Vibration Diagnosis Featuring Blade-Shaft Coupling Effect of Turbine Rotor Models

As is well known, zero and one nodal diameter (⁠$k=0$ and $k=1$⁠) modes of a blade system interact with the shaft system. The former couples with torsional and/or axial shaft vibrations, and the latter with bending shaft vibrations. This paper addresses the latter. With respect to $k=1$ modes, we discuss, from experimental and theoretical viewpoints, in-plane blades and out-of-plane blades attached radially to a rotating shaft. We found that when we excited the shaft at the rotational speed of $Ω=|ωb−ωs|$ (where $ωb$ is the blade natural frequency, $ωs$ the shaft natural frequency, and $Ω$ is the rotational speed), the exciting frequency $ν=ωs$ induced shaft-blade coupling resonance. In addition, in the case of the in-plane blade system, we encountered an additional resonance attributed to deformation caused by gravity. In the case of the out-of-plane blade system, we experienced two types of abnormal vibrations. One is the additional resonance generated at $Ω=ωb/2$ due to the unbalanced shaft and the anisotropy of bearing stiffness. The other is a flow-induced, self-excited vibration caused by galloping due to the cross-sectional shape of the blade tip because this instability disappeared in the rotation test inside a vacuum chamber. The two types of abnormal vibrations occurred at the same time, and both led to the entrainment phenomenon, as identified by our own frequency analysis technique.