Assessment of Two Harmonic Balance MethodBased Numerical Strategies for BladeTip/Casing Interactions: Application to NASA Rotor 67

Abstract

The study presented in this paper focuses on the analysis of rubbing interactions—including unilateral contact and dry friction—between a rotating fan blade and a rigid casing by frequency domain methods. Two previously published Harmonic Balance Methodbased methodologies are assessed: (1) an approach relying on augmented Lagrangians and (2) a second method using a regularized penalty law combined with a Lanczos σapproximation filter. As a reference point for this comparison, a timedomain numerical strategy relying on a Lagrange multiplierbased contact treatment is considered. All computations are run with the NASA rotor 67 fan blade, an open industrial blade geometry. As it undergoes structural contacts, this blade features an intricate dynamics response, thus making it a challenging case study for nonlinear iterative solvers. The contact scenario is chosen to be an ovalization of the casing with no external forcing. This scenario induces highly nonlinear responses of the blade and complex phenomena such as isolated frequency response curves. The results presented underline a very good agreement of the different strategies with the reference time marching approach. An indepth comparison is made with an emphasis on nonlinear frequency response curves (NFRC) and time signals. Finally, a physical analysis of the encountered isolas is presented through an indepth investigation of the main modal contributions for each computed solution. In the end, this paper provides new qualitative elements allowing for a better understanding of rubbing interactions that may not be efficiently obtained with time marching procedures.