Application of Numerical Bifurcation Tracking Strategy to Blade-Tip/Casing Interactions in Aircraft Engines

Abstract

Building on the regularized-Lanczos harmonic balance method (RL-HBM), a previously developed frequency method, this paper presents a numerical bifurcation tracking strategy dedicated to high-dimensional nonlinear mechanical systems. In order to demonstrate its applicability to industrial applications, it is here used to obtain original results in the context of blade-tip/casing interactions in aircraft engines. The emphasis is put specifically on the tracking of predicted limit point (LP) bifurcations as key parameters—such as the amplitude of the aerodynamic forcing applied on the blade, the friction coefficient or the operating clearances—vary. Overall, presented results underline that the employed frequency method is well-suited to tackle the numerical challenges inherent to such computations on high-dimensional systems. For the mechanical system of interest, the industrial fan blade National Aeronautics and Space Administration (NASA) rotor 67, it is shown that the application of the presented strategy yields an efficient way to identify isolated branches of solutions, which may be of critical importance from a design standpoint.