Accurate one dimensional beam modeling method for a rotor shaft with stepped cross-sections in the finite element method

Abstract

The bending stiffness at the stepped cross-section of a rotor decreases in accordance with the elasticity in the face of the cross-section. This study proposes a method to deal with this decrease in bending stiffness in one dimensional (1D) beam modeling. The 1D beam modeling is widely used in practice to predict the rotor vibration characteristics represented by the eigenvalues because reasonable accuracy can be obtained in shorter computational time compared to three dimensional (3D) modeling—this is applicable to precisely predict the vibration including the cross-sectional face elasticity. Furthermore, the 1D beam modeling is especially useful to save computational time for identifying optimum rotor shapes or dimensions in which iterative complex eigenvalue calculations are required. In the 1D beam modeling, however, the decrease in bending stiffness is not included unless a special treatment is introduced into it. In this paper, the authors propose an accurate and easy-to-use 1D beam modeling method which takes into account the cross-sectional face elasticity of a rotor shaft with stepped cross-sections. This newly proposed method considerably reduces the calculation error regarding the rotor's bending stiffness—an inherent functional limitation of the 1D beam modeling.