Rotating blade-casing rubbing simulation considering casing flexibility

Abstract

In the traditional rubbing model, the overall displacement (rigid body displacement) of the casing is always taken into account, while the local flexible deformation is either ignored or simply assumed as a spring element. Due to the small thickness of the casing (about 2–4 mm), there may exist a large error for predicting the normal rubbing force using the traditional model, which can lead to the error when the local deformation and wear extent are calculated. Aiming at this phenomenon, this paper deduces an improved rotating blade-casing rubbing model based on elastic compatibility conditions. During the derivation, the centrifugal stiffening, spin softening and rubbing softening are considered and the quasi-static bending displacement of blade is calculated based on the theory of mechanics of materials. The casing is regarded as a flexible ring with spring support in the radial direction, and the displacements are composed of rigid-body and flexible displacements. Ignoring the effects of the kinetic energy, according to Hamilton principle, the structural stiffness of the casing under the quasi-static condition is obtained. The proposed model is verified by comparing with the experimental data obtained from both rigid casings and flexible casings in published references. Based on a rotating-blade-flexible-casing system, the rubbing-induced vibration behaviors from both finite element (FE) model in ANSYS software and the proposed model are figured out and compared with each other for testing the effectiveness of the proposed model again. A frequency sweep is performed in order to better understand the resonances of the blade and casing. Vibration responses obtained from the traditional rubbing model and the proposed model are also compared with each other so that the advantages of the proposed model is emphasized. The comparison results show that the normal rubbing forces obtained from the proposed model are closer to the experimental results because the proposed rubbing model can accurately describe the flexible deformations of the casing under both quasi-static and dynamic conditions. The rubbing-induced blade vibration responses obtained from the traditional and proposed rubbing models agree well, however, the dynamic rubbing forces obtained from the proposed model are smaller than those from the traditional model. In addition, different combined nodal-diameter modes of the casing can be excited under different rotating speeds.