Abstract
This paper considers the interaction between a rotating bladed-disc and static casing, specifically a synchronisation phenomenon called wave speed coincidence. Through tip rub, travelling waves in the bladed-disc and casing can interact and cause large amplitudes of vibration. Previous work has analysed this phenomenon using time integration methods, which are often too computationally expensive for early design stages, and frequency domain approaches such as the harmonic balance method, which require simplification in the periodicity of the problem limiting the usefulness of such methods. This paper demonstrates the use of a power method and consideration of periodicity over a contact cycle. This allows the problem to still be considered as a periodic behaviour, but without the loss of generality associated with conditional harmonic balance methods. This is useful as a faster screening method for preliminary design stages and a way to down-select high risk cases, where further time integration analyses can be performed. The method is also applied to cases with asymmetric casings, allowing quantitative assessment of the effect of asymmetry in the future. In this case, as a result of the asymmetry, the interaction quickly became non-wave speed coincidence. Nevertheless positive power into the casing continued to be observed in some cases, suggesting potential instability from the subsequent blade rubs.
