Nous étudions dans cette thèse le problème de l’exploration parallèle d’un graphe à l’aide des multiples, synchronisés et mobiles agents. Chaque agent est une entité individuelle qui peut, indépendamment des autres agents, visiter les sommets du graphe ou parcourir ses arêtes. Le but de ensemble des agents est de visiter tous les sommets de graphe.Nous étudions d’abord l’exploration du graphe dans un modèle où chaque agent est équipé de mémoire interne, mais les noeuds n’ont pas de mémoire. Dans ce modèle les agents sont autorisés à communiquer entre eux en échangeant des messages. Nous présentons des algorithmes qui s’exécutent dans un minimum de temps possible pour polynomiale nombre d’agents (polynomiale en nombre de sommets du graphe). Nous étudions aussi quelle est l’impact de différentes méthodes des communications. Nous étudions des algorithmes où les agents peuvent se communiquer à distance arbitraire,mais aussi où communication est possible seulement entre les agents situés dans le même sommet. Dans les deux cas nous présentons des algorithmes efficaces. Nous avons aussi obtenu des limites inférieures qui correspondent bien à la performance des algorithmes.Nous considérons également l’exploration de graphe en supposant que les mouvements des agents sont déterminés par le soi-disant rotor-router mécanisme. Du point de vue d’un sommet fixé, le rotor- router envoie des agents qui visitent les sommet voisins dans un mode round-robin. Nous étudions l’accélération défini comme la proportion entre le pire des cas de l’exploration d’un agent unique et des plusieurs agents. Pour générales graphes, nous montrerons que le gain de vitesse en cas de multi-agent rotor-router est toujours entre fonction logarithmique et linéaire du nombre d’agents. Nous présentons également des résultats optimaux sur l’accélération de multi-agent rotor-router pour cycles, expanseurs, graphes aléatoires, cliques, tores de dimension fixé et une analyse presque optimale pour hypercubes.Finalement nous considérons l’exploration sans collision, où chaque agent doit explorer le graphe de manière indépendante avec la contrainte supplémentaire que deux agents ne peuvent pas occuper le même sommet. Dans le cas où les agents sont donnés le plan de graphe, on présente un algorithme optimal pour les arbres et un algorithme asymptotiquement optimal pour générales graphes. Nous présentons aussi des algorithmes dans le cas de l’exploration sans collision des arbres et des générales graphes dans la situation où les agents ne connaissent pas le graphe. Nous fermons la thèse par des observations finales et une discussion de problèmes ouverts liés dans le domaine de l’exploration des graphes. / In this thesis we study the problem of parallel graph exploration using multiple synchronized mobile agents. Each mobile agent is an entity that can, independently of other agents, visit vertices of the graph and traverse its edges. The goal of the agents is to visit all vertices of the graph. We first study graph exploration in the model where agents are equipped with internal memory but no memory is available at the nodes. Agents in this model are also allowed to communicate between each other by exchanging messages. We present algorithms working in a minimal possible time for a team of polynomial size (in the number of vertices of the graph). We also study the impact of the available range of communication by analysing algorithms for agents which can communicate at arbitrary distance, or only with other agents located at the same node. We present efficient algorithms and lower bounds that almost match our positive results in both communication models. We also consider graph exploration when movements of agents are determined according to the so-called rotor-router mechanism. From the perspective of a fixed node, the rotor-router sends out agents which visit the node along its outgoing edges, ina round-robin fashion. We study the speedup which is the ratio between the worst-case exploration of a single agent and of multiple agents. We first show that the speed up for general graphs for the multi-agent rotor-router is always between logarithmic and linear in the number of agents. We also present a tight analysis of the speedup for the multi-agent rotor-router for cycles, expanders, random graphs, cliques, constant dimensional tori and an almost-tight analysis for hypercubes. Finally we consider collision-free exploration, where each agent has to explore the graph independently with the additional constraint that no two agents can occupy the same node at the same time. In the case when agents are given the map of the graph, we show an optimal algorithm for trees and an asymptotically optimal algorithm for general graphs. We also present algorithms for collision-free exploration of trees and general graphs in the case when agents have no initial knowledge about the graph. We close the thesis with concluding remarks and a discussion of related open problems in the area of graph exploration.

This thesis involves the study of four problems in the area of nonlinear vibrations, using the asymptotic method of multiple scales(MMS). Accordingly, it consists of four sequentially arranged parts. In the first part of this thesis we study some nonlinear dynamics related to the amplitude control of a lightly damped, resonantly forced, harmonic oscillator. The slow flow equations governing the evolution of amplitude and phase of the controlled system are derived using the MMS. Upon choice of a suitable control law, the dynamics is represented by three coupled ,nonlinear ordinary differential equations involving a scalar free parameter. Preliminary study of this system using the bifurcation analysis package MATCONT reveals the presence of Hopf bifurcations, pitchfork bifurcations, and limit cycles which seem to approach a homoclinic orbit. However, close approach to homoclinic orbit is not attained using MATCONT due to an inherent limitation of time domain-based continuation algorithms. To continue the limit cycles closer to the homoclinic point, a new algorithm is proposed. The proposed algorithm works in phase space with an ordered set of points on the limit cycle, along with spline interpolation. The algorithm incorporates variable stretching of arclength based on local curvature, through the use of an auxiliary index-based variable. Several numerical examples are presented showing favorable comparisons with MATCONT near saddle homoclinic points. The algorithm is also formulated with infinitesimal parameter increments resulting in ordinary differential equations, which gives some advantages like the ability to handle fold points of periodic solution branches upon suitable re-parametrization. Extensions to higher dimensions are outlined as well. With the new algorithm, we revisit the amplitude control system and continue the limit cycles much closer to the homoclinic point. We also provide some independent semi-analytical estimates of the homoclinic point, and mention an a typical property of the homoclinic orbit. In the second part of this thesis we analytically study the classical van der Pol oscillator, but with an added fractional damping term. We use the MMS near the Hopf bifurcation point. Systems with (1)fractional terms, such as the one studied here, have hitherto been largely treated numerically after suitable approximations of the fractional order operator in the frequency domain. Analytical progress has been restricted to systems with small fractional terms. Here, the fractional term is approximated by a recently pro-posed Galerkin-based discretization scheme resulting in a set of ODEs. These ODEs are then treated by the MMS, at parameter values close to the Hopf bifurcation. The resulting slow flow provides good approximations to the full numerical solutions. The system is also studied under weak resonant forcing. Quasiperiodicity, weak phase locking, and entrainment are observed. An interesting observation in this work is that although the Galerkin approximation nominally leaves several long time scales in the dynamics, useful MMS approximations of the fractional damping term are nevertheless obtained for relatively large deviations from the nominal bifurcation point. In the third part of this thesis, we study a well known tool vibration model in the large delay regime using the MMS. Systems with small delayed terms have been studied extensively as perturbations of harmonic oscillators. Systems with (1) delayed terms, but near Hopf points, have also been studied by the method of multiple scales. However, studies on systems with large delays are few in number. By “large” we mean here that the delay is much larger than the time scale of typical cutting tool oscillations. The MMS up to second order, recently developed for such large-delay systems, is applied. The second order analysis is shown to be more accurate than first order. Numerical integration of the MMS slow flow is much faster than for the original equation, yet shows excellent accuracy. A key point is that although certain parameters are treated as small(or, reciprocally, large), the analysis is not restricted to infinitesimal distances from the Hopf bifurcation. In the present analysis, infinite dimensional dynamics is retained in the slow flow, while the more usual center manifold reduction gives a planar phase space. Lower-dimensional dynamical features, such as Hopf bifurcations and families of periodic solutions, are also captured by the MMS. The strong sensitivity of the slow modulation dynamics to small changes in parameter values, peculiar to such systems with large delays, is seen clearly. In the last part of this thesis, we study the weakly nonlinear whirl of an asymmetric, overhung rotor near its gravity critical speed using a well known two-degree of freedom model. Gravity critical speeds of rotors have hitherto been studied using linear analysis, and ascribed to rotor stiffness asymmetry. Here we present a weakly nonlinear study of this phenomenon. Nonlinearities arise from finite displacements, and the rotor’s static lateral deflection under gravity is taken as small. Assuming small asymmetry and damping, slow flow equations for modulations of whirl amplitudes are developed using the MMS. Inertia asymmetry appears only at second order. More interestingly, even without stiffness asymmetry, the gravity-induced resonance survives through geometric nonlinearities. The gravity resonant forcing does not influence the resonant mode at leading order, unlike typical resonant oscillations. Nevertheless, the usual phenomena of resonances, namely saddle-node bifurcations, jump phenomena and hysteresis, are all observed. An unanticipated periodic solution branch is found. In the three dimensional space of two modal coefficients and a detuning parameter, the full set of periodic solutions is found to be an imperfect version of three mutually intersecting curves: a straight line, a parabola, and an ellipse. To summarize, the first and fourth problems, while involving routine MMS involve new applications with rich dynamics. The second problem demonstrated a semi-analytical approach via the MMS to study a fractional order system. Finally, the third problem studied a known application in a hitherto less-explored parameter regime through an atypical MMS procedure. In this way, a variety of problems that showcase the utility of the MMS have been studied in this thesis.

Incorporating uncertainties in the aeroelastic analysis increases the confidence levels of computational predictions and reduces the need for validation with experimental or flight test data. Helicopter rotor blades, which play a dominant role in the overall vehicle performance, are routinely made of composites. The material properties of composites are uncertain because of the variations in manufacturing process and other effects while in service, maintenance and storage. Though nominal values are listed, they are seldom accurate. In this thesis, the effect of uncertainty in composite material properties on the computational predictions of cross-sectional properties, natural frequencies, blade tip deflections, vibratory loads and aeroelastic stability of a four-bladed composite helicopter rotor is studied. The effect of material uncertainty is studied with the composite rotor blades modeled as components of soft-inplane as well as stiff-inplane hingeless helicopter rotors. Aeroelastic analysis based on finite elements in space and time is used to evaluate the helicopter rotor blade response in hover and forward flight. Uncertainty analysis is performed with direct Monte Carlo simulations based on a sufficient number of random samples of material properties. It is found that the cross-sectional stiffness parameters and natural frequencies of rotor blades show considerable scatter from their baseline predictions. The uncertainty impact on the rotating natural frequencies depends on the level of centrifugal stiffening of each mode. The propagation of material uncertainty into aeroelastic response causes large deviations from the baseline predictions. The magnitudes of 4/rev vibratory loads show deviations of 10 to 600 percent from their baseline predictions. The aeroelastic stability in hover and forward flight conditions also show considerable uncertainty in the predictions. In addition to the effects of material uncertainty, various factors influencing the propagation of material uncertainty are studied with the first-order based reliability methods. The numerical results have shown the need to consider the uncertainties in the helicopter aeroelastic analysis for reliable computational predictions. Uncertainty quantification using direct Monte Carlo simulation is accurate but computationally expensive. The application of response surface methodologies to reduce the computational cost of uncertainty analysis is studied. Response surface approximations of aeroelastic outputs are developed in terms of the composite material properties. Monte Carlo simulations are then performed using these computationally less expensive response surface models. The results of this study show that the metamodeling techniques can effectively reduce the computational cost of uncertainty analysis of composite rotor blades. In the last part of the thesis, an aeroelastic optimization method to minimize the vibration level is developed with due consideration to material uncertainty. Second-order polynomial response surfaces are used to approximate the objective function which smooths out the local minima or numerical noise in the design space. The aeroelastic optimization is carried out with the nominal values of composite material properties and the performance of final design is found to be optimum even for the perturbed values of material properties.

The resolution of the complex physics of rotating configurations is critical for any engineering analysis that requires multiple frames of reference. Two well-known applications are in the rotorcraft and wind energy industries. Rotor wake impingement from rotor-fuselage and wind turbine-tower interactions impact structural and acoustic characteristics. Additionally, parasite drag resulting from rotorcraft hubs may result in severe limitations on forward flight vehicle performance. Complex turbulent wakes from rotors and hubs impinging on downstream empennage can create adverse aeroelastic behavior and can affect handling qualities. Numerical simulations of these flows require state-of-the-art Navier Stokes methods using dynamic overset grids. However, many current methods typically used in industry result in wakes that dissipate essential features. In order to address these concerns, two advancements are introduced in this thesis. Feature-based grid adaptation on dynamic overset grids has been developed and demonstrated with an unstructured Navier Stokes solver. The unique feature of the adaptation technique is that it is applied globally on the overset grid system except within the boundary layer. In concert with grid adaptation, an efficient parallelized search algorithm for solution interpolation over massively distributed systems has been created. This results in cost-effective interpolation that retains the numerical order of accuracy and has been verified in both space and time. The improvements have been demonstrated for rotor-fuselage interaction and a generic rotating hub. Detailed analysis of convergence of the methodology and sensitivity of the results to relevant parameters have also been included.

Dans l’évolution actuelle de mini-drones à décollage et atterrissage vertical, configurations convertibles de type “tilt-rotors” et “tilt-body” sont de plus en plus souvent utilisées. Ces configurations se sont avérées être très sensibles à l’effet du vent latéral quand ils sont en vol de transition ou tout simplement en vol à basse vitesse. Pour cette raison, une bonne compréhension du comportement d’un proprotor et de l’interaction proprotor-voilure à incidence est nécessaire pour la conception de ce type de drones. Un modèle à l’échelle du mini-drone MiniREC a été testée à la soufflerie S4 de type Eiffel de l’ISAE pour comprendre le comportement de la charge aérodynamique du proprotor au cours de la transition du vol vertical au vol horizontal. Aussi, pour observer l’effet d’échelle et étudier le type de proprotor utilisé normalement par les MAV, une deuxième expérience pour proprotors à incidence a été réalisée à la soufflerie SaBRE. Un anémomètre à film chaud a été utilisé pour caractériser le sillage de l’hélice. Les résultats expérimentaux ont montré la grande incidence de ces forces sur la stabilité longitudinale du drone à des angles d’incidence élevés. Il a également été montré que l’écoulement généré par un proprotor au incidence est de nature très instable, cequi rend sa modélisation complexe. D’un point de vue numérique, l’étude de l’hélice à l’incidence a été faite en utilisant l’hypothèse de Glauert pour un disque actuateur au incidence. Les résultats analytiques sont comparés avec les résultats expérimentaux obtenus à partir des mesures à film chauden 2D et une simulation CFD d’un disque actuateur au incidence chargé avec une charge moyenne équivalente aux valeurs de poussée expérimentales SaBRE et une simulation URANS CFD de l’hélice complète. En outre, les résultats de l’expérience S4 ont été comparés au modèle de Ribner pour les hélices en lacet et le modèle de Young qui est une modification statistique de l’analyse Ribner. La modification proposée du modèle de Ribner donne de bons résultats pour les rotors seul, même à des angles d’attaque élevés. Toutefois, il a été clairement démontré que son amélioration ou un nouveau modèle sont nécessaires afin de prévoir correctement la poussée et les forces produites par proprotors simples et co-axiaux. Pour cela un méthode quasi-stationnaire du premier ordre basée sur la théorie de la dynamique des éléments pales a été développée. Enfin, un prototype aérodynamique avec une sensibilité réduite au vent latéral a été conçu, construit et testé dans la soufflerie S4. Le test a montré que la première conclusion à propos de la contribution du proprotor à la sensibilité longitudinaletotale des mini-drones était justifiée et que la nouvelle configuration fait un candidat idéal pour lesconceptions futures de mini-drones basculant à décollage et atterrissage vertical. / In the current development of VTOL mini-UAS and MAVs, configurations like tilt proprotors and tilt-body are being applied more and more often. These types of configurations have shown to be very sensitive to the effect of the lateral wind when they are in transition flight or simply in low speed flight. For this reason a correct understanding of the behavior of a proprotor and the proprotor-wing interaction at incidence is necessary for the design and conception of this type ofUAS. A scaled model of the MiniREC mini-UAS was tested at the ISAE S4 Eiffel type wind tunnel to understand the aerodynamic load behavior of the proprotor during the transition from vertical flight to horizontal flight. Also, to observe the effect of the scale and study the type of proprotor usednormally by MAVs, a second experiment for proprotors at incidence was conducted at the SaBRE wind tunnel. A hot film anemometer was used to characterize the propeller wake. The experimental results showed the great impact of these loads over the longitudinal stability of the drone at highangles of incidence. It was also shown that the nature of the flow for a proprotor at incidence ishighly unsteady which makes its modeling a complex process. From a numerical point of view the study of the propeller at incidence was done using the Glauert’s hypothesis for an actuator disk at incidence. The analytic results are compared with experimental results obtained from the 2D hot film measurements and a CFD simulation of an actuator disk at incidence loaded with a mean load equivalent to experimental SaBRE thrust values and URANS CFD simulation of the full propeller. The results of the S4 experiment were also compared to Ribner’s model for propellers in yaw and the Young’s model which is a statistical modification of Ribner’s analysis. The present modification of Ribner’s model gives good results for single rotors even at high angles of attack. However it wasclearly shown that some improvement or a new model were needed to correctly predict the thrustand the off-axis loads produced by single and coaxial proprotors. For this a first order quasi-steady method based on blade element momentum theory was developed. Finally an aerodynamic prototype(with reduced sensitivity to the lateral wind) was designed on these bases, built and tested in theS4 wind-tunnel. The test showed that the initial conclusion about the contribution of the proprotorto the total longitudinal sensitivity of the mini-UAS were justified and that the new configuration showed a reduced sensitivity to the lateral wind which makes it a perfect candidate for future designs of tilt-body VTOL mini-UAS .

Made available in DSpace on 2014-12-17T14:56:08Z (GMT). No. of bitstreams: 1 ValciFV_TESE.pdf: 3670403 bytes, checksum: d8b060478983488207d8885853eac60d (MD5) Previous issue date: 2012-11-05 / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior / Electrical Motors transform electrical energy into mechanic energy in a relatively easy way. In some specific applications, there is a need for electrical motors to function with noncontaminated fluids, in high speed systems, under inhospitable conditions, or yet, in local of difficult access and considerable depth. In these cases, the motors with mechanical bearings are not adequate as their wear give rise to maintenance. A possible solution for these problems stems from two different alternatives: motors with magnetic bearings, that increase the length of the machine (not convenient), and the bearingless motors that aggregate compactness. Induction motors have been used more and more in research, as they confer more robustness to bearingless motors compared to other types of machines building with others motors. The research that has already been carried out with bearingless induction motors utilized prototypes that had their structures of stator/rotor modified, that differ most of the times from the conventional induction motors. The goal of this work is to study the viability of the use of conventional induction Motors for the beringless motors applications, pointing out the types of Motors of this category that can be more useful. The study uses the Finite Elements Method (FEM). As a means of validation, a conventional induction motor with squirrel-cage rotor was successfully used for the beringless motor application of the divided winding type, confirming the proposed thesis. The controlling system was implemented in a Digital Signal Processor (DSP) / Motores el?tricos transformam energia el?trica em energia mec?nica com relativa facilidade. Em algumas aplica??es particulares, necessita-se de motores el?tricos para trabalhar com flu?dos sem contamina??o, em regime de altas velocidades, em condi??es in?spitas, ou, ainda, em locais de dif?cil acesso e ? profundidade bastante consider?vel. Nestes casos, os motores com mancais mec?nicos, cujo desgaste ocasiona a necessidade de manuten??es, n?o s?o adequados. Uma solu??o poss?vel para este problema adv?m de duas alternativas: motores com mancais magn?ticos, que t?m o inconveniente de aumentar o comprimento da m?quina, e motores-mancais, que agregam compacidade. Motores de indu??o t?m sido cada vez mais utilizados em pesquisas, pois conferem maior robustez aos motores-mancais comparados a esses tipos de m?quinas constru?das com outros motores. As pesquisas j? realizadas com motores-mancais de indu??o utilizaram prot?tipos, cujas estruturas do estator e/ou rotor foram modificadas, diferindo em grande parte dos motores de indu??o convencionais. ? objetivo deste trabalho, estudar a viabilidade do uso dos motores de indu??o convencionais para a aplica??o de motores-mancais, apontando os tipos de motores dessa categoria que mais se ad?quam. O estudo utiliza o M?todo dos Elementos Finitos FEM. Como comprova??o, um motor de indu??o convencional com rotor gaiola de esquilo foi utilizado com sucesso para a aplica??o de motor-mancal do tipo enrolamento dividido, ratificando a tese proposta. O sistema de controle foi implementado em um Processador Digital de Sinais DSP

Les ensembles turbo-alternateurs des centrales électriques sont de grandes machines tournantes de plus de 50 mètres de long et de plusieurs centaines de tonnes. Lors du fonctionnement normal d'une telle machine, une probabilité non nulle existe d'un détachement accidentel d'une aube. Dans une telle situation, un balourd important est généré et du contact apparaît entre les parties tournantes et non tournantes de la machine. Il est alors capital de pouvoir simuler efficacement la dynamique de ce type d'évènement faisant intervenir de fortes non linéarités dans le système. Cette thèse a été réalisée dans le cadre du projet ANR (Agence Nationale de la Recherche) IRINA (SImulation et maîtRise des rIsques en coNception des mAchines tournantes) et en particulier entre le LaMCoS (LAboratoire de Mécanique des Contacts et des Structures) de l'INSA de Lyon et le département AMA (Analyses Mécaniques et Acoustiques) d'EDF R et D à Clamart. Elle a pour objectif de mettre au point une technique rapide de simulation du comportement des lignes d'arbres de machines tournantes en cas de présence de non linéarité de type contact entre rotor et stator. Pour atteindre cet objectif, une double démarche a été mise en place. La première consiste à mettre au point des modèles simplifiés afin de réduire le nombre de degrés de liberté du problème. De surcroît, une technique de réduction de modèle adaptée au cas de non linéarité localisée est utilisée afin de réduire encore plus la taille du système à résoudre. La seconde démarche consiste à mettre au point une technique de résolution rapide du système réduit afin d'obtenir la solution encore plus rapidement. Pour cela, au lieu d'utiliser les traditionnelles techniques d'intégration temporelle directe, c'est la méthode de la balance harmonique qui est mise à profit. Cette technique permet d'obtenir directement la réponse stabilisée du système grâce à une résolution des équations dans le domaine fréquentiel. Dans ce cadre, une maquette numérique a été mise au point mettant en oeuvre les fonctionnalités citées. Cette dernière permet de reproduire les phénomènes physiques périodiques ainsi que quasi-périodiques et de déterminer leur stabilité. Des études paramétriques sur des exemples de problèmes de contact rotor-stator viennent illustrer cette démarche. Enfin, une application sur un cas industriel de groupe turbo alternateur EDF est présentée. / Power plants turbo-generator sets are large rotating machines of more than 50 meters long and weight several hundred tons. During normal operation of such a machine, there is a nonzero probability of an accidental disconnection of a blade. In such a situation, a significant imbalance is generated and contact may occur between the rotating and non-rotating parts. It is therefore essential to be able to effectively simulate the dynamics of this type of event involving strong nonlinearities in the system. This PhD was conducted within the framework of the ANR (Agence Nationale de la Recherche) IRINA (Simulation and risk control in rotating machinery design) and in particular between the LaMCoS (LAboratory of Contact Mechanics and Structures) of the INSA Lyon and the AMA department (Mechanical and Acoustic Analysis) at EDF R and D in Clamart. It aims to develop a fast technique for simulating the behavior of shafts of rotating machinery in case of presence of non-linearity of contact between rotor and stator. To achieve this goal, a dual approach was implemented. The first is to develop simplified models to reduce the number of degrees of freedom of the problem. In addition, a model reduction technique suitable for the case of localized nonlinearity is used to further reduce the size of the system to be solved. The second approach is to develop a technique for efficient resolution of the reduced system to obtain the solution more quickly. To do this, instead of using the traditional direct temporal integration techniques, the harmonic balance method is put to use. This technique allows to directly obtain the stabilized response of the system thanks to a resolution of the equations in the frequency domain. In this context, a numerical model has been developed to implement the features mentioned. The latter allows to reproduce the physical periodic and quasi-periodic phenomena and to determine their stability. Parametric studies of examples of problems of rotor-stator contact will illustrate this approach. Finally, an application on an industrial case of turbo generator EDF is presented.

L’une des principales sources d’inconfort dans un hélicoptère sont les vibrations transmises par le rotor à la structure de l’appareil. En vol d’avancement, des efforts aérodynamiques cycliques sont subis par l’ensemble des pales en tête rotor et génèrent de très fortes vibrations basse fréquence (aux alentours des 17Hz) transmises aux passagers via la boîte de transmission principale puis le fuselage lui-même. Afin de garantir le confort des membres d’équipage et des passagers, de nombreux systèmes antivibratoires ont été conçus. Ces systèmes sont généralement passifs car la majorité de l’énergie vibratoire transmise à la structure se situe à une fréquence unique ωc correspondant à bΩ avec b le nombre de pales et Ω la fréquence de rotation du rotor. Cependant, les appareils modernes évoluent et le régime rotor jusqu’alors fixe durant toutes les phases de vol varie à présent pour des préoccupations de performances et de consommation (variation de l’ordre de +/-10% autour de bΩ). Cette nouvelle contrainte dans la conception des hélicoptères rend pertinente la technologie des systèmes antivibratoires actifs, pouvant s’adapter à la sollicitation en termes d’amplitude et fréquence. Lors de ces travaux de thèse, la suspension passive SARIB de Airbus Helicopters basée sur le principe du DAVI (Dynamic Antiresonant Vibration Isolator) est modifiée afin d’être rendue active par ajout d’une partie actuation/commande. La théorie des lois et algorithmes de contrôle utilisés dans ces travaux, est présentée en détail afin de poser solidement les bases du contrôle actif du prototype de suspension conceptualisé ici à savoir le contrôle FXLMS (adaptatif) et le contrôle optimal LQG. Afin de simuler le fonctionnement du système, un modèle tridimensionnel de la suspension active est construit, couplé à la structure souple de l’hélicoptère (NH90). Sur ce modèle sont alors appliquées les différentes lois de commande introduites auparavant et leurs performances comparées dans différents cas de chargement en tête rotor et surtout pour différentes fréquences de sollicitation. De même, pour chaque algorithme, différentes localisations des capteurs d’erreur sont étudiées afin de converger vers une configuration optimale. Les simulations démontrent que l’algorithme FXLMS feedforward est très bien adapté au contrôle des perturbations harmoniques et permet de réduire très significativement le niveau vibratoire du plancher cabine, sans réinjection parasite dans le reste de la structure. Une comparaison de l’efficacité du SARIB actif avec les systèmes d’absorbeurs en cabine est ensuite effectuée pour démontrer la pertinence d’utiliser le principe du DAVI comme base d’un système actif. Les travaux de cette thèse traitent également des essais réalisés en laboratoire sur le prototype échelle 1 de la suspension SARIB active avec contrôle FXLMS. / One of the main causes of discomfort in helicopters are the vibrations transmitted from the rotor to the structure. In forward flight, the blades are submitted to cyclic aerodynamic loads which generate low frequency (around 17Hz) but high energy mechanical vibrations. These vibrations are transmitted from the rotor to the main gearbox, then to the structure and finally to the crew and passengers. In order to maintain acceptable comfort for crew members and passengers, a lot of antivibration devices have been developed since the last 30 years. These systems are generally passive because most of the mechanical energy transmitted to the structure is at only one frequency ωc which is equal to the product bΩ with b the number of blades and Ω the rotor rotational speed. However, modern helicopters evolve and the rotor rpm, which has always been considered as fixed during flight is now a function of time, depending on the flight phases in order to increase performances and reduce energy consumption (variation bandwidth of Ω +/- 10%). This new constraint on the design of helicopters makes the active antivibration technology completely relevant with its capacity to adapt in terms of amplitude and frequency to the perturbation. During this thesis, the passive suspension called SARIB from Airbus Helicopters, based on the DAVI principle (Dynamic Antiresonant Vibration Isolator) is modified in order to implement active components and command (actuation). The theory of the control algorithms used in this thesis is presented in detail in order to define the theoretical tools of the active DAVI control which are : FXLMS control (adaptive control) and LQG (optimal control). To simulate the complete system, a 3D multibody model of the active suspension has been set up, coupled to a the flexible structure of a NH90 (Airbus Helicopters). On this model are applied the different control algorithms presented before and their performances are compared for different loads with variable frequency on the rotor hub. In the same way, different locations for the error sensors in the structure are studied to find the optimal control configuration. The simulations show that the FXLMS algorithm is well suited for the control of harmonic perturbations and reduce significantly the dynamic acceleration level on the cabin floor, without parasite reinjection on other parts of the structure. A comparison of the active SARIB with classical cabin vibration absorbers is also made in terms of efficiency in order to show the advantages of using the DAVI system as a base for an active antivibration device. Finally, this thesis also presents the experiments realized in the dynamics laboratory of Airbus Helicopters on a 1:1 scale prototype of the active SARIB suspension with FXLMS control. The results demonstrate the efficiency of the active suspension architecture and control algorithms.

Lors de la phase de certification d’un turbomoteur, le motoriste doit démontrer que la perte d’une pale de rotor ne conduit pas au "Knocking-Off", c’est à dire à la rupture en cascade des pales suiveuses. Cette démonstration est faite en général par un essai au banc coûteux car partiellement destructif. Grâce à l’amélioration des moyens de calcul, il devient possible de simuler la réponse transitoire de la structure soumise à ce type de chargement très complexe. En tant que point d’entrée sur la simulation, la connaissance du comportement des matériaux est primordiale. Or, peu d’études sont publiées sur le comportement dynamique des superalliages à base nickel monocristallins et, de surcroît, à des températures élevées de l’ordre de 1000°C. Pour prédire efficacement les conséquences d’impacts sur des pales de turbines, des travaux expérimentaux et numériques ont été réalisés sur un monocristal couramment utilisé par Turbomeca. Des essais de compression dynamique à haute température sur barres de Hopkinson permettent d’estimer le seuil de plasticité et l’écrouissage du matériau en fonction de l’orientation du cristal, de la vitesse de déformation et de la température. Les paramètres d’une loi visco-plastique anisotrope sont identifiés pour modéliser efficacement le comportement macroscopique du MC2 sous des chargements intenses et fortement multi-axiaux. Une campagne d’essais balistiques au banc de Safran Snecma a été réalisée sur des plaques et des pales monocristallines à hautes températures. Afin de prendre en compte la fragmentation des profils dans les calculs de perte de pale, un critère en déformation plastique dépendante du taux de triaxialité des contraintes est calibré puis validé par confrontation aux essais de tirs sur plaques. Des mesures de stéréo-corrélation postmortem et des enregistrements à la caméra rapide permettent de valider les simulations. Une pratique de modélisation de la perte d’une pale avec l’outil LS-Dyna a été établie et appliquée à un cas industriel de perte de pale en service. Enfin, en vue de justifier le découplage temporel entre les dommages primaires, liés aux impacts directs sur les premières pales suiveuses, et secondaires, liés aux effets de l’excentration, une approche de dynamique d’ensemble de ligne d’arbre a été développée puis validée. / During the certification process of a turbo engine, the engine manufacturer has to demonstrate that the loss of a rotor blade does not lead to the "knocking-off" phenomenon, in other words to the cascading failure of the successive blades. Generally, this demonstration is carried out through a costly rig test driving to the partial destruction of the engine. Thanks to the improvement of computational resources, it is now possible to simulate the transient response of the structure subjected to this complex loading. The knowledge of material behavior turns out to be the essential starting point for the simulation. However, only a few studies have been published on the dynamic behavior of nickel-based single crystal superalloys at high temperature reaching 1000°C. With a view to efficiently predicting the consequences of impacts on turbine blades, experimental and numerical works have been conducted on a single crystal frequently used by Turbomeca. High-temperature dynamic compressive tests on Split Hopkinson Pressure Bars (SHPB) have enabled to estimate the material plasticity level and hardening, depending on the crystal orientation, strain rate and temperature. The parameters of a viscoplastic anisotropic law have been identified to effectively model the MC2 macroscopic behavior under highly intense and multiaxial loading. At Safran Snecma Villaroche, ballistic tests have been undertaken on both single crystal plates and blades under high temperatures. In order to consider the fragmentation of profiles in blade-off simulations, a plastic strain criterion depending on stress triaxiality has been calibrated and validated by comparison with the impacts on blades. Post-mortem digital images correlation measurements and high-speed camera recordings have confirmed these simulations. Using LS-Dyna solver, a blade-off modeling strategy has been created and applied to an actual blade-off industrial case. Finally, a rotordynamics approach has been developed and validated with the aim of separately analyzing the primary damage, caused by direct impacts on the first following blades, and the secondary damage due to the effects of unbalance on a flexible rotor.

Ce travail est le produit d’une collaboration entre le LMFA (Laboratoire de Mécanique des Fluides et d’Acoustique, École Centrale de Lyon – France), Snecma et le Cerfacs. Il vise à étudier l’écoulement se développant dans le compresseur haute-vitesse axial de 3.5 étages CREATE (Compresseur de Recherche pour l’Etude des effets Aérodynamique et TEchnologique – vitesse de rotation : 11543 tr/min, vitesse en tête de rotor 1 : 313 m/s), conçu et construit par Snecma et étudié au LMFA sur un banc d’essai de 2 MW. Pour étudier l’écoulement, des mesures stationnaires de pression et température, de la vélocimétrie laser et des mesures rapides de pression statique et totale ont été utilisées. L’analyse se concentre sur deux aspects principaux : l’étude de l’écoulement aux points de fonctionnement stables, avec un intérêt tout particulier pour les interactions rotor-stator, et l’étude des instabilités apparaissant dans la machine à faibles débits.La description de l’écoulement instationnaire aux points stables est faite par le biais de mesures de pression statique en parois, de pression totale et de vitesse, mais également de température totale, entropie et angle d’incidence du fluide. Il est montré que la complexité et l’instationnarité de l’écoulement dans un compresseur multiétagé augmente fortement à l’arrière de la machine à cause des interactions entre les roues fixes et mobiles. Ainsi, une méthode d’analyse modale basée sur la décomposition de Tyler et Sofrin a été développée pour analyser ces interactions. Elle est d’abord appliquée aux mesures de pression afin d’extraire les contributions de chaque roue. Il est ainsi montré que les interactions complexes de pression dans CREATE peuvent être réduites à trois principaux types d’interactions. La méthode de décomposition est enfin appliquée au champ d’entropie dans toute la machine extrait de calculs CFD URANS réalisés par le Cerfacs, afin d’évaluer l’impact des interactions sur les performances de CREATE en terme de génération de pertes.La dernière partie de ce travail est dédié à l’analyse des instabilités apparaissant dans CREATE à faible débit. Il est montré que des ondes de pression tournantes apparaissent aux points stables et augmentent en amplitude à mesure qu’on se rapproche de la ligne de pompage, jusqu’à atteindre une taille critique induisant l’apparition d’une cellule de décollement tournant sur toute la hauteur de veine. Cette cellule entraîne la machine en pompage en seulement quelques tours. L’étude de ces ondes de pression, et la compréhension de leur véritable nature sont réalisées grâce à l’application d’un modèle analytique aux mesures expérimentales. Une description précise du déclenchement et du cycle du pompage est également faite grâce aux mesures de pression statique au dessus des rotors. Un système de contrôle anti-pompage développé au laboratoire et basé sur la détection de l’amplitude des ondes de pression est finalement décrit. / The present work is a result of collaboration between the LMFA (Laboratoire de Mécanique des Fluides et d’Acoustique, Ecole Centrale de Lyon – France), Snecma and the Cerfacs. It aims at studying the flow in the 3.5-stages high-speed axial compressor CREATE (Compresseur de Recherche pour l’Etude des effets Aérodynamique et TEchnologique - rotation speed: 11543 RPM, Rotor 1 tip speed: 313 m/s), designed and built by Snecma and investigated at LMFA on a 2-MW test rig. Steady measurements, as well as laser velocimetry, fast-response wall static and total pressure measurements have been used to experimentally investigate the flow. The analysis focuses on two main aspects: the study of the flow at stable operating points, with a special interest on the rotor-stator interactions, and the study of the instabilities arising in the machine at low mass flow rates.The description of the unsteady flow field at stable operating points is done through measurements of wall-static pressure, total pressure and velocity, but also total temperature, entropy and angle of the fluid. It is shown that the complexity and unsteadiness of the flow in a multistage compressor strongly increases in the rear part of the machine, because of the interactions between steady and rotating rows. Therefore, a modal analysis method developed at LMFA and based on the decomposition of Tyler and Sofrin is presented to analyze these interactions. It is first applied to the pressure measurements, in order to extract the contributions of each row. It shows that all the complex pressure interactions in CREATE can be reduced to three main types of interactions. The decomposition method is then applied to the entropy field extracted from URANS CFD calculations performed by the Cerfacs, in order to evaluate the impact of the interactions on the performance of the machine in term of production of losses.The last part of this work is devoted to the analysis of the instabilities arising in CREATE at low mass flows. It shows that rotating pressure waves appear at stable operating points, and increase in amplitude when going towards the surge line, until reaching a critical size provoking the onset a full span stall cell bringing the machine to surge within a few rotor revolutions. The study of these pressure waves, and the understanding of their true nature is achieved through the experimental results and the use of some analytical models. A precise description of the surge transient through wall-static pressure measurements above the rotors is also provided, as well as a description of a complete surge cycle. An anti-surge control system based on the detection of the amplitude of the pressure waves is finally proposed.