<p>One strategy frequently considered by aircraft engines manufacturers to increase aerodynamic efficiency is to reduce the clearance between blade tips and the surrounding casings. However, this solution comes at the expense of increasing the risk of harmful structural interactions. Indeed, contacts may stem from high amplitude vibrations thus yielding to a significant reduction of blades life-span. In order to mitigate potentially prejudicial interactions, advanced numerical strategies are deployed to take into account contact-induced nonlinearities along the blade tip. Aircraft engine manufacturers in particular need reliable predictive numerical vibration tools. There exists several numerical frameworks in which blade-tip/casing contacts may be analyzed. One may distinguish two classes of numerical methods: time integration based strategies and frequency methods. Time integration is costly but advantageously does not rely on any assumption with respect to the system's response; it is still commonly used today in the industry. To the contrary, frequency methods typically rely on an assumption of periodicity but may provide fast and reliable results. More importantly, frequency methods such as the harmonic balance method, when coupled to continuation algorithms, are able to provide a qualitative view of a system's dynamics which is key for understanding underlying physical phenomena. Parametric explorations including bifurcation analyses thus become within reach. In this study, a frequency-domain approach using the harmonic balance method coupled to a predictor-corrector continuation algorithm is implemented. Unilateral contact and dry friction are taken into account by means of a regularized penalty law. In order to enhance the robustness of the methodology, particular attention is paid to the mitigation of the Gibbs phenomenon. The traditional AFT scheme is here improved by a Lanczos sigma-approximation so that the computed nonlinear contact forces do not feature detrimental oscillations. This approach is applied considering the reduced-order model of an industrial compressor blade, namely a blade of the NASA rotor 37. Obtained results are compared to a well-calibrated time-integration based numerical strategy. The developed tool paves the way for accurate, fast and robust assessment of a blade vibration response following contacts; which is key for modern engine designs.</p>

Development of a Harmonic Balance Based Methodology for Blade-Tip/casing Interactions: Application to Nasa Rotor 37

Paper Proceedings: https://asmedigitalcollection.asme.org/GT/GT2021/volume/84898

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