The influence of disk's flexibility on coupling vibration of shaft–disk–blades systems

The coupling vibrations among shaft-torsion, disk-transverse and blade-bending in a shaft–disk–blades unit are investigated. The equations of motion for the shaft–disk–blades unit are first derived from the energy approach in conjunction with the assumed modes method. The effects of disk flexibility, blade's stagger angle and rotational speed upon the natural frequencies and mode shapes are particularly studied. Previous studies have shown that there were four types of coupling modes, the shaft–blade (SB), the shaft–disk–blades (SDBs), the disk–blades (DB) and the blade–blade (BB) in such a unit. The present research focuses on the influence of disk flexibility on the coupling behavior and discovers that disk's flexibility strongly affects the modes bifurcation and the transition of modes. At slightly flexible disk, the BB modes bifurcate into BB and DB modes. As disk goes further flexible, SB modes shift into SDB modes. If it goes furthermore, additional disk-predominating modes are generated and DB modes appear before the SDB mode. Examination of stagger angle β   proves that at two extreme cases; at β=0°β=0° the shaft and blades coupled but not the disk, and at β=90°β=90° the disk and blades coupled but not the shaft. In between, coupling exists among three components. Increasing β may increase or decrease SB modes, depending on which, the disk or shaft's first mode, is more rigid. The natural frequencies of DB modes usually decrease with the increase of β. Rotation effects show that bifurcation, veering and merging phenomena occur due to disk flexibility. Disk flexibility is also observed to induce more critical speeds in the SDBs systems.