A dynamic model for simulating rubbing between blade and flexible casing

Considering the effects of blade rotation and casing flexibility, a new blade-casing rubbing model is proposed. The blade is assumed to be clamped on a rigid disk and simulated by the twisted-shape plate model with a stagger angle, while the casing is simulated by the cylindrical shell model. Considering the influences of the centrifugal stiffening, spin softening and Coriolis force, the equations of motion of the rotating blade are obtained by Hamilton's principle and Galerkin method; the equations are coupled with flexural, radial and swing vibrations. Based on Sanders' shell theory, the cylindrical shell casing with elastic constraints is established where the elastic constraints are described using a set of springs on casing edges. Both models are verified by the result comparisons obtained from the finite element (FE) model or the published literature. The blade-tip is divided into n points along the chordwise direction of the blade, and whether rubbing occurs or not can be determined by judging the position relations between the blade-tip points and the corresponding casing points. The rubbing-induced vibration responses between the rotating blade and the flexible casing are also compared with those obtained from the rubbing model with the rigid casing and the FE model with the flexible casing. The results show that, compared with the rigid casing model using lumped mass points, the cylindrical shell casing model can consider the flexibility of the casing, and the nodal diameter vibration of the casing induced by rubbing can be observed. Moreover, both the rubbing force and the vibration response of the blade contacting with the flexible casing will decrease compared with those contacting with the rigid casing. Finally, based on the proposed model, the effects of rotational speed, blade shape, blade-tip geometry and asymmetric support boundary of casing on the rubbing responses of the system are also analyzed. (C) 2019 Elsevier Ltd. All rights reserved.