Natural Frequncies of Coupled Blade‐Bending and Shaft‐Torsional Vibrations

Abstract

In this study, the coupled shaft-torsional and blade-bending natural frequencies are investigated using a reduced order mathematical model. The system-coupled model is developed using the Lagrangian approach in conjunction with the assumed modes method to discretize the blade bending deflection. The model accounts for the blade stagger (setting) angle, the system rotating speed and its induced stiffening effect. The coupled equations of motion are linearized based on the small deformation theory for the blade bending and shaft torsional deformation to enable calculation of the system natural frequencies for various combinations of system parameters. The obtained coupled eignvalue system is ready for use as a reference for comparison for larger size finite element simulations and for the use as a fast check on natural frequencies for the coupled blade bending and shaft torsional vibrations in the design and diagnostics processes. Some results on the predicted natural frequencies are graphically presented and discussed pertinent to the coupling controlling factors and their effects. In addition, the predicted coupled natural frequencies are validated using the Finite Element Commercial Package (Pro-Mechanica) where good agreements are found.

Steady-state coupling vibration analysis of shaft–disk–blade system with blade crack

“…As shown in Table 6, the natural frequency of TB coupling mode is 832. 23 Hz and the natural frequency of BB coupling mode is 832.30 Hz, which means the effect of shaft torsion on blade vibration is so weak that can be neglected [17]. Additionally, because of the inevitable weak errors induced by the geometrical and material parameters in the process of design and fabrication, there is weak mistuning in the RSDB test rig which results in the presence of weak dispersion for the natural frequency between different blades.…”

“…Besides, the physical mechanism of the coupling RSDB system can be mathematically formulated by the analytical model, while the numerical model cannot offer physical mechanism interpretation directly based on the mathematical expressions. As a result, the analytical model is extensively adopted in the most literatures [9,20,[22][23][24][25][26], while only few are based on the numerical model [21].…”

“…Based on the continuum beam theory, some scholars explored the coupling vibration modeling of RSDB system [20,22], free vibration of RSDB system [17,23], abnormal vibration of blade-casing rubbing [9,25], vibration localization of mistuned RSDB system [24,26], etc. For example, Huang [22] established a coupling dynamic model of shaft torsional vibration and blade bending vibration based on Eluer beam theory.…”