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Modélisation dynamique des systèmes disque aubes multi-étages : Effets des incertitudes

Abstract : Recent designs in turbomachinery tend to have more flexible inter-stage rims and to be more lightly damped, resulting in configurations where modes might not be confined to only one stage. In general, multi-stage rotors have no particular axial symmetry property and the computationally costly analysis of the whole structure becomes mandatory. However, a multi-stage cyclic symmetry approach can be used for reducing the cost of modeling rotors composed of several stages even when the stages have different numbers of sectors. This approach takes advantage of the inherent cyclic symmetry of each stage and uses a specific assumption that results in decoupled subproblems for each spatial Fourier harmonic. The methodology proposed in this work allows including uncertainties in the analysis of multi-stage rotors using the multi-stage cyclic symmetry approach and the Polynomial Chaos Expansion. Uncertainties in rotors may arise from in-use wear of blades, temperature changes or manufacturing tolerances. As a first approach, only uncertainties arising from uniform in-use wear of the set of blades are included. These may be modeled by considering a global variation of the material properties of the set of blades of a particular stage. The multi-stage cyclic symmetry approach can then be used since the underlying assumption of identical sectors is respected. The positiveness of the random matrices involved is reached by using gamma-distributed random variables which imply the use of Laguerre's polynomials as basis for the polynomial chaos. Numerical examples representative of various types of turbomachinery are introduced in order to assess the robustness of the method of multi-stage cyclic symmetry. Uncertainties results for the free and forced response analyses obtained by the polynomial chaos are validated by comparison with Monte Carlo simulations. The considered uncertainties induce variations on the mode shapes that evolve between different families of modes in areas of high modal density. These variations result in significant changes in the global dynamics of the structure and must be considered in the context of robust designs.
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Bartolomé Segui Vasquez. Modélisation dynamique des systèmes disque aubes multi-étages : Effets des incertitudes. Autre. INSA de Lyon, 2013. Français. ⟨NNT : 2013ISAL0057⟩. ⟨tel-00961270⟩

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