abstract: Monte Carlo simulations are traditionally carried out for the determination of the amplification of forced vibration response of turbomachine/jet engine blades to mistuning. However, this effort can be computationally time consuming even when using the various reduced order modeling techniques. Accordingly, some investigations in the past have focused on obtaining simple approximate estimates for this amplification. In particular, two of these have proposed the use of harmonic patterns of the blade properties around the disk as an approximate alternative to the many random patterns of Monte Carlo analyses. These investigations, while quite encouraging, have relied solely on single degree of freedom per sector models of the rotor. In this light, the overall focus of the present effort is a revisit of harmonic mistuning of rotors focusing first the confirmation of the previously obtained findings with a more detailed model of the blisk in both conditions of an isolated blade-dominated resonance and of a veering between blade and disk dominated modes. The latter condition cannot be simulated by a single degree of freedom per sector model. Further, the analysis will consider the distinct cases of mistuning due to variations of material properties (Young's modulus) and geometric properties (geometric mistuning). In the single degree of freedom model, both mistuning types are equivalent but they are not, as demonstrated here, in more realistic models. The difference arises because changes in geometry induce not only changes in natural frequencies of the blades alone but of their modes and the importance of these two sources of variability is discussed with both Monte Carlo simulation and harmonic mistuning results. The present investigation focuses also on the possible extension of the harmonic mistuning concept and of its quantitative information that can be derived from such analyses. From it, a novel measure of blade-disk coupling is introduced and assessed in comparison with the coupling index introduced in the past. In conclusions, the low cost of harmonic mistuning computations in comparison with full Monte Carlo simulations is demonstrated to be worthwhile to elucidate the basic behavior of the mistuned rotor in a random setting. / Dissertation/Thesis / Masters Thesis Mechanical Engineering 2014

The application of laser Doppler vibrometry to high speed rotating structures has been hampered by technical limitations. Whereas full-field three-dimensional velocity measurements can be made on stationary structures, the capability on rotating structures is limited to low speed, one-dimensional, steady state operation. This work describes the implementation of a self-tracking laser vibrometry system which overcomes many of the limitations of current techniques for vibration measurements on rotating structures. A model of the self-tracker is developed and used to predict the effects of static misalignments on the position and velocity errors. These predictions are supported by experimental results and simplified models of the self-tracker. NOTE: (02/2011) An updated copy of this ETD was added after there were patron reports of problems with the file. / Ph. D.

Lightweight designs in engineering applications give rise to flexible structures with extremely low internal damping. Vibrations of these flexible structures due to an unwanted excitation of system resonances may lead to high cycle fatigue failure and noise propagation. A common method to suppress the vibrations is to increase the damping of the system using one of the classical control techniques i.e. passive, active, and/or hybrid. Passive techniques are those control systems that are simply integrated into the structures with no need of external power source for their operations, like viscoelastic damping, piezoelectric and electromagnetic shunt damping, tuned mass damper, etc. However, the control performance of these systems, in terms of the damping ratio and the robustness to uncertainties, is highly limited to the system properties. For example, viscoelastic damping may not perform well at low frequencies and the performance of shunt damping is dependent on the electromechanical coupling between the structure and the transducer. To overcome the limitations associated with passive controls, it has been proposed to use active control systems, which are less sensitive to the system's parameters, to improve the control performance. It requires an integration of sensors and actuators with a feedback loop containing control laws. However, the high requirement of the external power source is not favorable for engineering applications where energy efficiency is the key parameter. The combination of active and passive strategies, known as hybrid control systems, can provide a fail-safe configuration with a high control performance and low power consumption. The price to pay for such configurations is the complexity of the design. This doctoral thesis first investigates the conceptual designs of all kinds of classical control systems for a simplified mechanical system. They include 1) the passive shunt using an electromagnetic transducer, 2) the active control system using positive and negative feedback, and 3) the hybrid electromagnetic shunt damper using both an active voltage source as well as an active current source. The next part of this thesis is focused on bladed structures as real-life applications which highly require vibration control due to their low internal damping. Because of practical reasons, piezoelectric transducers are used for the application of control systems. The finite element model of the structure is made first without piezoelectric patches to optimize the best locations of piezoelectric patches. Then, the model is updated with the piezoelectric patches to numerically simulate different control strategies. The experiments are performed to validate the numerical designs. / Doctorat en Sciences de l'ingénieur et technologie / info:eu-repo/semantics/nonPublished

High cycle fatigue (HCF) failure has been studied extensively over the last two decades. Its impact on jet engines is severe enough that may result in engine losses and even life losses. The main requirement for fatigue life predictions is the stress caused by mechanical vibrations. One of the factors which have major impact on the vibratory stresses of bladed disk assemblies is a phenomenon called &ldquo / mistuning&rdquo / which is defined as the vibration localization caused by the loss of cyclic periodicity which is a consequence of inter&amp / #8208 / blade variations in structural properties. In this thesis, component mode synthesis method (CMSM) is combined with nonlinear forced response analysis in modal domain. Newton&amp / #8208 / Raphson and arc length continuation procedures are implemented for the solution. The component mode synthesis method introduces the capability of imposing mistuning on the modal properties of each blade in the assembly. Forced response analysis in modal domain reduces the problem size via mode truncation. The main advantage of the proposed method is that it is capable of calculating nonlinear forced response for all the degrees&amp / #8208 / of&amp / #8208 / freedom at each blade with less computational effort. This makes it possible to make a stress analysis at resonance conditions. The case studies presented in this thesis emphasize the importance of number of modes retained in the reduced order model for both CMSM and nonlinear forced response analysis. Furthermore, the results of the case studies have shown that both nonlinearity and mistuning can cause shifts in resonance frequencies and changes in resonance amplitudes. Despite the changes in resonance conditions, the shape of the blade motion may not be affected.

No description available.

<p>Two state of the art finite element reduction techniquespreviously validated against the direct finite element method,one based on classical modal analysis and another based oncomponent mode synthesis, are applied for efficient mistunedfree vibration and forced response analysis of several bladeddisk geometries. The methods are first applied to two testcases in order to demonstrate the differences in computationalefficiency as well as to validate the methods againstexperimental data. As previous studies have indicated, nonoticeable differences in accuracy are detected for the currentapplications, while the method based on classical modalanalysis is significantly more efficient. Experimental data(mistuned frequencies and mode shapes) available for one of thetwo test cases are compared with numerical predictions, and agood match is obtained, which adds to the previous validationof the methods (against the direct finite element method).</p><p>The influence of blade-to-blade coupling and rotation speedon the sensitivity of bladed disks to mistuning is thenstudied. A transonic fan is considered with part span shroudsand without shrouds, respectively, constituting a high and alow blade-to-blade coupling case. For both cases, computationsare performed at rest as well as at various rotation speeds.Mistuning sensitivity is modelled as the dependence ofamplitude magnification on the standard deviation of bladestiffnesses. The finite element reduction technique based onclassical modal analysis is employed for the structuralanalysis. This reduced order model is solved for sets of randomblade stiffnesses with various standard deviations, i.e. MonteCarlo simulations. In order to reduce the sample size, thestatistical data is fitted to a Weibull (type III) parametermodel. Three different parameter estimation techniques areapplied and compared. The key role of blade-to-blade coupling,as well as the ratio of mistuning to coupling, is demonstratedfor the two cases. It is observed that mistuning sensitivityvaries significantly with rotation speed for both fans due toan associated variation in blade-to-blade coupling strength.Focusing on the effect of one specific engine order on themistuned response of the first bending modes, it is observedthat the mistuning sensitivity behaviour of the fan withoutshrouds is unaffected by rotation at its resonant condition,due to insignificant changes in coupling strength at thisspeed. The fan with shrouds, on the other hand, shows asignificantly different behaviour at rest and resonant speed,due to increased coupling under rotation. Comparing the twocases at resonant rotor speeds, the fan without shrouds is lessor equally sensitive to mistuning than the fan with shrouds inthe entire range of mistuning strengths considered.</p><p>This thesis’scientific contribution centres on themistuning sensitivity study, where the effects of shrouds androtation speed are quantified for realistic bladed diskgeometries. However, also the validation of two finite elementreduction techniques against experimental measurementsconstitutes an important contribution.</p>

One of the most important problems that plague turbomachinery rotors is the existence of rogue blades -- lone blades that exhibit unexpected fatigue failure. It has been recognized that rotor mistuning might be the cause of rogue blades through a phenomenoncalled normal mode localization, whereby vibration energy is confined to a few blades of the assembly. The goals of this dissertation are (1) to achieve a thorough understanding of the fundamental mechanisms governing mistuning effects, (2) the development of mathematical models of turbomachinery rotors suitable for mistuning analysis, and (3) the development of techniques for designers interested in the mistuning sensitivity of a particular rotor design.

Bladed disks are critical structural components in jet engines and other turbomachinery. The nominal design for a bladed disk is typically assumed to have identical blades. However, there are always small, random variations in the blade properties due to manufacturing tolerances, material defects, and operational wear. These blade-to-blade discrepancies, called mistuning, can have a dramatic effect on bladed disk vibration. In particular, mistuning can cause localization of the response in a small region of the bladed disk, leading to higher blade stress and high-cycle fatigue concerns. While comprehensive analytical and computational studies of mistuning have been performed, relatively few experimental investigations have been conducted. The primary objective of this research is to experimentally investigate the fundamental structural dynamics of mistuned bladed disks, and to achieve a physical understanding of mistuning effects by accounting for the influence of important phenomena that have been largely neglected in previous mistuning models and system identification algorithms. First, a systematic experimental approach is presented to validate a new mistuning identification and model updating algorithm for single-piece bladed disks, or blisks. It is shown that only a few system response measurements taken at resonant frequencies are required to identify the blade stiffness mistuning parameters and the model updating parameters referred to as cyclic modeling error. By incorporating a model updating procedure, the accuracy of the mistuning identification results are significantly improved. Second, an alternative approach for vibration testing of many mistuning patterns is proposed and validated. In particular, varying the external forcing function provided to the blades is used to mimic the influence of structural blade property mistuning on the vibration response. Since it is much easier and more efficient to vary the external excitation than to physically alter the blades, this work opens the possibility of running an experimental analogue of a Monte Carlo simulation. Finally, the mistuning identification method is extended to also identify the forcing amplitude and phase applied to each blade. This approach shows promise as a powerful tool for accelerating calibration procedures, as well as for improving the accuracy and capability of experimental methods for bladed disks.

Crack initiation and propagation in the bladed disks of aero-engines caused by high-cycle fatigue under cyclic loads could result in the breakdown of the engines if not detected at an early stage. Although a number of fault detection methods have been reported in the literature, it still remains very challenging to develop a reliable online technique to accurately diagnose defects in bladed disks. One of the main challenges is to characterize signals contaminated by noises. These noises caused by very dynamic engine operation environment. This work presents a new technique for engine bladed disk crack detection, which utilizes advanced analysis of clearance and time-of-arrival signals acquired from blade tip sensors. This technique involves two stages of signal processing: 1) signal pre-processing for noise elimination from predetermined causes; and 2) signal post-processing for characterizing crack initiation and location. Experimental results from the spin rig test were used to validate technique predictions.

Les disques aubagés, que l’on trouve dans les turbomachines, sont des structures complexes dont le comportement vibratoire est généralement déterminé par l’exploitation de conditions de symétrie dans leur configuration nominale. Cette symétrie disparaît lorsque l’on assemble plusieurs de ces disques pour former un rotor ou que l’on introduit une variabilité spatiale des paramètres mécaniques (on parle de désaccordage intentionnel ou non). Le raffinement des maillages, nécessaire à une évaluation correcte de la répartition des contraintes, conduirait à des modèles de rotor complet de taille prohibitive (plusieurs dizaines de millions de degrés de liberté). L’objectif de cette thèse est donc l’introduction de méthodologies de réduction qui par combinaison de calculs acceptables permettent d’étudier de façon fine la dynamique d’ensemble sur des modèles 3D fins multi-étages et potentiellement désaccordés. L’étude des transformations de Fourier séparées des réponses de chaque étage permet, dans un premier temps, de bien comprendre les effets de couplage inter-harmonique liés au couplage inter-disque et au désaccordage. A partir de ce constat, une première méthode utilise les résultats de calculs en symétrie cyclique et à secteur encastré pour construire un modèle de secteur exact pour certains modes dits cibles et de très bonne qualité pour les autres modes. Cette méthode est ensuite étendue au cas multi-étage en construisant des bases de réduction de secteur par combinaison de solutions mono-harmoniques. Les illustrations montrent que la méthodologie proposée permet le traitement de modèles de très grande taille, tout en restant compatible avec une grande richesse de post-traitements (calculs de modes, calculs de réponses forcées, analyses de leur contenu harmonique spatial, répartition d’énergie et effets de localisation...). La méthodologie est enfin étendue à la gestion de modèles paramétrés en vitesse de rotation. L’enrichissement des ensembles de modes cibles par des calculs à trois vitesses permet ainsi une reconstruction rapide de l’évolution des fréquences pour l’ensemble d’un intervalle. / Bladed disks found in turbomachines are complex structures whose vibration characteristics are generally determined by exploiting the symmetry properties of their nominal configuration. This symmetry no longer exists either when disks are assembled to form a rotor or when discrepancies in the mechanical parameters are introduced (intentional or unintentional mistuning). Fine meshes required to correctly evaluate stress distributions would lead to prohibitive model sizes (typically a few million degrees of freedom). The objective of this thesis is to introduce model reduction techniques that rely on the combination of separate computations of acceptable size. This provides a means for in-depth studies of the behaviour of dense 3D models of multi-stage bladed rotors with possible mistuning. At first, Fourier transforms performed separately on each individual disk allows to understand the inter-harmonic coupling induced by inter-stage coupling and mistuning. From this study, a first method uses cyclically symmetric solutions plus sector modes with fixed inter-sector interfaces to build a reduced sector model. The latter is exact for target modes and very accurate for others. This method is extended to multi-stage assemblies by employing multi-stage mono-harmonic eigensolutions. Illustrations focus on the proposed methodology that enables to deal with large scale industrial models while remaining compatible with various post-processing procedures (free or forced response computations, analysis of their spatial harmonic content, energy distributions and localization effects...). This methodology is finally extended to the handling of parametric models depending on the rotation speed. The enrichment of the initial sets of target vectors with computations at three rotation speeds enables a fast and accurate recovery of the evolution of the eigenfrequencies with respect to the rotation speed in any operating range.