Vibration Diagnosis Featuring Blade-Shaft Coupling Effect of Turbine Model Rotors

Abstract

It is well known that zero and one nodal diameter (k = 0 and k = 1) modes of a blade system interact with the shaft system. The former is coupling with torsional and/or axial shaft vibrations, and the latter with bending shaft vibrations. This paper deals with the latter. With respect to k = 1 modes, we discuss experimentally and theoretically 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 = blade natural frequency, ωs = shaft natural frequency and Ω = 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-exited vibration caused by galloping due to the cross-section shape of the blade tip, because this instability disappeared at the rotation test inside a vacuum chamber. Both occurred at the same time, and both led to the entrainment phenomenon, which was identified by our own frequency analysis technique.