A General shaft-blade coupled vibration analysis using reduced blading model obtained by 3D – finite element method

Abstract

Selected from various eigenmodes of blading, nodal diameter κ= 0 and κ= 1 are both related to shaft torsional and/or axial vibration and shaft bending vibrations respectively. In order to avoid the possibility of 2f (f=power system frequency) from torsional vibration resonance, ISO regulates the final calculation results considering the combination betweenκ= 0 blade and torsional shaft vibration. The combination between κ= 1 blade and shaft bending vibration may become increasingly problematic as industry moves toward blade upsizing. This study explains a global method for blade-shaft coupled vibration analysis governing bothκ= 0 and κ= 1 in a systematic manner. According to our methods, the uncoupled blade vibration is first calculated for eigenvalue solutions using a general-purpose code of 3D-FEM (Finite Element Method), such as Nastran®. This solution provides a simplified blade model based on the concept of mode synthesis. Based on this blade model of our small scale test rotor, coupled vibration analysis was completed using the following two methods: -1) A simplified model of a shaft system was also prepared in a similar manner, and the two reduced models were then combined to understand the blade-shaft coupling system. 2) A 1D-FEM code specialized for shaft vibration analysis, defined as only beam elements, was connected with the prepared blade model to analyze the coupling effect. - These two methods provide numerical solutions that are approximate and within practical accuracy. As a result, it is a suitable alternative when a 3D-FullFEM evaluation is not possible on actual machines like large scale turbine generator sets.

Keywords

• blade vibration
• nodal diameter κ=0/1
• shaft torsion/axial/bending vibration
• coupling effect