Time domain analysis of a viscoelastic rotor using internal variable models

Damping in the stator of a rotating machine is able to reduce the unbalance response, and increase the speed where the stability limit is reached. However, damping in the rotor is destablising and the analysis of rotors with internal viscous damping is well established. The drive towards composite and laminated rotors mean that the viscous damping model is not always appropriate, and viscoelastic material models whose properties depend on frequency should be used. These properties may be measured experimentally and the analysis of structures containing viscoelastic material materials may be performed in the time domain using the ADF, ATF or GHM methods. This paper extends this analysis to rotors containing viscoelastic materials using the ATF approach. Other internal variable formulations for viscoelastic material may be used following the approach adopted in this paper with only slight modifications. Viscous damping in the rotor produces a skew-symmetric component in the ‘stiffness’ matrix; for viscoelastic models the skew-symmetric term appears in the internal variable equations. This paper gives an example to demonstrate the calculation of the stability limit speed for a machine.