Blade/Casing Rub Interaction in Turbomachinery: Structural Parameters’ Influence on Stability

Abstract

This paper studies the dynamics induced by interactions of rotating blades and the surrounding casing in turbomachinery such as aeroengines. Also known as “blade/casing rub dynamics,” this phenomenon results in vibrations that contribute to fatigue failure, especially in blades. Recently, it was proposed that the underlying dynamics of these interactions is analogous to internal milling operations. This introduces the concept of chatter and its intrinsic time-delay component in the dynamics, which is known to invite some nontrivial instability characteristics. The present paper investigates how the structural properties of the blade and casing components influence the stability of the combined interaction. The cluster treatment of characteristic roots paradigm is used for a delay-dependent stability analysis in the space of the operational parameters. An in-depth analysis reveals important aspects of the stability, which may provide valuable tools for designers. Analytical expressions are derived to calculate the sensitivities of the stability boundaries with respect to certain structural parameters, for the first time in literature to the best knowledge of the authors. Interesting mathematical features of the sensitivity analysis method are also discussed, which can be exploited for improved computational efficiency. The devised theory is demonstrated in a numerical case study.