Vibration response analysis of a rotational shaft–disk–blade system with blade-tip rubbing

• Effects of blade stagger angles on the blade rubbing-induced responses are analyzed.
• Amplitude amplification phenomena and super-harmonic resonances can be observed.
• Period-doubling bifurcation phenomenon can be observed under the large casing stiffness.
• Torsional vibration is sensitive to blade-tip rubbing relative to the system lateral vibration.

This paper aims at the blade-casing rubbing in a shaft–disk–blade (SDB) system including shaft, disk, blade and bearing, and focuses the effects of stagger angles of blades, rotational speeds and casing stiffness on the rubbing-induced vibration responses of the SDB system and casing. Firstly, a finite element (FE) model of an SDB system is developed, and the rubbing between the blade-tip and casing is simulated using contact dynamics theory. In the proposed model, Timoshenko beam elements are adopted to simulate the shaft and the blade, and shell elements to simulate the disk, and spring-damping elements to simulate the ball bearings. A point–point contact element is adopted to simulate the blade-casing rubbing. Moreover, the augmented Lagrangian method is utilized to deal with contact constraint conditions, and the Coulomb friction model is used to simulate the friction between the blade and casing. The proposed model is also validated by comparing the natural frequencies with those obtained from the published literature. The results indicate that (1) amplitude amplification phenomena can be observed when the multiple frequency components coincide with the torsional natural frequency of the SDB system and the bending natural frequencies of the blades under rotational state; (2) the torsional vibration features of the SDB system with blade-tip rubbing are more significant than the lateral vibration features of the shaft; (3) the torsional vibration of the SDB system increases, and the blade bending vibration reduces with the increase of the stagger angle of the blade; (4) period-2 motion may appear under the large casing stiffness and high rotational speeds, and the torsional vibration of the SDB system and blade bending vibration tend to increase with the increasing casing stiffness.