Calculation method for natural frequency of rotors considering load distribution in stepped parts

Abstract

To improve the product performance of turbomachinery and ensure vibration reliability, we propose a method for predicting natural frequencies that considers the decrease in the stiffness of the rotor stepped part. We developed a modeling method that divides the stepped part into a conical part that is responsible for stiffness and a shoulder part that is modeled as an additional mass. We then formulated the stiffness of the conical element based on the static deformation considering the cross-sectional change and verified the stiffness for various conical beams. We also developed a method that determines the boundary between the conical part and the shoulder part based on the axial load distribution in the rotor when the tensile distribution load is applied to the small diameter part of the end face of the stepped part. The primary bending natural frequency under free-free conditions was evaluated for rotors with a large diameter part in the center and small diameter parts at both ends. The calculation accuracies using a conventional model composed of beam elements, a model that reproduces the conical stiffness parts with 100-divided beam elements, and a model using the formulated conical elements were compared and verified with the 3D FEM analysis results. Our findings showed that the stiffness calculation error of the conical element based on the static deformation was 2.81% or less. In addition, the natural frequency calculation error when modeling the stepped parts with the proposed conical elements was 2.3% or less, thus demonstrating that the natural frequency can be predicted accurately.