3-D solid finite element modeling of rotating shafts

In this paper, three-dimensional (3-D) solid finite elements instead of beam or rod theories are employed to analyse the dynamic response of rotating hollow shafts. The equations of motion of a flexible rotating shaft have been consistently derived in a rotating frame. A new defined superelement representing a very short shaft can be formed to allow the use of reduction procedures with small matrix operations for such a chain-like structure. Not only bending but also torsional and axial vibrations can be analysed through appropriate superelement discretization. Computed natural bending frequencies show good agreements with the closed form solution using Timoshenko beam theory for a uniform shaft, and the measured results for a tapered one. For the modes of transverse vibrations, the translational motion in the rotating frame can be defined as forward or backward whirl. Its trajectories vary with frequencies of a an exciting force and become circular when resonance occurs. The criterion of critical speeds is also given.