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

Abstract

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.

Stability Analysis of an Industrial Blade Accounting for a Blade-Tip/Casing Nonlinear Interface

“…Results obtained with the RL-HBM for industrial blade models are in agreement with those obtained with time integration [8]. They also advantageously yield an accurate estimate of a blade's actual nonlinear resonance as it impacts the surrounding casing [9].…”

“…In this context, the recent development of a harmonic balance method-based approach [8,9]-referred to as RL-HBM (Regularized-Lanczos Harmonic Balance Method) in the remainder-for the analysis of blade-tip/casing contact interactions is promising. While it may allow to efficiently combine distinct nonlinear interfaces within a homogeneous solution framework, the RL-HBM also opens new avenues to provide designers with a much needed qualitative understanding of blade-tip/casing contacts.…”

Methodology for the Redesign of Compressor Blades Undergoing Nonlinear Structural Interactions: Application to Blade-Tip/Casing Contacts

“…3 Redesign of NASA rotor 37 NASA rotor 37 is a transsonic compressor blade for which a peak in vibration amplitude was numerically identified when blade-tip/casing contacts occur over an angular speed range located close to the intersection of its first bending mode and the fourth engine order [22]. As a case study for the proposed redesign methodology, it is here optimized with respect to its clearance consumption.…”

“…As in previous works [13,22], the material properties of a 18Ni 200-grade maraging steel are used for all rotor 37 models: Young's modulus E = 180 GPa, Poisson's ratio ν = 0.3, and density ρ = 8000 kg•m −3 . FE meshes of all considered blade models feature 20781 nodes and 6384 elements.…”

“…With respect to the contact scenario, a deformed rigid casing with two privileged contact areas is considered. Parameters issued from a previous publication are used [22]; in particular, blade-tip/casing clearance at rest is 5 × 10 −4 m. For the considered angular speed range, highest displacements are observed at the leading edge, thus motivating the choice of this particular location in the remainder.…”