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Développement de modèles numériques de roues aubagées désaccordées dans un contexte non-linéaire

Abstract : Aircraft engines are composed of bladed disks rotating at high speed and isolated from the external environment by the casing. The clearance between the blades and the casing favors the formation of vortices, resulting in aerodynamic losses. In order to improve overall engine efficiency, manufacturers are therefore seeking to reduce this clearance. However, the reduction of clearances favors the occurrence of contacts between the blades and the casing. The resulting non-linear vibrations are particularly detrimental to the proper operation of the engine due to the high relative speeds between the components. Thus, understanding these non-linear phenomena is a major industrial issue. Although blades are designed to be identical, small variations in mechanical properties are inevitably generated during manufacturing or due to in-service wear. This symmetry break, known as mistuning, induces changes in the vibratory behavior of the bladed disk, compared to that expected for a tuned bladed disk. In particular, the vibration amplitudes are greatly amplified, thus reducing the engine operating life. Stochastic approaches, made possible by the development of numerical simulations, are used in order to characterize the vibrations of mistuned bladed disks. To date, little research has been conducted on the study of non-linear vibrations — due to friction or contact — and mistuning. However, these two aspects greatly modify the dynamic behavior of bladed disks, so that taking them into account greatly improves the predictability of the simulations. The most recent researches rely on deterministic approaches to study the influence of mistuning on the non-linearities occurring inside the bladed disk, with low relative speeds. The influence of mistuning on non-linear vibrations has not been studied with a stochastic approach so far, nor by considering the contact nonlinearities between the blades and the casing, which imply high relative speeds. The present research thus represents the first combined analysis of mistuning and blade/casing contact non-linearities. Numerical modeling are performed using the finite element method. The equations of motion are solved by a time integration algorithm and the contact management is performed by the Lagrange multiplier method. Firstly, a stochastic study is carried out on a phenomenological model to validate the proposed methodology. Vibration amplifications due to mistuning in the non-linear framework are much higher than those obtained in the linear framework. Moreover, the non-linear interactions predicted on the tuned model are robust to small mistuning. A reduced order technique is then developed to generate mistuned models with a contact interface, at a negligible calculation cost. This development makes stochastic calculations possible on an industrial model, studied in a nominal configuration. Changes in the vibratory behavior of the blades are highlighted as the mistuning level increases, leading to high levels of vibration amplifications. Stress fields are also analyzed, indicating that the stress levels in the bladed disk increase significantly for the highest mistuning levels considered. Finally, the contact management methodology used, coupled with the reduced detuned model generation method developed, allows to generate Blade Tip-Timing data. The results obtained show that the methodology can be used to study stochastically the robustness of the mistuning identification algorithms, and to develop new algorithms for the analysis of non-linear phenomena.
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Jeanne Joachim. Développement de modèles numériques de roues aubagées désaccordées dans un contexte non-linéaire. Génie mécanique [physics.class-ph]. Ecole Polytechnique de Montréal, 2020. Français. ⟨tel-02888893⟩

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