Development of a Harmonic Balance Method-Based Numerical Strategy for Blade-Tip/Casing Interactions: Application to NASA Rotor 37

In this study, a frequency-domain approach based on the harmonic balance method coupled to a predictor-corrector continuation algorithm is implemented for the qualitative analysis of blade-tip/casing contacts in aircraft engines. Unilateral contact and dry friction are taken into account through a regularized penalty law. To enhance the robustness of the methodology, particular attention is paid to the mitigation of the Gibbs phenomenon. To this end, the employed alternating frequency/time scheme features a Lanczos σ-approximation so that spurious oscillations of the computed nonlinear contact forces become negligible. This approach is applied in combination with a model reduction technique on an industrial compressor blade: NASA rotor 37. In order to assess the influence of both the contact law regularization and the Lanczos σ-approximation, obtained results are thoroughly compared to an existing time integration-based numerical strategy relying on a Lagrange multiplier-based approach for contact treatment and that was previously confronted to experimental results. Presented results underline the very good agreement between the proposed methodology and the reference time integration numerical strategy. The proposed developments thus complement existing results on blade-tip/casing contact adding a much needed qualitative understanding of the interaction and an accurate assessment of the contact stiffening phenomenon.