Comparison of rubbing induced vibration responses using varying-thickness-twisted shell and solid-element blade models

In aircraft engines, small gaps between the rotating blade and casing can improve the overall efficiency, but may also cause blade-casing rubbings, which usually induce damages of the blade and casing, or generate excessive vibrations of rotor. Numerical simulation is the most commonly used method in analyzing blade-casing rubbings, but the simulation results are highly affected by blade modeling techniques. In this study, two finite element (FE) models of blade, i.e., a variable-thickness-twisted shell (VTTS) model and a solid element model are developed on the platform of ANSYS software, and rubbing induced vibration responses using the two FE models are compared. In these two models, the blade-tip is equally divided into 20 elements, and the corresponding casing is equally divided into 21 two-degree-of-freedom lumped mass points (LMPs) along the axis of rotation, which are rigidly connected (i.e., these mass points have the same vibration displacements) to describe the global casing vibration. Rubbing induced vibration responses of the blade and casing are investigated based on these models, where the angle misalignment, radial misalignment, radial elongation of the blade-tip and casing vibration are taken into account. Considering the effects of angle misalignment, blade-casing rubbing is simulated during the run-up process from 0 RPM to 10,000 RPM. The results exhibit that the VTTS model has higher calculation efficiency than the solid model in the rubbing simulation. For example, for the rubbing simulation during the run-up process, the calculation time using the VTTS model decreases by almost 23% comparing with the solid element model under the same element numbers (400 elements). In these two models, the rubbing-induced vibration characteristics, such as super-harmonic resonances and flexural-torsional coupled vibrations, are almost the same. The errors between the primary and super-harmonic resonance speeds are all less than 1%, and the maximum error between the amplitudes corresponding to these resonance speeds is about 1.23%. In addition, because the different centrifugal loads acting on model nodes lead to different blade-tip deformations rooting in the nonuniformity of the blade thickness along the chordwise direction, different rubbing positions are also detected by using these two models.