Modelling of rotors with axisymmetric solid harmonic elements

In rotating machinery analysis, the rotating shaft is typically modeled by a series of line or beam elements. These beam elements are formulated from classical beam theory, with a basic assumption that “plane sections remain plane” during bending. However, when the rotor has abrupt changes in the diameter, this assumption is not valid; local distortion occurs near the section change, resulting in an increase in the overall bending flexibility of the shaft. In this paper the bending stiffness and natural frequencies of several shaft geometries with stepped diameter changes are compared using several modelling assumptions. The comparison includes beam approximations with both transfer matrix and finite element approaches, and available experimental data. In addition, the conceptual approach of using an axisymmetric solid model of the shaft is reviewed. Results are included for a commercial four-node element, and for a cubic element developed for this work. The effective use of matrix reduction in conjunction with an axisymmetric model is shown. The importance of non-planar distortion near section changes is reviewed.