work concerns the development, optimization and validation of a finite element model of a dynamic vibration absorber using a viscoelastic material as the damping component. The dynamic absorber consists of a ring of viscoelastic material interposed between two rings of steel, which is fixed to the free end of a rotary system represented by a flexible shaft supported by two bearings, on which are fixed two discs equally spaced in the center of both bearings. The finite element model of the rotating system is validated with experimental data from the actual model and its critical speeds are determined based on the Campbell diagram and in its response to the imbalance. The initial model of the dynamic absorber is replicated from a model of the literature and the responses to an impulse excitation are compared. The developed model matches the literature one for frequencies up to 600 Hz, range comprising the critical speeds to be damped. The absorber\'s optimization is accomplished through variations of its geometry and influence curves of each parameter over its natural frequencies are drawn. Based on these curves, combined influence analyzes of the geometrical parameters over such frequencies are performed. From the results obtained, it can be seen the possibility of achieving a model that acts on specific bending modes of the rotation system, reducing the vibration amplitudes of the critical speeds corresponding to each mode. Once obtained the dynamic absorbers models corresponding to the first two modes of vibration of the rotatative system, both models are coupled to the system and it is observed great reduction of the amplitude of the first bending mode peaks, while the second mode suffer low peaks reduction.

Ces dernières décennies de nombreux modèles de paliers à feuilles ont été développés. Aujourd'hui, la limite de ces modèles est apparente notamment au niveau de la compréhension des comportements non linéaire du système rotor palier et de la quantification de sa dissipation énergétique. Il est essentiel pour les développements futurs de maîtriser les instabilités liées au fonctionnement de ces paliers. Grâce à une approche variationnelle et la MEF, la structure flexible a été modélisée comme une structure mince soumise à la pression d'un fluide compressible, isotherme, laminaire puis turbulent. Nous tenons compte dans cette étude, des frottements secs internes en utilisant la loi de Coulomb et la méthode du Lagrangien augmenté. Le modèle de structure est couplé avec équations de Reynolds des films minces afin de déterminer le comportement du rotor à l'aide du principe fondamental de la dynamique. Nous avons montré la pertinence de l'approche choisie, notamment l'utilisation du modèle de structure mince sur le comportement dynamique du rotor et sur le champ de pression hénéré dans le palier. On démontre aussi l'intéraction entre les déflections des bumps et le frottement sec. L'action du flambage est doublement accentué par le phénomène de frottement présent entre les feuilles, modifiant ainsi la dissipation d'énergie dans le palier. Le second objectif a été d'identifier l'origine des phénomènes subsynchrones afin de développer des nouveaux paliers en se dédouanant des instabilités qu'elles engendrent. / These last decades numerous model for airfoil bearings have been developed. But nowadays, these models are not sufficiently accurate for the rotor response prediction in the presence of non linearities. It is essential for the future developments to control the instabilities due to the non linear behavior in order to quantify the energy dissipation in the bearings. By means of a variational approach, the flexible structure is modeled as a thin media subjected to a compressible fluid pressure, isothermal and in a laminar then turbulent regime. The model is built up using FEM for the foils response. the internal dry friction is taken into account with Coulomb’s law and the updated Lagrangian method. The structure model is coupled with Reynolds equation to calculate the rotor motions, thanks to the basic principle of dynamics (B.P.D). This work is performed, first, to put in evidence the influence of thin structure approach on the rotor behavior and on the field pressure. The link between bumps deflections and dry friction is established. The structure buckling is twice increased by the phenomenon of friction between sheets and energy dissipation. The second objective is to identify the subsynchronous frequencies in order to establish the relevance of the new airfoil model for non linear and instabilities investigations.

The healthy condition of a rotating machine leads to safe and cheap operation of almost all industrial facilities and mechanical systems. To achieve such a goal, vibration-based condition monitoring has proved to be a well-accepted technique that detects incipient fault symptoms. The conventional way of On-Bearing Vibration Measurement (OBVM) captures symptoms of different faults, however, it requires a relatively expensive setup, an additional space for the auxiliary devices and cabling in addition to an experienced analyst. On-Shaft Vibration Measurement (OSVM) is an emerging method proposed to offer more reliable Faults Diagnosis (FD) tools with less number of sensors, minimal processing time and lower system and maintenance costs. The advancement in sensor and wireless communications technologies enables attaching a MEMS accelerometer with a miniaturised wireless data acquisition unit directly to the rotor without altering the machine dynamics. In this study, OSVM is analysed during constant speed and run-up operations of a test rig. The observations showed response modulation, hence, a Finite Element (FE) analysis has been carried out to help interpret the experimental observations. The FE analysis confirmed that the modulation is due to the rotary motion of the on-shaft sensor. A demodulation method has been developed to solve this problem. The FD capability of OSVM has been compared to that of OBVM using conventional analysis where the former provided more efficient diagnosis with less number of sensors. To incorporate more features, a method has been developed to diagnose faults based on Principal Component Analysis and Nearest Neighbour classifier. Furthermore, the method is enhanced using Linear Discriminant Analysis to do the diagnosis without the need for a classifier. Another faults diagnosis method has been developed that ensures the generalisation of extracted faults features from OSVM data of a specific machine to similar machines mounted on different foundations.

During the assembly of aircraft engines, some clearance is left in the rolling bearings mainly to reduce friction. However this clearance might allow the rolling element to vibrate during flight. Indeed, unwanted vibrations called non-synchronous vibrations (NSV) appear on the data recorded by the sensors on some development engines. NSV can be dangerous for the engine so they are closely monitored.  To prevent the appearance of the NSV, they are investigated by the engineers as soon as they appear during tests. The main source of the NSV is most likely to be the rolling bearings in the rotor because they induce a non-linear behaviour. The bearings of development engines were investigated on Finite Element Method (FEM) software for example but other methods could bring a contribution for the understanding of the NSV.  In this study, a multibody modelling software is used to try to model and explain the observed sub-synchronous vibrations considered as NSV. A model of the rotor of a prototype engine on a FEM software is provided and then reduced to be implemented in the new software. The behaviour of this new model is tested through modal analysis and response to imbalance.  Once the model is properly set, a parametric study is performed to see the effect of the thrust, gravity, imbalance weight and clearance on the system. It shows that clearance and gravity are key parameters while thrust and the imbalance weight have a minor impact on the NSV. This study has also helped to fix the parameters used to reproduce the NSV observed in the experiments.  Then, a second study focus on the influence of the clearance of the roller bearings on the NSV. This study defines a range of clearance that can be implemented on the engine to avoid the NSV. It also proved that the vibrations were very sensitive to a small change in the clearance values.  Finally, by studying the previous configurations, a link between the stiffness of the bearing and the occurrence of the NSV was established. In fact, the NSV appear only when the two roller bearings both have no stiffness because the clearance is not filled by the radial load. The rolling element is thus free to vibrate in its ring. It was noticed that the NSV has more chance to occur if it has already come out earlier in the run-up of the engine.  The multibody software is therefore perfectly able to reproduce the vibrations in a rotor. It is now a tool that can be used during the development process. / Vid montering av flygplansmotorer lämnas ett spelrum i rullningslagren främst för att minska friktionen. Detta spelrum kan emellertid tillåta att rullelementet vibrerar under flygning. Faktum är att oönskade vibrationer som kallas non-synchronous vibrations (NSV) visas på data som registreras av sensorerna på utveckling motorerna. NSV kan vara farligt för motorn och övervakas därför noggrant.För att förhindra uppkomsten av NSV utreds de regelbundet av ingenjörerna. Den huvudsakliga källan till NSV är troligen rullager i rotorn eftersom de inducerar ett icke-linjärt beteende. Lagren för utveckling motorer undersöktes till exempel med Finita Element-metoden (FEM) programvara men andra metoder skulle kunna bidra till förståelsen av NSV. I denna studie används en multibody-modelleringsprogramvara för att försöka modellera och förklara de observerade subsynkrona vibrationerna som betraktas som NSV. En modell av rotorn till en utveckling motor tillhandahålls i ett FEM-program och reduceras sedan för att implementeras i den nya mjukvaran. Beteendet hos denna nya modell testas genom modal analys och respons på obalans. När modellen är inställd utförs en parametrisk studie för att se effekten av dragkraften, gravitationen, obalansvikten och frigången i systemet.Den visar att frigång och gravitation är nyckelparametrar medan dragkraft och obalansvikt har en mindre inverkan på NSV. Denna studie har också hjälpt till att bestämma de parametrar som används för att reproducera NSV som observerats i experimenten. Därefter fokuserar en andra studie på inverkan av rullagernas frigång på NSV. Denna studie definierar ett intervall av spelrum som kan implementeras på motorn för att undvika NSV. Det visade sig också att vibrationerna var mycket känsliga för en liten ändring av frigångsvärdena.Slutligen, genom att studera de tidigare konfigurationerna, etablerades en koppling mellan lagrets styvhet och förekomsten av NSV. Faktum är att NSV endast visas när de två rullagren båda inte har någon styvhet eftersom spelet inte fylls av den radiella belastningen. Rullelementet är således fritt att vibrera i sin ring. Det märktes att NSV har större chans att inträffa om den redan sker tidigare i motorns start. Multibody-mjukvaran är därför perfekt för att reproducera vibrationerna i en rotor. Det är nu ett verktyg som kan användas under utvecklingsprocessen.

A análise de vibrações nos sistemas estruturais e rotativos permite detectar problemas indesejáveis, como a fadiga estrutural e o desgaste excessivo, que contribuem para a redução da vida útil do sistema e seus componentes. Tradicionalmente, a medição das vibrações é realizada por sensores de contato (acelerômetros e extensômetros), que possuem como inconveniente a adição de sua massa no sistema. Como alternativa, existem os sensores de não contato (LVD e ESPI), que são equipamentos de custo elevado. Este trabalho visa o desenvolvimento de um equipamento de baixo custo que realize medições multi-pontos sem contato do comportamento vibratório de estruturas e eixos rotativos. O método proposto utiliza como base os princípios da fotogrametria em conjunto com técnicas de subamostragem, que são utilizadas em estruturas ou máquinas com frequências de vibração conhecidas (e.g máquinas rotativas). A metodologia foi inicialmente aplicada em uma viga engastada-livre, excitada periodicamente por um shaker eletrodinâmico e posteriormente em um sistema rotativo montado em um bancada de testes. A viabilidade em se utilizar o método foi verificada comparando os resultados obtidos com as medições realizadas por um vibrômetro laser Doppler, no caso do sistema estrutural, e por sensores de proximidade indutivo nas vibrações do eixo rotativo. Com base nos comparativos, conclui-se que este método, mesmo apresentando limitações de resolução, pode ser perfeitamente empregado em medições de sistemas estruturais e rotativos assim como na análise modal operacional de estruturas. / The analysis of vibrations in structural and rotating systems allows the detection of undesirable problems, such as the structural fatigue and excessive wear, which contribute to the reduction of the useful life of the systems and their components. Traditionally, the measurement of vibrations is carried out by contacting sensors (accelerometers and strain gauges), which have the inconvenience of adding mass into the system. Alternativelly, there are the non-contacting sensors (LVD and ESPI), which are high cost equipments. This work aims at developing a low cost equipment that carry out multi-point non-contact measurements of the vibratory behavior of structures and rotating shafts. The proposed method uses as a basis the principles of photogrammetry together with sub-sampling techniques, which are used in structure or machines with known vibration frequencies (e.g rotating machines). The methodology was initially applied on a cantilever beam, periodically excited by an electrodynamic shaker and later in a rotating system mounted on a test bench. The feasibility of using the method was verified comparing the results obtained with measurements from a laser Doppler vibrometer, in the case of the structural system, and with inductive proximity sensors in the rotating shaft vibration. Based on the comparison analysis, one observes that this method can be perfectly used in vibration measurements in structural and rotating systems even with limitations in resolution as well as in operational modal analysis of structures.

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.

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.

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.

The sustainability, smooth operation and operational life of rotating machinery significantly rely on the techniques that detect the symptoms of incipient faults. Among the faults in rotating systems, the presence of a crack is one of the most dangerous faults that dramatically decreases the safety and operational life of the rotating systems, thereby leading to catastrophic failure and potential injury to personnel if it is undetected. Although many valuable techniques and models have been developed to identify a crack (or cracks) in stationary and rotating systems, finding an efficient technique (or model) that can identify a unique vibration signature of the cracked rotor is still a great challenge in this field. This is because of the unceasing necessity to develop high performance rotating machines and driving towards significant reduction of the time and cost of maintenance. Most of the crack identification techniques and models in the available literature are based on vibration-based methods. The main idea of the vibration-based method is that the presence of a crack in a rotor induces a change in the mass, damping, and stiffness of the rotor, and consequently detectable changes appear in the modal properties (natural frequencies, modal damping, and mode shapes). Among all these modal properties, the choice of the modal natural frequency change is more attractive as a tool for crack identification. The changes in natural frequencies due to a crack can be conveniently measured from just a few accessible points on the cracked rotor. Furthermore, measuring the natural frequencies does not require expensive measuring instruments, and the natural frequency data is normally less contaminated by experimental noise. However, the change that a crack induces in the natural frequencies is usually very small and can be buried in the ambient noise. Moreover, the natural frequencies are not affected if the crack is located at the nodes of modes or far from the location of inertia force and out-of-unbalance force that the disc generates in the shaft. To overcome these problems (or limitations), therefore, this study is conducted using the idea of the roving mass (roving disc in rotor case). The modal natural frequencies are used for the identification and location of cracks of various severities at different locations in both stationary and rotating shafts. The fundamental idea of the roving disc is that an extra inertia force is traversed along the cracked rotor to significantly excite the dynamics of the rotor near the crack locations. In other words, the location of a crack can be anywhere on the shaft which is contrary to the developed techniques in the available literature in which the location of a crack should be close to the disc. Along with the roving disc idea, three crack identification techniques are developed in this study using the natural frequencies of the cracked and intact shafts. Each of these techniques has its merits and limitations for crack identification. These techniques are implemented using data that are numerically generated by the finite element method based on the Bernoulli-Euler shaft elements and experimentally validated in the laboratory environment. The numerical and experimental results clearly demonstrate the capability of the suggested approach for the identification and location of cracks in stationary and rotating shafts.