Coupling Vibrations in Rotating Shaft-Disk-Blades System

Applications that have coupling among shaft, disk, and blades are investigated. A shaft-disk-blades unit often seen in engineering is presented. The governing relations for shaft torsion, disk bending, and blade bending are derived. Free vibration is then studied and the results show that shaft-blade (SB), shaft-disk-blades (SDB), disk-blades (DB), and blade-blade (BB) type coupling modes exist. The SDB and DB modes are observed to be evolved from the original SB and BB modes in a previously studied case of a rigid disk case. The effects of stagger angle $(β)$ on the coupling of the components are also examined. In the two extremes at $β=0$⁠, the disk is uncoupled, and at $β=π∕2$⁠, the shaft is uncoupled. In between, the three components are coupled. As $β$ increases, the disk participates more strongly, but the shaft behaves in exactly the opposite way. A SB mode at $β=0$ will transfer into a SDB mode as $β$ increases, eventually becoming a DB mode at $β=π∕2$⁠. Basically, as $β$ increases, the disk flexibility contributes more and reduces the natural frequencies. The effect of rotation is the last to be discussed and the results show that frequency bifurcation and loci veering occur as the rotation rate increases because of disk flexibility. For SD and SDB modes, the frequency loci veer and merge at certain rotational speeds. In these regions, there exist mode exchange and instability problems.